1

Incentive Mechanisms for Federated Learning:

From Economic and Game Theoretic Perspective
Xuezhen Tu, Kun Zhu, Member, IEEE, Nguyen Cong Luong, Dusit Niyato, Fellow, IEEE,
Yang Zhang, Member, IEEE, and Juan Li, Member, IEEE
arXiv:2111.11850v1 [cs.GT] 20 Nov 2021

Abstract—Federated learning (FL) becomes popular and has computing and storage capabilities [5] of end devices and edge
shown great potentials in training large-scale machine learning servers are utilized to make model training closer to where data
(ML) models without exposing the owners’ raw data. In FL, the is generated. This paradigm has promoted the emergence of a
data owners can train ML models based on their local data and
only send the model updates rather than raw data to the model new class of ML techniques that exploit the participation of
owner for aggregation. To improve learning performance in terms numerous clients without exposing the original data. One most
of model accuracy and training completion time, it is essential to famous distributed machine learning framework is Federated
recruit sufficient participants. Meanwhile, the data owners are Learning (FL). FL allows each client with data source, i.e.,
rational and may be unwilling to participate in the collaborative data owner, to train a local model, and a global model is
learning process due to the resource consumption. To address
the issues, there have been various works recently proposed to obtained through model aggregation. This process will be
motivate the data owners to contribute their resources. In this repeated until an accuracy target of the model is reached. FL
paper, we provide a comprehensive review for the economic and usually adopts client-server architecture for this interaction. By
game theoretic approaches proposed in the literature to design this way, it decouples ML from acquiring, storing, and training
various schemes for incentivizing data owners to participate in FL data in data centers, overcoming the limitations of traditional
training process. In particular, we first present the fundamentals
and background of FL, economic theories commonly used in approaches.
incentive mechanism design. Then, we review applications of In spite of the aforementioned great benefits of FL, it
game theory and economic approaches applied for incentive still faces several critical challenges. On the one hand, the
mechanisms design of FL. Finally, we highlight some open issues data owners, i.e., clients, typically consume their resources,
and future research directions concerning incentive mechanism e.g., computing and communication resources, for the local
design of FL.
training. This prevent self-interested clients from contributing
Index Terms—Federated learning, incentive mechanisms, eco- their resources for FL model training, unless they can obtain
nomic theories, game theoretic models. sufficient economic compensation. On the other hand, some
unreliable clients may perform undesirable behaviours, which
I. I NTRODUCTION affect the performance of global model of a FL task. In
particular, the client may launch a poisoning attack [6]–[8]
I N the past few years, we have witnessed the rapid devel-
opment of machine learning (ML) in the field of artificial
intelligence (AI) applications, such as computer vision, au-
that sends malicious updates to mislead the global model
parameters leading to the failure of current collaborative
tomatic speech recognition, natural language processing and learning. In addition, the privacy can not be guaranteed, i.e,
recommendation system [1]–[3]. The success of these machine participants information is still in danger of exposure. For
learning technologies, especially deep learning (DL), builds example, a generative adversarial network attack [9] could
on large volume of data (i.e., big data). With the advent be launched in FL, in which an adversary can pretend to be
of the Internet of Things (IoT), massive data is collected a participant engaging in the model training and learn other
by Internet connected smart devices with limited resources participants’ data.
(e.g., smartphones, sensors, etc.). In most traditional ML As a result, designing an efficient incentive mechanism for
technologies, the local data collected by smart devices need to FL is of crucial importance due to the following reasons.
be transmitted and processed at a cloud or data center to train First, to train and update the local models, the clients need
effective inference models. However, this causes excessive to consume the computing resource and network resource.
computation and storage costs, and the smart devices also Thus, the clients need to paid by reward or money to motivate
suffer from serious privacy leakage risk [4]. them for their contributions. Second, the clients are different
To address the aforementioned issues, mobile edge com- in behaviour, and thus they may be free to join and drop out
puting (MEC) has been proposed as a solution where the the FL platform. This significantly impacts the accuracy and
the delay of the training. Thus, a high incentive motivates
X. Tu, K. Zhu, Y. Zhang and J. Li are with the College of Computer Science more clients to join the FL platform and improves the training
and Technology, Nanjing University of Aeronautics and Astronautics, Nanjing
210016, China (email: {tuxz98, zhukun, yangzhang, juanli}@nuaa.edu.cn). performance.
N. C. Luong is with the Faculty of Computer Science, PHENIKAA Univer- There are two challenging tasks for incentive mechanism
sity, Hanoi 12116, Vietnam (email: luong.nguyencong@phenikaa-uni.edu.vn). designs in FL. The first is how to motivate and maintain more
D. Niyato is with School of Computer Science and Engineering, Nanyang
Technological University, Singapore 639798 (email: dniyato@ntu.edu.sg). participants from the participants’ perspective. That is, how
K. Zhu is the corresponding author. to provide a participating opportunity that a high reward is
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allocated to the clients and the privacy of the clients can be TABLE I
guaranteed. The second challenge is how to evaluate the par- M AJOR A BBREVIATIONS
ticipants’ contribution from the FL task publisher/platform’s Abbreviation Description
perspective. The demands of different FL task are various, thus BB Budge Balance
how to maximize the sustainable operation of the federation CE Computational Efficiency
while minimizing the incentive cost is challenging. DO(s) Data Owner(s)
To address the aforementioned challenges, many work has ED(s) Edge Node(s)
EMD Earth Mover’s Distance
been done from different aspects. Also, there are related
IC Incentive Compatibility
surveys including economic and pricing models for edge IR Individual Rationality
computing [10], FL [11], and incentive mechanism design for KKT Karush-Kuhn-Tucker
FL [12], [13], but they do not focus on how to adopt economic MDP(s) Mobile Device Group(s)
and game models to determine optimal interactions among MO(s) Model Owner(s)
buyers and sellers. To the best of our knowledge, there is no NE Nash Equilibrium
such a survey discussing the incentive mechanism design of FL SE Stackelberg Equilibrium
SP(s) Service Provider(s)
specifically from economic and game aspects. This motivates SV Shapley Value
us to deliver the survey with the aim of providing a guide for SWM Social Welfare Maximization
the relevant researchers engaged in the study of FL incentive WBB Weak Budge Balance
mechanism. We hope the reader will understand how economic
and game theoretic approaches can be adopted to effectively
design incentive mechanisms for FL. new global model is sent to participants for the next
The remainder of this paper is structured as follows. Sec- global training.
tion II reviews the background of FL such as the defini-
tion, architecture, advantages and incentive mechanisms in The step 2 and 3 are repeated until the global model reaches
FL. Fundamentals of the economic and game theory for an accuracy target.
incentive mechanisms in FL are given in Section III. In As an emerging distributed training framework, FL has been
Section IV, different game theoretic models used for incentive attracting great attentions. Multiple architectures of FL have
mechanisms in FL are discussed, including Stackelberg game, been proposed based on different networks, such as client-
non-cooperative game, etc. Section V reviews the auction server network and P2P network. However, for the works in
approaches for incentive mechanisms in FL. Applications of this survey, the client-server network based architecture (as
contract and matching theory for incentive mechanisms in FL shown in Fig. 1) is mainly considered, which consists of the
are discussed in Section VI. Section VII summarizes potential following entities:
future research directions. Finally, conclusions are drawn in • Clients: This layer is composed of devices, such as mo-
Section VIII. The list of abbreviations frequently used in this bile devices, sensors, and vehicles. Their functions are to
paper is given in Table I. contribute resources, i.e, training data and computational
resource to the FL process. Then, they act as the data
II. I NCENTIVE M ECHANISM D ESIGN FOR F EDERATED owners (DOs) to train a model from the FL service
L EARNING platform, i.e., the model owner (MO), by using their
A. Fundamentals of Federated Learning collected data.
• Communications and networking: This layer includes
The concept of FL was proposed by Google [14], [15]– data communication and networking infrastructures for
[17] which aims to build ML models based on distributed delivering the model parameters between clients and FL
datasets across multiple devices while protecting data privacy. service platform.
In general, FL refers to a collaborative learning method that • FL service platform: This layer consists of sufficient data
enables participants to interact and cooperate with each other storage and computational resource to firstly aggregate
for generating a global model without data sharing. The FL the local model update from the clients, and then broad-
process generally consists of three steps: casts the updated global model to all clients. Meanwhile,
• Step 1 (Model initialization): In this phase, the central the platform provides FL services to service requesters
server broadcasts the initialized global model to the or service users, e.g., through application interfaces.
selected local clients that are known as participants. • Service users/requesters: This layer contains the users
• Step 2 (Local model update): Each client trains its local who request FL service.
model based on the shared global model and local dataset.
After the training, the clients upload their local models With the above architecture, FL brings following benefits
to the server. compared with conventional centralized learning scheme and
• Step 3 (Model aggregation): Upon receiving the local
individual learning scheme:
models from the participants, the server uses model ag- • Privacy protection: Since the FL process does not involve
gregation algorithms, e.g., Federated Averaging algorithm the direct exchange or collection of raw data among
(FedAvg) which averages the parameters of the local participants, the privacy of participants is guaranteed to
models, to generate an updated global model. Then, the a certain extent. In a long-run, the privacy protection can
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• Computation efficiency (CE): It means that the incentive

Users/requesters mechanism can complete the participant selection and
reward allocation in the polynomial time.
• Fairness: It means that the incentive mechanism achieves
the property of fairness when some predefined fairness
functions, e.g., contribution fairness [18], regret distri-
FL service platform
bution fairness [19], [20], are minimized or maximized.
Ċ Cloud Fairness is the key to keep FL sustainable. A fair in-
centive mechanism can optimally assign the reward to
participants [21].
To achieve the aforementioned properties, the incentive
Communications mechanism needs to be well designed. In the following, the
/networking definition of incentive mechanism and the main design phase
are introduced in detail.
1) Definition of Incentive Mechanism in FL: An incentive
mechanism in FL system can be simply formulated as a triplet
Clients I = (P, C, R). P represents a set of potential FL participants
which could provide contributed training resources, i.e., Q,
for the FL process. C denotes a method that is used to
measure the contribution of each participant. R represents the
reward assigned to each participant based on the measured
Fig. 1. A general model of FL.
contribution according to C.
Specifically, designing an incentive mechanism aims to
better motivate participation, which further improves the determine the optimal participation level Q of participants and
performance of the FL system. the optimal reward R to maintain the sustainability of FL.
• Efficient model training: For the large-scale FL-based Optimization problems (e.g., utility maximization problem) are
training, only the model parameters (or model parameter designed to obtain the optimal strategy.
updates) are sent to the model owner, which reduces According to the above discussions, it can be known that
the communication overhead. Besides, FL helps to solve the incentive mechanism includes two phases, i.e., contribution
the problem of training failure caused by the resources evaluation and reward allocation. Both of them are introduced
shortage. in the following.
• Lower local inference latency: All participants can re- 2) Contribution Evaluation: In FL, selft-interested DOs
ceive a better global model compared with self-training have a higher incentive to join FL if they receive higher
model. Besides, compared with the centralized model, in rewards. However, this cause high incentive cost to the model
FL, making decisions can arise on local devices which owner. Thus, the contribution evaluation is important. Various
leads to lower local inference latency. methods have been proposed. In particular, the work in [22]
presented an exploratory analysis on honest DOs’ contribution,
malicious DOs’ behaviors and the defense mechanism of
B. Incentive Mechanism Design for Federated Learning: Con-
attacks. The work in [23] adopted the attention mechanism
cepts, Definitions, and Motivations
to evaluate the contribution of gradients provided by DOs
In the practical implementation of FL, participants may be in vertical FL. This approach can obtain real-time contri-
reluctant to participate without receiving compensation due to bution measurement for each DO with the high sensitivity
the resource-consuming training model and the risk of privacy on data quantity and data quality. Reference [24] presented
leakage. Additionally, there exists information asymmetry an intuitive contribution evaluation method based on step-
between the FL server and participants. Therefore, incentive wise contribution calculation. In [25], the authors proposed a
mechanisms design is crucial for FL to encourage the clients reinforcement learning-based accurate contribution evaluation
for their participations and to reduce the potential adverse method. Particularly, the work in [26] proposed a method
impacts of information asymmetry. In general, a desirable named pairwise correlated agreement based on the idea of
incentive can be characterized by the following properties: peer prediction to evaluate user contribution in FL without a
• Incentive compatibility (IC)/Truthfulness: It means that test dataset, which perform it using the statistical correlation
each participant can obtain the optimal compensate when of the model parameters uploaded by users.
they truthfully report their contributed resources and cost However, the approaches in [22]–[24] assumed that a trust
types. In other words, each of them can not improve their central server will honestly measure the contribution of each
revenue by submitting the false information. DO, which lack transparency and may hinder the success of
• Individual rationality (IR): It means that the utility of FL in practice. To address this issue, blockchain-based peer-
each participant is non-negative when they join in FL. to-peer payment system [27], [28] was proposed to enable
• Budget balance (BB): It means that the total payment for SV-based profit allocation through consensus protocol which
participants is no more than the given budget. replaces the traditional third party. Also, to prevent malicious
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behaviors, the authors in [29] proposed a scoring rule based of this approach is to solve a value-minus regret drift
framework to incentivize DOs to upload their model updates optimization problem, which achieves contribution fair-
in a trustworthy way. ness, regret distribution fairness, and expectation fairness,
The major contribution evaluation strategies in existing FL simultaneously.
system can be divided into the following categories: Summary: In this section, we provide a brief introduction
• Self-report based Contribution Evaluation: Self-report of FL that consists of a typical FL training process, general
based contribution evaluation is the most straight-forward architecture, and its advantages. In addition, the fundamentals
way, in which the DO actively reports the amount of of incentive mechanism for FL are discussed, e.g., concepts,
its contributed resources to the MO. In the context definitions and motivations. The next section presents some
of self-reporting, there are multiple metrics to evaluate basic and fundamentals of economic and game models.
DOs’ contribution, such as the capacity of computational
resource [30] and the data size [31]. III. OVERVIEW AND F UNDAMENTALS OF E CONOMIC AND
• Shapley Value based Contribution Evaluation: Shapley
G AME T HEORY FOR I NCENTIVE M ECHANISMS D ESIGN
value [32] is a marginal method based on contribution
which takes into account the impact of the participation Economic and game theoretic approaches based incentive
order of DOs, to fairly evaluate their marginal contribu- mechanism design for FL have received significant attentions.
tion to the federation. This method is usually adopted in This section presents the fundamentals and background of
cooperative game. The SV of DO is denoted as: the economic and game models commonly used for incentive
X
mechanism design. A taxonomy of the economic and game
|S|!(|N | − |S| − 1)!
ψi (N, v) =
N!
(v(S ∪ {i}) − v(S)), (1) models is provided in Fig.2.
S⊆N \{i}

