Markov Decision Processes: Discrete Stochastic Dynamic Programming
Markov Decision Processes: Discrete Stochastic Dynamic Programming
Friend-or-Foe Q-learning in General-Sum Games
ICML '01 Proceedings of the Eighteenth International Conference on Machine Learning
Fast Planning in Stochastic Games
UAI '00 Proceedings of the 16th Conference on Uncertainty in Artificial Intelligence
Nash q-learning for general-sum stochastic games
The Journal of Machine Learning Research
Efficient algorithms for online decision problems
Journal of Computer and System Sciences - Special issue: Learning theory 2003
Settling the Complexity of Two-Player Nash Equilibrium
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
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 7th international joint conference on Autonomous agents and multiagent systems - Volume 2
Computing an approximate jam/fold equilibrium for 3-player no-limit Texas Hold'em tournaments
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
Learning to Coordinate Efficiently: a model-based approach
Journal of Artificial Intelligence Research
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
Computing equilibria by incorporating qualitative models?
Proceedings of the 9th International Conference on Autonomous Agents and Multiagent Systems: volume 1 - Volume 1
Game theory for cyber security
Proceedings of the Sixth Annual Workshop on Cyber Security and Information Intelligence Research
Computing pure Bayesian-Nash equilibria in games with finite actions and continuous types
Artificial Intelligence
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Computing a Nash equilibrium in multiplayer stochastic games is a notoriously difficult problem. Prior algorithms have been proven to converge in extremely limited settings and have only been tested on small problems. In contrast, we recently presented an algorithm for computing approximate jam/fold equilibrium strategies in a three-player nolimit Texas hold'em tournament--a very large real-world stochastic game of imperfect information [5]. In this paper we show that it is possible for that algorithm to converge to a non-equilibrium strategy profile. However, we develop an ex post procedure that determines exactly how much each player can gain by deviating from his strategy and confirm that the strategies computed in that paper actually do constitute an ε-equilibrium for a very small ε (0.5% of the tournament entry fee). Next, we develop several new algorithms for computing a Nash equilibrium in multiplayer stochastic games (with perfect or imperfect information) which can provably never converge to a non-equilibrium. Experiments show that one of these algorithms outperforms the original algorithm on the same poker tournament. In short, we present the first algorithms for provably computing an ε-equilibrium of a large stochastic game for small ε. Finally, we present an efficient algorithm that minimizes external regret in both the perfect and imperfect information cases.