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After studying this chapter you will be able to

- Define and identify oligopoly
- Explain two traditional oligopoly models
- Use game theory to explain how price and output are determined in oligopoly
- Use game theory to explain other strategic decisions

PC War Games

- In some markets there are only two firms. Computer chips are an example.
- The chips that drive most PCs are made by Intel and Advanced Micro Devices.
- How does competition between just two chip makers work?
- Do they operate in the social interest, like the firms in perfect competition?
- Or do they restrict output to increase profit, like a monopoly?

What Is Oligopoly?

- The distinguishing features of oligopoly are
- Natural or legal barriers that prevent entry of new firms
- A small number of firms compete

What is Oligopoly?

- Barriers to Entry
- Either natural or legal barriers to entry can create oligopoly.
- Figure 13.9 shows two oligopoly situations.
- In part (a), there is a natural duopoly—a market with two firms.

What is Oligopoly?

- In part (b), there is a natural oligopoly market with three firms.
- A legal oligopoly might arise even where the demand and costs leave room for a larger number of firms.

What is Oligopoly?

- Small Number of Firms
- Because an oligopoly market has a small number of firms, the firms are interdependent and face a temptation to cooperate.
- Interdependence: With a small number of firms, each firm’s profit depends on every firm’s actions.
- Cartel: A cartel and is an illegal group of firms acting together to limit output, raise price, and increase profit.
- Firms in oligopoly face the temptation to form a cartel, but aside from being illegal, cartels often break down.

What is Oligopoly?

- Examples of Oligopoly
- Figure 13.10 shows some examples of oligopoly.
- Four largest firms
- Next four largest firms
- Next 12 largest firms
- An HHI that exceeds 1,000 is usually an oligopoly.
- An HHI below 1,000 is usually monopolistic competition.

Two Traditional Oligopoly Models

- The Kinked Demand Curve Model
- In the kinked demand curve model of oligopoly, each firm believes that if it raises its price, its competitors will not follow, but if it lowers its price all of its competitors will follow.

Two Traditional Oligopoly Models

- Figure 13.11 shows the kinked demand curve model.
- The firm believes that the demand for its product has a kink at the current price and quantity.

Two Traditional Oligopoly Models

- 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 firm’s prices change in line with the price of the firm shown in the figure.

Two Traditional Oligopoly Models

- The kink in the demand curve means that the MR curve is discontinuous at the current quantity—shown by that gap AB in the figure.

Two Traditional Oligopoly Models

- Fluctuations in MC that remain within the discontinuous portion of the MR curve leave the profit-maximizing quantity and price unchanged.
- For example, if costs increased so that the MC curve shifted upward from MC0 to MC1, the profit-maximizing price and quantity would not change.

Two Traditional Oligopoly Models

- The beliefs that generate the kinked demand curve are not always correct and firms can figure out this fact.
- If MC increases enough, all firms raise their prices and the kink vanishes.
- A firm that bases its actions on wrong beliefs doesn’t maximize profit.

Two Traditional Oligopoly Models

- Dominant Firm Oligopoly
- In a dominant firm oligopoly, there is one large firm that has a significant cost advantage over many other, smaller competing firms.
- The large firm operates as a monopoly, setting its price and output to maximize its profit.
- The small firms act as perfect competitors, taking as given the market price set by the dominant firm.

Two Traditional Oligopoly Models

- Figure 13.12 shows10 small firms in part (a). The demand curve, D, is the market demand and the supply curve S10 is the supply of the 10 small firms.

Two Traditional Oligopoly Models

- At a price of $1.50, the 10 small firms produce the quantity demanded. At this price, the large firm would sell nothing.

Two Traditional Oligopoly Models

- But if the price was $1.00, the 10 small firms would supply only half the market, leaving the rest to the large firm.

Two Traditional Oligopoly Models

- The demand curve for the large firm’s output is the curve XD on the right.

Two Traditional Oligopoly Models

- The large firm can set the price and receives a marginal revenue that is less than price along the curve MR.

Two Traditional Oligopoly Models

- The large firm maximizes profit by setting MR = MC. Let’s suppose that the marginal cost curve is MC in the figure.

Two Traditional Oligopoly Models

- The profit-maximizing quantity for the large firm is 10 units. The price charged is $1.00.

Two Traditional Oligopoly Models

- The small firms take this price and supply the rest of the quantity demanded.

Two Traditional Oligopoly Models

- In the long run, such an industry might become a monopoly as the large firm buys up the small firms and cuts costs.