where ψi (N, v) is the average marginal contribution of

A. Game Theory
DO i related to all possible subsets of federation, S
represents the different cooperation modes in the large Game theory is able to model the multi-participant inter-
coalition N , v(S) is the utility of model collaboratively active decision making problem in which the decision of a
trained by the subset S. Recently, there has been many participant (i.e., player) potentially affects the decisions of
works on SV-based contribution evaluation of DOs [33], other players. In the context of FL, the participants can be
[34], and its improvements [35], [36]. the MO (e.g., BS, MEC server, and SP) and the DO (e.g.,
• Influence and Reputation based Contribution Evaluation: mobile device, edge node, and users). In the following, we
The influence of the client is defined formally as the briefly present game theory-based incentive approaches which
effect of its contribution on the loss function of the FL have widely been used to determine the best reward for
model [37]. If the contribution is a model update (or participants of FL. To interpret the definition of the game,
data) the improvement of the loss function is achieved some terminologies are defined below.
through applying the update (adding the data to the • Player: A player is a decision maker which chooses its
training set). The work in [38] defines a novel notion, actions, and is considered to be rational if it always plays
Fed-Influence, to quantify the influence of each individual in a way which maximizes its own payoff.
client in terms of model parameters, and it can well on • Payoff: The payoff refers to the benefits (e.g., profit,
both convex and non-convex loss functions. Reputation utility, interest) that a player can obtain from the game,
mechanism is introduced and combined with blockchain which can be positive or negative.
to select the reliable and trustworthy participants [39]– • Strategy: Player’s strategy is a complete plan of actions
[42]. The reputation of the DO can be classified into that the player can choose to achieve a desired outcome.
direct reputation opinion and recommended reputation The payoff relies on not only the player’s own actions
opinion, which can be calculated using the subjective but also the actions of others.
logic model [43]. • Equilibrium: Equilibrium means that each player in the
3) Reward Allocation: After evaluating the contribution of game achieves the maximum utility they think, in which
DOs, the MO should assign reward as the return of each DO everyone has no an incentive to change its strategy. It
to remain and enhance the participation level of high-quality reflects the stability of the game result.
DOs. 1) Non-cooperative Game: In a non-cooperative game,
• Offered Reward: It considers the case where the MO each player is considered to be selfish which only cares
offers reward to the DO before training model, in which about the maximization of its own payoff rather than the
the reward can be determined according to the quality of social welfare of the FL system. In such games, there is not
the contributed resources [44], or through voting [45]. cooperation or agreements among players.
• Payoff Sharing: It considers the scenario that the MO Consider the pricing in a FL service market as an example.
allocates the reward to the DOs when completing the The mobile devices as sellers (i.e., DOs) can set the price
FL task [46]. Considering that payment delay may re- for providing computational resources to the MO as buyer.
duce the enthusiasm of participants in this scenario, A non-cooperative game among the competitive sellers can be
the payoff sharing scheme [19], [20] is proposed which modeled and defined as a triplet G = (Pi , ui , i ∈ N ), in which
can dynamically divide a given budget. The objective N represents N competitive sellers, Pi is a set of pricing
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Economic and game theoretic approaches

for incentive mechanism design in FL

Game theory based Auction based Contract theory Matching theory

incentive incentive based incentive based incentive

Non-cooperative Stackelberg Coalitional Sealed-bid Forward Reverse Double Combinatorial

game game game auction auction auction auction auction

Fig. 2. A taxonomy of economic and game approaches for incentive mechanism design in FL.
strategies of player i, and ui is the payoff of player i given game, BNE can be obtained where each player selects a
i’s chosen strategy and the others’ strategies. Let pi ∈ Pi be strategy that maximizes its expected payoff given its beliefs
any possible strategy of player i. about the type and strategies of other players. Because the
non-cooperative game models the conflict of selfish players,
Definition 1: Denote p∗i as the best response of player i to the the game in the FL market where the DOs are competitive
chosen strategies of other N − 1 players, i.e., p∗−i . Then, the and the budget of the MO is limited can be formulated as the
set of strategies (p∗i , ......, p∗N ) is termed a Nash equilibrium non-cooperative game. The corresponding Nash equilibrium
(NE) of this game, meaning that no player can gain higher allows DOs to have an optimal participation strategy. In the
payoff by deviating its current strategy when the strategies of context of FL, it is used for the computation resource trading
the other players remain the same, that is [47], with competitive prediction service provider as proposed in
[54].
ui p∗i , p∗−i > ui pi , p∗−i , ∀pi ∈ Pi .



