CHAPTER 15
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 firstmover 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 (nonstable) 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.
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 Spring '09
 Smith
 Game Theory, Nash

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