Lectures (Video)
- 1. Introduction
- 2. Putting yourselves into other people's shoes
- 3. Iterative deletion and the median-voter theorem
- 4. Best responses in soccer and business partnerships
- 5. Nash equilibrium: bad fashion and bank runs
- 6. Nash equilibrium: dating and Cournot
- 7. Nash equilibrium: shopping, standing and voting on a line
- 8. Nash equilibrium: location, segregation and randomization
- 9. Mixed strategies in theory and tennis
- 10. Mixed strategies in baseball, dating and paying your taxes
- 11. Evolutionary stability: cooperation, mutation, and equilibrium
- 12. Evolutionary stability: social convention, aggression, and cycles
- 13. Sequential games: moral hazard, incentives, and hungry lions
- 14. Backward induction: commitment, spies, and first-mover
- 15. Backward induction: chess, strategies, and credible threats
- 16. Backward induction: reputation and duels
- 17. Backward induction: ultimatums and bargaining
- 18. Imperfect information: information sets and sub-game
- 19. Subgame perfect equilibrium: matchmaking and strategic investments
- 20. Subgame perfect equilibrium: wars of attrition
- 21. Repeated games: cooperation vs. the end game
- 22. Repeated games: cheating, punishment, and outsourcing
- 23. Asymmetric information: silence, signaling and suffering education
- 24. Asymmetric information: auctions and the winner's curse
Game Theory - Lecture 9
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Lecture 9 - Mixed strategies in theory and tennis
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.
Prof. Ben Polak
ECON 159 Game Theory, Fall 2007 (Yale University: Open Yale) http://oyc.yale.edu Date accessed: 2009-01-15 License: Creative Commons BY-NC-SA |
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