Lecture 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.