Session 9 - Mixed strategies in theory and tennis
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We continue our discussion of mixed strategies. First we discuss the payoff to a mixed strategy, pointing out that it must be a weighed average of the payoffs to the pure strategies used in the mix. We note a consequence of this: if a mixed strategy is a best response, then all the pure strategies in the mix must themselves be best responses and hence indifferent. We use this idea to find mixed-strategy Nash equilibria in a game within a game of tennis.
ECON 159: Game Theory
| Lecture 9 - Mixed strategies in theory and tennis |
Overview:
We continue our discussion of mixed strategies. First we discuss the payoff to a mixed strategy, pointing out that it must be a weighed average of the payoffs to the pure strategies used in the mix. We note a consequence of this: if a mixed strategy is a best response, then all the pure strategies in the mix must themselves be best responses and hence indifferent. We use this idea to find mixed-strategy Nash equilibria in a game within a game of tennis.
Reading assignment:
Strategies and Games: Theory And Practice. (Dutta): Chapters 8-9
Strategy: An Introduction to Game Theory. (Watson): Chapter 11
Thinking Strategically. (Dixit and Nalebuff): Chapter 7
Class lecture:
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