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: 3508
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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Reviews and comments:

Comment1 Nia Muller, June 17, 2022 at 7:28 p.m.:

The basic idea of this lecture is that we need to be able to talk about the imperfections in the information sets. The standard way we do this is by talking about sub game perfection, which means that there is a unique equilibrium point in which all players are rational and all payoffs are maximized. We then say that there is perfect information, because it's easy to prove that no player can get better than perfect information. The first thing you should do when you have decided to play at a casino, is to read the reviews at https://wageringadvisors.ca/low-depos... website. There are many different websites that provide reviews of different casinos but that one is the best.

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