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Imperfect Competition: A Game-Theoretic Approach

Chapter 13. Imperfect Competition: A Game-Theoretic Approach. 13- 1. Chapter Outline. An Introduction to the Theory of Games Some Specific Oligopoly Models Competition When There are Increasing Returns to Scale Monopolistic Competition A Spatial Interpretation of Monopolistic Competition

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Imperfect Competition: A Game-Theoretic Approach

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  1. Chapter 13 Imperfect Competition:A Game-Theoretic Approach 13-1

  2. Chapter Outline • An Introduction to the Theory of Games • Some Specific Oligopoly Models • Competition When There are Increasing Returns to Scale • Monopolistic Competition • A Spatial Interpretation of Monopolistic Competition • Historical Note: Hotelling’s Hot Dog Vendors • Consumer Preferences and Advertising 13-2

  3. Prisoner's Dilemma • Two prisoners are held in separate cells for a serious crime that they did in fact commit. The prosecutor has only enough hard evidence to convict them of a minor offense, for which the penalty is a year in jail. • Each prisoner is told that if one confesses while the other remains silent, the confessor will go scot-free while the other spends 20 years in prison. • If both confess, they will get an intermediate sentence 5 years. 13-3

  4. Dominant Strategy • Dominant strategy:the strategy in a game that produces better results irrespective of the strategy chosen by one’s opponent. The Nash Equilibrium Concept • Nash equilibrium:the combination of strategies in a game such that neither player has any incentive to change strategies given the strategy of his opponent. • A Nash equilibrium does not require both players to have a dominant strategy! • The Maximin Strategy Maximin strategy:choosing the option that makes the lowest payoff one can receive as large as possible. 13-4

  5. Tit-for-Tat • Tit-for-tat strategy- • The first time you interact with someone, you cooperate. In each subsequent interaction you simply do what that person did in the previous interaction. • Thus, if your partner defected on your first interaction, you would then defect on your next interaction with her. • If she then cooperates, your move next time will be to cooperate as well. • Requirement: there not be a known, fixed number of future interactions. 13-5

  6. Sequential Games • Sequential game: one player moves first, and the other is then able to choose his strategy with full knowledge of the first player’s choice. • Example - United States and the former Soviet Union (USSR) during much of the cold war. • Strategic entry deterrence – they change potential rivals’ expectations about how the firm will respond when its market position is threatened. 13-6

  7. Figure 13.1: Nuclear Deterrenceas a Sequential Game 13-7

  8. Figure 13.2: The Decision to Buildthe Tallest Building 13-8

  9. Figure 13.3: Strategic Entry Deterrence 13-9

  10. Figure 13.4: The Profit-Maximizing Cournot Duopolist • The Cournot Model--oligopoly model in which each firm assumes that rivals will continue producing their current output levels. • Main assumption - each duopolist treats the other’s quantity as a fixed number, one that will not respond to its own production decisions. • Reaction function- a curve that tells the profit-maximizing level of output for one oligopolist for each amount supplied by another. 13-10

  11. Figure 13.5: Reaction Functionsfor the Cournot Duopolists 13-11

  12. Figure 13.6: Deriving the Reaction Functions for Specific Duopolists The Bertrand Model Bertrand model - oligopoly model in which each firm assumes that rivals will continue charging their current prices. 13-12

  13. Stackelberg Model Figure 13.7: The Stackelberg Leader’s Demand and Marginal Revenue Curves Figure 13.8: The Stackelberg Equilibrium 13-13

  14. Comparison Of Outcomes--Table & Graph Figure 13.9: Comparing Equilibrium Price and Quantity 13-14

  15. Competition When There Are IncreasingReturns To Scale • In markets for privately sold goods, buyers are often too numerous to organize themselves to act collectively • Where it is impractical for buyers to organize direct collective action, it may nonetheless be possible for private agents to accomplish much the same objective on their behalf. Figure 13.10: Sharing a Market with Increasing Returns to Scale 13-15

  16. The Chamberlin Model • Assumption: a clearly defined “industry group,” which consists of a large number of producers of products that are close, but imperfect, substitutes for one another. • Two implications: • Because the products are viewed as close substitutes, each firm will confront a downward-sloping demand schedule. • Each firm will act as if its own price and quantity decisions have no effect on the behavior of other firms in the industry. 13-16

  17. Figure 13.11: The Monopolistic Competitor’s Two Demand Curves Figure 13.12: Short-Run Equilibrium for the Chamberlinian Firm 13-17

  18. Figure 13.13: Long-Run Equilibriumin the Chamberlin Model 13-18

  19. Perfect Competition Versus ChamberlinianMonopolistic Competition • Competition meets the test of allocative efficiency, while monopolistic competition does not. • Monopolistic competition is less efficient than perfect competition because in the former case firms do not produce at the minimum points of their long-run average cost (LAC) curves. • In terms of long-run profitability the equilibrium positions of both the perfect competitor and the Chamberlinian monopolistic competitor are precisely the same. 13-19

  20. Figure 13.14: An Industry in Which Location is the Important Differentiating Feature The Optimal Number of Locations The number of outlets that emerges from the independent actions of profit-seeking firms will in general be related to the optimal number of outlets in the following simple way  • Any environmental change that leads to a change in the optimal number of outlets (here, any change in population density, transportation cost, or fixed cost) will lead to a change in the same direction in the equilibrium number of outlets. 13-20

  21. Figure 13.16: The Optimal Number of Outlets Figure 13.15: Distances with N Outlets 13-21

  22. Figure 13.17: A Spatial Interpretationof Airline Scheduling • Why not have a flight leaving every 5 minutes, so that no one would be forced to travel at an inconvenient time? • The larger an aircraft is, the lower its average cost per seat is. • If people want frequent flights, airlines are forced to use smaller planes and charge higher fares. 13-22

  23. Figure 13.18: Distributing the Costof Variety 13-23

  24. Figure 13.19: The Hot Dog Vendor Location Problem 13-24

  25. Consumer Preferences And Advertising • Because products are differentiated, producers can often shift their demand curves outward significantly by advertising. • The revised sequence -- the corporation decides which products are cheapest and most convenient to produce, and then uses advertising and other promotional devices to create demand for them. 13-25

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