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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

Nash Equilibrium

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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)

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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 TableMultiple 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

Game Theory: Kinked Demand Curve and Nash Equilibrium

Firm B(Competitor)

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%

Firm A(You)

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%14

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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 (non-cooperative)– 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-to-Sales Ratio for Selected Products and

Industries

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Game Theory Modelsof 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.