SCHOOL OF ECONOMICS AND MANAGEMENT

ECONOMICS WORKING PAPER 2007-8

Overconfidence and Moral Hazard

Leonidas Enrique de la Rosa

UNIVERSITY OF AARHUS
BUILDING 1322 - 8000 AARHUS C - DENMARK
+45 8942 1133
 Overcon…dence and Moral Hazard

Leonidas Enrique de la Rosa

delaRosa@econ.au.dk

April 10, 2007

Abstract

In this paper, I study the e¤ects of overcon…dence on incentive contracts in a moral-hazard

framework in which principal and agent knowingly hold asymmetric beliefs regarding the prob-
ability of success of their enterprise. Agent overcon…dence can have con‡icting e¤ects on the
equilibrium contract. On the one hand, an overcon…dent agent disproportionately values success-
contingent payments, and thus prefers higher-powered incentives. On the other hand, if the
agent is overcon…dent in particular about the extent to which his actions a¤ect the likelihood of
success, lower-powered incentives are su¢ cient to induce any given e¤ort level. If the agent is
overall moderately overcon…dent, the latter e¤ect dominates; because the agent bears less risk
in this case, he actually bene…ts from his overcon…dence. If the agent is signi…cantly overcon-
…dent, the former e¤ect dominates; the agent is then exposed to an excessive amount of risk,
which is harmful to him. An increase in overcon…dence— either about the base probability of
success or the extent to which e¤ort a¤ects it— makes it more likely that high levels of e¤ort are
implemented in equilibrium.

Keywords: overcon…dence, heterogeneous beliefs, moral hazard.

JEL Classi…cation: A12, D81, D82.

School of Economics and Management, University of Aarhus. A version of this paper is part of my Ph.D. disser-
tation at the University of California, Berkeley. I am particularly grateful to Benjamin Hermalin, Matthew Rabin,
and especially Botond K½oszegi for their insightful comments. I am also very grateful to Robert Anderson, Peter
Ove Christensen, Ulrike Malmendier, Dayanand Manoli, John Morgan, Terrance Odean, Yuliy Sannikov, Chris Shan-
non, Adam Szeidl, and seminar participants at University of Aarhus, UC Berkeley, CIDE, EPGE–FGV, Melbourne
Business School, Oberlin College, and Queen’s University for helpful comments and discussion.

1
1 Introduction

It is not uncommon to observe incentive contracts that appear puzzling in the light of a standard
principal-agent model. For instance, in 1995 Continental Airlines o¤ered $65 to every hourly
employee in every month that Continental’s on-time performance ranked amongst the top …ve
in the industry. This seemingly small incentive had, rather surprisingly, notable results.1 More
generally, low- and middle-rank employees receive performance bonuses that are relatively small
but seem to “get the job done”: they induce the employees to exert e¤ort at work and act with
the company’s best interest in mind. At the same time, millions of dollars in many top executives’
compensation packages acutely depend on their company’s performance. I argue that allowing for
heterogeneous beliefs— agent overcon…dence in particular— will aid our understanding of incentives
in contracts.
Consider the problem facing a business owner when hiring a manager as her agent. If the owner
(the principal) cannot monitor the actions undertaken by the manager (the agent) and these actions
a¤ect pro…ts, she will o¤er an incentive contract (e.g. consisting of a salary and a performance
bonus). In the standard treatment of this moral-hazard problem, it is usually assumed either that
the parties hold identical beliefs regarding the distribution of pro…ts conditional on the manager’s
actions, or that asymmetries in beliefs arise solely from private information. Motivated by extensive
psychological evidence that people are overcon…dent about their ability and future prospects2 , this
paper introduces heterogeneous beliefs of which principal and agent are aware: they “agree to
disagree.”
Section 2 introduces the main assumptions of the model, devoting special attention to the
assumption that principal and agent knowingly hold asymmetric beliefs, which is crucial in the
model and implies there can be no further updating of beliefs upon observing each other’s actions.
There are two dimensions on which the asymmetry of beliefs is important in the model: an (overall)
overcon…dent agent can be overcon…dent about the base probability of success of the project— over
all possible choices of e¤ort available to him— and he can be overcon…dent about the value of his
1
Knez and Simester (2001) study Continental’s case. The authors argue that mutual monitoring among employees
was the main reason behind the success of the incentive scheme. We will see that such e¤ectiveness of low-powered
incentives can also be explained within a setting of agent overcon…dence.
2
In the psychology literature, a technical use of the term “overcon…dence”refers to overestimating the precision of
one’s forecast. In this paper, we will refer to overestimating the probability of favorable outcomes following the agent’s
actions as “agent overcon…dence.” Some literature refers to this type of self-serving bias as unrealistic optimism (or
simply optimism). Others share the use of the term with this paper. When discussing ability and the repercussions
of one’s actions, I believe that overcon…dence is a more appropriate term than optimism, which suggests a passive
role in relation to outcomes.

2
e¤ ort— the marginal contribution of his e¤ort to the probability of success.3
Section 3 develops the main results of the model, exploring the e¤ects of overcon…dence in
a setting in which several principals compete to contract with the agent. Competition between
principals will drive their expected pro…ts to zero in equilibrium, which allows for an intuitive
exposition of the e¤ects of overcon…dence.4
Because of the parties’ awareness about the asymmetry in beliefs, there are no signaling or
screening concerns in my model, so the e¤ects of overcon…dence on optimal contract design are
isolated from its consequences in terms of adverse selection.5 Agent overcon…dence about the
probability of success of the enterprise can have con‡icting e¤ects on the equilibrium contract. On
the one hand, when the agent is overcon…dent in particular about the marginal contribution of his
e¤ort to the project’s probability of success, lower-powered incentives are su¢ cient to induce any
given e¤ort level. This is the incentive e¤ ect of overcon…dence, and it pushes the equilibrium
contract to exhibit lower-powered incentives. On the other hand, because an overcon…dent agent
disproportionately values success-contingent payments, he …nds high-powered incentive contracts
more attractive than a “realistic” agent. Because the principal believes that she will pay the
bonus infrequently, she …nds such a contract— with a higher performance bonus and a lower base
salary— an inexpensive way of hiring the agent. This consequence of the divergence in evaluating
payments is the wager e¤ ect of overcon…dence, and it pushes the equilibrium contract to exhibit
higher-powered incentives.
3
The agent could even be undercon…dent about the value of e¤ort, while still being overcon…dent overall. Imagine,
for example, an agent who believes he has the “Midas touch”: just because he’s involved, the enterprise must succeed.
This agent is overall very overcon…dent in the sense that he always overestimates the probability of success of the
project, but at the same time underestimates the contribution of his e¤ort to increasing the probability of success.
4
Section 5 studies the case of a principal making a take-it-or-leave-it o¤er to the agent, and Section 6 extends the
model to allow for a continuum of e¤ort levels that the agent can choose from. Section 4 is a discussion about the
welfare e¤ects of agent overcon…dence, which is particularly relevant in the competing-principals framework.
5
Recent studies allow for asymmetric beliefs in principal-agent models, but the main focus has been on the e¤ects
of asymmetric beliefs in an adverse-selection framework. Fang and Moscarini (2005) allow for overcon…dent agents
in an adverse selection model, and …nd that a principal might prefer not to di¤erentiate wages to avoid the negative
e¤ects that revealing her private information about the agents’true ability may have on workers’morale. Koufopoulos
(2002) suggests that bias in the perception of risk might explain some empirical observations related to asymmetric
information in competitive insurance markets. Maskin and Tirole (1990) and (1992) introduce private information
held by the principal regarding the extent to which she values the agency relationship in an adverse-selection model.
Villeneuve (2000) considers the possibility that the principal is better informed than the agent in an insurance-market
setting, which he refers to as “reverse adverse selection.” Van den Steen (2005) considers asymmetric beliefs in the
absence of private information (as this paper does) when there is disagreement about the best course of action. I
consider disagreement about outcome distribution conditional on actions, but in my model the parties agree about
which one generates a better distribution.

3
 The degree of overall overcon…dence determines which of these e¤ects dominates in equilibrium.
The incentive e¤ect dominates when the agent is only slightly overcon…dent overall. When the
agent is signi…cantly overcon…dent, however, incentive provision becomes secondary to the fact that
principal and agent value outcome-contingent payments di¤erently. As a consequence, the wager
e¤ect dominates, and greater agent overcon…dence about either the base probability of success or
the e¤ect of the agent’s e¤ort on the probability of success results in higher-powered incentives in
equilibrium. Because of the potentially con‡icting e¤ects of overcon…dence, the power of incentives
of the equilibrium contract depends both on the degree and the kind of agent overcon…dence. In
contrast, the level of e¤ort implemented by the equilibrium contract unambiguously increases with
overcon…dence.6
Section 4 discusses the welfare e¤ects of overcon…dence in the competing-principals framework.
As it turns out, moderate overcon…dence can be welfare-enhancing in this setting. Because an
agent who is only slightly overcon…dent about the value of e¤ort receives more insurance than
an agent who holds realistic beliefs, he actually bene…ts from the e¤ects of his overcon…dence on
the equilibrium contract. An agent who is undercon…dent about the value of e¤ort or signi…cantly
overcon…dent overall, in contrast, bears an excessive amount of risk, so his overcon…dence is harmful
to him. Subsection 4.2 is a brief discussion on how the results carry over when we allow the
competing principals to hold asymmetric beliefs amongst themselves.
Section 5 studies the implications of the model when one principal can make a take-it-or-leave-it
o¤er to an agent— the standard setting in the moral-hazard literature. The main di¤erence is that
an exogenous agent-participation constraint replaces the endogenous one generated by competing
contract o¤ers, so the principal faces a remarkably similar optimization problem to the one faced by
a principal who competes with others. The qualitative e¤ects of overcon…dence on the equilibrium
contract in the one-principal case thus mirror the results discussed in the competing-principals
framework. Subsection 5.1 discusses the welfare e¤ects of agent overcon…dence in the one-principal
setting; because the principal extracts all the surplus from the agency relationship, these e¤ects
are quite di¤erent than in the case in which principals compete. Subsection 5.2 discusses the
implications of the model in a situation in which the principal has a choice regarding which agent
to hire from a pool of agents with di¤erent levels of ability and overcon…dence. Subsection 5.3
studies the possibility that it is the agent who designs the contract and makes a take-it-or-leave-it
o¤er to the principal.
6
There is a caveat to this statement. Formally, the implemented level of e¤ort (or the probability that high e¤ort
is implemented in equilibrium in the two-action case) unambiguously increases, ceteris paribus, with overcon…dence
of each kind. Given the two kinds of overcon…dence, this does not mean that agents who are more overcon…dent
overall always exert more e¤ort in equilibrium.

4
 Section 6 extends the one-principal, one-agent framework to allow for a continuum of e¤ort
levels that the agent can choose from. The incentive and wager e¤ects of overcon…dence carry
over to this setting. A consequence of both e¤ects is that, if the problem has an interior solution,
the implemented level of e¤ort is (continuously) increasing in each kind of overcon…dence. For
this reason, in contrast to the discrete-choice case, the power of incentives of the optimal contract
might increase with overcon…dence about the value of e¤ort even when the agent is only slightly
overcon…dent overall.
Section 7 concludes. Interesting applications of the model could include entrepreneurship and
executive compensation, and the results seem to be consistent with recent empirical observations.
I also discuss some potentially interesting avenues for further research.