Oligopoly Games

- Game theory is a tool for studying strategic behavior, which is behavior that takes into account the expected behavior of others and the mutual recognition of interdependence.
- The Prisoners’ Dilemma
- The prisoners’ dilemma game illustrates the four features of a game.
- Rules
- Strategies
- Payoffs
- Outcome

Oligopoly Games

- Rules
- 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 (Art and Bob) have been caught committing a petty crime.
- Each is held in a separate cell and cannot communicate with each other.

Oligopoly Games

- Each is told that both are suspected of committing a more serious crime.
- If one of them confesses, he will get a 1-year sentence for cooperating while his accomplice get a 10-year sentence for both crimes.
- If both confess to the more serious crime, each receives 3 years in jail for both crimes.
- If neither confesses, each receives a 2-year sentence for the minor crime only.

Oligopoly Games

- Strategies
- Strategies are all the possible actions of each player.
- Art and Bob each have two possible actions:
- 1. Confess to the larger crime.
- 2. Deny having committed the larger crime.
- With two players and two actions for each player, there are four possible outcomes:
- 1. Both confess.
- 2. Both deny.
- 3. Art confesses and Bob denies.
- 4. Bob confesses and Art denies.

Oligopoly Games

- Payoffs
- Each prisoner can work out what happens to him—can work out his payoff—in each of the four possible outcomes.
- We can tabulate these outcomes in a payoff matrix.
- A payoff matrix is a table that shows the payoffs for every possible action by each player for every possible action by the other player.
- The next slide shows the payoff matrix for this prisoners’ dilemma game.

Oligopoly Games

- Outcome
- If a player makes a rational choice in pursuit of his own best interest, he chooses the action that is best for him, given any action taken by the other player.
- If both players are rational and choose their actions in this way, the outcome is an equilibrium called Nash equilibrium—first proposed by John Nash.
- The following slides show how to find the Nash equilibrium.

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 13.13 on the next slide describes the demand and cost situation in a natural duopoly.

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

- Collusion
- 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 the 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 strategies that firms in a cartel can pursue are to
- Comply
- Cheat
- Because each firm has two strategies, there are four possible combinations of actions for the firms:
- 1. Both comply.
- 2. Both cheat.
- 3. Trick complies and Gear cheats.
- 4. Gear complies and Trick cheats.

Colluding to Maximize Profits

Firms in a cartel act like a monopoly and maximum economic profit.

Oligopoly GamesTo find that profit, we set marginal cost for the cartel equal to marginal revenue for the cartel. Oligopoly Games

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 firm’s 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. The blue rectangle shows each firm’s 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

- One Firm Cheats on a Collusive Agreement
- Suppose the cheat increases its output to 3,000 units. Industry output increases 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 makes an increased economic profit.

Oligopoly Games

- Both Firms Cheat
- Suppose that both increase their output to 3,000 units.

Oligopoly Games

- Industry output is 6,000 units, the price falls, and both firms make zero economic profit—the same as in perfect competition.

Oligopoly Games

- Possible Outcomes
- If both comply, each firm makes $2 million a week.
- If both cheat, each firm makes 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.

Oligopoly Games

- Nash Equilibrium
- The Nash equilibrium is that both firms cheat.
- The quantity and price are those of a competitive market, and the firms make zero economic 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.

Oligopoly Games

- Here is the payoff matrix for the Pampers Versus Huggies game.

Oligopoly Games

- The Disappearing Invisible Hand
- In all the versions of the prisoners’ dilemma that we’ve examined, the players end up worse off than they would if they were able to cooperate.
- The pursuit of self-interest does not promote the social interest in these games.

Oligopoly Games

- A Game of Chicken
- In the prisoners’ dilemma game, the Nash equilibrium is a dominant strategy equilibrium, by which we mean the best strategy for each player is independent of what the other player does.
- Not all games have such an equilibrium.
- One that doesn’t is the game of “chicken.”

Repeated Games and Sequential Games

- A Repeated Duopoly Game
- If a game is played repeatedly, it is possible for duopolists to successfully collude and make 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.

Repeated Games and Sequential Games

- One possible punishment strategy is a tit-for-tat strategy.
- A tit-for-tat strategy is one 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.
- A trigger strategy is one 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

- Table 13.5 shows that a tit-for-tat strategy is sufficient to produce a cooperative equilibrium in a repeated duopoly game.
- 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.

Repeated Games and Sequential Games

- Figure 13.17 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 makes zero economic 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.

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