Econ 201
Oligopolies & Game Theory
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Figure 12.4 Duopoly Equilibrium in
a Centralized Cartel
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Duopoly
• What are the strategic options and the payoffs?
– Form a cartel
• Forego additional profits from increasing output beyond
assigned quota
– Cheat on the Cartel
• Increase production unilaterally (output effect)
– If only you increase output, price doesn’t fall too much (price effect)
– Compete on price
• Final equilibrium moves towards competitive market price
– No monopoly rents (or + economic profits)
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Game Theory
• Game theory is a methodology that can
be used to analyze both cooperative and
non-cooperative oligopolies.
– Recognizes the interdependence of the firms’
actions
• Using a payoff matrix to describe options
(strategies) and payoffs
– Firms are profit maximizers!
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Figure 12.7 Xbox and PlayStation
2 Payoff Matrix for Advertising
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Nash Equilibrium
•
Nash equilibrium
a solution to a non-cooperative game involving two or more players
• each player is assumed to know the equilibrium strategies of the other
players
• no player has anything to gain by changing only his own strategy
unilaterally
Hence, a Nash equilibrium will be stable (once you get there!)
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Determining the Dominate
Strategy (Single Nash)
• A dominant strategy occurs when one
strategy is best for a player regardless of
the rival’s actions. (rival’s actions don’t
matter)
– Dominate strategy equilibrium—neither
player has reason to change their actions
because they are pursuing the strategy that is
optimal under all circumstances.
• Here the dominant strategy is for each firm
to advertise (it is also a Nash Equilibrium) 7
Multiple Equilibria
• Sometimes there are come cases where there
are multiple Nash equilibria.
– In this case, the outcome is uncertain.
– Firms will have an incentive to collude.
• An example:
– Sony/Microsoft can add one of two new features
• One feature appeals only to YOUTH market
• Other feature appeals only to TEEN market
• Incentive to reach agreement on both firms offering the same
new (one only) feature
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Payoff Table
Multiple Nash Equilibria
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Prisoner's Dilemma
• A prisoner’s dilemma occurs when the
dominate strategy leads all players to an
undesired outcome.
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Figure 12.9 Prisoners’
Dilemma
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Best Outcome
• Neither confesses
– But without collusion/agreement – how do you
guarantee this outcome?
• Enforcement issues (price, output, quotas)
– Law & Order
• Why we keep suspects separated!
– Prevent collusive agreements
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An Economic Application of Game
Theory: the Kinked-Demand Curve
• Above the kink, demand is relatively elastic because all other firm’s
prices remain unchanged. Below the kink, demand is relatively
inelastic because all other firms will introduce a similar price cut,
eventually leading to a price war. Therefore, the best option for the
oligopolist is to produce at point E which is the equilibrium point
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Game Theory: Kinked Demand
Curve and Nash Equilibrium
Firm B
(Competitor)
Firm A
(You)
Raise Price
Don’t Change
Lower Price
(-5%)
(-1%->+5%)
(-2%->+1%)
Raise Price
(A) -5%
(A) -5%
(A)-5%
(-5%)
(B) -5%
(B) +5%
(B)+1%
Don’t Change
(A) +5%
(A) 0
(A)-1%
(-1%->+5%)
(B) -5%
(B) 0
(B)+1%
Lower Price
(A) +1%
(A)+1%
(A) -2%
(-2%->+1%)
(B) -5%
(B) -1%
(B) -2%
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Nash Equilibrium
• If firm facing kinked demand curve tries to
raise price:
– Other firms do not
– As demand is highly elastic and other firms
are “close” substitutes
– Loses market share and revenues
• If firm lowers price
– Competitors match price decreases
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Nash Equilibrium
• If firm facing kinked demand curve tries to
raise price:
– Other firms do not
– As demand is highly elastic and other firms
are “close” substitutes
– Loses market share and revenues
• If firm lowers price
– Competitors match price decreases
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Features of a
Nash Equilibrium
• In a non-cooperative oligopoly, each firm
has little incentive to change price.
• This represents a Nash Equilibrium,
where each firm’s pricing strategy remains
constant given the pricing strategy of the
other firms.
– Firms have no incentive to change
their strategy.
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Non-Cooperative Cartels
Either
• Some degree of price competition
– Firms engage in highly competitive pricing
• Similar outcome as perfect competition
– Firms have some market power
• Resembles monopolistic competition
– Bilateral monopoly with price competition
• or Stable prices prevail
– Non-collusive
– Firms choose not to compete because of kinked
demand curve
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Non-cooperative Oligopolies
• Competitive/psuedo-competitive behavior (noncooperative)
– Perfect Competition (almost): firms undercut each
other’s prices
• competition between sellers is fierce, with relatively low
prices and high production
– Outcome may be similar to PC or Monopolistic Competition
– Nash equilibrium
• Firms avoid “ruinous” price competition by keeping prices
stable and avoiding price competition (undercutting each
others prices)
• May lead to product proliferation and/or extensive advertising
(non-price competition)
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Figure 12.3 U.S. 2003 Advertising-toSales Ratio for Selected Products and
Industries
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Game Theory Models
of Oligoploy
• Stackelberg's duopoly. In this model the firms move
sequentially (see Stackelberg competition).
• Cournot's duopoly. In this model the firms
simultaneously choose quantities (see Cournot
competition).
• Bertrand's oligopoly. In this model the firms
simultaneously choose prices (see Bertrand
competition).
• Monopolistic competition. A market structure in which
several or many sellers each produce similar, but slightly
differentiated products. Each producer can set its price
and quantity without affecting the marketplace as a
whole.
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