(2)
2) Stackelberg Game: Stackelberg game [55] is a
The inequality (2) implies that NE is a stable outcome of sequential-move game in which the players acting as the
the game in which the sellers at the equilibrium have no an leaders move first and then other players acting as followers
incentive to change their strategies since they cannot improve move after observing leaders’ moves. Therefore, it is also
their payoffs unilaterally. Note that, there could be no NE termed as leader-follower game [53]. The Stackelberg game
or multiple NE in a game. This makes players difficult to aims to model multi-agent decision making processes and
predict the outcome of the game. Therefore, it is important maximize the utility of both the leader and the followers given
to check the existence and uniqueness of the NE when using the leader’s strategy.
the non-cooperative game. It has been proven that a unique Consider again the scenario in Section III-A with two
NE exists if the strategy space of each player is a convex mobile devices as players, i.e., computational resource sellers.
set which is non-empty, closed, and bounded, and if its P1 and P2 denote the sets of the pricing strategies of players
payoff function is a continuous and quasi-concave function 1 and 2, respectively. Both mobile devices 1 and 2 aim to
[48]–[50]. The existence and uniqueness of NE can also be maximize its own utility ui (p1 , p2 ) , i ∈ 1, 2, where p1 and
proved by adopting the Kakutani’s fixed point theorem [50] p2 are their chosen strategies from P1 and P2 , respectively.
or the Brouwer’s fixed point theorem [51]. Because the non- Assume that player 1 chooses its strategy at stage 1, and thus
cooperative game formulates the conflict relationship among acts as the leader. Player 2 chooses its strategy at stage 2, and
self-interest players, the incentive problem among competitive acts as the follower. The optimization problem of the leader
participants of collaborative learning under limited budget was and the follower together form the Stackelberg game, and their
modeled as non-cooperative game [52]. solutions construct the Stackelberg equilibrium (SE).
The non-cooperative game assumes that information such
Definition 2: Let p∗1 and p∗2 denote the solutions of the
as feature, payoff function and strategy of the players are
optimization problems of the leader and the follower, respec-
the common knowledge among players, which is termed a
tively. Then, the point (p∗1 , p∗2 ) is the SE for the Stackelberg
complete information game. However, in practice, a player
game if any (p1 , p2 ) with p1 > 0 and p2 > 0, we have
may not be fully aware of this information of other players,
u1 (p∗1 , p∗2 ) > u1 (p1 , p∗2 ) and u2 (p∗1 , p∗2 ) > u2 (p∗1 , p2 ).
only knowing the occurrence probability of each type. Such a
game is known as an incomplete information game. In FL mar- The backward induction method [56] is commonly used to
ket, the prior knowledge about Dos’ reliability or reputation derive the SE. In the above example, given p1 , the optimization
that helps allocate rewards may be unknown for the MO. A problem of the follower is solved first to find p∗2 , and then the
typical example is the Bayesian game [53] where the outcome p∗1 is obtained through substituting p∗2 in the leader problem.
of the game can be predicted using Bayesian game analysis. Since player 1 takes advantage of knowing player 2 knows
The equilibrium solution of such a game is Bayesian Nash p1 , player 1 imposes a solution which will facilitate itself.
equilibrium (BNE). Similar to NE in a complete information Therefore, the utility of the leader at the SE is higher than that
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of the follower, called the first mover advantage. Accordingly, • Utility: The buyer’s utility is the difference between
when reaching SE, the leader could achieve a payoff at least its valuation of the requested commodity and its final
as high as the one obtained from the corresponding NE. payment. The seller’s utility, i.e., revenue, refers to the
This feature makes the Stackelberg game suitable for the total payment received from the buyers. In FL markets,
incentive mechanism design in FL. For example, it allows the utility of the buyer, e.g., model owner, can be propor-
the mobile devices (i.e., the followers) to determine optimal tional to the accuracy of the global model and inversely
computational resource prices after knowing the amount of proportional to the total payment that the model owner
CPU resources that the MO (i.e., the leader) needs as proposed pays the data owners.
in [30] or the reward offered by the MO as proposed in [57]. • Social welfare: It refers to the sum of utilities of the users
3) Coalitional Game: In a cooperative game, players coop- (i.e., both buyers and sellers) in an auction.
erate with each other with the aim of maximizing a common
Auction mechanism has been widely applied in many fields,
objective of the coalition. Moreover, enforceable contracts
such as resource allocation in wireless systems [59], secure
are made among the players. In this case, the players can
data offloading [60], and network security [61]. For the rest of
coordinate strategies and reach an agreement on how to assign
this section, we introduce the detail of auction types commonly
the total payoff to the players in a coalition. The objective of
applied to incentive mechanism design in FL.
a coalitional game is to find a stable solution which ensures
that the outcome of the game is immune to changes of groups 1) Sealed-bid Auction: Different from the open-cry auction
of players (i.e., each player has no incentive to move from its (e.g., English auction and Dutch auction), the bids of the
current coalition to another coalition). buyers are open to each other during the auction, in a sealed-
bid auction, the buyers submit sealed bids simultaneously to
the auctioneer. Accordingly, no bidder can know the bidding
B. Auction information of others and cannot change its own bid. There
An auction is an economic mechanism, the goals of which three types of sealed-bid auctions.
are to allocation commodities (e.g., training data, computa- • First-price sealed-bid (FPSB) auction: The bidder with
tional resource, and bandwidth) and establish corresponding the highest bid is the winner who can receive the item
prices via a process known as bidding [58]. An auction consists and pays the highest bid.
of an explicit set of rules which determine resource allocation • Second-price sealed-bid (SPSB) auction or Vickrey auc-
and prices of the basis from market participants [58]. There tion: In this auction, the winner only pays the second-
are following terminologies used in the auction: highest bid rather than the highest bid that it submitted
• Bidder: A bidder is a buyer who wants to purchase items [62]. Since the winner pays the price less than its ex-
in the auction. In the FL market, bidders can be model pected price, the Vickrey auction motivates buyers to bid
owners or FL service requesters. truthfully. The auction thus achieves truthfulness. This
• Seller: A seller offers services or resources to the buyers. feature enables Vickrey auction to be widely used for
In FL markets, the sellers are typically data owners or the incentive mechanism design in FL to prevent the
clients who use their local data to train the shared model misbehaviors of unreliable clients.
required by the model owner. • Vickrey-Clarke-Groves (VCG) auction: A VCG auction is
• Auctioneer: An auctioneer is an intermediate agent which a generalized Vickrey auction with multiple commodities.
conducts the auction, i.e., price and winner determination. In the VCG auction, the commodities are allocated so-
In many cases, the seller itself is the auctioneer. cially optimal manner, and the winner pays for the loss
• Price: A price in an auction may be an asking price of the social value owing to winning the commodities.
or a bidding price. The asking price is the price of a Such payment rule enables bidders to give their true value
commodity that the seller wants to obtain, and the bidding for the commodities. The VCG is thus a strategy-proof
price is the price that the buyer wants to pay for his or truthful mechanism. In FL, VCG mechanism can be
requested commodity. Hammer price is the price at which used to motivate IoT devices (the Dos) to report their true
the buyer and the seller agree to make a deal, i.e., final valuations to the network operator for maximizing social
payment. welfare as proposed in [63].
• Commodity: An auction commodity refers to the object
2) Forward, Reverse and Double Auction: The auction
traded between a buyer and a seller. Each commodity has
mentioned above are classified as the forward auctions from
a value at which the buyer/seller wants to buy/sell. In FL
the seller’s side. Considering the buyer’s side, there are re-
markets, the commodity can be a data unit (a training
verse and double auctions. In particular, there are following
data sample) or a computing resource unit that the data
definitions:
owner offers.
• Valuation: In an auction, the valuation refers to monetary • Forward auction: In the forward auction, multiple buyers
valuation of commodities. Different buyers and sellers submit their bids, i.e., bidding price, to compete for the
may value commodities with different valuations depend- requested items offered by one seller.
ing on their preferences. The valuation of a participant • Reverse auction: In the reverse auction, multiple sellers
can be private that is unknown to the other’s participants submit their asks, i.e, asking price, to compete for selling
or public that is known to the others. the items to the single buyer. The reverse auction is
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often used together with other auction mechanisms, e.g., have been widely applied in incentive mechanism design for
sealed-bid reverse auctions. FL. A three-dimensional contract incentive mechanism that
• Double auction: In FL market, there may exists multiple jointly considers the task expenditure and privacy issue is
MOs and multiple DOs, the double auction can be used to design as proposed in [70]. A two-period incentive mechanism
match the supply and demand. In a double auction, buyers based on dynamic contract is proposed in [71] to incentivize
and sellers simultaneously submit their bids, i.e., bidding users with different willingness to participate. The contract-
price, and asks, i.e, asking price, to an auctioneer [64]. based personalized privacy-preserving incentive for FL in [72]
The auctioneer determines a price p, i.e., the transaction can provide customized payments for workers with different
price, to clear the market, at which the asking prices privacy preferences.
from sellers are less than p while the bidding prices from 2) Matching Theory: Matching theory aims to optimally
buyers are more than p. The transaction price is typically match two disjoint sets of agents together, given their individ-
set as p = (pb + ps ) /2, where pb is the bidding price ual utilities. In the general allocation game model, there could
of one buyer and ps is the asking price of one seller. be multiple agents in both sides of the matching, and agents
The buyers receive resources, and the sellers gain the from one side have transactions with agents in the opposite
transaction price. The process is repeated until no more side. Therefore, such a game is called two-sided matching. In
transactions occur or a predetermined end time achieves. matching theory, agents compete with each other to maximize
3) Combinatorial Auction: In combinatorial auction, each their own utility, i.e, selfishness, and always make decisions
bid of a buyer indicates a bundle of multiple commodities that can increase their utilities, i.e, rationality. In FL, it is used
rather than an individual commodity [65]. Based on the for the task allocation withe the aim of minimizing the system
information included in the bid as well as the capacity latency of multiple-task FL in MEC [73], [74].
of commodities from sellers, the auctioneer determines the Summary: This section has introduced the basis of eco-
optimal allocation strategy as well as the winner of the nomic and game theoretic approaches proposed to design
auction. However, solving winner determination problem is incentive mechanisms for FL. Specifically, we provide the
a challenge for the combinatorial auction since the problem is definitions, mechanism descriptions, and rationality behind
generally NP-hard, which means that there is no polynomial- the use of these approaches for incentive mechanisms. In the
time algorithm to find the optimal allocation. There are many subsequent sections, we provide comprehensive reviews on the
algorithms that have been proposed to obtain the approximate applications of economic and game theoretic approaches for
solutions for the problem, such as the Lagrangian relaxation incentive mechanism design in FL.
approach [66]. In FL, the combinatorial auction is used to
allocate network operator’s bandwidth to multiple FL SP as
proposed in [67].
IV. A PPLICATIONS OF G AME T HEORY FOR I NCENTIVE
M ECHANISM D ESIGN IN FL
C. Contract and Matching Theory
Contract theory [68] and matching theory [69] have been In the FL service market, there are multiple partici-
regarded as two powerful tools to model the dynamic and pants/stakeholders which may belong to different entities, i.e.,
mutually beneficial relations among different types of rational service users, FL service providers (also MOs), and data
and selfish agents. In particular, they can effectively deal with providers (also DOs). Each participant determines the optimal
the high dynamics of trading market, selfish and competitive strategy and through constantly interacting with other agents
participants. In the following, the brief introductions of con- to achieve different objectives. The objectives include the
tract theory and matching theory which have been used to revenue, utility, cost, and system performance. The interaction
design incentive mechanism in FL is presented. among entities is complex and their objectives often conflict
1) Contract Theory: Contract theory is an economical with each other, which makes game-theoretic approaches
theory that regards all transaction and institutions as a kind of become effective tools for designing incentive mechanisms
contract [22]. It is widely used where the asymmetric infor- with low complexity for FL. With the traditional methods,
mation is available between employer and employees (i.e., the it is difficult to incorporate economic implication into the
futures of an employee is not known exactly to the employer). solutions. Therefore, when the rationality of the stakeholders
In the FL market, since the employees are selfish and they in the FL system are important, the traditional methods may
may not reveal their true bids as well as the property of not be suitable.
privacy protection of FL mechanism, there exists information Game models that are commonly adopted in incentive mech-
asymmetry. Contract theory can design the optimal contract anism of FL consists of Stackelberg game, non-cooperative
to reduce the moral hazard, adverse selection, and extortion game, and coalition game. Specifically, the Stackelberg game
of the parties amid information asymmetry. This characteristic is used to maximize the utility of the MOs and the DOs.
makes the contract theory suitable for the incentive mechanism Otherwise, the non-cooperative game is used in the case each
designs in FL. In the context of FL, an employer can be a player, i.e., the DO or the MO, aims to maximize its own
model owner who wants to recruit workers to complete the FL utility. To form a stable DO federation, the coalition game
model training. Similarly, an employee can be any client (data can be used. The game approaches are reviewed, discussed,
owner) who wants to participate in the FL. The contract theory and analyzed in the following sections.
 8

BS(leader) FL data owners(followers)


Sense and collected data
MEC server
Encrypted local Upper-level
gradient update game Reward
Reward Reward Reward
& training reward

Learning Learning Learning

FL service provider(leader)
service service service

FL service & Lower-level Service

A(follower) B(follower) C(follower) service price game demand values
& payment
UEs
FL servicer users(followers)
Fig. 3. Stackelberg game-based incentive scheme in crowdsourcing frame-
work. 

A. Incentive Mechanisms Based on Stackelberg Game Fig. 4. Market-oriented architecture for motivating information trading with
federated learning based on hierarchical game.
In an FL system, the MO hires the DOs for model training.
Thus, the MO acts as a buyer, and the DOs are sellers. The
MO can first set a reward, and then the DOs decide its level Newton-Raphson method. The simulation results show that the
of participation. To stimulate both the MO and the DOs to proposed game approach outperforms the heuristic approach
participate in the FL system, the Stackelberg game is adopted. up to 22% gain in the offered reward while achieving the
The first work of Stackelberg game can be found in [75]. same target accuracy. However, the proposed game approach
The system model is shown in Fig. 3 in which the BS, i.e., is constrained to a single leader, i.e., an MEC server.
the MO, is the leader, and the user equipments (UEs), i.e., Opposite to the model in [76], in [77], the MEC servers
the DOs, are the followers. The BS as the buyer first sets of operators act as sellers (leaders), that cooperatively train a
a monetary reward to maximize its utility. Given the BS’s global model from a coordinator at the cloud, i.e., the buyer
reward, each UE determines its local training strategy, i.e., the (the follower), based on the sensing data from IoT sensors
amount of CPU resources, to maximize its utility. Here, the that are distributed by the coordinator. The interaction process
UE’s utility is a concave function of its local training accuracy can be summarized as follows. First, each MEC operator in-
and the BS’s reward, and the BS’s utility is a strictly concave dividually sets its optimal price to maximize its utility, i.e, the
function of the number of global iterations required to reach payment from the coordinator minus its power consumption
the global accuracy and the reward. A unique NE among UEs for local training, accounting its residual computational re-
can be obtained by taking the first-order condition. Given source. Given the price and configuration profile of operators,
the UEs’ best responses, the BS updates the global model the coordinator allocates the sensing data from IoT sensors
and adjusts its reward to maximize its utility. The backward to maximize its utility while satisfying the latency constraint
induction method is applied to solve the game. The simulation of the distributed learning process. The coordinator’s utility is
results show that an increase in the reward incentivizes the UEs defined as the difference between the gain owing to the model
to generate more local models that leads to a higher global training and the payment to operators. To find an optimal data
accuracy. However, the BS needs to pay a higher incentive distribution strategy for the coordinator, the KKT is used. The
cost to the UEs. theoretical analysis proves the existence of a unique SE for the
The same system model and Stackelberg game approach two-level game. The simulation results show that the operators
can also be in [76] where the MO is an MEC server, i.e., can increase the prices to improve their utilities. However, if
the buyer, that offers the reward. Also, the utility of the UE the prices are too high, their utilities seem not to increase,
is the difference between the reward offered by the server since the coordinator reduces the amount of distributing input
and the local training cost. To obtain the best responses of the sensing data.
UEs, Karush-Kuhn-Tucker (KKT) and the first-order condition Consider a general scenario, the authors in [78] proposed to
are used. Given the best responses, the server determines adopt a two-layer Stackelberg game to model the interactions
the reward to maximize its utility under the limitation of a among an FL SP (SP), users, and DOs. The system model
fixed number of global iterations. Given the constraint, to is shown in Fig. 4. In the lower-layer game, the SP is the
achieve the desired training result, a threshold accuracy of leader, and the users are the followers. Each user determines
the local training at the UEs is set. The UEs whose local its optimal demand value of learning service to maximize its
accuracies are higher than a threshold are selected for the utility. The competition among users is modeled as a non-
training. The threshold is optimized using the Lagrangian and cooperative game. The NE solution of the game is obtained
 9

TABLE II
A PPLICATIONS OF S TACKELBERG G AME FOR I NCENTIVE M ECHANISM D ESIGN IN FL

Market Structure Stackelberg Game

Ref. Scenarios Method of Solution
Seller Buyer Item Leader Follower Objective
Communication efficiency, global model The first-order
Edge UEs’ CPU
UEs BS BS UEs accuracy improvement for the leader, condition, backward
[75] Networks resource
revenue improvement for the followers induction method
Mobile The first-order
Communication efficiency, global model
Crowd- MEC MEC condition, KKT
UEs CPU resource UEs accuracy improvement for the leader,
[76] sourcing server server condition, and backward
revenue improvement for the followers
Network induction method
KKT condition and
MEC MEC Cloud co- Computational MEC Cloud co- Revenue improvement for both leader and
backward induction
[77] Network operators ordinator resource operators ordinator followers, FL latency requirement guarantee
method
Data
General FL service, The first-order
SP, data Service workers, Revenue improvement for both leader and
FL workers’ model SP derivative, backward
[78] workers users service followers
system updates induction method
users
The first-order
General
Mobile Mobile Revenue improvement for both leaders and optimality condition,
FL MO Training data MO
[31] devices devices follower and exterior point
system
method.
Air- Reliable local model update for the leader, The first-order
Ground Local model Ground
ground UAVs UAVs revenue improvement for both leader and derivative, and the
[79] clients update clients
networks followers second-order derivative
The first-order derivative
General
Mobile Cloud Cloud Mobile Privacy protection, revenue improvement for , the second-order
FL FL service
[80] devices server server devices both leader and followers derivative, and bisection
system
/Newton’s method.
Internet
Improved fairness, and revenue An ADMM-based
of Vehicles RSUs Training data RSUs Vehicles
[81] improvement for both leaders and followers iterated algorithm
Vehicles
Wireless Transmission power feasibility, reward The first-order
WPT MEC MEC WPT
charging Power resource feasibility, revenue improvement for both derivative, the
[82] nodes node node nodes
network leader and followers second-order derivative
The first-order
Edge Edge Cloud Cloud Edge Revenue improvement for both leader and derivative, the
[83] Traning data
network nodes server server nodes followers second-order derivative,
[57]
and DRL

