Oligopoly Games and Strategy Chapter 13: Oligopoly Games and Strategy

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 Understanding real world markets Students have no difficulty seeing monopolistic competition in the world all around them. Emphasize that the work they’ve just done understanding the models of perfect competition and monopoly are not wasted because the real-world situation of monopolistic competition, as its name implies, is a mixture of both extremes. Some of what they learned in each of the two previous chapters survives and operates in the middle ground of monopolistic competition.

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 Game Theory Game theory is an entirely different approach to modeling a firm’s output and price decisions. It allows for the expected actions of all other firms in the market to be explicitly considered in the firm’s decision-making process. Game theory is a big step for the student and need a significant amount of time to develop. This chapter is designed to be flexible and provide you with many options on just how far to go. 1.We noted above that if you wish you can avoid game theory completely and stop at page 292. 2.You might want to introduce only the prisoner’s dilemma game. Pages 293–294 enable you to do that. 3.You might want to spend serious time applying the prisoner’s dilemma to a cartel game. Pages 295–299 enable you to do that. 4.You might want to extend the range of examples and apply the prisoner’s dilemma to a real-world research and development game. Pages 299–300 enable you to do that. 5.Finally, you might want to introduce repeated and sequential games and some of their applications and implications. Pages 301–303 enable you to do that. 6.Each of the steps laid out above is optional, but cumulative. You can stop at any point, but shouldn’t try to skip one step with the exception that you can teach the R&D game based on the general introduction to the prisoner’s dilemma without teaching the longer and more complex cartel game.

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. The prisoners’ dilemma Take things a step at a time and begin by playing the prisoner’s dilemma game. A good Web version of the game can be found on a site operated by a group called Serendip at Bryn Mawr College in Pennsylvania. The URL is http://serendip.brynmawr.edu/playground/pd.html. If you can use the Web in your classroom, open two browsers and go to this site twice. Get two teams trying to beat Serendip.

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.

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

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

Prisoners’ Dilemma Payoff Matrix

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.

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. 52

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. A Cartel Game. The prisoner’s dilemma to a cartel game on pages 295–299 has been carefully designed to get the maximum payoff from the knowledge your students have of the perfect competition and monopoly results of the two preceding chapters and to introduce them to game theory in a setting that is as close to the previously studied settings as possible. 1. The natural duopoly setting ensures that there is a zero profit equilibrium that corresponds to perfect competition and monopoly profit equilibrium. 2. Instead of just asserting a payoff matrix, the numbers in the matrix come directly from monopoly profit-maximising and competitive outcomes. You need to do a bit of work (and so do your students) to generate the payoff numbers, but the whole story hangs together so much better when the student can see where the numbers come from and can see the connection between the oligopoly set up and those of competition and monopoly. 3. Start with Figure 13.8 (page 295) and after you’ve explained the cost and demand conditions shown in the figure, ask the students what they think the price and quantity will be in this industry. There will be differences of opinion. This diversity of opinion motivates the need for a model of the choices the firms make. 4. The game is set up so that the competitive equilibrium is the Nash equilibrium. You might want to emphasize, that this outcome is efficient even though it is not the best joint outcome for the firms.

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.

Costs and Demand Individual Firm Industry MC ATC D 10 10 6 6 1 2 3 4 5 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 1 2 3 4 5 1 2 3 4 5 6 7 Quantity (thous. of switchgears/week) Quantity (thous. of switchgears/week) 59

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

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. 60

Colluding to Make Monopoly Profits Figure 13.2 Individual Firm Industry MC ATC 10 10 9 9 Collusion achieves monopoly outcome Economic Profit MC1 8 Price and cost (thous. of $/ unit) Price and cost (thous. of $/ unit) 6 6 D MR 1 2 3 4 5 1 2 3 4 5 6 7 Quantity (thous. Of switchgears/week) Quantity (thous. of switchgears/week) 63

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

One Firm Cheats Complier Cheater Industry ATC ATC D Figure 13.3 10 10 10 8 8 Price & cost Price & cost Economic loss 7.5 7.5 7.5 Price & cost Economic profit 6 Complier’s output Cheat’s output D 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 6 7 Quantity (thousands of switchgears/week) Quantity (thousands of switchgears/week) Quantity (thousands of switchgears/week) 69

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.

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.

Duopoly Payoff Matrix 76

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 The R&D Game. This example really happened. You can flesh out the time line of developments in this industry at http://www.gpoabs.com.mx/cricher/timeline.htm.

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. The repeated prisoners’ dilemma and punishment The interesting fact about this extension of the prisoners’ dilemma is that punishment strategies can support a cooperative equilibrium, lead to maximum (monopoly) profit, and an inefficient allocation of resources.

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.

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 Entry game The textbook uses the simplest possible example to illustrate the sequential entry game in a contestable market. It doesn’t explicitly explain the backward induction method of solving such a game, but it implicitly uses that method. You might want to be explicit.

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

END CHAPTER 13