Backward Induction: Ultimatums and Bargaining

Lecture Description

We develop a simple model of bargaining, starting from an ultimatum game (one person makes the other a take it or leave it offer), and building up to alternating offer bargaining (where players can make counter-offers). On the way, we introduce discounting: a dollar tomorrow is worth less than a dollar today. We learn that, if players are equally patient, if offers can be in rapid succession, and if each side knows how much the game is worth to the other side, then the first offer is for an equal split of the pie and this offer is accepted. But this result depends on those assumptions; for example, bargaining power may depend on wealth.

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 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