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ECON 159: Game Theory

Lecture 10 - Mixed Strategies in Baseball, Dating and Paying Your Taxes. We develop three different interpretations of mixed strategies in various contexts: sport, anti-terrorism strategy, dating, paying taxes and auditing taxpayers. One interpretation is that people literally randomize over their choices. Another is that your mixed strategy represents my belief about what you might do. A third is that the mixed strategy represents the proportions of people playing each pure strategy. Then we discuss some implications of the mixed equilibrium in games; in particular, we look how the equilibrium changes in the tax-compliance/auditor game as we increase the penalty for cheating on your taxes. (from oyc.yale.edu)

Lecture 10 - Mixed Strategies in Baseball, Dating and Paying Your Taxes

Time Lecture Chapters
[00:00:00] 1. Mixed Strategy Equilibria: Example (Continued)
[00:12:49] 2. Mixed Strategy Equilibria: Other Examples in Sports
[00:23:41] 3. Mixed Strategy Equilibria Interpretation 1: Literal Randomization
[00:28:17] 4. Mixed Strategy Equilibria Interpretation 2: Players' Beliefs about Each Other's Actions
[00:47:04] 5. Mixed Strategy Equilibria Interpretation 3: Prediction of Split on Two or More Courses of
... Action in a Large Population
[00:59:52] 6. Mixed Strategy Equilibria: Policy Applications

References
Lecture 10 - Mixed Strategies in Baseball, Dating and Paying Your Taxes
Instructor: Professor Ben Polak. Resources: Handout on ESS in Pure Strategies [PDF]; Blackboard Notes Lecture 10 [PDF]. Transcript [html]. Audio [mp3]. Download Video [mov].

Go to the Course Home or watch other lectures:

Lecture 01 - Introduction: Five First Lessons
Lecture 02 - Putting Yourselves into Other People's Shoes
Lecture 03 - Iterative Deletion and the Median-Voter Theorem
Lecture 04 - Best Responses in Soccer and Business Partnerships
Lecture 05 - Nash Equilibrium: Bad Fashion and Bank Runs
Lecture 06 - Nash Equilibrium: Dating and Cournot
Lecture 07 - Nash Equilibrium: Shopping, Standing and Voting on a Line
Lecture 08 - Nash Equilibrium: Location, Segregation and Randomization
Lecture 09 - Mixed Strategies in Theory and Tennis
Lecture 10 - Mixed Strategies in Baseball, Dating and Paying Your Taxes
Lecture 11 - Evolutionary Stability: Cooperation, Mutation, and Equilibrium
Lecture 12 - Evolutionary Stability: Social Convention, Aggression, and Cycles
Lecture 13 - Sequential Games: Moral Hazard, Incentives, and Hungry Lions
Lecture 14 - Backward Induction: Commitment, Spies, and First-Mover Advantages
Lecture 15 - Backward Induction: Chess, Strategies, and Credible Threats
Lecture 16 - Backward Induction: Reputation and Duels
Lecture 17 - Backward Induction: Ultimatums and Bargaining
Lecture 18 - Imperfect Information: Information Sets and Sub-Game Perfection
Lecture 19 - Subgame Perfect Equilibrium: Matchmaking and Strategic Investments
Lecture 20 - Subgame Perfect Equilibrium: Wars of Attrition
Lecture 21 - Repeated Games: Cooperation vs. the End Game
Lecture 22 - Repeated Games: Cheating, Punishment, and Outsourcing
Lecture 23 - Asymmetric Information: Silence, Signaling and Suffering Education
Lecture 24 - Asymmetric Information: Auctions and the Winner's Course