Econ 201

1. Econ 201 Oligopolies & Game Theory

2. Figure 12.4 Duopoly Equilibrium in a Centralized Cartel

3. 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)

4. 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!

5. Figure 12.7 Xbox and PlayStation Dominant Strategy

6. 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!)

7. 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) • Dominant 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) • BUT there is no incentive for the firms to collude – hence no Anti-trust violation! (at least on the cooperation side; maybe still on anti-competitive pricing)

8. Figure 12.7 Xbox and PlayStation Dominant Strategy

9. 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

10. Payoff TableMultiple Nash Equilibria Requires collusion – agree no to compete in each other’s market

11. Prisoner's Dilemma • A prisoner’s dilemma occurs when the dominant strategy leads all players to an undesired outcome.

12. Figure 12.9 Prisoners’ Dilemma Optimal - each would prefer to serve minimal time. Each has to “not confess” But: if one does remains silent and the other does confess -> not optimal. Hence each will choose to confess -> sub-optimal

13. Best Outcome • Neither confesses • But without collusion/agreement – how do you guarantee this outcome? • Enforcement issues (price, output, quotas) • In our duopoly game: • Each firm pursues “cheating” (here confessing) as can’t rely on other firm not to cheat • Supoptimal (from firm’s perspective) -> competitive equilibria • Law & Order • Why we keep suspects separated! • Prevent collusive agreements • In Economics – wiretaps, e-mail and Sherman Anti-trust Act

14. An Economic Application of Game Theory: the Kinked-Demand Curve:Prisoner’s dilemma (sub-optimal) • 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 Prisoner’s Dilemma

15. 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

16. Game Theory: Kinked Demand Curve and Nash Equilibrium

17. 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.

18. 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

19. 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)

20. U.S. 2003 Advertising-to-Sales Ratio for Selected Products and Industries

21. 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.