Using Double-Oracle Method and Serialized Alpha-Beta Search for Pruning in Simultaneous Move Games

We focus on solving two-player zero-sum extensive-form games with perfect information and simultaneous moves. In these games, both players fully observe the current state of the game where they simultaneously make a move determining the next state of the game. We solve these games by a novel algorithm that relies on two components: (1) it iteratively solves the games that correspond to a single simultaneous move using a double-oracle method, and (2) it prunes the states of the game using bounds on the sub-game values obtained by the classical Alpha-Beta search on a serialized variant of the game. We experimentally evaluate our algorithm on the Goofspiel card game, a pursuit-evasion game, and randomly generated games. The results show that our novel algorithm typically provides significant running-time improvements and reduction in the number of evaluated nodes compared to the full search algorithm.

[1]  Avrim Blum,et al.  Planning in the Presence of Cost Functions Controlled by an Adversary , 2003, ICML.

[2]  U. Dulleck,et al.  μ-σ Games , 2012, Games.

[3]  Dana S. Nau,et al.  An Analysis of Forward Pruning , 1994, AAAI.

[4]  Oriol Carbonell-Nicolau.  Games and Economic Behavior , 2011 .

[5]  Michael Buro,et al.  Solving the Oshi-Zumo Game , 2003, ACG.

[6]  D. Koller,et al.  Efficient Computation of Equilibria for Extensive Two-Person Games , 1996 .

[7]  Michael L. Littman,et al.  Markov Games as a Framework for Multi-Agent Reinforcement Learning , 1994, ICML.

[8]  Ariel Rubinstein,et al.  A Course in Game Theory , 1995 .

[9]  Peter Norvig,et al.  Artificial Intelligence: A Modern Approach , 1995 .

[10]  Olivier Teytaud,et al.  Upper Confidence Trees with Short Term Partial Information , 2011, EvoApplications.

[11]  B. Stengel,et al.  Efficient Computation of Behavior Strategies , 1996 .

[12]  Michael Buro,et al.  Heuristic Search Applied to Abstract Combat Games , 2005, Canadian Conference on AI.

[13]  Laurent Bartholdi,et al.  Computer Solution to the Game of Pure Strategy , 2012, Games.

[14]  Branislav Bosanský,et al.  Extending Security Games to Defenders with Constrained Mobility , 2012, AAAI Spring Symposium: Game Theory for Security, Sustainability, and Health.

[15]  Yoav Shoham,et al.  Multiagent Systems - Algorithmic, Game-Theoretic, and Logical Foundations , 2009 .

[16]  Vincent Conitzer,et al.  A double oracle algorithm for zero-sum security games on graphs , 2011, AAMAS.

[17]  Milind Tambe,et al.  Security and Game Theory - Algorithms, Deployed Systems, Lessons Learned , 2011 .

[18]  Aaas News,et al.  Book Reviews , 1893, Buffalo Medical and Surgical Journal.

[19]  Duane Szafron,et al.  Efficient Monte Carlo Counterfactual Regret Minimization in Games with Many Player Actions , 2012, NIPS.

[20]  Martin Müller,et al.  Fuego—An Open-Source Framework for Board Games and Go Engine Based on Monte Carlo Tree Search , 2010, IEEE Transactions on Computational Intelligence and AI in Games.

[21]  Michael Buro,et al.  Alpha-Beta Pruning for Games with Simultaneous Moves , 2012, AAAI.

[22]  Michael R. Genesereth,et al.  General Game Playing: Overview of the AAAI Competition , 2005, AI Mag..

[23]  Milind Tambe.  Security and Game Theory: EFFICIENT ALGORITHMS FOR MASSIVE SECURITY GAMES , 2011 .

[24]  Ruck Thawonmas,et al.  Monte Carlo Tree Search for Collaboration Control of Ghosts in Ms. Pac-Man , 2013, IEEE Transactions on Computational Intelligence and AI in Games.