Fast algorithms for finding randomized strategies in game trees

Interactions among agents can be conveniently described by game trees. In order to analyze a game, it is important to derive optimal (or equilibrium) strategies for the di erent players. The standard approach to nding such strategies in games with imperfect information is, in general, computationally intractable. The approach is to generate the normal form of the game (the matrix containing the payo for each strategy combination),and then solve a linear program (LP) or a linear complementarity problem (LCP). The size of the normal form, however, is typically exponential in the size of the game tree, thus making this method impractical in all but the simplest cases. This paper describes a new representation of strategies which results in a practical linear formulation of the problem of two-player games with perfect recall (i.e., games where players never forget anything, which is a standard assumption). Standard LP or LCP solvers can then be applied to nd optimal randomized strategies....

• Type: Conference
• Year: 1994
• Where: STOC
• Authors: Daphne Koller, Nimrod Megiddo, Bernhard von Stengel
• Keywords: Algorithms, Almaden Research Center, Game Tree, Normal Form, STOC 1994