2 Framework

The main assumption of the model that di¤ers from those in conventional moral-hazard models
is that principal and agent hold heterogeneous beliefs regarding the distribution of outcomes, and
both are aware of this asymmetry. Therefore, principal and agent do not update their beliefs upon
play of the game (principal and agent simply “agree to disagree”). Because this assumption is
crucial to the results of this paper, I will discuss its validity before moving on to setting up the
model.
There are both empirical and methodological reasons for assuming that parties do not fully
update their beliefs upon learning the beliefs held by others. This assumption may be very ap-
propriate in a moral-hazard framework; in relation to the agent’s ability, arguments like “I know
myself better than anybody else” for the agent and “everyone thinks they’re better than average”
for the principal would allow them both to rationalize not revising their beliefs. Consider, for
example, the extreme situation in which the principal judges the agent’s ability according to the
population mean, knowing that agents tend to be overcon…dent. If she believes that agents’beliefs
are independent of their underlying ability, she will disregard those beliefs as uninformative. In this
scenario, the principal’s beliefs are independent of the individual agent’s true ability, so the agent
can also disregard them as uninformative. Principal and agent have nothing to teach each other
in terms of the agent’s true ability in a one-shot game. Furthermore, the assumption allows me to
study the e¤ects of overcon…dence on the equilibrium incentive contract, isolating them from any
signaling or screening concerns.
Heterogeneous posterior beliefs can also result from di¤ering prior beliefs. Morris (1995) dis-
cusses the assumption of heterogeneous priors in the context of economic models, and makes a case

5
for allowing this possibility. An alternative explanation involves errors in processing information.
If players update their beliefs in a non-Bayesian way following the observation of a given signal
(for example, each participant in a private-information game overestimates the informative value of
their own private signal), their posterior beliefs will di¤er even if all private information is revealed
in equilibrium. Eyster and Rabin (2005) explore another channel through which participants can
maintain asymmetric posterior beliefs: if players in a private-information game fail to interpret
other players’actions as conveyors of private information, asymmetric posterior beliefs will survive
even in fully-separating equilibria of the game.
In the presentation of the results, I focus on the case of agent overcon…dence: the agent holds
overly optimistic beliefs, relative to the principal, regarding the probability of success of the project.
The propositions, however, accommodate the possibility of a relatively pessimistic agent. Research
in the …eld of psychology suggests that individuals tend to overestimate the probability of favorable
events, and that such bias is more pronounced when they have some control over the likelihood of
those events. Weinstein (1980) found that students were overly optimistic about the likelihood of
good or bad events happening to them relative to same-gender students in their school— such as
enjoying their post-graduation job or attempting suicide. He also found that the degree of such
“unrealistic optimism”depended, among other things, on a notion of control over the likelihood of
a given event. Taylor and Brown (1988) present a review of psychology literature that supports
the view that, in general, individuals’ assessment of their own abilities, talents, and social skills
are overly optimistic. Fiske and Taylor (1991), and Kunda (1999) also discuss the tendency of
individuals to be overcon…dent, referencing both theoretical and empirical studies in psychology.
Researchers in business and economics have also taken notice of the propensity of individuals
to be overcon…dent. Larwood and Whittaker (1977) found company managers to be unrealistically
optimistic about the future performance of their …rms relative to the competition. Cooper, Woo,
and Dunkelberg (1988), in a survey of nearly three thousand entrepreneurs, report that entrepre-
neurs are notably optimistic about their chances of success when setting up a business. Evidence
from experimental economics supports the case for overcon…dence as well: Camerer and Lovallo
(1999), for example, …nd that there is excess entry into a hypothetical capacity-constrained market
when participants’ payo¤s after entering depend on skill, but not when they depend on chance.
This suggests that agents not only hold overcon…dent beliefs, but also act on them.7
7
There are theoretical approaches to overcon…dence in the economics literature as well. Gervais and Odean (2001)
explain overcon…dence in a dynamic framework in which agents overweight success and underweight failure when
updating their beliefs about their own ability. Bénabou and Tirole (2002) model a self-deception game in which
multiple equilibria regarding the level of overcon…dence may arise. Goel and Thakor (2002) explore the costs and
bene…ts of overcon…dence in a tournament setting.

6
 The other assumptions of the model are in line with the standard treatment of moral hazard.
Assume there is a project that can be undertaken by a principal and an agent if they decide to
enter a contractual relationship. There are two possible outcomes: the project can succeed or fail.
The project yields revenue x0 if it fails, and revenue x1 > x0 if it succeeds. The probability of
success of the project depends on a non-contractible action e chosen by the agent, which can be
interpreted as his choice among e¤ort levels.
The principal’s utility is expected revenue from the project net any payments made to the agent
(the principal is risk neutral). The agent’s utility is separable in money and e¤ort, so that his utility
after receiving payment s from the principal and exerting e¤ort level e is

u (s) c (e) ,

where c (e) denotes the disutility to the agent from exerting e¤ort. I assume that u : R ! R has
full range, and that it is continuous and twice continuously di¤erentiable, with u0 > 0 and u00 < 0
(the agent is risk averse).
As previously noted, principal and agent knowingly hold asymmetric beliefs regarding the prob-
ability of success of the project. The principal believes that, conditional on the agent choosing e¤ort
level e 2 [0; 1], the project will succeed with probability Pr (x1 j e) = q + ve. Let a tilde denote
f (x1 j e) = q~ + v~e.
the agent’s beliefs: he believes that the conditional probability of success is Pr
This particular parameterization will prove to be subsequently useful for the analysis, because it
highlights the two dimensions (levels and di¤erences) on which the asymmetry in beliefs is relevant
in the model. The parameters q, q~, v, and v~ are assumed to be positive; the probability of success
of the project is perceived by both parties to be increasing in e¤ort. Beliefs are also restricted to
q + v < 1 and q~ + v~ < 1.8
There are two ways in which the beliefs held by principal and agent can di¤er. The agent is
said to be overcon…dent about the base probability of success if q~ > q. The agent is said to be
overcon…dent about the value of e¤ ort if v~ > v; he believes that the marginal contribution of his
e¤ort to the probability of success is greater than what the principal believes. We will refer to these
as di¤erent kinds of overcon…dence, and say that the agent is overcon…dent overall if q~ > q and
q~+ v~ > q +v. The possibility of agent undercon…dence about the value of e¤ort (~
v < v) is consistent
with overall overcon…dence and may be relevant according to some views regarding self-enhancing
biases. Hoorens (1993) notes that most self-enhancing biases seem to be motivated by a desire to
8
The assumption that q~ + v~ < 1 avoids the possibility of a trivial forcing contract— one that in…nitely punishes
the agent in case of project failure and thus trivially implements e¤ort at …rst-best cost. Assuming q + v < 1 (so that
principal and agent agree on the subset of outcomes that occur with probability zero) avoids the possibility that the
principal can unboundedly increase the agent’s perceived expected utility at no cost to herself.

7
see oneself as particularly “good”and consequently a perception of superiority (pp. 131–2). A sense
of superiority might lead an agent to believe that the probability of success of a project in which he
engages is very high, independent of e¤ort level, (a very high q~) and underestimate the value of his
e¤ort (~
v < v). The agent’s beliefs about the value of e¤ort a¤ect his perception of the rewards to
e¤ort of a given incentive contract. Even though I am partial to interpret the evidence regarding
overcon…dence as pointing to overcon…dence about the value of e¤ort, it is useful to remain open
to the possibility of overall overcon…dence coupled with undercon…dence of this kind.
I will consider both the case of many principals who compete to contract with an agent, and
the case of one principal making a take-it-or-leave-it contract o¤er to an agent. The timing of
the game is as follows: the principal(s) …rst make contract o¤er(s) to the agent. The agent then
decides whether to accept one or reject all o¤ers. If he accepts an o¤er, he then chooses how much
e¤ort to exert. The outcome of the project is then realized, payo¤s are distributed according to the
contract’s terms, and the agency relationship ends. The solution concept used is subgame-perfect
Nash equilibrium: at every decision node of the game, the relevant player chooses an optimal
response, even if she had expected not to reach that node in equilibrium. I focus on pure-strategy
equilibria of the game (in particular, each principal o¤ers a given contract with probability one in
equilibrium); this is a substantive assumption in terms of the equilibrium strategy, but does not
a¤ect the main message of the model.9 Without loss of generality, I restrict attention to contract
o¤ers of the form hs1 ; s0 i— a schedule of outcome-contingent payments to the agent— given that
project outcome is the only mutually-observable signal in the model.10
9
In the model with one principal, she always o¤ers the optimal contract to the agent. In the case that principals
compete to contract with the agent, it will be shown that in equilibrium principals receive zero expected pro…ts. The
principals will therefore be indi¤erent between o¤ering what is characterized as the equilibrium contract, or any other
contract that yields zero expected pro…ts (e.g. one that is rejected by the agent). Equilibrium requires, however, that
the agent accepts the characterized equilibrium contract with probability 1; if the agent accepted a di¤erent contract
with positive probability, there would be a pro…table deviation for some principal.
10
See Holmstrom (1979) for a discussion about observability and contracting under moral hazard. Because of the
agent’s risk aversion, it is in general not optimal to introduce unnecessary “noise”to the payment structure. If signals
besides project outcome are observable by both parties, the terms of the equilibrium contract may be contingent on
those as well. Under asymmetric beliefs, if there is some signal that the agent believes to be correlated with his e¤ort,
the principal can reduce the cost of implementing e¤ort by o¤ering payments that are also contingent on this signal,
even if she believes it to be completely uninformative. I assume that outcome is the only signal that principal and
agent can contract on.

8
 3 Competing Principals

Consider the case of multiple principals who compete to contract with one agent. This setup is
appropriate if agents are scarce in the sense that there are more principals who wish to hire an
agent than there are quali…ed agents. If we are concerned with particularly talented or specialized
agents (superstar occupations for example), this model will be more suitable than the standard
one-principal, one-agent framework. This model is also useful when considering a situation in
which the agent has proprietary rights over the project, rather than the principal. Imagine, for
example, a risk-averse entrepreneur deciding whether or not to set up a business. There are potential
principals (banks or venture capital funds) willing to bear some of the risk inherent to the enterprise.
Establishing an agency relationship in which the principal absorbs some of this risk would be
mutually bene…cial.

principals if agent accepts payo¤s are distributed

simultaneously an o¤er he chooses according to
o¤er contracts action e the contract’s terms
.........................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................

agent project time

accepts one o¤er succeeds
or rejects all or fails

Figure 1: Timing of the model when principals compete

The timing of the model is as follows. First, principals make simultaneous contract o¤ers to
the agent. The agent then chooses which o¤er (if any) to accept. If the agent chooses to accept
a contract o¤er, he chooses some action that a¤ects the outcome distribution of the project. The
outcome of the project is realized and observed by both parties. Payo¤s are then distributed
according to the provisions in the contract, and the agency relationship ends. If the agent chooses
not to accept any contract, the project will not be undertaken, and the players receive payo¤s
according to some outside option. The participants’ outside option is their opportunity cost of
entering the contractual relationship. The outside option for each principal is not contracting with
the agent, which yields zero pro…ts. I assume that the outside option for the agent is low enough
so that he always accepts an o¤er in equilibrium, and thus the equilibrium contract is independent
of his outside option.
Assume the agent has two actions to choose from; e 2 f0; 1g.11 A straightforward way to
interpret this two-action space is that the agent can simply choose whether or not to exert e¤ort.
11
Section 6 presents an extension of the model in which the agent’s action choice set is the continuous unit interval.

9
I normalize the cost of not exerting e¤ort to zero so that c (0) = 0 and c (1) = c.
Principals and agent evaluate any given contract according to their own beliefs. Assume that
competing principals share the same beliefs about the probability of success of the project; I discuss
the possibility of di¤erent principals holding di¤erent beliefs in Subsection 4.2 below. Each principal
wishes to maximize her expected pro…ts. Expected pro…ts for the principal whose contract o¤er
hs1 ; s0 i is accepted by the agent in equilibrium, conditional on each of the agent’s possible e¤ort
levels, are:

E [ j e = 1] = (q + v) (x1 s1 ) + [1 (q + v)] (x0 s0 )

E [ j e = 0] = q (x1 s1 ) + [1 q] (x0 s0 ) .

The agent’s objective is to maximize his expected utility when choosing which contract o¤er to
accept and how much e¤ort to exert once he engages the project. After accepting a given contract
o¤er hs1 ; s0 i, the agent’s expected utility conditional on his choice of e¤ort is:

~ [u (sx ) j e = 1]
E c = (~
q + v~) u (s1 ) + [1 (~
q + v~)] u (s0 ) c
~ [u (sx ) j e = 0] = q~u (s1 ) + [1
E q~] u (s0 ) .

We can now turn to characterizing the equilibrium contract. After accepting the contract o¤er
that the agent …nds most attractive, he chooses whichever action he believes will yield him higher
expected utility given the terms of the contract. The competing principals take this into account
when designing their o¤ers. In particular, if a principal wishes to induce e¤ort, the contract must
be “incentive compatible”— the contract terms must be such that, if the agent accepts it, he …nds
it in his best interest to exert e¤ort:

(~
q + v~) u (s1 ) + [1 (~
q + v~)] u (s0 ) c q~u (s1 ) + [1 q~] u (s0 ) .

