Poker is a family of games that exhibit imperfect information, where players do not have full knowledge of past events. Whereas many perfect information games have been solved (e.g., Connect Four and checkers), no nontrivial imperfect information game played competitively by humans has previously been solved. Here, we announce that heads-up limit Texas hold’em is now essentially weakly solved. ...

We derive a recursive formula for expected utility values in imperfectinformation game trees, and an imperfectinformation game tree search algorithm based on it. The formula and algorithm are general enough to incorporate a wide variety of opponent models. We analyze two opponent models. The “paranoid” model is an information-set analog of the minimax rule used in perfect-information games. The...

We study the complexity of nding the values and optimal strategies of mean payoo games on graphs, a family of perfect information games introduced by Ehrenfeucht and Mycielski and considered by Gurvich, Karzanov and Khachiyan. We describe a pseudo-polynomial time algorithm for the solution of such games, the decision problem for which is in NP \ co-NP. Finally, we describe a polynomial reductio...

We consider infinitary two-player perfect information games defined over graphs of configurations of a pushdown automaton. We show how to solve such games when winning conditions are Boolean combinations of a Büchi condition and a new condition that we call unboundedness. An infinite play satisfies the unboundedness condition if there is no bound on the size of the stack during the play. We sho...

The paper provides a framework for representing belief-contravening hypotheses in games of perfect information. The resulting t-extended information structures are used to encode the notion that a player has the disposition to behave rationally at a node. We show that there are models where the condition of all players possessing this disposition at all nodes (under their control) is both a nec...

Article history: Received 12 June 2012 Available online 13 February 2013 JEL classification: C70 C72

This paper shows how uncertainty aversion can resolve ties in extensive games of perfect information, and thereby re"ne subgame-perfection in such games. This is done by assuming that (a) players are rational with multi-prior expected utility functions of Gilboa and Schmeidler (1989), (Journal of Economic Theory 48, 221}237); and (b) a player's plan of the game corresponds to set-valued acts at...

We prove that any strictly competitive perfect-information two-person game with n outcomes is solvable in n−1 steps of elimination of weakly dominated strategies— regardless of the length of the game tree. The given bound is shown to be tight using a variant of Rosenthal's centipede game.

Following Kohlberg-Mertens [8, 1986], we investigate an axiomatic approach to non-cooperative solution concepts. A basic question in this program is identifying a backward-induction axiom (for general games). We show that three axioms—Existence, Rationality, and Difference—together characterize backward induction in perfect-information games satisfying a “single payoff condition.” We discuss im...