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Game Theory - Lecture 18

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

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.

Prof. Ben Polak
ECON 159 Game Theory, Fall 2007
(Yale University: Open Yale)
Date accessed: 2009-01-15
License: Creative Commons BY-NC-SA

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1. Problem set 8



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