We can rewrite the incentive-compatibility constraint above as

v~ (u (s1 ) u (s0 )) c. (IC)

Intuitively, the perceived expected utility gain for the agent from exerting e¤ort (receiving excess
utility (u (s1 ) u (s0 )) with additional probability v~), must be no less than his disutility from
exerting e¤ort. I will refer to the di¤erential u (s1 ) u (s0 ) as the contract’s power of incentives.
Note that the power of incentives necessary to induce e¤ort is decreasing in v~. It is, however,
independent of q~: the agent’s beliefs regarding the base probability of success does not a¤ect his
perception of the rewards to e¤ort of a given incentive scheme.

10
 An equilibrium contract is such that no other contract can (i) attract the agent by o¤ering him
terms that he strictly prefers and (ii) yield higher expected pro…ts for the o¤ering principal (i.e.
there is no pro…table deviation for any principal from an equilibrium contract). Because principals
compete in o¤ering contracts to the agent and they all evaluate pro…ts based on the same beliefs,
expected pro…ts for the principal whose o¤er is accepted by the agent in equilibrium must be zero
(equal to the principals’outside option).

Lemma 1 If principals share the same beliefs regarding outcome distribution conditional on the
agent’s actions, in equilibrium expected pro…ts will be zero for all principals according to their
beliefs.

All formal proofs are relegated to the appendix. Intuitively, if a principal made positive expected
pro…ts, another principal could outbid that contract o¤er— provide a slightly higher expected pay-
ment to the agent— without a¤ecting incentives, thus attracting the agent and earning positive
expected pro…ts. When principals do not share the same beliefs, this zero-expected-pro…ts condi-
tion will no longer hold, but the intuition behind the results carries over to such a setting. We
relax the assumption that principals share the same beliefs in Subsection 4.2.
The equilibrium contract depends crucially on the e¤ort level that is implemented in equilibrium.
I will, in turn, characterize the equilibrium contract assuming that e¤ort is not implemented and
assuming that e¤ort is implemented, and subsequently analyze the e¤ect of overcon…dence on the
level of e¤ort actually implemented in equilibrium.
Assume …rst that e¤ort is not implemented in equilibrium. If principals and agent held identical
beliefs, the risk-neutral principal would absorb all the risk from the project, and o¤er a …xed
payment to the agent (i.e. independent of project outcome). If the agent is overcon…dent about
the base probability of success, however, he will be exposed to risk in equilibrium.

Proposition 1 Assuming e¤ ort is not implemented in equilibrium, the only equilibrium contract
hs1 ; s0 i is characterized by the conditions

q~ u0 (s1 ) q
0
=
1 q~ u (s0 ) 1 q

and q (x1 s1 ) + [1 q] (x0 s0 ) = 0. The agent bears risk in equilibrium if q~ 6= q.

Consider the case of agent overcon…dence about the base probability of success, in which q~ >
q. The intuition of Proposition 1 is that an overcon…dent agent is willing to wager on success
against the (relatively pessimistic) principal. Starting from a riskless contract (one that speci…es
s1 = s0 ), because the marginal cost for the agent from bearing additional risk is zero at that point,

11
principal and agent evaluate marginal changes in payments based on their e¤ect only in terms of
expected payment. Consider, then, an increase in the success-contingent payment, coupled with
a decrease in the failure-contingent payment, that leaves expected payment unchanged according
to the principals’beliefs. The agent is relatively optimistic about receiving the success-contingent
payment, so according to his beliefs such deviation yields a higher expected payment. When q~ > q,
there is a …rst-order gain perceived by the agent from such higher expected payment, and only a
second-order loss from higher risk exposure, compared to a riskless contract. Therefore, an agent
who is overcon…dent about the base probability of success bears risk in equilibrium.
Because of the disagreement between principal and agent regarding the probability of success of
the project, the agent is willing to be exposed to more risk in equilibrium than a “realistic”agent.
This wager e¤ ect pushes the equilibrium contract towards higher-powered incentives. Note that,
absent moral-hazard concerns, the equilibrium contract allows for Pareto-optimal risk sharing. In
the identical-beliefs case, this implies that the risk-neutral principal will absorb all of the risk. In
the heterogeneous-beliefs case, it implies that the agent bears risk in proportion to the disagreement
in beliefs.12
If the contract characterized in Proposition 1 satis…es the incentive-compatibility constraint
q~ u0 (s1 ) q
(IC), it must be the case that the agent exerts e¤ort in equilibrium. Whenever 1 q~ u0 (s0 ) > 1 q and
hs1 ; s0 i does not implement e¤ort, hs1 ; s0 i cannot be an equilibrium contract. A principal could
deviate and o¤er a higher-powered incentive contract that will both attract the agent and yield
positive expected pro…ts. Not implementing e¤ort might thus be infeasible under heterogeneous
beliefs.
Assume now that e¤ort is implemented in equilibrium. If principals and agent held identical
beliefs, the equilibrium contract o¤er would be characterized by zero expected pro…ts for the o¤ering
principal and the binding incentive-compatibility constraint (IC). There is a tradeo¤ between
incentives and insurance: if not for the incentive-provision problem, e¢ ciency gains would result
from providing more insurance to the agent (i.e. reducing the power of incentives). Implementing
e¤ort requires that the agent be exposed to a discrete amount of risk. The e¢ ciency loss that arises,
12
Another way to frame the wager e¤ect is from the viewpoint of asset trading under uncertainty. Principal and
agent have the opportunity to trade payments in the “success” and “failure” states of the world. The principal,
being risk neutral, is willing to trade in…nitely at what she believes to be the actuarially fair price of these securities.
Principal and agent evaluate each trade di¤erently. In particular, a trade of higher payment to the agent in the
“success” state coupled with a lower payment in the “failure” state that the principal judges to be actuarially fair is
regarded as better than actuarially fair by the agent. Because of his risk aversion, the agent is not willing to trade
in…nitely at that price— only as long as the gains from a higher perceived expected payment compensate him for the
additional risk he bears. Adrian and Wester…eld (2005) uncover the wager e¤ect in a continuous-time agency model.

12
given the agent’s risk aversion, is referred to as the cost of agency; if the agency relationship was
not necessary, this cost would be avoided (for instance, if the risk-neutral principal could undertake
the project on her own and carry out the agent’s task).
Given this incentive-insurance tradeo¤, the contract analogous to the identical-beliefs equi-
librium contract is a natural candidate for a potential equilibrium contract when we allow for
heterogeneous beliefs.

De…nition 1 Let hs1 ; s0 i denote the contract that satis…es (IC) with equality and yields zero ex-
pected pro…ts according to the principals’ beliefs:

v~ (u (s1 ) u (s0 )) = c

(q + v) (x1 s1 ) + [1 (q + v)] (x0 s0 ) = 0.

This contract will in fact be the equilibrium contract when the beliefs held by the agent di¤er
only slightly from the principals’beliefs. In other words, if the agent is only slightly overcon…dent
overall, the contract with incentives just powerful enough to implement e¤ort will be the equilibrium
contract. The intuition from the identical-beliefs setting carries over to this case: a principal cannot
provide more insurance to the agent without destroying the incentives for the agent to exert e¤ort.

Proposition 2 Assuming e¤ ort is implemented in equilibrium, hs1 ; s0 i is the only equilibrium con-
q~+~v u0 (s1 ) q+v
tract if 1 (~ v ) u0 (s0 )
q +~ 1 (q+v) .

q~+~v u0 (s1 ) q+v

Given that s1 > s0 , the condition 1 (~ v ) u0 (s0 )
q +~ 1 (q+v) holds for some values q~ + v~ > q + v. If
this is the case, we will say that the agent is only “slightly overcon…dent overall,”since q~+ v~ 6 q +v.
There is no pro…table deviation from hs1 ; s0 i. To see why, note that providing more insurance
to the agent (by decreasing s1 and increasing s0 ) would destroy the incentives for the agent to
exert e¤ort, increasing both payments would decrease expected pro…ts, and a contract with lower
payments would not attract the agent away from hs1 ; s0 i. Consider then an increase in s1 coupled
with a decrease in s0 , so that e¤ort is still implemented and expected pro…ts do not decrease.
Providing less insurance to the agent would never be pro…table in the identical-beliefs framework,
but such deviation could seem attractive to an overcon…dent agent because of the wager e¤ect.
The condition in Proposition 2 above illustrates how each party evaluates marginal changes in
payments at hs1 ; s0 i. The agent perceives that a marginal increase in s1 increases his utility by
u0 (s1 ) with probability (~
q + v~), and that a marginal decrease in s0 decreases his utility by u0 (s0 )
with probability [1 (~
q + v~)]. The principal believes, on the other hand, that she will pay the
marginal increase in s1 with probability (q + v) and save the marginal decrease in s0 with probability

13
[1 (q + v)]. If the inequality holds, a principal cannot draw the agent away from hs1 ; s0 i and
increase expected pro…ts by providing less insurance. Intuitively, it is too costly for the principal to
compensate the agent for bearing more risk. Because marginal utility is assumed to be decreasing,
the fact that there is no pro…table marginal deviation from hs1 ; s0 i implies that there is no pro…table
discrete deviation from hs1 ; s0 i either.
When the condition in Proposition 2 holds, overcon…dence about the value of e¤ort (~
v > v)
allows a principal to provide more insurance to an overcon…dent agent without destroying incentives
compared to a “realistic”agent. This is the incentive e¤ ect of overcon…dence. Any contract that
implements e¤ort exposes the agent to a discrete amount of risk, so as to give him su¢ cient
incentives to exert e¤ort. Even though the wager e¤ect implies that an overcon…dent agent is
willing to bear some risk when contracting with a principal, this amount of risk is continuous in
the degree of disagreement in beliefs. If the agent is only slightly overcon…dent overall, the amount
of risk required by incentive provision is greater than the amount of risk he would willingly bear as
a consequence of the wager e¤ect. The incentive e¤ect therefore dominates the wager e¤ect in this
case, and the power of incentives of the equilibrium contract depends solely on the agent’s beliefs
about the value of e¤ort.
When the agent is only slightly overcon…dent overall, the incentive-insurance tradeo¤ present
in the case of identical beliefs remains. If the agent is overcon…dent about the value of e¤ort,
lower-powered incentives are su¢ cient to implement e¤ort than if he held “realistic”beliefs; a prin-
cipal can then o¤er a contract that provides more insurance (thus reducing the cost of agency)
without destroying incentives. If, however, the agent is undercon…dent about the value of e¤ort,
the incentive e¤ect implies that higher-powered incentives will be necessary to implement e¤ort.
ds1 ds0
Applying Lemma 1, we can say that d~
v < 0 and d~
v > 0 when the agent is only slightly overcon-
…dent overall. Therefore, the power of incentives of the equilibrium contract decreases
in overcon…dence about the value of e¤ort when the agent is only slightly overcon…-
dent overall. The agent’s beliefs regarding the base probability of success (~
q ) do not a¤ect the
equilibrium contract in this case. The principals’ beliefs do not a¤ect the power of incentives of
the equilibrium contract either, but they do a¤ect the agent’s expected payment. If the principals
are optimistic and judge the probability of success to be high, they believe the project’s expected
revenue is high, and can o¤er a higher expected payment to the agent accordingly.
The degree of asymmetry in beliefs held by principals and agent de…ne whether or not the
agent is only slightly overcon…dent overall. As the next proposition shows, if the agent is instead
signi…cantly overcon…dent overall, the equilibrium contract exhibits excessively powerful incentives.
Because of the wager e¤ect, a very overcon…dent agent substantially overestimates the probability

14
of success, so he prefers a contract that rewards him handsomely for success and punishes him
harshly for failure over the hs1 ; s0 i contract (which provides as much insurance as possible while
implementing e¤ort). He judges the higher expected payment from an excessively risky contract as
su¢ cient to compensate him for the cost of bearing more risk.

q~+~v u0 (s1 ) q+v

Proposition 3 Assuming e¤ ort is implemented in equilibrium, if 1 (~ v ) u0 (s0 )
q +~ > 1 (q+v) then
hs1 ; s0 i is not an equilibrium contract. The only equilibrium contract hs1 ; s0 i is characterized by
q~ + v~ u0 (s1 ) q+v
=
1 (~ q + v~) u0 (s0 ) 1 (q + v)
and (q + v) (x1 s1 ) + [1 (q + v)] (x0 s0 ) = 0. The equilibrium contract has higher-powered
incentives than necessary to implement e¤ ort.

