Computing Maxmin Strategies in Extensive-form Zero-sum Games with Imperfect Recall
نویسندگان
چکیده
Extensive-form games with imperfect recall are an important game-theoretic model that allows a compact representation of strategies in dynamic strategic interactions. Practical use of imperfect recall games is limited due to negative theoretical results: a Nash equilibrium does not have to exist, computing maxmin strategies is NP-hard, and they may require irrational numbers. We present the first algorithm for approximating maxmin strategies in two-player zero-sum imperfect recall games without absentmindedness. We modify the wellknown sequence-form linear program to model strategies in imperfect recall games resulting in a bilinear program and use a recent technique to approximate the bilinear terms. Our main algorithm is a branch-andbound search that provably reaches the desired approximation after an exponential number of steps in the size of the game. Experimental evaluation shows that the proposed algorithm can approximate maxmin strategies of randomly generated imperfect recall games of sizes beyond toy-problems within few minutes.
منابع مشابه
Combining Incremental Strategy Generation and Branch and Bound Search for Computing Maxmin Strategies in Imperfect Recall Games
Extensive-form games with imperfect recall are an important model of dynamic games where the players are allowed to forget previously known information. Often, imperfect recall games are the result of an abstraction algorithm that simplifies a large game with perfect recall. Unfortunately, solving an imperfect recall game has fundamental problems since a Nash equilibrium does not have to exist....
متن کاملSolution Concepts in A-Loss Recall Games: Existence and Computational Complexity
Imperfect recall games represent dynamic interactions where players forget previously known information, such as history of played actions. The importance of imperfect recall games stems from allowing a concise representation of strategies compared to perfect recall games where players remember all information. However, most of the algorith-mic results are negative for imperfect recall games – ...
متن کاملAn Algorithm for Constructing and Solving Imperfect Recall Abstractions of Large Extensive-Form Games
We solve large two-player zero-sum extensive-form games with perfect recall. We propose a new algorithm based on fictitious play that significantly reduces memory requirements for storing average strategies. The key feature is exploiting imperfect recall abstractions while preserving the convergence rate and guarantees of fictitious play applied directly to the perfect recall game. The algorith...
متن کاملFinding Equilibria in Games of No Chance
We consider finding maximin strategies and equilibria of explicitly given extensive form games with imperfect information but with no moves of chance. We show: 1. A maximin pure strategy for a two-player extensive form game with perfect recall and no moves of chance can be found in time linear in the size of the game tree. In contrast, it is known that this problem is NP-hard for games with cha...
متن کاملAn Exact Double-Oracle Algorithm for Zero-Sum Extensive-Form Games with Imperfect Information
Developing scalable solution algorithms is one of the central problems in computational game theory. We present an iterative algorithm for computing an exact Nash equilibrium for two-player zero-sum extensive-form games with imperfect information. Our approach combines two key elements: (1) the compact sequence-form representation of extensiveform games and (2) the algorithmic framework of doub...
متن کامل