by taking the first-order derivative. The utility of user is the maximize its profit. Here, the profit is the difference between
benefit gained from the direct network effect caused by all the the revenue obtained from providing the learning service to the
users in the system and the benefit gained from the indirect MO and the relay service to other mobile users and the energy
effect caused by other participants minus the negative impact consumption cost. The experimental results show that the route
on service quality as well as the payments from the users. In selection of model transmission among the mobile devices
the upper-layer game, the SP acts as the leader and the DOs can significantly improve the performance of the model and
act as the followers. Based on the DOs’ required charging make mobile users gain the best benefit. In the future, power
price and users’ service demand, the SP decides its service optimization can be considered to construct a energy-efficient
price to maximize its utility, i.e., its profit, which is defined cooperative FL system.
as the payment obtained from users minus its fixed processing Different from the aforementioned works, the authors in
cost and rewards to the workers. Given the SP’s price, each [79] considered an FL network in which the MO is an un-
DO determines its charging price to maximize its utility, i.e., manned aerial vehicle (UAV) as the leader, and the data owners
profit, which is the difference between the total remuneration are ground clients as the followers. The interaction between
received from SP and the additional rewards obtained owing to the leader and the followers is as follows. First, the UAV,
joining FL training and its cost for perceiving and collecting i.e., the buyer, offers a reward when it publishes the FL task.
data. The first order derivative is used again to obtain the op- Then, each client decides its participating level to maximize its
timal strategies of the SP and the DOs. The optimal solutions utility that is the difference between the reward and the cost for
of all three entities constitute the SE. However, this work does training FL task. The clients’ optimal strategies are determined
not consider constrained computing resources of DOs. using the first-order and the second-order derivative. Given the
In a practical FL network, a mobile user can be out of the clients’ responses, UAV determines its reward to maximize
coverage range of the MO. In this case, the mobile user can ask its utility. Here, the utility is defined as the total benefit
other mobile users (i.e., relay node) in the network to forward gained from the training of clients minus its payment to
its local model to the MO. In this scenario, the authors in [31] these clients. The theoretical analysis has proved the existence
adopted the Stackelberg game in which the MO is the follower and uniqueness of NE among the clients as well as the SE
(i.e., the buyer) and the mobile users are the leaders (i.e., the between the UAV and the clients. To further adapt to the
sellers). The MO determines the size of dataset provided by dynamics of air-ground network, the authors design a dynamic
the mobile users to maximize its utility. The utility of the MO incentive mechanism to adaptively select the optimal number
is a function of the total data size of all the users and the prices of clients, taking into account the limitation of drone coverage.
paid to the mobile users. Given the data size, each mobile user The difference between the two incentive mechanisms is the
determines the optimal price for one training data sample to definition of the clients’ loss. The simulation results show
 10

that the social welfare obtained by the dynamic incentive Service request
FL service
mechanism is higher than that obtained by the static incentive ĂĂ
Charging reward
Charging price
mechanism. The reason is that dynamic incentive mechanism AI service requesters
Energy supply
Energy payment
can always select the optimal clients adapting to the time- Energy supplier MEC node
varying environment. (leader)
WPT node
Considering the privacy leakage issue in FL, a Stackelberg (follower)
game-based incentive mechanism to motivate users with sen- Wireless
Renewable
sitive data to participate in FL with guaranteed privacy is charging
energy
channel
proposed in [80]. The system model includes a cloud server, Renewable
energy Stationary
WPT node
i.e., the MO, and mobile users, i.e., the data owners. Specif- (follower) charing mode

ically, the server publishes an FL task and announces a total Edge device Mobile device
reward for attracting users. Given the server’s reward, each Dynamic
user determines its desired privacy budget, i.e, the monetary charging mode

compensation for privacy loss, to maximize its own utility.

The utility of a user is defined as the payment obtained Fig. 5. Energy-knowledge trading framework based on Stackelberg game.
from the server minus its cost. The payment depends on
not only the total reward but also the privacy budgets of
users. A stable privacy budget strategy for each user can be However, the training time constraints that affect the service
obtained by taking the first-order and second- order derivative. delay of the intelligent transportation system are not consid-
Based on the optimal strategies of users, the server decides ered.
an optimal total reward that maximizes its utility, which is a To ensure the learning performance of energy-constrained
function of the global model accuracy and the reward paid edge devices, the authors in [82] proposed a novel wirelessly-
to the users. The optimal reward can be calculated through powered edge intelligence framework (WPEG). As shown in
either the bisection method or Newton’s method [84]. As Fig. 5, the system model consists of edge devices which
shown in the numerical results, with the increasing number provide learning services, MEC nodes which is an interme-
of users, the users’ utility decreases, while the server’s utility diary between the AI service requester and edge devices, and
increases. However, this work only considers the users’ cost wireless power transfer (WPT) nodes which provide charging
associated with the privacy budget, while other costs, such as services to edge devices via wireless channel. The goal of
communication and computation cost, are not considered. the WPEG is to obtain the optimal power transmission and
To preserve the privacy of the clients, blockchain has economic rewards for jointly maximizing the utility of both
recently been integrated with the FL as proposed in [81], which WPT nodes and the MEC node. The utility of WPT nodes is
considers an Internet of Vehicular (IoV) system. This system defined as the reward obtained from the MEC node minus the
consists of one top chain and ground chains. In each ground energy cost paid to the energy supplier, and the utility of the
chain, a multi-leader and multi-follower Stackelberg game is MEC node is the difference between the profit that it achieves
used to motivate vehicles to join in the FL. Specifically, the by participating in the AI service and the reward given the
Roadside Units (RSUs) act as the leaders which are named WPT nodes. The optimization problem is modeled as a two-
as FL RSUs (FRs) and vehicles act as the followers which stage Stackelberg game that could be regarded as energy-
are namely FL vehicles (FVs). Each FR competes with with knowledge trading, in which the MEC node is the leader and
each other and sets price for vehicular training results, while the WPT nodes act as followers. That is, to obtain knowledge
FVs collect surrounding data for sale. Given the bid prices inferred from the data of edge devices, the MEC node needs
of all FRs and other FVs’ training data sizes, one FV aims to purchase the energy from WPT nodes. Given the economic
to minimize the amount of its collected data that maximizes reward, each WPT node as a seller determines its power
its utility. The utility of an FV is the difference between the transmission strategies to optimize the self-revenue. With the
revenue by selling knowledge (i.e., the learning parameters WPT nodes’ responses, the MEC node as the buyer adjusts
of the FV’s local model) to FRs according to their asking its reward to maximize its utility. A low complexity gradient-
price and the computation cost for collecting and training data. based searching algorithm is designed to find the NE of the
Given the data size of all FVs and other FRs’ pricing strategies, game. Numerical results show that in terms of the average
the goal of an FR is to minimize its bid price for purchasing utility of the MEC node, the proposed incentive scheme
FVs’ knowledge while gaining more benefits. The utility of improves up to 32.38 %, 14.42 %, 41.37 %, and 110.19%,
an FR is defined as the further learning reward that gains compared with the random federated edge learning scheme
from BSs in top chain layer minus the computation cost for in which the MEC node offers random incentives to WPT
further learning as well as the cost for the FVs’ knowledge. An nodes, and uniform federated edge learning scheme in which
iterated algorithm based on the Alternating Direction Method a uniform incentive is offered to WPT nodes. However, the
of Multipliers (ADMM) is adopted to deal with the proposed proposed work does not consider the edge devices’ mobility.
multi-leader and multi-player game. Simulation results demon- To address the challenges of the non-publicity of individual
strate that based on the game-theoretic incentive mechanism, participation strategy and ambiguous contribution evaluation,
the proposed hierarchical FL algorithm can achieve about 10% deep reinforcement learning (DRL)-based Stackelberg game
more accuracy improvement over conventional FL algorithms. can be adopted as proposed in [83]. The system model consists
 11

of a server at the cloud that publishes an FL model and

Price strategy Upper-level
rewards, and multiple edge nodes that cooperatively train the
differential game
FL model. The interaction among the server and edge nodes
is modeled as a Stackelberg game where the server acts as a
leader and the edge nodes act as followers. Given the server’s
reward and other nodes’ decisions, each edge node decides an
optimal training data size to maximize its utility. The utility of
a edge node is defined as the reward received from the server
minus its cost of data collection and model training. Given
the optimal data sizes of the edge nodes, the server calculates
an optimal reward to maximize its utility, which is defined
as the gain of model accuracy minus the total reward paid to
edge nodes. Theoretical analysis proves the existence of NE
among the edge nodes and a unique SE of the entire game. MOs (Buyers) MDGs(Sellers)
Then, an actor-critic DRL model based on the proximal policy MDG selection Lower-level
optimization is adopted to find the SE of the game based on evolutionary game
the past strategies. The numerical results show that the DRL-
based incentive mechanism can learn the optimal strategies
for the server and edge nodes at which the server’s utility Fig. 6. Federated learning training service market based on dynamic game.

obtained by the proposed DRL approach is higher than those

obtained by the random and greedy approaches. However, how
the proposed approach improves the utility of the edge nodes pricing strategies of MDGs are formulated as a higher-level
is not discussed. differential game. Given the MDGs’ price, each MO adjusts
The same system model and hierarchical game can be its selections according to the price and time-varying observed
found in [57]. However, different from [83], in [57], given the model accuracy to maximize their utility. The utility of MO
server’s reward, each edge nodes determines its contributed is defined as a net profit function, i.e., the gain of accuracy
computational resources to the model training to maximize from the MDG minus the price paid for the training service
its utility. The utility of a edge node in each round is the and congestion punishment from MDG. Given the MOs’
difference between the payment from the server and its total selections, each MDG optimizes its price as the best response
CPU energy consumption for the local training to satisfy to MOs’ selections and other MDGs’ pricing strategies so
the local accuracy requirement. The optimal computational as to maximize their accumulative profits gained from the
resources allocation strategy can be obtained by taking the training services. The profit of the MDG is defined as the
first-order derivative. Given the best contributed resources of difference between the payment for selling data and the
the edge nodes, the server optimize its rewards strategy to cost for training. The differential game can be regarded as
minimize its total cost, which is a function of the total time of an optimal control problem which can be solved by using
one global iteration and the total payment to edge nodes. Using the iterative numerical algorithm [87]. The simulation results
the KKT conditions, the best reward strategy is obtained. A show that the accumulative profits of MDGs obtained by
DRL-based model is also designed to learn an optimal reward the differential game approach are much higher than those
strategy for the server. The experiment results demonstrated obtained by the static non-cooperative game.
comparing with greedy, random and traditional single-round Considering the same FL system as described in [85], the
optimization approaches, the DRL-based approach can achieve evolutionary game model [88] is formulated to analyze the
the best results. dynamic training strategies of the mobile devices with bounded
rationality. The competitive evolution of individuals (mobile
users) in the population is modeled. However, unlike [85],
B. Incentive Mechanisms Based on Non-cooperative Game the utility, i.e., the payoff, that one mobile device can receive
In the non-cooperative game, all the players simultaneously from the MO is proportional to the data size that the mobile
decide their strategies, while in the Stackelberg game, one or device uses for the training. The objective of each mobile
some players as leaders decide their strategies before other device is to maximize its individual utility, and to achieve it,
players (followers). the mobile device dynamically adapts its strategy according
In [85] and [86], the authors considered a federated learning to its utility. In particular, each mobile device compares its
training service market. The system model is shown in Fig. 6 utility with the average utility, and if the utility is less than
which consists of multiple MOs and multiple mobile device the average, it will select another strategy in the next period.
groups (MDGs). The MOs as buyers select MDGs, i.e., the The uniqueness and stability of the evolutionary equilibrium
sellers that have access to a federation of enormous mobile is proved by using the Cauchy-Lipschitz theorem [89] and
devices, to complete the FL training service. A two-level Lyapunov’s second method for stability [90], which allows
dynamic game is adopted to formulate the interactions in the mobile users to have the optimal strategies. Numerical
this training service market. In particular, the MDG selection results show that the utilities fluctuate first over time and then
are modeled as a lower-level evolutionary game, while the converge to the evolutionary equilibrium and the learning rate
 12

