Oligopoly Games An Oligopoly 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. Figure 13.8 on the next slide describes the demand and cost situation in a natural duopoly. A Cartel Game. The prisoner’s dilemma to a cartel game on pages 291–295 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-maximizing 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 291) 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 Part (a) shows each firm’s cost curves. Part (b) shows the market demand curve.

Oligopoly Games This industry is a natural duopoly. Two firms can meet the market demand at the least cost.

Oligopoly Games How does this market work? What is the price and quantity produced in equilibrium?

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 the United States and are undertaken in secret. Firms in a collusive agreement operate a cartel.

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 The first possible outcome—both comply—earns the maximum economic profit, which is the same as a monopoly would earn.

Oligopoly Games To find that profit, we set marginal cost for the cartel equal to marginal revenue for the cartel. Figure 13.9 shows this outcome.

Oligopoly Games The cartel’s marginal cost curve is the horizontal sum of the MC curves of the two firms and the marginal revenue curve is like that of a monopoly.

Oligopoly Games The firms maximize economic profit by producing the quantity at which MCI = MR.

Oligopoly Games Each firm agrees to produce 2,000 units and each firm shares the maximum economic profit.

Oligopoly Games When each firm produces 2,000 units, the price is greater than the firm’s marginal cost, so if one firm increased output, its profit would increase.

Oligopoly Games Figure 13.10 shows what happens when one firm cheats and increases its output to 3,000 units. Industry output rises to 5,000 and the price falls.

Oligopoly Games For the complier, ATC now exceeds price. For the cheat, price exceeds ATC.

Oligopoly Games The complier incurs an economic loss. The cheat earns an increased economic profit.

Oligopoly Games Either firm could cheat, so this figure shows two of the possible outcomes. Next, let’s see the effects of both firms cheating.

Oligopoly Games Figure 13.11 shows the outcome if both firms cheat and increase their output to 3,000 units.

Oligopoly Games Industry output is 6,000 units, 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.

Payoff Matrix

Trick’s view of the world Tell the story in the same way as for the prisoner’s dilemma.

Trick’s view of the world

Gear’s view of the world

Gear’s view of the world

Equilibrium

Oligopoly Games Other Oligopoly Games An R & D Game 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 Oligopoly Games Advertising and R & D games are also prisoners’ dilemmas. An R & D Game Procter & Gamble and Kimberley Clark play an R & D game in the market for disposable diapers. 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 (rather than simultaneously as in the prisoner’s dilemma), 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 and lead to maximum (monopoly) profit and an inefficient allocation of resources.

Repeated Games and Sequential Games One possible punishment strategy is a tit-for-tat strategy, in which one player cooperates this period if the other player cooperated in the previous period but cheats in the current period if the other player cheated in the previous period. 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 Price wars might result from a tit-for-tat strategy where there is an additional complication—uncertainty about changes in demand. A fall in demand might lower the price and bring forth a round of tit-for-tat punishment.

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. 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.

Repeated Games and Sequential Games Figure 13.12 shows the game tree for a sequential entry game in a contestable market.

Repeated Games and Sequential Games In the first stage, Agile decides whether to set the monopoly price or the competitive price.

Repeated Games and Sequential Games In the second stage, Wanabe decides whether to enter or stay out.

Repeated Games and Sequential Games In the equilibrium of this entry game, Agile sets a competitive price and earns a normal profit to keep Wanabe out. A less costly strategy is limit pricing, which sets the price at the highest level that is consistent with keeping the potential entrant out.