q~+~v u0 (s1 ) q+v

If q~ + v~ q + v, so that 1 (~ v ) u0 (s0 )
q +~ > 1 (q+v) , we will say that the agent is “signi…cantly
overcon…dent overall.” If this is the case, he is actually content to bear more risk in equilibrium
than he would under contract hs1 ; s0 i. Parallel to the analysis in the case of slight overcon…dence,
consider a deviation from hs1 ; s0 i towards less insurance: a marginal increase in s1 together with
a marginal decrease in s0 . Recall that the agent perceives such a change as an increase in utility
of u0 (s1 ) with probability (~
q + v~) and a decrease in utility of u0 (s0 ) with probability [1 (~
q + v~)].
Because the agent considerably overestimates the likelihood of receiving the success-contingent
payment, a principal can o¤er less insurance to the agent and attract the agent away from hs1 ; s0 i,
while increasing her expected pro…ts. Since hs1 ; s0 i maximizes the agent’s perceived expected utility
subject to the zero-expected-pro…ts condition, there is no pro…table deviation from this contract.
Because of the wager e¤ect, if the agent is signi…cantly overcon…dent overall, he judges the hs1 ; s0 i
contract to yield a signi…cantly higher expected payment than the hs1 ; s0 i contract— so much higher
that it more than compensates him for the excessive amount of risk he bears.
When the agent is signi…cantly overcon…dent overall, the agent’s bias in evaluating payments
overshadows the incentive-insurance tradeo¤ present in the identical-beliefs case. In that setting, the
principal is prevented from providing more insurance to the agent because of the need to provide
appropriate incentives. When the agent is signi…cantly overcon…dent overall, there is no such
tradeo¤ in equilibrium. The agent’s relative bias then overrides his risk aversion when evaluating
payo¤s, and thus incentive provision becomes secondary to the di¤erence in how principal and
agent evaluate outcome-contingent payments. As in the case in which no e¤ort is implemented, the
equilibrium contract allows for Pareto-optimal risk sharing; the amount of risk the agent bears as
a consequence of the heterogeneity in beliefs is more than enough to provide incentives.
In contrast to the e¤ect of overcon…dence about the value of e¤ort on the power of incentives
ds1 ds0 ds1
when the agent is slightly overcon…dent, now d~
v > 0 and d~
v < 0. Likewise, d~q > 0 and

15
ds0
d~q < 0. Because it is the wager e¤ect of overcon…dence that dominates in this case, the power
of incentives of the equilibrium contract increases in overcon…dence of either kind
when the agent is signi…cantly overcon…dent overall. The equilibrium contract exhibits
excessively powerful incentives— more powerful than necessary to induce e¤ort— independent of
the composition of agent overcon…dence. As before, we would expect more-optimistic principals to
o¤er a higher expected payment to the agent. Given that in this case it is the degree of divergence
in beliefs that drives contract design, however, the power of incentives is decreasing in both q and
v: the divergence is smaller when principals are more optimistic.
Whether or not e¤ort is implemented in equilibrium depends on which of the potential equi-
librium contracts identi…ed above gives the agent higher perceived expected utility (recall that
principals always receive zero expected pro…ts in equilibrium). The incentive e¤ect reduces the
cost of implementing e¤ort, and a higher degree of overcon…dence of either kind makes the poten-
tial equilibrium contract that implements e¤ort relatively more attractive to the agent. Therefore,
higher levels of overcon…dence of either kind increase the likelihood that e¤ort is implemented in
equilibrium.

Proposition 4 Ceteris paribus, higher levels of overcon…dence of either kind increase the likelihood
that e¤ ort is implemented in equilibrium: if e¤ ort is implemented given agent beliefs (~
q ; v~), then
e¤ ort will be implemented when his beliefs are (~
q ; v~ ) for any v~ v~ or (~
q ; v~) for any q~ q~.

For di¤erent reasons, the potential equilibrium contract that implements e¤ort becomes rel-
atively more attractive to the agent as overcon…dence of either kind increases, whether it is the
incentive or the wager e¤ect of overcon…dence that dominates. Recall that when the incentive e¤ect
dominates, higher overcon…dence about the value of e¤ort reduces the cost of implementing e¤ort.
The agent reaps the bene…ts of this e¢ ciency gain when principals compete. Higher overcon…dence
about the base probability of success increases the agent’s perceived expected utility under the
contract that does not implement e¤ort; however, because he receives a higher success-contingent
payment under the contract that does implement e¤ort, there is a greater increase in his perceived
expected utility under this contract. For this same reason, higher overcon…dence of either kind
makes the contract that implements e¤ort comparatively more attractive to the agent when the
wager e¤ect dominates.13
13
Note that Proposition 4 does not imply that e¤ort is more likely to be implemented, in general, when dealing
with an overall more overcon…dent agent. Imagine, for example, a case in which e¤ort would be implemented if the
agent held “realistic” beliefs. Suppose that the agent is overall slightly overcon…dent, but undercon…dent about the
value of e¤ort. Because higher-powered incentives are then necessary to implement e¤ort, the increase in the cost of
agency reduces the likelihood that e¤ort is implemented in equilibrium.

16
4 Welfare Analysis

This section studies the welfare e¤ects of agent overcon…dence. Principals and agent hold hetero-
geneous beliefs, so at least one of them must be incorrect. The e¤ects of this deviation from a
strong interpretation of rationality on the participants’well being are not immediately clear. For
expositional purposes, Subsection 4.1 analyzes the welfare e¤ects of overcon…dence in which all
principals share the same beliefs, as was assumed in the previous section. Subsection 4.2 extends
the analysis to allow for principals holding di¤ering beliefs.

4.1 Principals Sharing the Same Beliefs

An overcon…dent agent will have a biased outlook on his expected utility; in what follows, I evaluate
the agent’s actual expected utility based on the true probabilities of success and failure. I believe
that this is a good initial measure of the agent’s ex-ante well being. If the agent cares solely about
the actual payments that he receives (in addition to his cost of e¤ort), this is the appropriate
measure— it is the actual expected value of his future utility. Further considerations about factors
that in‡uence individuals’well being have con‡icting implications in terms of welfare analysis. If the
agent derives utility from anticipating how richly he will be rewarded once the project succeeds,
along the lines of K½oszegi (2005), an overcon…dent agent will enjoy higher utility than what I
calculate as his actual expected utility. On the other hand, once payo¤s are realized, the agent
will be disappointed whenever he does not receive the success-contingent payment he so con…dently
anticipates. An agent could evaluate receiving the low failure-contingent payment not only for its
own worth, but also as a loss relative to his “reference point” as introduced by K½oszegi and Rabin
(2005). In this case, the agent would be worse o¤ than what I calculate. One could also imagine
a concept of welfare consistent with individual sovereignty: we could calculate each participant’s
expected utility based on their subjective beliefs. Such analysis, however, ignores the fact that
individuals do care about utility derived from actual consumption made possible by income, and
not just their expectations about future utility.
Assume, for now, that the principals hold accurate beliefs. This assumption is convenient be-
cause the zero-expected-pro…ts condition implies that social welfare depends solely on the agent’s
well being and that the agent’s beliefs only a¤ect the power of incentives of the equilibrium
contract— not the actual expected payment the agent receives. We will relax this assumption
in short. When principals compete, the agent receives expected payment equal to the project’s ex-
pected revenue. Because, given some implemented level of e¤ort, the agent’s expected payment is
independent of the terms of the equilibrium contract, his actual expected utility depends exclusively

17
on the implemented level of e¤ort and the amount of risk he bears in equilibrium.
Keeping with the structure of the previous section, I …rst identify the welfare e¤ects of overcon-
…dence assuming that e¤ort is not implemented in equilibrium, and that changes in overcon…dence
do not a¤ect the implemented level of e¤ort. In that case, zero expected pro…ts and the assump-
tion that principals hold accurate beliefs imply that actual expected payment to the agent is the
project’s expected revenue:
qx1 + (1 q) x0 .

As shown in Proposition 1, as a consequence of the wager e¤ect, an agent who is overcon…dent about
the base probability of success always bears risk in equilibrium, so any level of overcon…dence of
this kind harms the risk-averse agent.
Assume now that e¤ort is implemented in equilibrium, and that changes in overcon…dence do
not a¤ect the implemented level of e¤ort. Actual expected payment to the agent is then

(q + v) x1 + [1 (q + v)] x0 .

When the agent is only slightly overcon…dent overall, the equilibrium contract is characterized by
Proposition 2. If this is the case, the power of incentives depends solely on the agent’s beliefs
regarding the value of e¤ort. Due to the incentive e¤ect, an agent who is overcon…dent about
the value of e¤ort is exposed to less risk in equilibrium than he would be if he held realistic
beliefs because lower-powered incentives are su¢ cient to induce e¤ort. Thus, the agent’s well being
increases with overcon…dence regarding the value of e¤ort. Slight overcon…dence about the value
of e¤ort is therefore bene…cial to the agent: he bene…ts from the e¢ ciency gain of a lower cost
of agency. The agent’s beliefs about the base probability of success do not a¤ect the equilibrium
contract if he remains only slightly overcon…dent overall.
When the agent is signi…cantly overcon…dent overall, the equilibrium contract is characterized
by Proposition 3. As a consequence of the wager e¤ect, the amount of risk that the agent is exposed
to increases in overcon…dence of either kind. Thus, when the agent is signi…cantly overcon…dent,
his well being decreases with overall overcon…dence. Higher overcon…dence increases the agent’s
exposure to what is already an excessive amount of risk.
As shown by Proposition 4, another e¤ect of higher overcon…dence of either kind is that it makes
e¤ort more likely to be implemented. If higher agent overcon…dence drives e¤ort to be implemented
in equilibrium, the actual expected payment to the agent increases (by as much as expected revenue
does) because e¤ort exertion increases the probability of success of the project. A marginal increase
in overcon…dence that drives e¤ort to be implemented might, therefore, bene…t the agent. This will
only be the case, however, if the increase in actual expected payment compensates the agent for the

18
disutility of exerting e¤ort (e¤ort must therefore be the …rst-best action, so that v (x1 x0 ) > c)
and the additional risk he bears.
When principals compete to contract with the agent, some overcon…dence about the value of
e¤ort bene…ts the agent because lower-powered incentives are then su¢ cient to induce e¤ort. A
risk-neutral principal can provide more insurance without destroying incentives. In contrast, if the
agent is undercon…dent about the value of e¤ort or signi…cantly overcon…dent overall, he bears an
excessive amount of risk (which is costly to him).
Allowing for principals to hold inaccurate beliefs, the e¤ects of overcon…dence outlined above
are reinforced if principals are overly optimistic about the probability of success of the project.
When this is the case, higher-powered incentive contacts that yield zero expected pro…ts according
to the principals’ beliefs yield lower actual expected payment to the agent. As the agent holds
higher stakes in the project, his actual expected payment decreases from the optimistic principals’
estimate of expected revenue towards actual expected revenue.14 . The agent’s welfare therefore
decreases as the power of incentives of the equilibrium contract increases, even more sharply than
in the case in which principals hold accurate beliefs. The e¤ects of agent overcon…dence on his
well being are therefore reinforced when principals are overly optimistic: the agent bene…ts from
moderate overcon…dence about the value of e¤ort because he bears less risk and he receives a higher
actual expected payment in equilibrium. Undercon…dence about the value of e¤ort or signi…cant
overall overcon…dence harm the agent both because he is exposed to a higher amount of risk and
because he receives a lower actual expected payment in equilibrium.
If the principals are overly pessimistic relative to the true probability of success, the e¤ects of
agent overcon…dence on his well being are ambiguous. In this case, when expected pro…ts are zero
according to the principals’beliefs, higher-powered incentive contracts yield higher actual expected
payment to the agent. As the agent holds higher stakes in the project, his actual expected payment
now increases from the overly pessimistic principals’estimate of expected revenue towards actual
expected revenue. Changes in overcon…dence that result in lower power of incentives still bene…t
the agent by shielding him from risk, but provide him with a lower actual expected payment.
Conversely, changes in overcon…dence that result in higher power of incentives expose the agent to
more risk but also provide higher actual expected payment to him. For instance, a signi…cantly
overcon…dent agent may actually bene…t from his overcon…dence when contracting with an overly
pessimistic principal, particularly if his beliefs are close to the true outcome distribution and he
14
This is true as long as s1 < x1 and s0 > x0 . I assume that this is the case for the remainder of the paper, but
brie‡y discuss the alternative in Subsection 4.2 below. Common sense, if not legal provisions, should prevent the
agent from signing a contract in which he takes on more risk than the intrinsic risk of the project.

19
has high risk tolerance.

