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GAME THEORY MODELS OF PRICING The first six problems for this chapter are intended to illustrate the concept of Nash equilibrium in a variety of contexts. Many of them have only modest economic content, but are traditional game theory problems. The remaining problems (15.7–15.12) in the chapter show how game theory tools can be applied to models of pricing. Many of these represent extensions or generalizations of the results illustrated in Chapter 14. Comments on Problems 15.1 The classic “Stag Hunt” game attributed to Rousseau. The most interesting aspect of the game is the decline in the value of cooperation as the number of players expands. 15.2 A simple game with continuous strategies in which there are multiple Nash equilibria. 15.3 A continuation of Example 15.2 that shows how mixed strategy equilibria depend on the payoffs to “The Battle of the Sexes” game. 15.4 This is a problem based on Becker's famous “Rotten Kid Theorem.” The problem provides a good illustration of backward induction. 15.5 The “Chicken” game. This game illustrates the importance of credible threats and pre- commitments. 15.6 An illustration of an auction game. A more detailed example from auction theory is provided in problem 15.12. 15.7 An illustration of how competitive results do not arise in Bertrand games if marginal costs are not equal. 15.8 This is an entry game with important first-mover advantages. 15.9 This is a game theory example from the theory of cartels. Because the stable price is so low, cartels may seek enforcement mechanisms to maintain higher (non-stable) prices. 15.10 This is an extension of Example 15.5. In this case, the firms must consider the expected value of profits when choosing trigger price strategies. 15.11 This problem provides a numerical example of Bayesian Nash equilibrium in which demand (rather than costs) is uncertain for player B. 79
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This note was uploaded on 11/06/2009 for the course ECON ECON111 taught by Professor Smith during the Spring '09 term at Punjab Engineering College.

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