Yale / Political Science

Nash Equilibrium: Shopping, Standing and Voting on a Line

By Benjamin Polak | Game Theory Lecture 7 of 24

GRADED BY 46 USERS grade it
get flash player

Lecture Description

We first consider the alternative "Bertrand" model of imperfect competition between two firms in which the firms set prices rather than setting quantities. Then we consider a richer model in which firms still set prices but in which the goods they produce are not identical. We model the firms as stores that are on either end of a long road or line. Customers live along this line. Then we return to models of strategic politics in which it is voters that are spread along a line. This time, however, we do not allow candidates to choose positions: they can only choose whether or not to enter the election. We play this "candidate-voter game" in the class, and we start to analyze both as a lesson about the notion of equilibrium and a lesson about politics.

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, Handouts, and Reading Assignment

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
Leave Feedback