4.2 Principals With Di¤ering Beliefs

I derived the results of the model assuming that all competing principals hold identical beliefs. This
simpli…ed the analysis because competition then resembles Bertrand competition, so that expected
pro…ts are driven to zero when as few as two principals compete. Given that I am allowing for
principal and agent to hold heterogeneous beliefs, this assumption seems particularly strong. If we
allow for principals to knowingly hold disagreeing beliefs regarding the probability distribution of
outcomes, two main complications arise.15
First, so long as the number of competing principals is …nite, expected pro…ts according to
the beliefs of the principal whose o¤er is accepted in equilibrium will generically be positive. The
most optimistic principal needs only to ensure that her contract o¤er yields zero expected pro…ts
according to the beliefs of the second-most-optimistic principal. The second-most-optimistic prin-
cipal is not willing to outbid some o¤ers that yield positive expected pro…ts to the most optimistic
principal if they hold heterogeneous beliefs.16 When allowing for principals to hold disagreeing be-
liefs, it is generally in each principal’s best interest to hold accurate beliefs, which will allow her to
design her contract o¤er optimally. If the second-most-optimistic principal overestimates the true
probability of success, the most optimistic principal (whose contract is accepted in equilibrium) will
su¤er losses in expectation. Optimistic bias will therefore tend to harm the principal. An overly
pessimistic principal, on the other hand, will tend to be outbid by more optimistic principals. If
all principals are pessimistic relative to the actual probability of success, any principal whose o¤er
is rejected in equilibrium would bene…t from correctly updating her beliefs; she could then attract
the agent and earn positive expected pro…ts.
The second complication is pinpointing the o¤er which is accepted by the agent in equilibrium.
If we assume monotonic bidding strategies by the principals, then the o¤er made by the most
15
When the principals hold heterogeneous beliefs, it would be optimal for them to set up a secondary side-betting
market on project outcome (if it is publicly observable). Because of risk neutrality, this side-betting would be
unbounded— and so would expected pro…ts from each principal’s point of view. We assume that such a side-betting
market is infeasible, so that principals behave optimally in the contract-o¤er-design stage.
16
Note that the result of generically-positive perceived expected pro…ts for the principal whose o¤er is accepted
in equilibrium does not depend on the assumption that principals are aware of each others’ beliefs. Dropping this
assumption (if principals know only the agent’s and their own beliefs), competition would then resemble a …rst-price
sealed-bid auction. If there are …nitely many principals, each of them knows that some contract o¤ers which yield
strictly positive expected pro…ts will be accepted by the agent with positive probability. Each principal will therefore
o¤er a contract to the agent that, conditional on being accepted, gives the principal strictly positive perceived expected
pro…ts according to her own beliefs.

20
 optimistic principal will tend to be the one accepted in equilibrium. There is, however, an extreme
case in which the o¤er made by the most pessimistic principal could be the one accepted by the
agent: if the agent is fairly risk neutral and very overcon…dent relative to the most pessimistic
principal, the hs1 ; s0 i contract as characterized in Proposition 3 could be such that s1 > x1 and
s0 < x0 — the principal bets on project failure.17 If this is the case, the principal earns higher pro…ts
when the project fails than when it succeeds. The principal would then have incentives to sabotage
the project if possible, and the agent should be wary of accepting such a contract o¤er. This extreme
seems unrealistic, for the same reason that contracts with payments that are non-monotonic in the
principal’s objective variable (e.g. output) seem unrealistic: one of the participants would then
have incentives to destroy output.

5 One Principal and One Agent

Consider now the setting that tends to be discussed more often in agency literature, in which
one principal can make a take-it-or-leave-it contract o¤er to one agent. Owing to her bargaining
power, the principal extracts all the surplus from the agency relationship. This framework is more
appropriate than the competing-principals setting when the pool of potential agents is large relative
to the number of principals. The case of salespeople in retail could be an example of such a situation.

principal if agent accepts payo¤s are distributed

makes contract o¤er he chooses according to
o¤er to the agent action e the contract’s terms
..........................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................

agent accepts project time

or rejects o¤er succeeds
or fails

Figure 2: Timing of the model with one principal and one agent

The timing of the model is as follows. First, the principal makes a take-it-or-leave-it contract
o¤er to the agent. The agent can accept or reject the o¤er. If he accepts it, he chooses whichever
action maximizes his perceived expected utility given the terms of the contract. The outcome of
the project is then realized, payo¤s are distributed according to the terms of the contract, and the
agency relationship ends. If the agent rejects the principal’s o¤er, both will receive utility according
17
This case may be so extreme that holding excessively pessimistic beliefs could be better than holding accurate
beliefs for a principal: she then “wins” and earns the chance to bilk the agent for pro…t, whereas the o¤er made by
a principal holding accurate beliefs would be rejected.

21
to their outside option. I assume that the agent’s outside option is exogenous and independent of
his overcon…dence.18 The principal’s outside option does not a¤ect the equilibrium contract as long
as the agency relationship yields su¢ cient surplus for her to engage in it; I assume this to be the
case.
Let u denote the agent’s perceived expected utility from his outside option. The principal’s
contract o¤er, if it is to be accepted by the agent, must provide him perceived expected utility no
lower than u. This participation, or “individual rationality”— IR— constraint restricts the possible
optimal contract o¤ers to those that satisfy

(~
q + v~e) u (s1 ) + [1 (~
q + v~e)] u (s0 ) c (e) u, (IR)

where e is the action (freely chosen by the agent) that the principal wishes to implement. The
incentive compatibility constraint that the contract must satisfy if the principal wishes to implement
e¤ort remains unchanged:
v~ (u (s1 ) u (s0 )) c. (IC)

The principal’s objective when designing the optimal contract o¤er is to maximize expected
pro…ts, taking into account the relevant constraints:

max (q + ve) (x1 s1 ) + [1 (q + ve)] (x0 s0 )

e;s1 ;s0

subject to

v~ (u (s1 ) u (s0 )) c if e = 1,

v~ (u (s1 ) u (s0 )) c if e = 0, and

(~
q + v~e) u (s1 ) + [1 (~
q + v~e)] u (s0 ) c (e) u.

Note that the problem of a principal who competes with others to contract with the agent,
studied in Section 3, can be reinterpreted as follows: she wishes to maximize expected pro…ts,
taking into account that the agent chooses e optimally and that he will accept the o¤er only if it
is better than the next-best contract o¤er. This maximization problem can be written as:

max (q + ve) (x1 s1 ) + [1 (q + ve)] (x0 s0 )

e;s1 ;s0

18
This assumption allows me to isolate the e¤ect that overcon…dence, only regarding the probability of success of
the project, has on the equilibrium contract. If the agent was also overcon…dent about his outside option, he would
demand a higher perceived expected utility in order to accept any given o¤er by the principal.

22
subject to

v~ (u (s1 ) u (s0 )) c if e = 1

v~ (u (s1 ) u (s0 )) c if e = 0

(~
q + v~e) u (s1 ) + [1 (~
q + v~e)] u (s0 ) c (e) U (next-best o¤er),

where U (next-best o¤er) stands for the perceived expected utility that the agent would receive by
accepting the best alternative o¤er (and choosing his optimal e¤ort level accordingly).
The only di¤erence between these two problems is that the agent’s participation constraint
is exogenous when one principal makes a take-it-or-leave-it o¤er, and endogenously generated by
competing o¤ers in the case of competing principals. The results regarding the equilibrium contract
(Propositions 1–4) remain, except that the expected payment to the agent is determined by his
exogenous participation constraint (IR), rather than the zero-expected-pro…ts condition. Note in
particular that, given a set of parameters of the model, the e¤ort level implemented in equilibrium is
independent of market structure. Intuitively, there is no pro…table deviation from the equilibrium
contract in the competing-principals setting— there is no other contract that attracts the agent
(gives him higher perceived expected utility) and yields higher expected pro…ts for the o¤ering
principal. The optimal contract when one principal makes a take-it-or-leave-it o¤er is such that
no other contract retains the agent (gives him at least as much perceived expected utility as his
outside option) and yields higher expected pro…ts for the principal.
Because of the duality of this problem, the e¤ects of overcon…dence on the equilibrium contract
carry over from the competing-principals model accordingly. If the agent is only slightly overcon…-
dent overall, the incentive e¤ect dominates: if the agent is overcon…dent about the value of e¤ort,
then lower-powered incentives are su¢ cient to induce e¤ort, while if he is undercon…dent on this
dimension, higher-powered incentives are necessary to implement e¤ort. If the agent is signi…cantly
overcon…dent overall, the wager e¤ect dominates: the optimal contract exhibits excessively power-
ful incentives that increase with agent overcon…dence on either dimension. Finally, ceteris paribus,
increases in overcon…dence of either kind make it more likely that e¤ort is implemented under the
optimal contract. The optimal contract is derived explicitly in Subsection A.2 of the Appendix.

5.1 Welfare Analysis

Because the principal is able to extract all the surplus from the agency relationship, the welfare
e¤ects of overcon…dence di¤er from those in the competing-principals setting.19 In equilibrium,
19
In an independent study, Santos-Pinto (2006) analyzes the e¤ects of agent overcon…dence on …rm pro…ts in a
tournament setting. Our results in terms of welfare are consistent.

23
she o¤ers the agent perceived expected utility only as high as the utility he would derive from his
outside option. As before, …rst assume that the principal’s beliefs are accurate.
Recall that the cost of agency is reduced when the agent is overcon…dent about the value of
e¤ort. The principal bene…ts from this e¢ ciency gain because she captures all the surplus from
the relationship; it reduces the cost of satisfying the incentive-compatibility constraint. Further-
more, because an overcon…dent agent is overly optimistic about the probability of receiving the
success-contingent payment, overall agent overcon…dence reduces the principal’s cost of satisfying
his participation constraint. For this reason, even slight overcon…dence about the value of e¤ort
hurts the agent.20 Agent undercon…dence about the value of e¤ort increases the cost of agency.
Besides hurting the agent, who is exposed to more risk, it might reduce the principal’s expected
pro…ts if the increase in the cost of agency is greater than the savings in terms of an easier-to-satisfy
participation constraint.
When the agent is signi…cantly overcon…dent overall, he bears an excessive amount of risk in
equilibrium. This, coupled with a lower actual expected payment (consequence of overestimating
the probability of receiving the success-contingent payment), implies that his actual expected utility
quickly decreases with overcon…dence in this range. The principal’s expected pro…ts increase with
agent overcon…dence of either kind in this range, because it is cheaper for her in expectation to
provide the agent a perceived expected utility comparable to his outside option— whether or not
e¤ort is implemented in equilibrium.

5.2 Choosing From a Pool of Agents

Given that agent beliefs a¤ect the principal’s expected pro…t— even if we hold actual agent pro-
ductivity constant— the question regarding whether the principal prefers to contract with a more-
or less-overcon…dent agent follows naturally. Consider the problem that the principal faces when
choosing an agent from a pool of applicants with di¤erent levels of overcon…dence and true ability.
This question is particularly relevant when the pool of agents is large relative to the number of
principals willing to hire an agent, our main motivation for discussing the one-principal setting.
All else equal, the principal will prefer a more overcon…dent agent. Imagine a situation in
which many potential agents share the same underlying characteristics, but di¤er in their self-
con…dence— e.g. a group of individuals who pass several aptitude tests. The principal will choose
the most overcon…dent agent, because it is cheapest for her to satisfy his participation constraint.21
20
The assumption that the agent’s valuation of his outside option is independent of his level of overcon…dence is
crucial for this result. In some instances, one might expect an overcon…dent agent to be overcon…dent about the
opportunities that he passes by, just as he is about the project he actually engages.
21
As discussed before, if an agent is overcon…dent overall but undercon…dent about the value of e¤ort, the cost

24
Clearly, the assumption that the outside option is evaluated equally by agents with di¤erent beliefs
is crucial for this result: less overcon…dent agents could become attractive if overcon…dence also
a¤ects their perception regarding their outside option, since less overcon…dent agents would accept
contracts yielding lower perceived expected utility.
When facing a pool of agents who share the same beliefs about their ability, on the other hand,
the principal will hire the agent that she judges to be most able. An applicant who responds to
a job announcement, for example, probably believes he is well-suited for the position. Because
choosing a higher-ability agent (i.e. an agent who generates a better outcome distribution) yields
higher expected revenue and the cost of inducing any of these agents to exert e¤ort is the same,
the principal naturally prefers the most able agent.
In short: When the principal faces a pool of same-ability agents who di¤er only in their level
of overcon…dence, she will tend to hire the most overcon…dent agent. In contrast, when she faces
a pool of applicants who share the same beliefs but di¤er in underlying ability, the principal will
choose the least overcon…dent— most able— agent.

