Settling the Complexity of Two-Player Nash Equilibrium
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
Lossless abstraction of imperfect information games
Journal of the ACM (JACM)
A near-optimal strategy for a heads-up no-limit Texas Hold'em poker tournament
Proceedings of the 6th international joint conference on Autonomous agents and multiagent systems
Proceedings of the 6th international joint conference on Autonomous agents and multiagent systems
Proceedings of the 7th international joint conference on Autonomous agents and multiagent systems - Volume 2
AAAI'06 proceedings of the 21st national conference on Artificial intelligence - Volume 2
AAAI'07 Proceedings of the 22nd national conference on Artificial intelligence - Volume 1
Approximating game-theoretic optimal strategies for full-scale poker
IJCAI'03 Proceedings of the 18th international joint conference on Artificial intelligence
Proceedings of the 7th international joint conference on Autonomous agents and multiagent systems - Volume 2
Abstraction pathologies in extensive games
Proceedings of The 8th International Conference on Autonomous Agents and Multiagent Systems - Volume 2
Computing equilibria in multiplayer stochastic games of imperfect information
IJCAI'09 Proceedings of the 21st international jont conference on Artifical intelligence
Approximation guarantees for fictitious play
Allerton'09 Proceedings of the 47th annual Allerton conference on Communication, control, and computing
Using counterfactual regret minimization to create competitive multiplayer poker agents
Proceedings of the 9th International Conference on Autonomous Agents and Multiagent Systems: volume 1 - Volume 1
On the rate of convergence of fictitious play
SAGT'10 Proceedings of the Third international conference on Algorithmic game theory
Artificial Intelligence
Proceedings of the 2013 international conference on Autonomous agents and multi-agent systems
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A recent paper computes near-optimal strategies for two-player no-limit Texas hold'em tournaments; however, the techniques used are unable to compute equilibrium strategies for tournaments with more than two players. Motivated by the widespread popularity of multiplayer tournaments and the observation that jam/fold strategies are nearoptimal in the two player case, we develop an algorithm that computes approximate jam/fold equilibrium strategies in tournaments with three --- and potentially even more --- players. Our algorithm combines an extension of fictitious play to imperfect information games, an algorithm similar to value iteration for solving stochastic games, and a heuristic from the poker community known as the Independent Chip Model which we use as an initialization. Several ways of exploiting suit symmetries and the use of custom indexing schemes made the approach computationally feasible. Aside from the initialization and the restriction to jam/fold strategies, our high level algorithm makes no poker-specific assumptions and thus also applies to other multiplayer stochastic games of imperfect information.