Lecture 15 - Backward induction: chess, strategies, and credible threats

author: Benjamin Polak, Department of Economics, Yale University
recorded by: Yale University
published: Nov. 15, 2010,   recorded: September 2007,   views: 3215
released under terms of: Creative Commons Attribution No Derivatives (CC-BY-ND)
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Description

We first discuss Zermelo's theorem: that games like tic-tac-toe or chess have a solution. That is, either there is a way for player 1 to force a win, or there is a way for player 1 to force a tie, or there is a way for player 2 to force a win. The proof is by induction. Then we formally define and informally discuss both perfect information and strategies in such games. This allows us to find Nash equilibria in sequential games. But we find that some Nash equilibria are inconsistent with backward induction. In particular, we discuss an example that involves a threat that is believed in an equilibrium but does not seem credible.

Reading assignment:

Strategies and Games: Theory And Practice. (Dutta): Chapters 11-12

Strategy: An Introduction to Game Theory. (Watson): Chapter 21

Resources:

Blackboard Notes Lecture 15[PDF]

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