Users(buyers) distance between the local model transmitted by the client

and the aggregation model. Then, the NE property is applied
Prediction task request
to determine the probability of different strategies of the server
Ļ Decrypted aggregated
& Deposit for payment predictions
and clients. At the mixed Nash equilibrium, both the players
ķ TEEs-based server have no an incentive to change their strategies since they are
Encrypted aggregated
ĺ predictions not able to increase their expected payoff by selecting an
Prediction
& accuracy-aware alternate strategy. The simulation results show the proposed
serving contract
scores algorithm can detect 100% of the bad clients, and the test
Ĺ
Payment based ĸ accuracy of the proposed algorithm is at least 15.8% and
Local model-based
on the scores Deposit for
prediction results
2.3% better than the previous works (e.g., Multi-KRUM [93],
Ļ potential penalty Federated Averaging [94], and COMED [16]) for flipping and
Prediction service providers(sellers) noisy scenarios, respectively. The detection of the backdoor
attack where a malicious client can use model replacement to
introduce backdoor functionality into the global model can be
considered in the future work.
Considering the organization heterogeneity and non-
excludable public goods (i.e., resources of organizations), the
Fig. 7. Federated prediction serving framework based on Bayesian game. authors in [95] proposed an incentive mechanism for cross-silo
FL. As shown in Fig. 8, in cross-silo FL, each organization
is not only the data owner that cooperatively trains a global
decreases dramatically over time, which is consistent with the model from a third party entity, but also the owner of the
theoretical analysis. global model that utilizes the resources of organizations to gain
To motivate the self-interested MOs to provide truthful revenue from its market. In the proposed incentive scheme,
results for prediction services, a non-cooperative Bayesian each organization submits the message files, including the
game-based incentive mechanism is proposed in [54]. The number of training rounds that it can participate in and the
system model is shown in Fig. 7 which consists of prediction unit monetary reward per training round that it hopes to
SPs, users, server and a smart contract. Specifically, the SPs gain, to the server. Once receiving organizations’ message
who own various ML models monetize their prediction query profile, the server calculates and announces the processing
services on the blockchain. The user can query the prediction capacity used by each organization for local training and their
services through the smart contract. Moreover, the contract respective monetary transfer received from or paid to other
will assign the users’ deposit to the providers according to the organizations. Each organization optimizes its message profile
respective accuracy-aware scores calculated by the server. In to maximize its payoff, which is defined as its utility and
addition, if the SP does not offer the promised prediction, it additional monetary transfer minus the cost. The utility of
will be punished through submitting a deposit. The strategy the organization is a function of the difference between the
of the SP is to choose whether to participate in a prediction precision of the global model without training and that of the
service, and if participating, what quality level local model to trained global model. A non-cooperative game with perfect
provide. The utility is the difference between the payment from information is used to model the strategic interaction among
users and the cost for providing prediction and its deposit. To organizations, which is formulated as a social welfare maxi-
obtain the optimal behavior strategies of SPs, the objective of mization problem, i.e., maximizing the overall payoffs of all
the proposed mechanism is to maximize the overall probability organizations. In order to obtain the NE solution, a distributed
of Kullback-Leivler divergence between each SP’s prediction algorithm inspired by the distributed accelerated augmented
and the true prediction, subject to IR and BB. A Bayesian Lagrangian method [96] is proposed. The simulation results
NE can be obtained through applying the divergence-based show that the proposed mechanism can enable the organiza-
Bayesian Truth Serum method [91]. The simulation results tions to achieve a higher social welfare through participating
show that the participating SP who offers a truthful prediction in cross-silo FL. A scenario that the organizations determine
will receive sufficient incentives which demonstrates the ef- the numbers of participating rounds considering their valuation
fectiveness of the proposed pricing mechanism. However, the on precision and their computational and communication costs
scenario where the input data is injected into the imperceptible can be considered in the future.
perturbations is not considered.
To detect and discard bad updates provided by clients,
the authors in [92] model the aggregating process in the C. Incentive Mechanisms Based on Other Game Methods
FL system by a mixed-strategy game. The players are a To stimulate the users to participate in the FL system in
server and the clients. The valid strategies of the clients are a long-term, the fairness allocated to the users should be
to send good or bad updates while the server can accept guaranteed. To achieve fairness, hedonic game and coalitional
or ignore these updates. When a client sends good updates game are appropriate solutions. Similar to [83], the authors in
and the server accepts them, both of them will earn some [97] considered an FEL system in which edge devices are not
payoffs. A trustworthy metric is used to measure a good only producers but also consumers. Differently, they studied
or bad update. This metric is inversely proportional to the the utility maximization problem only for edge devices. This
 13

TABLE III
A PPLICATIONS OF N ON - COOPERATIVE G AME AND O THER G AMES FOR I NCENTIVE M ECHANISM D ESIGN IN FL

Market Structure
Ref. Scenario Game Model Mechanism Objective Solution
Seller Buyer Item
Individual utility
Evolutionary Hamilton
MDGs’ Given the training price offered by the maximization for
General game, solution,
[85] MDGs MOs learning MDGs, the evolutionary equilibrium MDG buyers, and the
FL system differential evolutionary
[86] service selection strategy for the MOs is determined. accumulative profits
game equilibrium
maximization for sellers
The training strategies selection problem of
Mobile the mobile devices is formulated as
General Evolutionary Mobile Sellers’ individual utility Evolutionary
MOs evolutionary game. The uniqueness and
devices’
[88] FL system game devices maximization equilibrium
datastability of the evolutionary equilibrium
solution is proved.
The strategic behaviors of participating
Truthfulness, individual
FL Non- The providers in federated prediction is modeled
rationality, budget Bayesian
prediction cooperative Prediction providers’ as a Bayesian game. The Bayesian Nash
Users feasibility, fair reward, Nash
[54] serving Bayesian SPs prediction equilibrium participation strategy is obtained
and sellers’ utility equilibrium
framework game service applying the idea of divergence-based BTS
maximization
method.
Sellers provide good or bad updates for the
Mixed
Clients’ buyer, and the buyer selects to accept or Payoff maximization for
Mix-strategy Central strategy
Robust FL Clients learning reject these updates. The probability that the both the sellers and the
[92] game server Nash
service clients provide good updates is calculated by buyer.
equilibrium
using mix-strategy game.
Once receiving the participated round and
monetary transfer from the organization, the Efficiency, individual
Non- Organizations’
Cross-silo central serve calculates them. The sellers rationality, budget Nash
cooperative Organizations Organizations learning
[95] FL determine their optimal decisions through balance, and sellers’ equilibrium
game service
solving the social welfare maximization payoff maximization
problem using the Lagrangian.
Global profit
Edge The equilibrium solution for the devices’
maximization for the
Cooperative Edge Edge devices’ participating strategy is derived through Equilibrium
FEL buyer, and guarantee
[97] game devices server learning decomposing the original problem and solution
incentive compatibility
service solving it.
for the sellers
Agents selects an optimum cluster that
Data Agents’
General Hedonic enable their utility to be improved to join, Stable cluster formation Nash
owner MAE learning
[98] FL system game and the utility of each players is allocated by and budget balance equilibrium
agents service
MAE according the marginal contribution.
Guarantee individual
The sellers choose optimum contract bundles
rationality, incentive
Contract for utility maximization and contribute the
FL in Workers’ compatibility and
theory, Model corresponding data to the training. The Optimal
mobile Workers training revenue improvement
[99] coalition owners buyers adjust their reward strategies and solution
networks data for workers, buyers’
game collaborative with other owners to form
marginal contribution
federation to maximize their payoffs.
maximization
Given the sellers’ data pricing, and then the
Data
buyers determine their optimum bid. The The utility maximization
Proof of Reverse Data Pool providers’ Optimal
Euler-Lagrange equation and variational for both buyers and
[100] FL game providers members training solution
method are used to obtained the best sellers
data
strategies of both parties.

a decision on whether to join a round of FEL so as to gain

a payoff, given other devices’ participation decisions. The
payoff of the device is the difference between the income
owing to serving the device users and the cost consumed
for local training and updating. The device’s objective is to
maximize its payoff with the optimal participation decision.
ĸ ĸ Considering the privacy among edge devices, a global profit
ĸ Local training Monetary
transfer
maximization (GPM) problem, i.e, maximizing the overall
Organization 2
Organization 3 expected profits of all devices, is formulated to find the best
Organization 1 Producers participation strategy for the device from the global viewpoint.
Consumers
And the definition of correlated equilibrium is introduced to
guarantee that no player can deviate from the assigned strategy
Users
to maximize its profit given others’ strategies. To solve the
(Buyer)
optimization problem in polynomial time, the original problem
is decomposed into several sub-GPM problems according to
Fig. 8. The trading market based on non-cooperative game in cross-silo FL the number of edge devices. The simulation results show that
system. Note that the diagram only shows the scenario that organization 1 the device who has larger data contribution than others is more
acts as the consumer which uses the model trained by all three organizations.
likely to participate in the FEL. However, the learning service
latency is not taken into account which is important to the
edge intelligence service.
relationship is modeled as a participation game, and each edge
device acts as a player. In the game, each edge device makes To deal with stable clustering problem of data owner agents
 14

contributing to federated training process, in [98], the hedonic In [100], a novel consensus mechanism, proof of FL, is
game is used to simulate the problem where the agents act proposed, in which the pool members are the buyers to coop-
as the players of the game and the clusters as the coalitions. eratively train a global model from the pool manager based
The system model includes multiple agents (i.e., sellers) which on their privacy data purchased from the data providers (i.e.,
cooperate with other agents selectively to form clusters and sellers). To guard against the risk of privacy data leakage in
train model, and a model aggregating entity which as a utility FL, a reverse game-based data trading mechanism is proposed
allocator (i.e., buyers) is responsible for assigning a utility to which enables a pool member (miner) to maximize its utility
all possible clusters. The utility of any cluster is the sum of only when it trains the model without any leakage. The
the raw utility and learning utility. The strategy of the agent strategy of the data provider is to determine an optimal data
is to decide which cluster to join with the aim of maximizing pricing rules to maximize its utility, which is the final price of
its utility, and the utility is the sum of the minimum payment the traded data minus the expected loss brought by sensitive
price that any agent can obtain if it join a cluster and the gain data leakage. Given the data provider’s pricing rules, the pool
owing to joining a specific cluster. To ensure the Nash-stability member calculates its optimal bid according to its real privacy
of the hedonic game, the definition of the Nash-stable set is information, i.e, the IC property, for maximizing its utility. The
introduced to design an effective utility allocation method for utility is the legally expected net profit from this data trading
agents. For all clusters, the utility allocation method satisfies and the expected profit of leaking sensitive data minus the
the property of budget balance since the overall utility of all final price of the traded data. The optimal strategies of both
agent in one cluster is not greater than the cluster’s utility. parties can be obtained through solving the Euler-Lagrange
The theoretical analysis prove that when the utility function equation of their utility by adopting the variational method.
of a cluster is superadditive and preferences of a play are The simulation results show that the higher reputation value
additively separable and symmetric, it always admit a Nash- of the pools , the bigger probability of successful data trading
stable coalition partition. and the higher utility of both parties.
Unlike [98] and [101] which studied the federation among Summary: In this section, we have reviewed the applica-
DOs, the federation of multiple MOs is considered in [99]. tions of game theory approaches for the incentive mechanism
Firstly, to motivate the worker to participate in FL, a contract design in FL. The objective is to find the equilibrium solution
theory-based incentive mechanism in mobile crowdsensing among players to achieve utility maximization, while satisfy-
network is proposed. In this system, the MOs (buyers) train ing IR, IC and BB. The Stackelberg game-based approaches
local models based on the data collected by workers (sellers), are summarized along with the references in Table II, and
and collaborate with other MOs selectively to form federations Table III summarizes the approaches based on non-cooperative
to maximize their own profits. Given the prevailing federation game and other games. As observed from the tables, the
parameters (i.e., others’ strategies for workers’ contribution), Stackelberg game are used to maximize the utilities for both
every MO’s contract-theoretic incentive mechanism is de- the MO and the DO while non-cooperative game is mostly
signed separately with the aim of maximizing their marginal adopted to maximize the utility of DOs with competitive
contribution while minimizing incentive cost paid to workers. relationship. In fact, auction is also an effective incentive
The strategy of the MO is to determine an optimal reward method to motivate the players to join in the FL, especially in
to maximize its profit, which is defined as its marginal a high competition environment with limited resources. The
contribution minus the incentive cost and resources cost for next section discusses how to apply auctions for incentive
model training. The marginal contribution of the MO is the mechanism design in FL.
utility it produces after joining the FL. Moreover, the strategy
of each worker is to determine its data quantity contribution V. A PPLICATIONS OF AUCTION FOR I NCENTIVE
to maximize its individual utility, i.e., the difference between M ECHANISM D ESIGN IN FL
the reward from the MO and the cost incurred by collecting Auctions have some good properties. For example, IC
data. Given a set of feasible data contribution subsequences, encourages the clients to report true cost that gain the utility of
the optimal reward strategy is obtained by using the approach the model owner or encourages the model owner to report its
in [102]. Using the optimization tool, i.e., cvxpy [103] or the true value of the computing resource, while IR guarantees that
Bunching and Ironing algorithm [104], an optimal set of data every client joining the FL has a non-negative utility. Thus,
contribution is obtained. Then, a coalitional game is designed auction is a very effective solution for the incentive mechanism
to model the problem of federation formation, and the merge in FL.
and split algorithm proposed in [105] is adopted to study
the stable federation partition given different characteristics
of data quantity and quality the MOs have. The numerical A. Incentive Mechanisms Based on Sealed-bid Auctions
results show that the reward of workers increases as its data In a sealed-bid auction, sealed bids from bidders are si-
contribution increases and there exists the federation formation multaneously sent to the auctioneer. This approach is mainly
equilibrium in the proposed mechanism design. However, applied in participant selections for FL. The MO sends a
there may be competing or malicious MOs which can affect request of FL task to the DOs. After receiving the service
the performance of a federation adversely. Furthermore, the request, each DO (as a bidder) submits a message to the MO
reputation mechanisms [106] can be introduced to choose (as the buyer/auctioneer), which includes data such as bidding
reliable MOs. information, cost, and computation capacity. Particularly, the
 15

