Chapter 6: Game Theory and
Oligopoly
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Game Theory
• Game theory is concerned with the general analysis of strategic interaction.
• The payoff of the agent is not only determined by the action of
himself/herself, but also determined
by the action of other persons.
• Game theory can be used to study
parlor games, political negotiation,
and economic behavior.
Normal-form Game
• Three factors of a game:
• Players
• Strategies
• Payoffs
Payoff Matrix
Best Response and Prisoner’s Dilemma
• Best response refers to the optimal strategy of a player given
the other player’s strategies.
Equilibrium
In equilibrium, everyone is simultaneously optimizing, so nobody would benefit by
changing his or her own behavior.
Dominant Strategy and Dominant Strategy Equilibrium
• When the best responses are the same in terms of every
possible strategy of the other player, the player has a
dominant strategy.
• If all the players’ strategies are dominant strategies in a
strategy profile, then the strategy profile is a dominant
strategy equilibrium.
• Prisoner’s dilemma is the unique dominant strategy
equilibrium!
Game without Dominant Strategy
• Players: McDonald's and KFC
• Strategies: advertise or not
• Payoffs:
Nash Equilibrium
• If each strategy chosen by the player is a best response with
respect to the partner’s strategy in the strategy profile, the
strategy profile is a Nash equilibrium.
• All the players know the game
and the payoff matrix.
• All the players know that all the
players know the game.
• …
Looking for Nash Equilibrium
Prisoner’s Dilemma is a dominant strategy Nash equilibrium.
Revisiting the Tragedy of Commons
• Players: Firm 1 and Firm 2
• Strategies: pollute or not
• Payoffs:
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Zero-Sum Game
• Players: spot kicker and goalkeeper
• Strategies: left or right
• Payoffs:
Zero-Sum Game
• Pure strategy: each player is making one choice and sticking to
it.
• Mixed strategy: players randomize their strategies - assign a
probability to each choice and play their choices according to
those probabilities.
• If an NE consists of pure strategies only, we call it a pure-
strategy NE; otherwise it is called a mixed-strategy NE.
Battle of Sexes
• Players: boy and girl
• Strategies: action movie or art movie
• Payoffs:
Meeting in an Airport
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A Beautiful Mind
https://www.youtube.com/watch?v=2d_dtTZQyUM
Extensive-Form Game
• The extensive form game is a game tree.
Decision nodes
Terminal nodes
Backward Induction
First-mover advantage
Commitment
A Trust Game Between You and Bernie
Evidence from List (2006)
BETWEEN MONOPOLY AND PERFECT COMPETITION
• Types of Imperfectly Competitive Markets
• Oligopoly
• Only a few sellers, each offering a similar or identical product to the others.
• Monopolistic Competition
• Many firms selling products that are similar but not identical.
MARKETS WITH ONLY A FEW SELLERS
• Because of the few sellers, the key feature of oligopoly is the
tension between cooperation and self-interest.
• Characteristics of an Oligopoly Market
• Few sellers offering similar or identical products
• Interdependent firms 4 fiums involved hwe the abilitytoinfluence
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• Best off cooperating and acting like a monopolist by producing a
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small quantity of output and charging a price above marginal cost
• A duopoly is an oligopoly with only two members. It is the
simplest type of oligopoly.
Table 1 The Demand Schedule for Water
Copyright © 2004 South-Western
• Price and Quantity Supplied
• The price of water in a perfectly competitive market would be driven
to where the marginal cost is zero:
• P = MC = $0
• Q = 120 gallons
• The price and quantity in a monopoly market would be where total
profit is maximized:
• P = $60
• Q = 60 gallons
• Price and Quantity Supplied
• The socially efficient quantity of water is 120 gallons, but a
monopolist would produce only 60 gallons of water.
• So what outcome then could be expected from duopolists?
• The duopolists may agree on a monopoly outcome.
• Collusion
• An agreement among firms in a market about quantities to produce or prices
to charge.
• Cartel
• A group of firms acting in unison.
• Although oligopolists would like to form cartels and earn
monopoly profits, often that is not possible. Antitrust laws
prohibit explicit agreements among oligopolists as a matter of
public policy.
Different Nash Equilibria in Oligopoly
• A Nash equilibrium is a situation in which economic actors
interacting with one another each choose their best strategy
given the strategies that all the others have chosen.
• Sequential Move Game
• Quantity leadership: Stackelberg equilibrium
• Price leadership
• Simultaneous Move Game
• Price: Bertrand equilibrium
• Quantity: Cournot equilibrium
The Equilibrium for an Oligopoly
• When firms in an oligopoly individually choose production to
maximize profit, they produce quantity of output greater than
the level produced by monopoly and less than the level
produced by competition.
• The oligopoly price is less than the monopoly price but greater
than the competitive price (which equals marginal cost).
How the Size of an Oligopoly Affects the Market Outcome
• How increasing the number of sellers affects the price and
quantity:
• The output effect: Because price is above marginal cost, selling more
at the going price raises profits.
• The price effect: Raising production will increase the amount sold,
which will lower the price and the profit per unit on all units sold.
• As the number of sellers in an oligopoly grows larger, an
oligopolistic market looks more and more like a competitive
market. seller ↑ oligopolistic marlet ompetitive marlet
• The price approaches marginal cost, and the quantity
produced approaches the socially efficient level.
PUBLIC POLICY TOWARD OLIGOPOLIES
• Cooperation among oligopolists is undesirable from the standpoint of
society as a whole because it leads to production that is too low and
prices that are too high.
• Antitrust laws make it illegal to restrain trade or attempt to monopolize
a market.
• Sherman Antitrust Act of 1890
• Clayton Act of 1914
• Antitrust policies sometimes may not allow business practices that have
potentially positive effects:
• Resale price maintenance
• Predatory pricing
• Tying
• Resale Price Maintenance (or fair trade)
• occurs when suppliers (like wholesalers) require retailers to charge a
specific amount
• Predatory Pricing
• occurs when a large firm begins to cut the price of its product(s) with
the intent of driving its competitor(s) out of the market
• Tying
• when a firm offers two (or more) of its products together at a single
price, rather than separately
