Factoring sparse multivariate polynomials
Journal of Computer and System Sciences
Graphical Models for Game Theory
UAI '01 Proceedings of the 17th Conference in Uncertainty in Artificial Intelligence
Exponentially Many Steps for Finding a Nash Equilibrium in a Bimatrix Game
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
Computing Nash equilibria of action-graph games
UAI '04 Proceedings of the 20th conference on Uncertainty in artificial intelligence
On the Complexity of Two-PlayerWin-Lose Games
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
A technique for reducing normal-form games to compute a Nash equilibrium
AAMAS '06 Proceedings of the fifth international joint conference on Autonomous agents and multiagent systems
Algorithms for rationalizability and CURB sets
AAAI'06 Proceedings of the 21st national conference on Artificial intelligence - Volume 1
A generalized strategy eliminability criterion and computational methods for applying it
AAAI'05 Proceedings of the 20th national conference on Artificial intelligence - Volume 2
IJCAI'03 Proceedings of the 18th international joint conference on Artificial intelligence
Generalization risk minimization in empirical game models
Proceedings of The 8th International Conference on Autonomous Agents and Multiagent Systems - Volume 1
Thesis summary: empirical game-theoretic methods for strategy design and analysis in complex games
AAAI'07 Proceedings of the 22nd national conference on Artificial intelligence - Volume 2
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Game theoretic reasoning about multi-agent systems has been made more tractable by algorithms that exploit various types of independence in agents' utilities. However, previous work has assumed that a game's precise independence structure is given in advance. This paper addresses the problem of finding independence structure in a general form game when it is not known ahead of time, or of finding an approximation when full independence does not exist. We give an expected polynomial time algorithm to divide a bounded-payout normal form game into factor games that isolate independent strategic interactions. We also show that the best approximate factoring can be found in polynomial time for a specific interaction that is not fully independent. Once known, factors aide computation of game theoretic solution concepts, including Nash equilibria (or ε-equilibria for approximate factors), in some cases guaranteeing polynomial complexity where previous bounds were exponential.