bidding information submitted by each DO is not open in the Buyer Devices Worker Devices
auction and FL trading process. In each round of auction, the (Bidders) (Sellers/Auctioneers)
MO selects the DO which meets the training conditions of
FL at this stage through solving a winner selection problem.
The selection process is repeated until the FL task can be
completed. Bids & Resource demand
1) FPSB Auction: To motivate data owners to contribute & Task delay deadline
their idle resources for the performance improvement of Phase 1
computation-intensive application, the authors in [39] designed Candidate result & Claimed
prices & Execution time
a double auction-based FEderated learning and Subjective
logic-driven distributed Task allocation system in mobile de- Selection result
vice cloud, namely FEST. In the FL market, it is necessary & Computational task
to match the bidders and the sellers since there are multiple Phase 2
bidders (model owners) and sellers (data owners). In FEST, Computational result
buyer devices as bidders recruit high-quality worker devices, Phase 3
i.e., sellers, with reliable and experienced execution perfor- Payment
mance to achieve the best system performance. The FEST-
auction process consists of three phases: bidder selection, task Fig. 9. Double auction based distributed task allocation in mobile device
allocation and worker payment assignment, as shown in Fig. 9. cloud.
In the first phase, after receiving the task requests (including
buyers’ task bid, resource requirement and delay requirement
of the task) from the bidder, each seller computes the priority to maximize the overall system performance or are selfish to
factor of each bidder, which is an integrated metric with maximize their own performance. For the cooperative FL SPs,
related to task bid, execution time and preference to seller. intra-service and inter-service resource allocations are consid-
Then each seller greedily selects bidders sorted based on ered. The optimal FL round length is obtained in intra-service
the descending order of priority factor until it satisfies the problem through optimizing the bandwidth allocation among
resource, energy and maximum workload constraints. In the the clients of each FL service. The optimal solution to the
second phase, a bidder only recruits one seller for a computing intra-service bandwidth problem is then used to solve the inter-
task. In fact, a bidder can win bids from multiple sellers. service problem, and the bandwidth allocated to each FL SPs
Therefore, each bidder chooses the best one from multiple is computed by using dual decomposition [110]. In addition,
candidate sellers which can maximize its utility. The utility of to address the selfishness issue among FL SPs, a multi-bid
the bidder is a composite function of the bidder’s valuation for auction mechanism is designed to allocate bandwidth to SPs
resources and the seller’s ask price for resources as well as its so as to maximize the SPs’ utilities. The network operator
execution time and reputation value. In addition, a payment (seller) finds an optimal allocation scheme to maximize each
policy based on the approach in [107] is designed where SP’s (buyer) utility through the use of the KKT condition.
the seller providing high-quality service is rewarded whereas Each SP is then charged according to the second-price auction
the seller failing to rendering the required task quality is payment policy. The simulation results show that the proposed
punished. Theoretical analysis proved that the proposed FEST two bandwidth allocation schemes are superior to benchmark
framework achieves the properties of CC, IR, truthfulness, and algorithms in terms of inherent fairness by design, where band-
BB. Simulation results imply that the FEST system achieve width is equally or proportionally allocated among clients and
performance improvement as high as 30% and 25% in terms SPs. However, when a client can simultaneously participate
of quality-of-experience and utility of the bidder, respectively, in multiple FL service, resource allocation should take into
compared with the truthful incentive mechanism (TIM) [108] account both bandwidth resource and client computational
and distributed truthful auction mechanism (DTAM) [109] resources.
schemes. FEST performs better than the two existing ap- Given the growing complexity and capacity of the future
proaches since they only consider the resource availability of network, it is difficult to completely model or solve the
sellers while not considering the quality-of-experience of the dynamic conditions in the network with the standard ap-
bidders. However, the growth of the number of FL worker will proaches. The authors in [111] proposed deep learning-based
lead to much higher computational complexity, which makes (DL) optimal auction incentive scheme, where multiple MOs
the FEST based auction approach not suitable to large-scale (buyers) intend to buy the 3C-L resources (i.e, communi-
FL applications. cation, computation, caching, and learning resources) from
2) SPSB Auction: The aforementioned works are for re- a worker (seller). In this incentive mechanism, the concept
sources allocation in which only a single FL service is consid- of information freshness, i.e., Age of Information (AoI) is
ered. However, as the diversification of ML-driven applications adopted. Meanwhile, the DL-based pricing scheme is proposed
develop and grow, it is predicted that the wireless network to price the workers contribution in terms of AoI, in which
will host multiple co-existing FL services. To fill the gap, both conditions of truthfulness and revenue maximization of
the authors in [67] considered a multi-FL service scenario, the seller are ensured. Although the proposed incentive scheme
where FL service providers (SPs) cooperate with each other uses the second-price auction to determine the winner, it allows
 16

the worker to earn higher revenue than that of the conventional Model owner
second-price auction scheme. The reason is the information (Buyer)
asymmetry among the buyer and the sellers can affect the
performance of the latter scheme, but the former can avoid
this issue through learning from the historical data so as to
improve the performance.
To overcome the issue of the failure of the communication Task
link and missing nodes that may affect the performance of Task
execution
Bids Distribution Payments
FL, a communication-efficient FL scenario where the UAVs results
ś
as wireless relays to improve the communication between IoV Ś Ŝ ŝ
components (workers, i.e., DOs) and the FL server is consid- Data owners
ered as proposed in [112] and [113]. The authors presented (Sellers)
a joint auction-coalition formation framework to allocate the
UAVs coalitions to cells of workers. Note that the payment that
a cell receives depends on the total time needed to complete
the FL task. Therefore, the workers in a cell have higher
incentive to bid for the UAV coalitions that can maximize
the utility of the cell(i.e., the difference between the valuation Fig. 10. Reverse auction based incentive mechanism for client selection in
of the cell for a coalition and its payment price), and then and FL.
pay them based on the second-price auction. Furthermore, the
UAVs aim to maximize sum of their individual profits through model for cooperative production of virtual products is pre-
finding a stable partition. To achieve the objective of both sented in [115] and [116]. Specifically, a mechanism similar to
cells and UAVs, a merge-and-split algorithm is proposed to FVCG, Procurement-VCG (PVCG) is proposed on the supply
find the optimal coalitional structure. Simulation results show side, and the Crémer-Mclean mechanism [117] is used to
that the proposed join auction-coalition scheme achieves the overcome the demand-side information asymmetry (the model
highest profit of coalition, compared with the merge-and-split users’ valuations on the trained FL model). Differently, in
with random allocation and random partitioning with second- PVCG, if one producer (i.e., the seller) cannot offer the data it
price auction. In the future, a joint trajectory optimization and claims at the time of bidding, the coordinator (the intermediary
energy efficient coalition formation game can be considered between producers and model users, i.e., the buyer) will
to complete the FL tasks more efficiently. impose a high punishment on it. The theoretical analysis
3) VCG Auction: In [114], the authors proposed Fair- demonstrated that the Crémer-Mclean mechanism, together
VCG (FVCG) as an improvement of VCG mechanism for with the procurement auction, maximizes producer surplus by
incentivizing DOs to contribute their data and truthfully report motivating producers to offer all their data to the federation
their cost in FL training processes. FVCG aims not only to and truthfully report their private information. However, when
maximize the social welfare but also minimize unfairness of the number of producers increase, more advanced algorithms
the learning federation without the FL server (buyer) knowing is required for FVCG and PVCG to learn the two payments.
the cost type and data quality of DOs (sellers). Guaranteeing In addition, the effectiveness and superiority of FVCG and
the fairness among DOs can encourage them to improve PVCG need to be verified compared with other sharing rule
their participation level. The proposed FVCG approach mainly (e.g., SV, [118], [119] and Labour Union [120]).
includes two steps: 1) the calculation of the data acceptance
vector, which illustrates the FL server decides how much data
to accept from each DO; 2) the calculation of the payment B. Incentive Mechanisms Based on Reverse Auctions
vector (including the VCG payment vector and the adjustment For reverse auction, sellers bid for the prices at which they
payment vector), which indicates the payment each DO can are willing to sell their resources. One of major advantages
receive from the server. In particular, the adjustment vector is of the reverse auction is to incentivize the participants, e.g.,
defined as the solution of a functional optimization problem, the data owners, to report their types, e.g., the cost of FL
which is difficult to solve. FVCG adopts an unsupervised training. This advantage is important to the model owner
and composite neural network based approach to solve the since it helps to reduce the incentive cost. As shown in Fig.
optimization problem since the neural network can approx- 10, there are four steps in a typical reverse auction based
imate continuous function with an arbitrary precision. The incentive mechanism including bidding, winner selection and
experimental evaluation results reveal the reasonableness of task assignment, feedback of the task results, and payment
FVCG and the proposed neural network-based approach. determination.
The proposed incentive mechanism in [114], i.e., FVCG, In [121], the authors modeled the incentive mechanism
overcomes the supply-side information asymmetry and ensures between the BS and multiple mobile users as a reverse
the fairness among the DOs in the FL process. In practice, combinatorial auction game, where the BS acts as the buyer
the information asymmetry is multidimensional including the (also the auctioneer) and the mobile users as the sellers are
demand side and the supply side, both of which affect the allowed to bid for the combination of resources. In particular,
sustainability of federation. For this reason, a game-theoretical each mobile user sends a message consisting of the required
 17

amount of resources, local accuracy, and the corresponding with the benchmark scheme only depending on the bidders’
energy cost to the BS. Given the maximum tolerable time of bid prices, and the social welfare is improved in DRLA.
FL (the upper bound of the total time of one global iteration), However, there is a drawback in the approaches mentioned
each mobile user determines the optimal bid, which includes in [122] and [124], i.e., it needs to obtain the global distribu-
the uplink transmission power, the CPU cycle frequency and tion of all data before calculating EMD, which is impractical
the local accuracy level, to minimize its energy cost. And a under the setting of FL. Therefore, the authors in [125] adopted
low-complexity iterative algorithm is proposed to obtain the the reputation mechanism to indirectly represent data quality.
optimal solution of the problem. Once receiving the bids from Based on this method, they designed an reverse auction-
all mobile users, the BS performs winner selection and pay- based incentive mechanism (RRAFL), which helps the task
ment determination by solving an social welfare maximization requester (i.e., the buyer) choose high-quality and reliable
(SWM) problem using the primal-dual based greedy algorithm. mobile devices (i.e., the sellers) for performing the task.
Note that the utility of BS is the difference between the BS’s RRAFL is mainly composed of four parts. In the first phase,
satisfaction level (based on the local accuracy that the user can the comprehensive reputation of mobile devices is calculated.
offer in the bid) and the payment for mobile users. Simulation The next phase is winner selection and payment. Based on the
results show that the social welfare obtained by the proposed reputation value, the candidates calculate their unit reputation
mechanism is 400% larger than by the fixed price scheme since bid price, and then they are sorted in a non-decreasing order
the fixed price mechanism heavily depends on the prices of of their price. The requester select K candidates as winners
the resources. from the ranking form from front to back which can maximize
To avoid the collusion between the untrustworthy third party its utility, and pay to them. The utility of the request is a
and the ENs, the authors in [122] presented a a decentralized function of the comprehensive reputation. After the model
and transparent blockchain-based resource trading system for training, the winners’ contribution is measured to reevaluate
FL in edge computing (EC). To encourage both the resource and update to their reputation value. The experimental results
requester (individuals or companies who need model training) show the effectiveness of RRAFL. In the future, the further
and ENs (the owner of data and computing capacity) to join in study on how to measure the participants’ contributions more
the system, the incentive problem among them is formulated reasonably can be considered.
as a data quality-driven reverse auction (DQDRA) with the Paying attention to the same problem as that in [125],
aim of maximizing the valuation of the requester about the the author in [126] proposed a cluster-based clients selection
model accuracy. Accordingly, ENs, i.e, sellers, determine the method. The system model consists of a cloud aggregation
optimal bids which can maximize their utilities (including data server and multiple edge clients, i.e., SPs. Accordingly, the
size, the EMD metrics, i.e., a metric for data distribution, clients with the similar initial gradient are divided to the same
and prices) and submit them to the requester, i.e, the only cluster firstly. Second, to overcome the excessive consumption
one buyer. Once receiving the ENs’ information, the requester caused by random selection, an auction-based clients selection
decides the winner and the payment to them based on the method is designed in each cluster, in which the clients as
proposed monotone greedy algorithm by marginal density bidders provide data services and computing services, and the
for its valuation maximization. The service valuation of the cloud server as an auctioneer (also the buyer) trains a global
requester is a function of training data size. The simulation model. In the auction, each client determines its optimal bid
results show that the valuation of the requester in DQDRA price that maximize the expected revenue through using the
is larger than the valuation of the requester in the GREEDY- first-order optimal condition. Then, the sever randomly selects
SM and RANDOM-SM mechanisms proposed in [123]. The a group, and selects K clients with the lowest bid in this group
trading market with multiple competitive requesters can be as winners. The minimum local data size among winners as
taken into account in the future. the threshold. The winner selection process is repeated among
The same system model and auction mechanism to that in clients with the data size greater than the threshold in each
[122] can be also found in [124]. However, in [124], the buyer group. The simulation results show that the auction-based
is an FL platform, and the sellers are DOs, i.e., FL workers, clients selection scheme can show a faster convergence rate
which report the requested wireless channel to communicate compared to randomly selecting a client from each groups.
with the platform. The FL training problem between the To motivate power users to participate in the interruptible
platform and DOs is converted to a SWM problem where the load management, the authors in [127] proposed a multi-
utility of the platform is the data utility minus the total cost and attribute sealed auction game to simulate the interaction be-
the total payments to workers. To tackle the SWM problem, tween the power company and the power users, with the aim of
the original auction is decomposed into a set of sub-auction maximizing the power company’s revenue and finally decide
in terms of EMD. After that, each group greedily selects the the list of participating users. The auction model consists
workers and determines the payments based on the marginal of two main phases, i.e., user bidding and user selection.
virtual social welfare density. To further improve the social In the first phase, each power user reports the amount of
welfare, the author proposed a DRL-based auction (DRLA) interruption and its quotation to the company. In the second
which use the graph neural network to extract the features from phase, the K-means clustering method is used to cluster the
workers’ reported types and automatically decides the service users according to each users’ load features. Based on the
allocation and payment. The experimental results show that the objective of minimizing the total expenditure, the company
DRLA and RMA can achieve higher social welfare compared chooses the users from various clusters considering the users’
 18

