Imperfect Information: Information Sets and Sub-Game Perfection

Lecture Description

We consider games that have both simultaneous and sequential components, combining ideas from before and after the midterm. We represent what a player does not know within a game using an information set: a collection of nodes among which the player cannot distinguish. This lets us define games of imperfect information; and also lets us formally define subgames. We then extend our definition of a strategy to imperfect information games, and use this to construct the normal form (the payoff matrix) of such games. A key idea here is that it is information, not time per se, that matters. We show that not all Nash equilibria of such games are equally plausible: some are inconsistent with backward induction; some involve non-Nash behavior in some (unreached) subgames. To deal with this, we introduce a more refined equilibrium notion, called sub-game perfection.

Course Description

This course is an introduction to game theory and strategic thinking. Ideas such as dominance, backward induction, Nash equilibrium, evolutionary stability, commitment, credibility, asymmetric information, adverse selection, and signaling are discussed and applied to games played in class and to examples drawn from economics, politics, the movies, and elsewhere.

Related Resources

Lecture Transcript, Reading Assignment, and Handouts

Course Index

1. Introduction to Game Theory
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
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 Advantages
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 Perfection
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