5.3 Comment on the Agent Designing the Contract

With a reinterpretation, the competing-principals framework of Section 3 can be used to study

the setting in which it is the agent who designs the contract and makes a take-it-or-leave-it o¤er
to a principal. The agent extracts all the surplus from the relationship, just as when principals
compete. Recall that competition drives expected pro…ts to zero, so the equilibrium contract in
that case maximizes the agent’s perceived expected utility among those that yield non-negative
expected pro…ts for the principal. This is precisely the agent’s objective when designing a take-it-
or-leave-it contract o¤er. If the agent is aware of the principal’s beliefs, the equilibrium contract
is identical to the equilibrium contract that would follow competition between several principals
sharing the same beliefs. If the overcon…dent agent was instead oblivious about the fact that the
principal holds di¤erent beliefs, he would o¤er a contract in line with the equilibrium of a standard
identical-beliefs model. The principal would reject such an o¤er if she was relatively pessimistic
about the probability of success, judging it to yield negative expected pro…ts.
of agency increases. The principal might choose a less (overall) overcon…dent agent if lower-powered incentives are
su¢ cient to induce this agent to exert e¤ort. More precisely, …xing actual agent ability and one kind of overcon…dence
across agents, the principal will prefer the agent with highest overall overcon…dence.

25
6 Extension: The Continuous-Action Case

In this section, I generalize the one-principal, one-agent model to allow the agent to choose from
a continuum of possible e¤ort levels. As we will see, most of the results of the two-action model
generalize to a continuous-action setting. The timing and other assumptions in this framework are
identical to those in the one-principal, one-agent setting studied in the previous section, except that
the agent has a continuum of possible e¤ort levels to choose from: he will choose some e 2 [0; 1]
if he accepts the principal’s contract o¤er. The disutility cost of e¤ort is a function c (e); assume
that c0 ( ) > 0 and c00 ( ) > 0. This assumption implies that the agent’s e¤ort level choice will be
proportionately related to the contract’s power of incentives as long as his choice is an interior
solution to his perceived expected utility maximization problem. Assume that c0 (0) = 0 and
lime!1 c0 (e) = 1 so that it is, in fact, an interior solution whenever s1 > s0 .22
As discussed before, because the principal who can make a take-it-or-leave-it o¤er to an agent
faces a very similar problem to the one faced by a principal who competes with others, the results
in a competing-principals setting and a one-principal setting di¤er only in the level of expected
payment to the agent. I focus on a continuous-action-space extension of the model in a one-
principal, one-agent setting. Because the agent receives perceived expected utility equal to that
of his (exogenous) outside option in equilibrium, his two possible outcome-contingent utility levels
have a fairly simple closed-form solution in this setting.
The principal’s problem when designing the optimal contract o¤er is to maximize her expected
pro…ts, taking into account that the agent will choose his e¤ort level optimally and that he will
accept the o¤er only if he judges it to yield expected utility no lower than his outside option.
If the agent accepts a given contract o¤er hs1 ; s0 i, he will subsequently choose his e¤ort level
so as to maximize his perceived expected utility:

max (~
q + v~e) u (s1 ) + [1 (~
q + v~e)] u (s0 ) c (e) .
e2[0;1]

The …rst-order condition for the agent’s problem is

v~ [u (s1 ) u (s0 )] = c0 (e) ,

which de…nes the agent’s choice of e¤ort after accepting contract o¤er hs1 ; s0 i. The incentive
e¤ect is apparent from this condition: a lower-powered incentive contract is su¢ cient to implement
any given e¤ort level e when the agent is overcon…dent about the value of e¤ort. The agent’s
22
Note that if the agent chose a corner solution (e = 0 or e = 1), as long as his choice of e¤ort remains at a given
corner or shifts discretely to the other, the analysis reduces to the two-action model studied before.

26
participation constraint can be written as:

(~
q + v~e) u (s1 ) + [1 (~
q + v~e)] u (s0 ) c (e) u,

where e is chosen optimally by the agent. Note that it must be binding in equilibrium. If not, the
principal could marginally reduce both payments s1 and s0 while keeping the power of incentives
[u (s1 ) u (s0 )] constant (so as to implement the same e¤ort level). The principal would then
increase expected pro…ts, which contradicts equilibrium.
In order to characterize the relationship between overcon…dence, the power of incentives, and
the implemented level of e¤ort under the optimal contract, it is useful to reinterpret the principal’s
problem.

De…nition 2 Given the agent’s e¤ ort-choice problem, and that the principal will optimally set the
participation constraint to bind, the best contract that implements e¤ ort level e, hs1 (e) ; s0 (e)i, is
implicitly de…ned by
c0 (e)
u (s1 (e)) = u + c (e) + [1 (~
q + v~e)] and
v~
c0 (e)
u (s0 (e)) = u + c (e) (~
q + v~e) .
v~

Taking this into account, we can reduce the principal’s problem to

max (q + ve) (x1 s1 (e)) + [1 (q + ve)] (x0 s0 (e)) .

e2[0;1]

Clearly, the power of incentives of the optimal contract depends not only on the agent’s beliefs
but also on the e¤ort level that the principal chooses to implement, which in turn depends on
all the parameters in the model (including the particular functional form of the agent’s utility
with respect to payments and disutility cost of e¤ort). While explicitly solving for the optimal
implemented level of e¤ort seems fruitless, it is possible to study the qualitative e¤ects of changes
in each kind of overcon…dence.
Assume that the principal’s pro…t-maximization problem when choosing which e¤ort level to
implement is well behaved : it has a unique, interior, local and global maximum. Let e denote the
e¤ort level that solves the principal’s pro…t maximization problem, at which the marginal revenue
from increasing the implemented level of e¤ort equals its marginal cost:

M Re = M Ce .

Note that the marginal revenue of e¤ort is constant:

M Re = v (x1 x0 ) .

27
By marginally increasing the implemented level of e¤ort, the additional revenue in the event of
project success (x1 x0 ) will come about with marginally higher probability (how much higher
depends on v, but not on the agent’s beliefs).
The marginal cost of implementing e¤ort, on the other hand, is

ds1 (e) ds0 (e)

M Ce = v (s1 (e) s0 (e)) + (q + ve) + [1 (q + ve)]
de de
where

ds1 (e) 1 c00 (e)

= 0 [1 (~ q + v~e)] , and
de u (s1 (e)) v~
ds0 (e) 1 c00 (e)
= (~
q + v
~ e) .
de u0 (s0 (e)) v~
Note, in particular, that the marginal cost of implementing e¤ort depends crucially on the agent’s
beliefs. It is clear that for the principal’s pro…t-maximization problem to be well behaved, it is
su¢ cient that the marginal cost of implementing e¤ort be an increasing function of e¤ort level.
Further discussion about the conditions under which the principal’s pro…t-maximization problem
is well behaved is relegated to Subsection A.3.1 of the Appendix.
Consider the e¤ect of marginally higher agent overcon…dence about the base probability of
success on the marginal cost of implementing e¤ort, evaluated at the optimal e :

@M Ce c00 (e ) 1 1
= (q + ve ) 0 + [1 (q + ve )] < 0.
@ q~ v~ u (s1 (e )) u0 (s0 (e ))
Given that the marginal revenue of implementing any e¤ort level is constant, and that the marginal
cost of implementing e¤ort increases with e¤ort level, it follows that the principal will choose
to implement higher e¤ort if dealing with an agent who is more overcon…dent about the base
de
probability of success: d~q > 0. This result is analogous to its counterpart in the two-action case,
summarized in Proposition 4. As a consequence of the wager e¤ect of overcon…dence, because a
more-overcon…dent agent prefers higher-powered incentive contracts, it is cheaper for the principal
to implement a higher level of e¤ort in the margin.
Consider now the comparable e¤ect of marginally higher agent overcon…dence about the value
of e¤ort:

@M Ce c00 (e ) 1 1
= e (q + ve ) 0 + [1 (q + ve )]
@~v v~ u (s1 (e )) u0 (s0 (e ))
1
v [(x1 s1 (e )) (x0 s0 (e ))] < 0.
v~
The …rst term of the equation above re‡ects the wager e¤ect of overcon…dence. Just as in the
case of overcon…dence about the base probability of success, it is less costly for the principal to

28
implement higher e¤ort levels. The second term of the equation re‡ects the incentive e¤ect of
overcon…dence. The contract hs1 (e ) ; s0 (e )i will implement some e¤ort level greater than e
following an increase in the agent’s overcon…dence about the value of e¤ort. This bene…ts the
principal as long as (x1 s1 (e )) (x0 s0 (e )).23 Implementing a higher level of e¤ort increases
the expected revenue of the project. As a consequence of both the wager and the incentive e¤ects
of overcon…dence, higher overcon…dence about the value of e¤ort results in a higher implemented
de
e¤ort level: d~
v > 0. This is analogous to the corresponding result in the two-action case, exposed
in Proposition 4.
The e¤ect of overcon…dence about the base probability of success on the power of incentives of
the optimal contract is straightforward. Given that a higher e¤ort level is implemented, and that
this kind of overcon…dence does not directly a¤ect the incentive structure of the contract holding
e¤ort constant, it follows that overcon…dence about the base probability of success always implies
higher-powered incentives. The wager e¤ect of overcon…dence drives the optimal contract towards
higher-powered incentives in the continuous-action case, even if the agent is only slightly overcon-
…dent overall, because the implemented e¤ort level continuously increases with overcon…dence.
The e¤ect of overcon…dence about the value of e¤ort on the power of incentives is, on the other
hand, ambiguous. This is because, as in the two-action case, the incentive e¤ect of overcon…dence
on this dimension pushes toward lower-powered incentives, while the wager e¤ect pushes toward
higher-powered incentives. Furthermore, both e¤ects of overcon…dence imply that the optimal
contract implements a higher e¤ort level, which also pushes toward higher-powered incentives. The
intuition can also be explained in terms of the two-action setting. In that case, an increase in
overcon…dence about the value of e¤ort that drives e¤ort to be implemented in equilibrium is likely
to result in a higher-powered incentive contract.
The actual change in the power of incentives of the optimal contract as a consequence of changes
in agent overcon…dence regarding the value of e¤ort is formally derived in Subsection A.3.2 of the
Appendix. Whether there is some range of overall slight overcon…dence over which the power of
incentives decreases in overcon…dence about the value of e¤ort depends on all the parameters of
the model. Such a range exists if the agent is very risk averse and the marginal cost of exerting
e¤ort does not increase sharply. Intuitively, because a small increase in the amount of risk born by
23
As argued in footnote 14 and the discussion that follows it in the text, it seems very reasonable to assume that
in equilibrium x1 x0 s1 (e ) s0 (e ), so that the agent is not exposed to more risk than inherent in the project.
If this assumption is violated, the principal would enjoy greater pro…ts in the case of project failure than in the case
of success, so may prefer to implement lower rather than higher e¤ort levels. Such a contract seems unrealistic, since
the principal would then have incentives to sabotage the project. Common sense, if not legal restrictions, should
prevent the agent from accepting such a contract.

29
the agent is su¢ cient to induce higher e¤ort exertion, and lower-powered incentives are su¢ cient
to implement any given e¤ort level, the power of incentives of the optimal contract decreases with
overcon…dence about the value of e¤ort. If, on the other hand, the agent is not very risk averse and
his marginal cost of exerting e¤ort increases sharply, the additional power of incentives necessary to
implement higher e¤ort is large, so there is no such range and the power of incentives is everywhere
increasing in overcon…dence of either kind.

