Chapter 13:

1. Chapter 13: Oligopoly Games and Strategy

2. Objectives After studying this chapter, you will be able to: • Use game theory as a tool for studying strategic behaviour • Use game theory to explain how price and output are determined in oligopoly • Use game theory to explain other strategic decisions • Explain the implications of repeated games and sequential games

3. Game Theory • Game theory is a tool for studying strategic behaviour, which is behaviour that takes into account the expected behaviour of others and the mutual recognition of interdependence. • What Is a Game? • All games share four features: • Rules • Strategies • Payoffs • Outcome

4. Game Theory • The Prisoners’ Dilemma • The prisoners’ dilemma game illustrates the four features of a game. • The rules describe the setting of the game, the actions the players may take, and the consequences of those actions. • In the prisoners’ dilemma game, two prisoners (Alf and Bob) have been caught stealing a car.

5. The Prisoner’s Dilemma • Rules of the game • Prisoners are put in separate rooms and cannot communicate with the other. • They are told that they are a suspect in the earlier crime. • If both confess, they will get 3 years. • If one confesses and the other does not, the confessor will get 1 year while the other gets 10.

6. The Prisoners’ Dilemma • Strategies (possible actions) • They can each: • Confess to the bank robbery • Deny having committed the bank robbery

7. The Prisoners’ Dilemma • Payoffs • 4 outcomes are possible: • Both confess. • Both deny. • Alf confesses and Bob denies. • Bob confesses and Alf denies. • The Payoff Matrix is illustrated on the following slide

8. Prisoners’ Dilemma Payoff Matrix

9. The Prisoners’ Dilemma • A dominant strategy emerges. • Alf and Bob should both deny, because: • If they both deny, they will only get 2 years—but they don’t know if the other will deny. • If Alf denies, but Bob does not, Alf will only get 1 year. • If Alf denies, but Bob confesses, Art will get 10 years. • They both eventually decide it is best to confess — Nash equilibrium.

10. The Prisoners’ Dilemma • In a Nash equilibrium, each player takes their best possible action given the action of their opponent. • In equilibrium, both will confess. Each thinks: • If I confess, but my accomplice does not, my sentence will only be 1 year. This is better for me than 2 years. • If my accomplice confesses, but I do not, my sentence will be 10 years. If I confess too, I will only have a 3-year sentence.

11. Oligopoly Games • A Price-Fixing Game • A game like the prisoners’ dilemma is played in duopoly. • A duopoly is a market in which there are only two producers that compete. • Duopoly captures the essence of oligopoly.

12. Oligopoly Games • Suppose that the two firms enter into a collusive agreement: • A collusive agreement is an agreement between two (or more) firms to restrict output, raise price, and increase profits. • Such agreements are illegal in Australia and are undertaken in secret. • Firms in a collusive agreement operate a cartel.

13. Costs and Demand Figure 13.1 Individual Firm Industry MC ATC 10 10 Price and cost (thous. of $/ unit) Price and cost (thous. of $/ unit) 6 6 D Minimum ATC 0 1 2 3 4 5 0 1 2 3 4 5 6 7 Quantity (thous. of switchgears/week) Quantity (thous. of switchgears/week)

14. Oligopoly Games • The possible strategies are: • Comply • Cheat • Because each firm has two strategies, there are four possible outcomes: • Both comply • Both cheat • Trick complies and Gear cheats • Gear complies and Trick cheats

15. Oligopoly Games • Colluding to Maximise Profits • These firms can benefit from colluding. • They maximise industry profits if they agree to set the industry output level equal to the monopoly output level. • They must agree on how much of the monopoly output each will produce. • For each firm, price is greater than MC. For the industry, MR = MC.

16. Collusion achieves monopoly outcome Economic Profit Colluding to Make Monopoly Profits Figure 13.2 Individual Firm Industry MC ATC 10 10 9 9 MC1 8 Price and cost (thous. of $/ unit) Price and cost (thous. of $/ unit) 6 6 D MR 0 1 2 3 4 5 0 1 2 3 4 5 6 7 Quantity (thous. Of switchgears/week) Quantity (thous. of switchgears/week)

17. Oligopoly Games • A Price-Fixing Game – one firm cheats on a collusive agreement • For the complier, ATC now exceeds price and for the cheat, price exceeds ATC. • The complier incurs an economic loss and the cheat earns an increased economic profit. • The industry output is larger than the monopoly output and the industry price is lower than the monopoly price

18. 7.5 Economic loss Complier’s output Cheat’s output Economic profit 0 1 2 3 4 5 0 1 2 3 4 5 5 0 1 2 3 4 6 7 One Firm Cheats Figure 13.3 Cheater Industry Complier ATC ATC 10 10 10 8 8 Price & cost Price & cost 7.5 7.5 Price & cost 6 D Quantity (thousands of switchgears/week) Quantity (thousands of switchgears/week) Quantity (thousands of switchgears/week)

19. Oligopoly Games • A Price-Fixing Game – both firms cheat • Industry output is increased, the price falls, and both firms earn zero economic profit—the same as in perfect competition.

20. Oligopoly Games • You’ve now seen the four possible outcomes: • If both comply, they make $2 million a week each. • If both cheat, they earn zero economic profit. • If Trick complies and Gear cheats, Trick incurs an economic loss of $1 million and Gear makes an economic profit of $4.5 million. • If Gear complies and Trick cheats, Gear incurs an economic loss of $1 million and Trick makes an economic profit of $4.5 million. • The next slide shows the payoff matrix for the duopoly game.

21. Duopoly Payoff Matrix

22. Oligopoly Games • The Nash equilibrium is where both firms cheat. • The quantity and price are those of a competitive market, and the firms earn normal profit. • Other games of strategy: • The Razor Blade R & D Game. • A Game of Chicken

23. Repeated Games and Sequential Games • A Repeated Duopoly Game • If a game is played repeatedly, it is possible for duopolists to successfully collude and earn a monopoly profit. • If the players take turns and move sequentially many outcomes are possible. • In a repeated prisoners’ dilemma duopoly game, additional punishment strategies enable the firms to comply and achieve a cooperative equilibrium, in which the firms make and share the monopoly profit.

24. Repeated Games and Sequential Games • A cooperative equilibrium might occur if cheating is punished • One possible punishment strategy is a tit-for-tat strategy. • A more severe punishment strategy is a trigger strategy in which a player cooperates if the other player cooperates but plays the Nash equilibrium strategy forever thereafter if the other player cheats.

25. Repeated Games and Sequential Games • A Sequential Entry Game in a Contestable Market • In a contestable market—a market in which firms can enter and leave so easily that firms in the market face competition from potential entrants—firms play a sequential entry game. • A Contestable Air Route • Example: Agile Air and Wanabe sequential entry game in a contestable market

26. Agile Versus Wanabe: A Sequential Entry Game in a Contestable Market

27. END CHAPTER 13