1. ECON 201 OLIGOPOLIES & GAME THEORY 1

2. FIGURE 12.4 DUOPOLY EQUILIBRIUM IN A CENTRALIZED CARTEL 2

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) 3

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! 4

5. FIGURE 12.7 XBOX AND PLAYSTATION DOMINANT STRATEGY 5

6. NASH EQUILIBRIUM 6 Nash equilibrium a solution to a non-cooperative game involving two or more playerssolution non-cooperative game each player is assumed to know the equilibrium strategies of the other playersequilibrium strategies 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) 7

8. FIGURE 12.7 XBOX AND PLAYSTATION DOMINANT STRATEGY 8

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 9

10. PAYOFF TABLE MULTIPLE NASH EQUILIBRIA 10 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. 11

12. FIGURE 12.9 PRISONERS’ DILEMMA 12 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 13

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 pointprice war 14 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 15

16. GAME THEORY: KINKED DEMAND CURVE AND NASH EQUILIBRIUM Firm B (Competitor) Raise PriceDon’t ChangeLower Price (-5%)(-1%->+5%)(-2%->+1%) Raise Price(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) -2% (-2%->+1%)(B) -5%(B) -1%(B) -2% 16

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. 17

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 18

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) 19

20. U.S. 2003 ADVERTISING-TO-SALES RATIO FOR SELECTED PRODUCTS AND INDUSTRIES 20

21. GAME THEORY MODELS OF OLIGOPLOY StackelbergStackelberg's duopoly. In this model the firms move sequentially (see Stackelberg competition).duopolyStackelberg competition CournotCournot's duopoly. In this model the firms simultaneously choose quantities (see Cournot competition).duopolyCournot competition BertrandBertrand's oligopoly. In this model the firms simultaneously choose prices (see Bertrand competition).Bertrand competition Monopolistic competitionMonopolistic 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. 21