7 Conclusion and Discussion

This paper attempts to provide insight into the e¤ects of overcon…dence in equilibrium within
a moral-hazard framework, which include potential bene…ts and pitfalls. It gives one possible
explanation to why we may observe incentive contracts that seem excessively powerful in some
situations, and others that seem surprisingly ‡at in other situations. It also helps explain why
overcon…dence can be valuable, not only for the agent, but also for the principal— even though she
is mainly concerned with the agent’s underlying ability.
The results of the paper suggest that incentive contracts are sensitive to the kind of overcon-
…dence, not only to the presence of overcon…dence per se. Because of this, experimental and …eld
studies exploring how (besides whether or not) individuals are overcon…dent would help our un-
derstanding about how incentive contracts respond to changes in beliefs. For instance, if agents
tend to be signi…cantly overcon…dent overall and agent overcon…dence is procyclical (as suggested
by Gervais and Odean [2001]), our model predicts that fast-paced growth should be followed by
more powerful incentive contracts being implemented. In contrast, if agents tend to be only slightly
overcon…dent about the value of e¤ort, less powerful incentives would follow.
Some recent empirical observations are consistent with the model. For example, in a survey of
almost three thousand entrepreneurs, Cooper, Woo, and Dunkelberg (1988) …nd that entrepreneurs
tend to overestimate the probability of success of their enterprise, and invest many hours in it (more
than 60 hours a week according to many of the respondents). In Weinstein’s (1980) terms, when
entrepreneurs form expectations they may be comparing themselves to a hypothetical entrepreneur
who chooses to enter an industry with merely good prospects and puts little e¤ort into making the
enterprise succeed. Given that the average success rate of businesses is readily available information,
entrepreneurs may use this average as their benchmark when forming expectations. When doing so,
they fail to internalize the fact that most other entrepreneurs choose to enter an industry which they
deem particularly pro…table and work hard towards success, just like they do. The results of my
model imply that entrepreneurs’choice of long hours could arise simply from their overcon…dence

30
rather than, for example, a particularly low cost of e¤ort for entrepreneurs because they enjoy their
work more than others.
Cooper, Woo, and Dunkelberg (1988) also …nd that the entrepreneurs’degree of overcon…dence
seems to be independent of factors that a¤ect their actual probability of success (like experience
in the industry and education level). This suggests an empirical test for the relevance of overcon-
…dence in entrepreneurs’ decisions: holding the beliefs of the entrepreneur constant, if the most
overcon…dent agents are signi…cantly overcon…dent (as implicitly de…ned by Proposition 3) then my
model can have implications opposite to those of a standard moral-hazard model which does not
allow for overcon…dence. A standard identical-beliefs model would predict a positive correlation
between the proportion of funds invested in the project by the entrepreneur and the probability
of success of the enterprise. Entrepreneurs who invest a higher proportion of their own funds face
more powerful incentives to exert e¤ort. In that case, there is less of an agency problem, so the
probability of success should always be positively correlated to the proportion of funds invested by
the entrepreneur. When we allow for overcon…dence, and given the observation that beliefs tend to
be fairly homogeneous, in this setting the most overcon…dent entrepreneurs (those with relatively
low underlying ability) will tend to “underinsure” and invest a higher proportion of their own
funds in the project. They will tend to have a lower success rate than more able, less overcon…dent
entrepreneurs who do not underinsure. Less overcon…dent entrepreneurs …nd the terms of the prin-
cipals’o¤ers (e.g. the terms of a bank loan) to be more in line with their own beliefs; because of a
smaller wager e¤ect of overcon…dence, they face less powerful incentives in equilibrium (they invest
a smaller proportion of their own funds). Thus, the probability of success of an enterprise may be
negatively correlated to the proportion of the entrepreneur’s own funds invested in it. Of course,
even allowing for overcon…dence, the e¤ect of incentives on the e¤ort that the entrepreneur exerts
pushes towards a positive correlation. Observing a negative correlation would strongly suggest that
overcon…dence is relevant in entrepreneurs’decision-making processes.
The model can serve to reinterpret some previous empirical results. Smith and Watts (1992)
present an empirical study which discusses executive compensation. One of their observations is
that …rms with larger “investment opportunity sets” pay their CEOs more, and are more likely
to use stock options and other forms of performance-contingent pay. They interpret this result in
light of a standard moral-hazard framework: they argue that a manager’s actions are less read-
ily observable if the …rm has more investment opportunities. In a world where overcon…dence is
relevant, it seems intuitive that a larger opportunity set will go hand-in-hand with higher CEO
overcon…dence about the chosen course of action, since he will tend to choose whichever action he
is most optimistic about. In this sense, my model is consistent with a positive correlation between

31
larger investment opportunity sets and higher-powered compensation packages, and the connection
more straightforward than monitoring problems that increase with the amount of possible invest-
ment projects. Moral hazard, however, does not seem to be the main driving force behind optimal
contract design in the context of executive compensation. A model in which the agent holds private
information regarding the best course of action seems more appropriate to study this topic. Gervais,
Heaton and Odean (2003) explore one such model and argue that the power of incentives should
be lower if a manager is overcon…dent than if he is realistic. Their insight is that an overcon…dent
manager will act in a less risk-averse manner, so lower-powered incentives are su¢ cient to align the
agent’s objectives to those of the principal. The wager e¤ect of overcon…dence identi…ed in this
paper, however, carries over to this setting. If the principal is aware that the agent tends to overes-
timate the probability of success after choosing a course of action, the wager e¤ect pushes towards
higher-powered incentives. I study the e¤ects of overcon…dence in an investment-decision setting
in de la Rosa (2006), and Van den Steen (2005) studies a similar problem (from the viewpoint of
intrinsic and extrinsic motivation).
Another direction for further research that could yield interesting results is overcon…dence in a
self-selection (or sorting) setting. According to adverse-selection models that allow for overcon…-
dence, the most overcon…dent agents are naturally attracted to riskier endeavors. This is consistent
with the fact that some agents in dangerous jobs do underestimate the probability of a bad out-
come, as noted by Akerlof and Dickens (1982). My model implies, however, that di¤erent kinds
of overcon…dence can have con‡icting e¤ects in terms of the amount of risk born by the agent in
equilibrium. If this is the case, agents with similar degrees of overall overcon…dence might sort
themselves into very di¤erent positions.

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34
A Appendix

A.1 Competing Principals

Lemma 1 If principals share the same beliefs regarding outcome distribution conditional on the
agent’s actions, in equilibrium expected pro…ts will be zero for all principals according to their beliefs.
Proof. Suppose not. Suppose that a principal o¤ers, and the agent accepts, a contract hs1 ; s0 i
in equilibrium that yields positive expected pro…ts for the o¤ering principal:

Pr (x1 j e) (x1 s1 ) + [1 Pr (x1 j e)] (x0 s0 ) > 0,

where e is chosen optimally by the agent. Other principals, whose contracts are not accepted by
the agent, receive zero pro…ts in equilibrium. Consider the following deviation by one of these
principals: o¤er contract hs1 + ; s0 i if hs1 ; s0 i implements e¤ort, and hs1 ; s0 + i if hs1 ; s0 i does not
implement e¤ort. In either case, the new contract implements the same e¤ort level as hs1 ; s0 i does,
makes the agent strictly better o¤, and will thus be accepted by the agent. For close enough to
zero, the principal making the new contract o¤er enjoys positive expected pro…ts. Given that there
is a pro…table deviation, hs1 ; s0 i cannot be the equilibrium contract.

Proposition 1 Assuming e¤ ort is not implemented in equilibrium, the only equilibrium contract
hs1 ; s0 i is characterized by the conditions

q~ u0 (s1 ) q
0
=
1 q~ u (s0 ) 1 q

and q (x1 s1 ) + [1 q] (x0 s0 ) = 0. The agent bears risk in equilibrium if q~ 6= q.

Proof. Assuming that e¤ort is not implemented in equilibrium, hs1 ; s0 i characterized by
q q~ u0 (s1 )
1 q = 1 q~ u0 (s0 ) and zero expected pro…ts for the principal maximizes the agent’s perceived ex-
pected utility subject to non-negative pro…ts for the o¤ering principal. It can be shown that, because
of the agent’s risk aversion, this contract is the unique global maximum. Any other contract that
does not implement e¤ort and gives non-negative expected pro…ts to the o¤ering principal therefore
yields strictly lower perceived expected utility to the agent. Conversely, any other contract that
does not implement e¤ort and yields the same perceived expected utility to the agent yields strictly
negative expected pro…ts for the o¤ering principal. Thus, there is no pro…table deviation from
hs1 ; s0 i.

Proposition 2 Assuming e¤ ort is implemented in equilibrium, hs1 ; s0 i is the only equilibrium

q~+~v u0 (s1 ) q+v
contract if 1 (~ v ) u0 (s0 )
q +~ 1 (q+v) .

35
 Proof. We need to show that there is no pro…table deviation from this contract; i.e. that no
other e¤ort-implementing contract exists such that the agent receives higher expected utility, and
the o¤ering principal enjoys positive expected pro…ts. This rules out contracts with higher payment
to the agent in both success and failure, and those with lower payment to the agent in both events.
The perceived expected utility for the agent under hs1 ; s0 i is

~ [u (sx ) j e = 1] = (~
E q + v~) u (s1 ) + [1 (~
q + v~)] u (s0 ) c.

A marginal change in payments that leaves the agent indi¤erent satis…es

q + v~) u0 (s1 ) ds1 + [1

(~ q + v~)] u0 (s0 ) ds0 = 0
(~

or
q~ + v~ u0 (s1 )
ds0 = ds1
1 (~ q + v~) u0 (s0 )
where necessarily ds1 > 0 and ds0 < 0, since the incentive compatibility constraint would be
otherwise violated. Such a change implies that the agent would bear more risk under the new
contract. Since the agent is risk-averse, he must be compensated with a higher expected payment,
which is why the increase in s1 must be more than actuarially fair according to his beliefs.
The change in expected pro…ts for the o¤ering principal from a marginal change in the payment
structure that leaves the agent indi¤erent is

(q + v) ds1 [1 (q + v)] ds0 =

q~ + v~ u0 (s1 )
(q + v) + [1 (q + v)] ds1 0.
1 (~ q + v~) u0 (s0 )
q~+~v u0 (s1 ) q+v
If 1 (~ v ) u0 (s0 )
q +~ 1 (q+v) , expected pro…ts decrease for the principal o¤ering the new contract
that exposes the agent to more risk than hs1 ; s0 i does. It follows that there is no pro…table marginal
u0 (s1 )
deviation from the hs1 ; s0 i contract. Given that u0 (s0 ) falls as s1 increases and s0 decreases, discrete
deviations from hs1 ; s0 i that implement e¤ort and leave the agent indi¤erent also imply expected
losses for the o¤ering principal. Therefore, hs1 ; s0 i is the only equilibrium contract.

q~+~v u0 (s1 ) q+v

Proposition 3 Assuming e¤ ort is implemented in equilibrium, if 1 (~ v ) u0 (s0 )
q +~ > 1 (q+v) then
hs1 ; s0 i is not an equilibrium contract. The only equilibrium contract hs1 ; s0 i is characterized by

q~ + v~ u0 (s1 ) q+v
0
=
1 (~ q + v~) u (s0 ) 1 (q + v)

and (q + v) (x1 s1 ) + [1 (q + v)] (x0 s0 ) = 0. The equilibrium contract has higher-powered

incentives than necessary to implement e¤ ort.

36
 Proof. The proof is analogous to the proof of Proposition 1. Assuming that e¤ort is im-
plemented in equilibrium, hs1 ; s0 i (uniquely) maximizes the agent’s perceived utility subject to
non-negative pro…ts for the o¤ering principal. It follows that any other contract that implements
e¤ort and yields the same perceived expected utility to the agent yields strictly negative expected
pro…ts for the o¤ering principal. There is no pro…table deviation from hs1 ; s0 i.
q+v q~+~v u0 (s1 )
Given that by assumption 1 (q+v) < 1 (~ v ) u0 (s0 ) ,
q +~ since u00 ( ) < 0, and expected pro…ts for
the principal are zero under both hs1 ; s0 i and hs1 ; s0 i, it follows that s1 > s1 and s0 < s0 . By
construction, v~ (u (s1 ) u (s0 )) = c, and thus

v~ (u (s1 ) u (s0 )) > c;

hs1 ; s0 i has higher-powered incentives than necessary to implement e¤ort.