TABLE IV
A PPLICATIONS OF S EALED -B ID AUCTION M ODEL FOR I NCENTIVE M ECHANISM D ESIGN IN FL

Market Structure
Ref. Auction Model Mechanism Objective
Seller Buyer Item
Based on buyers’ bids, the sellers determines buyer Execution time of FL task
Sealed-bid Worker Buyer Computational winning candidates by using the greedy approach. The minimization, Buyer devices’ utility
[39] double auction devices devices resources seller that can maximize the utility of the buyer is maximization, CC, IR, BB, and
selected. truthfulness
Buyers submit to the auctioneer their bids including the
Second-price
Network FL service requested bandwidth and the unit price, the auctioneer Utility maximization for SPs, IR, IC
sealed-bid Bandwidth
[67] operator providers allocates bandwidth to buyers based on the market and fairness
auction
cleaning price.
MOs’ bids are transformed to new bids satisfying IR
deep
3C-L and IC properties, the winners are decided based on Revenue maximization for the
learning-based Worker MOs
[111] resources second-price auction and the payment price of them is seller, IR, and IC, best matching
optimal auction
derived using ReLU.
Second-price Buyers submit their bids to UAV coalition with
Train Total profit maximization for sellers,
[112] sealed-bid UAVs Workers sufficient energy, and then each coalition is allocated to
resources IC,IR
[113] auction cells of workers.
Based on the data quality and privacy cost of sellers,
Training the buyer determine the amount of acceptable data to
VCG auction DOs FL server IR,IC, SWM, WBB and fairness
[114] data maximize its revenue. The payment function is derived
by using composite neural networks.
Sellers submit to the auctioneer their bids including
SWM, truthfulness, ex-post
Virtual their capacity and type parameters, the coordinator
VCG auction Producers Consumers allocative efficiency, ex-post IR,
[115] products determines the acceptance ratio and transfer payment to
WBB
sellers.

TABLE V
A PPLICATIONS OF R EVERSE AUCTION M ODEL FOR I NCENTIVE M ECHANISM D ESIGN IN FL

Market Structure
Ref. Scenario Mechanism Objective
Seller Buyer Item
Wireless Mobile devices submit their optimal bids for these
Mobile Training SWM, energy cost minimization for
cellular BS resources, and the winner selection problem is then
[121] users resources sellers, truthfulness, IR and CE
network solved by using primal-dual based greedy algorithm.
Service valuation maximization for
Edge Data The winner and their payment are determined based the buyer, utility maximization for
ENs Requester
[122] computing resources on the monotone greedy algorithm. sellers, budget feasibility,
truthfulness, and CE.
Wireless FL FL Data Same as [122], but the improvement of social welfare
DOs SWM, IC, IR, and CE
[124] service market platform resources is further studied based on DRL.
Mobile Data The winner selection and payment are determined Utility maximization for the buyer,
Horizontal FL Requester
[125] devices resources based on greedy algorithm. IC, IR, budget feasibility, and CE
The optimal bid prices for sellers can be determined
Edge Cloud Training
MEC using the first-order condition, and the K sellers with Revenue maximization for sellers
[126] clients server resources
lowest bid are selected as the winners.
Power demand Power Power The participating users are determined based on the The total cost minimization for the
Power
[127] response users company price and the expected response rate of users. power company, and fairness
The optimal uplink transmission power and CPU
Cellular Utility maximization for sellers,
Computational frequency of sellers can be obtained using iteration
wireless Users BS social cost minimization for the
[128] resources algorithm, and then the randomize auction scheme is
network buyer, truthfulness, IR, and CE.
used to tackle the winner selection problem.
Given the buyer’s scoring rule, sellers determine their Profit maximization for both sellers
Training optimal bids. Then, the buyer selects K sellers with and buyer, lightweight incentive
MEC ENs Aggregator
[129] resources the highest scores as winners by using Lagrange mechanism, IR, IC, and Pareto
multiplier method. efficiency
The learning tasks allocation and payment
The sum of quality of aggregated
Mobile FL Training determination are determined by solving the sum of
Horizontal FL model updates maximization,
[130] users platform resources quality of aggregated model updates maximization
truthfulness, IR and CE
problem based on the greedy algorithm.

bids and the expected response rate. Meanwhile, the fairness cost, to maximize its utility. The utility of the user is the
mechanism in the scenario where users have participated difference between the reward and the true cost. The optima
in multiple consecutive times is considered. The simulation uplink transmission power and CPU frequency can be obtained
results show that the proposed greedy approach can reduce using the iteration algorithm. The winner selection problem for
the expenses of power company and improve the selected the BS is formulated as a social cost minimization problem.
probability of small business and residential users. However, To deal with the NP-hard minimization knapsack problem,
the bidding sequence should be considered since it may affect the framework of randomized auction [131], [132] is adopted.
the user selection of long-term demand respond process. The simulation results demonstrate the proposed randomized
The system model in [75] is also considered in [128]. auction scheme can guarantee the approximation factor of the
However, the difference is that the interaction between the integrality to the optimal minimum cost. However, the work
BS and users is modeled as a randomized auction where the does not consider the privacy protection of bidders.
former is the buyer and the latters are the sellers. In particular, In [129], FMore, a multi-dimensional procurement auction-
each users determines its bid, consisting of the resources based incentive mechanism with only one buyer, was proposed
(uplink transmission power and CPU frequency) and training with the aim of motivating high-quality ENs with low cost
 19

to join in FL. The system model includes an aggregator is to maximize the SWM, the revenue of resources providers,
at the remote cloud, i.e., a buyer, which rents the data, and the FL system performance. The reviewed approaches
computation and communication resources for FL from ENs are summarized along with the references in Table IV and
i.e., sellers. Specifically, when receiving a bid request with Table V. As seen, the auction models are mostly used to
scoring function from the buyer, the ENs decide whether select high-quality participants to maximize the performance
to bid or not according to their available resources. The of FL system. However, the collusion problem is unfavourable
scoring function is related to the resources quality and sellers’ for auction-based incentive mechanisms. Thus, it is crucial to
expected payment. If one EN determines to join in FL, it will develop more effective methods to prevent dishonest bidding.
reply the aggregator the response message (ask) containing In the next section, we will discuss how to apply the contract
the resources quality and the corresponding prices according and matching theory for incentive mechanism design.
to sealed-bid auction. The K ENs with the best scores are
chosen for participating in collaborative learning, and the VI. A PPLICATIONS OF C ONTRACT AND M ATCHING
payment for these nodes is implemented according to the first- T HEORY FOR I NCENTIVE M ECHANISM D ESIGN IN FL
price auction policy. Note that the proposed multi-dimensional Due to the clear decision tree of duties and obligations,
auction has multiple winners which is different from [39]. contract theory is widely applied in FL systems. For the
Extensive simulations show that FMore can speed up federated contract theory based incentive scheme, the MO proposes a
learning via reducing training rounds by almost 51.3 %, and list of contracts to DOs. In particular, the MO is not informed
improve the model accuracy by 28% for the LSTM model about the private type of DOs when designing the contracts.
compared with the classic FL scheme, which enables FMore as Each DO then proactively selects the appropriate contract type
a lightweight resource auction approach for FL. However, the that maximizes its own utility based on the evaluation of their
budget constraint of the aggregator is not considered in FMore, own abilities. Besides, the matching theory is used to match
which is left to be extended for the future work. Moreover, the MO with the DO optimally for the efficient FL training.
for each EN, whether the selected probability should be the
same or different remains to be further studied.
Although the existing works that have applied the reputation A. Incentive Mechanisms Based on Contract Theory
mechanism can select the high-quality DOs to join in FL, none The contract theory-based incentive mechanism aims at
of them considers the learning quality of participants, which maximizing the payoff or utility of the MO. Generally, the
can significantly affect the performance of FL and the direction problem is to maximize the objective function, i.e., the MO’s
of incentive. To bridge this gap, the authors in [130] proposed utility, subject to IR constraint and IC constraint. The first
a novel distributed learning system named FAIR, i.e, Federated constraint indicates that the payoff gained by the DO under
leArning with qualIty awaReness. Particularly, FAIR integrates this contract is not less than its reservation payoff if not
the reverse auction-based incentive mechanism design and the participating. The second constraint means that the DO’s
quality-aware model aggregation algorithm, which allows it expected payoff is maximized when signing the contract.
to facilitate precise user incentive and model aggregation. The The authors in [134] proposed a contract-theoretic task-
system mainly consists of three components: the learning qual- aware incentive mechanism to model the tradeoff between
ity evaluation, incentive mechanism and model aggregation. preferences for service latency and AoI of different training
Specifically, the historical quality records are firstly leveraged tasks. The problem of training resource trading for the MO
to estimate the current learning quality. Based on the estimated having different preferences to the service latency and AoI is
quality, a reverse auction incentive mechanism is then estab- considered. The MO acts as the employer to set the contract for
lished to encourage mobile users participation, in which the the different FL tasks as (reward, the number of update cycles),
mobile users (the sellers) send their bids to the cloud platform and the workers as the employees which select one optimal
(the auctioneer). To maximize the collective learning quality of contract to participate in FL. Further, the authors considered
all the participants in each iteration, within the limited budget, to accurately design the reward structure, the update expense,
a learning quality maximization (LQM) problem is formulated. e.g., the energy consumption incurred in data collection and
A greedy algorithm based on Myerson’s theorem [133] of model training is required to be known. This asymmetric
truthfulness is designed to solve this NP-hard problem. Thus, information is tackled by using the contract theory. To obtained
the learning task allocation and reward assignment is deter- a feasible contract, the profit maximization problem for the
mined. What’s more, a new aggregation algorithm is proposed MO is built, subject to IR and IC constraints for the utility of
to filters out non-ideal model updates for the enhancement of worker. For the future work, the deviation from an ideal cache
the global model. The performance evaluation results show can be considered and then a caching scheme can be designed
that the performance of the ResNet model can be improved to better manage the AoI-service latency tradeoff.
by 68.9% using FAIR compared with the knapsack greedy and Considering the challenges when implementing the FL in
bid price first mechanisms. For the future work, integrating IoV networks (such as dynamic activities and the limited pay-
the communication and computation performance into FAIR ment budget), the authors in [135] proposed a novel economic
to enhance its robustness when employed in practical systems framework to address these issues. A multi-principal one-
can be considered. agent contract is designed where the best smart vehicles (SV,
Summary: In this section, we introduce the application of as principals) non-collaboratively offer contract agreements
auction model for incentive mechanisms in FL. The objective (containing information significance and offered payment) to
 20

