Game Theory with Ben Polak - 18. Imperfect information: information sets and sub-game perfection

Game Theory (ECON 159) 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. 00:00 - Chapter 1. Games of Imperfect Information: Information Sets 18:56 - Chapter 2. Games of Imperfect Information: Translating a Game from Matrix Form to Tree Form and Vice Versa 35:11 - Chapter 3. Games of Imperfect Information: Finding Nash Equilibria 49:59 - Chapter 4. Games of Imperfect Information: Sub-games 01:10:17 - Chapter 5. Games of Imperfect Information: Sub-game Perfect Equilibria Complete course materials are available at the Yale Online website: online.yale.edu This course was recorded in Fall 2007.