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

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

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.

Whenever you find yourself in a tree, play nash equilibrium. The idea of playing from a node to the choice of two nodes whereby when you choose, choose the NE. In a sub-game perfection ideal.

From a dominate, forward thought perspective determine and draw a sub-game perfection example.