the vehicular service provider (VSP). The VSP (as the agent) Unlike the contract-based incentive mechanisms that con-
is then in charge of optimizing the offered contracts. The sider single-dimensional privacy information, the work in
payment budget of the VSP is referred as the asymmetric [140] proposed the multi-dimensional contract theoretic ap-
information. Specifically, the VSP perform an SV selection proach which considers the user’s two-dimensional privacy
method to decide a set of the best SVs for the FL process information including training cost and communication delay.
according the significance of their current locations and in- The interaction between the FL serve and users is modeled
formation history. Then, each selected SV can collect on- as a labor market, in which the former act as the employer
road information and offer a payment contract to the VSP and the latter act as the employees. The key contribution
based on its collected QoI. This contract model is modeled of this approaches is summarizing users’ multi-dimensional
as a profit maximization problem for the VSP and SVs is private information into a one-dimensional criterion (i.e., the
formulated amid the limited payment budget and common server’s preference on different user’ types) that allows a
constraints (i.e., IR and IC). To find the optimal contracts for complete order of users. Three scenarios are considered in-
the SVs, the problem is transformed into an equivalent low- cluding complete informational scenario, weakly incomplete
complexity problem. The equilibrium solution is the found information scenario, and strongly incomplete information
based on the proposed iterative algorithm. The experiment scenario is considered. In the first scenario, the serve knows
results demonstrate that the proposed scheme can improve the each user’s type, the contract design is to minimize the server’s
social welfare of the network up to 27.2 times and convergence cost with the IR constraint. In the second scenario, the same
57% faster compared with those of random and round-robin objective with IR and IC constraints is considered since the
scheduling methods. server does not know which user belongs to which type. In the
The economic approach in [135] is also applied into the third scenario, the contract design is to minimize the expect
electric vehicle network as proposed in [136]. In this network, cost of the server, where the objective function is similar to
multiple charging stations (CSs), i.e., principals (employers), that in the second scenario excepted the expectation part. The
firstly implement the energy demand prediction method lever- simulation results show that all the designed contract in the
aging FL, and then reserve energy from the smart grid provider three information scenarios can achieve up to 73.72% cost
(SGP) in advance based on the prediction results to maximize reduction of uniform contract when the number of users is
their own profits. The profit of the CS is the difference between large.
the revenue for serving electric vehicles and the energy transfer The approach in [140] assumed that the data of user is IID,
payments to the SGP. Note that the competition among the CSs in fact, data distribution may have an impact on the server’s
and the willingness to transfer energy of the SGP is unknown cost. Therefore, the authors further studied the case where
for each other. The CS’s profit maximization problem is users have non-IID data in [141]. And the EMD metric is
modeled as a non-collaborative energy contract problem under used again. The author derived the server’s optimal contract
the unknown information and the common constraints of the with the non-IID data under complete and weakly incomplete
SGP. To find the optimal contracts for the CSs, the method of information scenarios, respectively. Compared with the case
solution in [135] is also used . The simulation results show IID in which the server only selects the most preferred type
that the proposed framework can outperform other economic under complete information, in the non-IID case, the server
models by 48% and 36% in terms of the CSs’ utilities and may choose more than one type. Meanwhile, they find that
social welfare (i.e., the total profits of all participating entities) weakly incomplete information does not increase the server’s
of the network, respectively. cost (comparing with the complete information scenario) when
To simulate the mobile devices with high-quality data training data is IID, but it in general does when data is
to participate in FL, the authors in [137] designed a con- non-IID. The experimental results of the non-IID case show
tract theory-based incentive mechanism, where mobile devices that the server’s cost in the proposed mechanism is lower
(DOs) are the employees and the monopolist operator (i.e., task than that in optimal uniform contract (OUC), reverse multi-
publisher) is the employer. The task publisher design specific dimensional auction mechanism (RMA) [124] and Stackelberg
contracts for different types of DOs with different levels of game mechanism (SBG) [31]. For the future work, deriving
data quality to maximize its profits, which is a function of the the optimal contract for the strongly incomplete information
time of the global iteration and the reward paid to DOs. Under scenario, and expanding existing researches to a general sce-
the constraints of IR and IC, the optimal CPU resources and nario with multiple competitive servers can be considered.
the corresponding reward can be derived using the substitution The authors in [142] leveraged on multi-dimensional con-
method and the convex optimization tools. The simulation tract theory to design a trustworthy incentive mechanism for
results show that the the task publisher can obtain higher profit the UAV-enable IoV network. The system model consists of
using the proposed contract-based method compared to the a MO, i.e., the employer, perform a time-sensitive task, and
Stackelberg game method in [138]. Based on this approach, multiple UAVs, i.e., the employees, implement sensing task
the reputation mechanism based on blockchain is introduced and transmit the collected data to the MO. The objective
in [139] to measure the reliability and trustworthiness of of this incentive is to maximize the profit for both the MO
the mobile devices, so as to motivate high-reputation DOs and UAVs. The profit of UAV is the difference between the
with high-quality data to join in model learning. To further contractual rewards and energy cost, and the profit of the
improve the accuracy of reputation computation, more weight MO is the total revenue obtained from UAV and the reward
parameters can be taken into consideration. expenses. In this incentive scheme, a UAV is categorized into
 21

a multi-dimensional type-(x, y, z, q), where x is traversal cost economic and game theoretic models have been widely applied
type, y is sensing cost type, z is computation cost type, and to design various incentive scheme in different scenario. How-
q is transmission cost type. The proposed contract design ever, incentive mechanism design is in its infancy. Thus, there
includes two phase, i.e, multi-dimensional contract design and are still open issues and new research directions on incentive
traversal cost compensation. In the first phase, the sensing cost mechanisms for FL as discussed in the following.
and computation cost is transformed into a single-dimensional 1) Online-Auction based Mechanism Design: Existing mon-
contract design problem, same as the method in [140]. In etary incentive schemes based on traditional auction method
the second, a fixed compensation is added to derive the final mostly are in offline, i.e., the auction starts only if a sufficient
contract bundles by considering additional traversal cost and number of bidders must be available. For example, in [129],
transmission cost. After obtaining the optimal contract, the the model aggragator starts to determine the winner when the
matching-based UAV-subregion assignment using the Gale- number of the bids from the ENs is sufficient or a predefined
Shapley algorithm [143] is considered to match the lowest users’ bids have to be synchronized. In such an auction, each
cost UAV to each subregion, i.e., target sensing region. The bidder may need to wait for a long time even if the bidder
simulation results demonstrate the IC property of the proposed does not win the auction. This discourages the bidder to join
contract design and show the efficiency of the matching. in the FL platform. Different from the offline auctions, online
auctions allow the auctioneer or the seller to makes decisions,
B. Incentive Mechanisms Based on Matching Theory i.e., on winner and prices, upon a bidder joins the auction.
The online auction can break the time and space constraints
Matching theory is widely used in the real market for its and save costs. Some recent works, e.g., [147] and [148], have
optimal two-side matching rule. This property is beneficial for investigated the online auction for mobile crowdsensing. Thus,
the worker selection of the requester of the FL service. the online auctions is a promising solution for the incentive
The author in [144] considered the network slicing place- mechanism design for FL.
ment strategy to offering customize service for different users’ 2) Advanced Contribution Evaluation Methods: To evaluate
heterogeneous requirements. In particular, the network slice the contribution of the data owners, Shapley value have been
controller (NSC), i.e., the seller, collects the requests from end commonly used. Based on the concept of the SV, many works
users (EU), i.e., buyers, and then deploys the virtual network have been done such as the federated SV [36] based on
functions (VNFs) to provider different communication services local model updates and contribution index [35] based on
for each of them. The proposed VNFs placement policy the intermediate results of the training process of FL. The
includes three modules, i.e., FL module, EUs behavior module, existing works demonstrate that the SV method in FL setting
and VNFs placement module. The first module is deployed has comparable performance. In addtion, a computation-and
among NSC and EUs designed to predict EUs’ VNFs demand communication-efficient estimation method is proposed in
information for each type of service. Based on the prediction [149]. The main focus of these works is to reduce the time
results, the network slice controller provide and place the complexity of the computing SV. Note that they assume that a
corresponding VNF to the area of EUs. A two-phase placement trusted server will honestly evaluate the contribution of each
strategy based on the matching theory is proposed to maximize participant. To establish a transparent evaluation mechanism,
the SP’s revenue. The SP revenue is the difference between blockchain-based SV [27] is adopted to overcome the mo-
the price payed by the EU based on its level of quality nopolistic behavior. However, all of the aforementioned works
of experience and the cost borne by the SP in provisioning do not consider the adversarial behaviours of the participants,
and placing the VNF in the service area. As shown in which may affect the the Shapley value calculation and lead
the simulation results, the proposed matching theory-based to the unfairness. More research works need to be investigated
assignment approach can reach a superior revenue compared for designing comprehensive and transparent contribution eval-
with the method based on Kolkata game [145] and potential uation mechanisms.
game [146]. 3) Incentive Mechanism with Privacy Protection: Existing
Summary: In this section, we discuss the applications of incentive mechanisms largely ignore the protection of pri-
contract and matching theory for incentive mechanism design vacy information, e.g., individual preferences, of data owners.
in FL. The objective is to maximize the seller’s utility or What’s worse, with the most current incentive mechanisms,
revenue, the buyer’s profit, and to minimize the latency of data owners who participate in the bidding process directly
FL training. The related works are summarized along with the reveal their privacy information. Meanwhile, the data owners
references in Table VI. As seen, the contract design mostly who lose in the bidding process receive no compensation at all
depend on the traditional optimization method, in the future, for their privacy revelation, which may reduce the participation
the DRL-based contract design can be considered to better enthusiasm of data owners. To protect data owners’ privacy
adapt to the changing user types. while maintaining high utility of trained models, some works
that consider the privacy problem have been done. The works
VII. S UMMARY, C HALLENGES , AND F UTURE R ESEARCH in [52], [150] proposed the game theoretic models for the FL
D IRECTIONS market, in which the data owners can obtain compensation
Different approaches reviewed in this survey show the according to their privacy loss quantified by local differential
effectiveness of economic and game theoretic models for the privacy. However, these frameworks may not be suitable
incentive mechanism design for the FL systems. Evidently, for some specific learning tasks. Thus, more research works
 22

TABLE VI
A PPLICATIONS OF C ONTRACT AND M ATCHING T HEORY FOR I NCENTIVE M ECHANISM D ESIGN IN FL

Market Structure
Ref. Scenario Mechanism Objective
Seller Buyer Item
For the tradeoff between the service latency and AoI,
Smart Training Profit maximization for the MO, IR
Workers MO the frequency of data update are stipulated in the
[134] industries resource and IC
optimal contract
Vehicles’ The optimal contract problem is converted a equivalent
Profit maximization for both buyer
Vehicular local low-complexity problem, and then the equilibrium
IoV network Vehicles and sellers, QoI improvement for
[135] SP training solution for vehicles is obtained using the iteration
sellers, IR and IC
results algorithm.
Electric vehicle Profit maximization for buyers,
SGP CSs Power Same as [135]
[136] networks IC,and IR
Profit maximization for the buyer,
Mobile Task Data The optimal contributed data size and reward are
[137] Mobile network guarantee latency requirement, IR
devices publisher resources obtained using the substitution method.
[139] and IC
Payoff maximization for sellers and
The The optimal contract can be derived by converting the
Data cost minimization for the buyer,
[140] Efficient FL Users central two-dimensional information into a single-dimensional
resources guarantee latency requirement, IR
[141] server criterion.
and IC
The optimal contract can be obtained using the same
UAV-enable Sensing Profit maximization for both sellers
UAVs MO method in [140], and the lowest cost UAV is allocated
[142] IoV network task and the buyer, IR and IC.
each subregion based on the Gale-Shapley algorithm.
Network Revenue maximization for sellers,
The NVFs placement strategy is modeled as a
Network slicing NSC EUs slice and guarantee the QoE requirement
[144] two-phase matching game
service of the buyer

need to be investigated for both incentiving data owners and and background of FL and incentive mechanism design. Then,
protecting their privacy. we have introduced fundamentals of various economic and
4) Comprehensive Incentive Scheme: The most of current game models with the aim to understand the motivations of
incentive mechanisms aim to optimize a single objective. For using the economic and game models in incentive mechanism
example, the works [57], [75], [151] aim to select the optimal design of FL. After that, we have provided detailed reviews,
participants for maximizing the performance of the FL system. analyses, and comparisons of the economic and game theoretic
Also, some works related to the Shapley value aim to evaluate approaches in designing variety of incentive mechanisms of
the contribution of the participants to guarantee the fairness. FL. Finally, we have discussed some open issues and future
In fact, multiple objectives should be considered in the FL. research directions.
For example, the participant selection and the contribution
evaluation should be jointly investigated to maximize both the
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