Proposition 4 Ceteris paribus, higher levels of overcon…dence of either kind increase the likelihood
that e¤ ort is implemented in equilibrium: if e¤ ort is implemented given agent beliefs (~
q ; v~), then
e¤ ort will be implemented when his beliefs are (~
q ; v~ ) for any v~ v~ or (~
q ; v~) for any q~ q~.
Proof. Overcon…dence a¤ects the implemented level of e¤ort di¤erently, depending on whether
the incentive or the wager e¤ect of overcon…dence dominates.
First, consider changes in agent overcon…dence regarding the value of e¤ort.
If hs1 ; s0 i is the potential equilibrium contract that implements e¤ort, the power of incentives
decreases with overcon…dence regarding the value of e¤ort. Expected pro…ts are zero in equilibrium,
so a marginal increase in v~ implies:
ds1 ds0
(q + v) [1 (q + v)] = 0,
d~
v d~
v
ds1 ds0
where d~
v < 0 and d~
v > 0. The e¤ect of such a change in the agent’s perceived utility when hs1 ; s0 i
is the potential equilibrium contract that implements e¤ort is
ds1 ds0
u (s1 ) q + v~) u0 (s1 )
u (s0 ) + (~ + [1 q + v~)] u0 (s0 )
(~ c > 0,
d~
v d~
v
q~+~v u0 (s1 ) q+v
taking into account that hs1 ; s0 i is the potential equilibrium contract only if 1 (~ v ) u0 (s0 )
q +~ 1 (q+v) .
If hs1 ; s0 i is the potential equilibrium contract that implements e¤ort, the envelope theorem
implies that the change in the agent’s perceived utility from a marginal increase in v~ is

u (s1 ) u (s0 ) > c > 0.

There is no change in the agent’s perceived expected utility under hs1 ; s0 i from a marginal
increase in v~. Therefore, if e¤ort is implemented given agent beliefs (~
q ; v~), then e¤ort will be
implemented when his beliefs are (~
q ; v~ ) for any v~ v~.

37
 Consider now changes in agent overcon…dence regarding the base probability of success.
If hs1 ; s0 i is the potential equilibrium contract that implements e¤ort, the power of incentives
is independent from overcon…dence regarding the base probability of success. A marginal increase
in q~ implies a change in the agent’s perceived expected utility of

u (s1 ) u (s0 ) = c.

If hs1 ; s0 i is the potential equilibrium contract that implements e¤ort, the envelope theorem
again implies that the change in the agent’s perceived utility from a marginal increase in q~ is

u (s1 ) u (s0 ) > c.

The change in the agent’s perceived expected utility following a marginal increase in q~ under
the potential equilibrium contract that does not implement e¤ort is

u (s1 ) u (s0 ) c.

Therefore, if e¤ort is implemented given agent beliefs (~

q ; v~), then e¤ort will be implemented
when his beliefs are (~
q ; v~) for any q~ q~.

A.2 One Principal and One Agent

Solving the principal’s pro…t-maximization problem explicitly

Assume that e¤ort is implemented in equilibrium. The principal’s problem is

max (q + v) (x1 s1 ) + [1 (q + v)] (x0 s0 )

s1 ;s0

subject to

v~ (u (s1 ) u (s0 )) c

(~
q + v~) u (s1 ) + [1 (~
q + v~)] u (s0 ) c=u

We can solve this problem by setting up a Lagrangian. Let denote the Lagrange multiplier
associated with the IC constraint, and the multiplier associated with the IR constraint. Since
the IR constraint binds in equilibrium, it follows that > 0.
If the IC constraint binds in equilibrium as well, so that > 0, then the IR and IC constraints
holding with equality de…ne the equilibrium contract. This contract is analogous to the contract
discussed in the previous section when the di¤erence in beliefs held by principal and agent was
small (which we denoted by hs1 ; s0 i). As before, when the beliefs held by principal and agent do
not diverge signi…cantly, the IC constraint will in fact bind, and the contract with incentives just

38
powerful enough to induce e¤ort exertion is the equilibrium contract. This result is analogous to
Proposition 2. The optimal contract is then characterized by

q~
u (s0 ) = u c
v~
1 q~
u (s1 ) = u + c.
v~

If the IC constraint binds, the incentive e¤ect of overcon…dence dominates. The power of
incentives is, as in the case of competing principals, decreasing in the agent’s estimation of the
value of his e¤ort (~
v ). The power of incentives is independent of the agent’s belief about the base
probability of success (~
q ), and of the principal’s beliefs. An agent who is overcon…dent about
the base probability of success (he overestimates q~) will, however, be paid less both in the event
of success and failure. Overcon…dence of this kind makes it cheaper for the principal to satisfy
the agent’s participation constraint, since the agent deems it more likely that he will receive the
“high”payment s1 . The incentive e¤ect of overcon…dence will in fact dominate— and the incentive
compatibility constraint will bind in equilibrium— if principal and agent hold beliefs that are not
signi…cantly divergent.
If the IC constraint is slack in equilibrium instead, so that = 0, the …rst-order conditions of
the principal’s maximization problem yield

q + v~) u0 (s1 ) = (q + v)
(~

[1 q + v~)] u0 (s0 ) = [1
(~ (~
q + v~)]

which substituting for yields

q+v q~ + v~ u0 (s1 )
= .
1 (q + v) 1 (~ q + v~) u0 (s0 )

This condition characterizes the power of incentives of the equilibrium contract when the beliefs
held by principal and agent di¤er signi…cantly. This result is analogous to Proposition 3 in the
case of competing principals. The expected payment in this case is grounded by the IR constraint
instead of the zero-expected-pro…ts condition.
When the agent is signi…cantly overcon…dent overall, the power of incentives of the optimal
contract o¤ered by the principal is increasing in overcon…dence of either kind.
Assume now that e¤ort is not implemented in equilibrium. The wager e¤ect of overcon…dence
implies that the agent will bear some risk in equilibrium. The equilibrium contract’s power of incen-
q q~ u0 (s1 )
tives are characterized by the expression 1 q = 1 q~ u0 (s0 ) . This result is analogous to Proposition
1. The expected payment to the agent is determined by the IR constraint.

39
 Finally, the likelihood that the principal will implement e¤ort is increasing in either kind of
overcon…dence. If the agent is overcon…dent about the value of e¤ort, the cost of agency when im-
plementing e¤ort is reduced, so the pro…ts for the principal when implementing e¤ort increase. Fur-
thermore, given that an overcon…dent agent overestimates the probability of receiving the success-
contingent payment, it is increasingly cheaper for the principal to satisfy the agent’s participation
constraint the higher this payment is; a contract that implements e¤ort is increasingly cheaper
(as overcon…dence increases) to implement for the principal relative to a contract that does not
implement e¤ort. The likelihood that e¤ort is implemented under the optimal contract is therefore
increasing in each kind of overcon…dence. This result is analogous to Proposition 4.

A.3 The Continuous-Action Case

A.3.1 Conditions for the principal’s pro…t-maximization problem to be well behaved

Recall that we can write the principal’s pro…t-maximization problem as:

max (q + ve) (x1 s1 (e)) + [1 (q + ve)] (x0 s0 (e)) .

e2[0;1]

subject to

c0 (e)
u (s1 (e)) = u + c (e) + [1 (~
q + v~e)]
v~
c0 (e)
u (s0 (e)) = u + c (e) (~
q + v~e) .
v~

Let e denote the solution to the …rst-order condition of this problem, the level of e¤ort at
which the principal’s marginal revenue equals her marginal cost of implementing e¤ort:

M Re = M Ce .

Recall that
M Re = v (x1 x0 ) ,

and
ds1 (e) ds0 (e)
M Ce = v (s1 (e) s0 (e)) + (q + ve) + [1 (q + ve)] ,
de de
where

ds1 (e) 1 c00 (e)

= 0 [1 (~ q + v~e)]
de u (s1 (e)) v~
ds0 (e) 1 00
c (e)
= (~
q + v~e) .
de u0 (s0 (e)) v~

40
 This problem will have a unique, interior, local and global maximum if the marginal cost of
implementing e¤ort is strictly increasing in implemented level of e¤ort.
The change in the marginal cost of increasing e¤ort is:

dM Ce ds1 (e) ds0 (e) d2 s1 (e) d2 s0 (e)

=v + (q + ve) + [1 (q + ve)] .
de de de de2 de2
ds1 (e) ds0 (e)
The …rst component of this expression is positive, since de > 0 and de < 0. Assuming for
simplicity that c00 (e) = k, a constant, the second and third components of the expression above
are:

" #
d2 s1 (e) k (~q + v~e)]2
u00 (s1 (e)) [1 k
= 0 1 ,
de2 u (s1 (e)) u0 (s1 (e)) v~2 u0 (s1 (e))
" #
d2 s0 (e) k q + v~e)2
u00 (s0 (e)) (~ k
= 0 1 .
de2 u (s0 (e)) u0 (s0 (e)) v~2 u0 (s0 (e))

If both of these components are positive, it follows that the marginal cost of implementing e¤ort
will be strictly increasing in e¤ort level. This will be the case if:

c00 (e) is large enough

If the cost to the agent of choosing higher levels of e¤ort is convex enough, then the cost to
the principal of implementing higher levels of e¤ort will be convex as well.

the agent is su¢ ciently risk averse

u00 (sx )
A large coe¢ cient of absolute risk aversion u0 (sx ) also makes it increasingly costly to im-
plement higher e¤ort, since the principal must compensate the agent for the higher risk he
must bear as higher levels of e¤ort are implemented.

the agent is wealthy

It is increasingly costly to power-up incentives and implement higher levels of e¤ort when
changes in the payments have little e¤ect on the agent’s utility level. When the agent is
wealthy, his marginal utility u0 (sx ) is relatively low.

A.3.2 The power of incentives and agent overcon…dence regarding the value of e¤ort

Recall that the solution to the agent’s problem yields

c0 (e )
[u (s1 (e )) u (s0 (e ))] = .
v~

41
The change in the power of incentives of the equilibrium contract is thus

d [u (s1 (e )) u (s0 (e ))] c00 (e ) de c0 (e )

= .
d~
v v~ d~
v v~2

Recall, as well, that the solution to the principal’s problem e is such that

M Re = M Ce ,

or
ds1 (e ) ds0 (e )
v (x1 x0 ) = v (s1 s0 ) + (q + ve ) + [1 (q + ve )] .
de de
Assume that c00 (e) = k, a constant. Taking the total derivative of the equation above with
respect to v~ yields

de [1 (~
q + v~e )] (~
q + v~e ) [1 (~ q + v~e )] (~
q + v~e )
0= + 0 v+ + 0 v
d~
v u0 (s1 (e )) u (s0 (e )) u0 (u (s1 (e ))) u (u (s0 (e )))
(q + ve ) [1 (q + ve )]
0
+ 0 v~
u (u (s1 (e ))) u (u (s0 (e )))
(
k u00 (u (s1 (e ))) (q + ve ) [1 (~ q + v~e )]2
+
v~ u0 (u (s1 (e ))) u0 (u (s1 (e )))
)!
u00 (u (s0 (e ))) [1 (q + ve )] (~ q + v~e )2
u0 (u (s0 (e ))) u0 (u (s0 (e )))
1 (q + ve ) [1 (~ q + v~e )] [1 (q + ve )] (~ q + v~e )
0
+ 0
v~ u (u (s1 (e ))) u (u (s0 (e )))
(q + ve ) [1 (q + ve )]
e + 0 .
u0 (u (s1 (e ))) u (u (s0 (e )))

Given that we are interested in the e¤ect of overcon…dence regarding the value of e¤ort on the
power of incentives when the agent is slightly overcon…dent, I evaluate the change in the power of
incentives of the equilibrium contract at the point that principal and agent agree in their beliefs:

d [u (s1 (e )) u (s0 (e ))] k de c0 (e )

=
d~
v v~=v;~
q =q v d~
v v2

[1 (q + ve )] (q + ve ) 1 1 v
= + v
u0 (s1 (e )) u0 (s0 (e )) 1 0 k
1
u00 (u (s1 (e ))) [1 (q + ve )] 00
u (u (s0 (e ))) (q + ve )
+
u0 (u (s1 (e ))) 1 u0 (u (s0 (e ))) 0
1 1 (q + ve ) [1 (q + ve )]
+ e
1 0 v 1 0
c0 (e )
v2

42
where
= (q + ve ) [1 (q + ve )] ; 1 = u0 (u (s1 (e ))) ; 0 = u0 (u (s0 (e ))) ;
1 1
note 1 0
> 0.
The expression above shows that the power of incentives will be decreasing in overcon…dence
about the value of e¤ort when the agent is only slightly overcon…dent overall if the agent’s action
is very responsive to the power of incentives. This will be the case if the agent is very risk averse
u00 (u(sx ))
(as measured by u0 (u(sx )) , which resembles the coe¢ cient of absolute risk aversion), or if the
increase in the marginal cost of e¤ort is su¢ ciently low (as measured by k = c00 (e )). The power
of incentives of the optimal contract will be everywhere increasing in both kinds of overcon…dence
if the agent is su¢ ciently risk neutral, or if the disutility cost of e¤ort rapidly increases.

43
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