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.

00:00:00 Games of Imperfect Information: Information Sets
00:18:56 Games of Imperfect Information: Translating a Game from Matrix Form to Tree Form and Vice Versa
00:35:11 Games of Imperfect Information: Finding Nash Equilibria
00:49:59 Games of Imperfect Information: Sub-games
01:10:17 Games of Imperfect Information: Sub-game Perfect Equilibria

Source: Ben Polak, Game Theory (Yale University: Open Yale Courses). Licensed under CC BY-NC-SA 3.0.