Lecture 18 - Imperfect information: information sets and sub-game perfection

author: Benjamin Polak, Department of Economics, Yale University
recorded by: Yale University
published: Nov. 15, 2010,   recorded: September 2007,   views: 3505
released under terms of: Creative Commons Attribution No Derivatives (CC-BY-ND)
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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.

Reading assignment:

Strategies and Games: Theory And Practice. (Dutta): Chapter 13

Strategy: An Introduction to Game Theory. (Watson): Chapters 15-16, 19

Resources:

Problem Set 8 [PDF]
Blackboard Notes Lecture 18 [PDF]

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