Multiagent Systems: Algorithmic, Game-Theoretic, and Logical Foundations
Multiagent Systems: Algorithmic, Game-Theoretic, and Logical Foundations
A new algorithm for generating equilibria in massive zero-sum games
AAAI'07 Proceedings of the 22nd national conference on Artificial intelligence - Volume 1
Smoothing Techniques for Computing Nash Equilibria of Sequential Games
Mathematics of Operations Research
A double oracle algorithm for zero-sum security games on graphs
The 10th International Conference on Autonomous Agents and Multiagent Systems - Volume 1
Trading Agents
Security and Game Theory: Algorithms, Deployed Systems, Lessons Learned
Security and Game Theory: Algorithms, Deployed Systems, Lessons Learned
Computing approximate Nash Equilibria and robust best-responses using sampling
Journal of Artificial Intelligence Research
Accelerating best response calculation in large extensive games
IJCAI'11 Proceedings of the Twenty-Second international joint conference on Artificial Intelligence - Volume Volume One
Solving extensive-form games with double-oracle methods
Proceedings of the 2013 international conference on Autonomous agents and multi-agent systems
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We investigate an iterative algorithm for computing an exact Nash equilibrium in two-player zero-sum extensive-form games with imperfect information. The approach uses the sequence-form representation of extensive-form games and the double-oracle algorithmic framework. The main idea is to restrict the game by allowing the players to play only some of the sequences of available actions, then iteratively solve this restricted game, and exploit fast best-response algorithms to add additional sequences to the restricted game for the next iteration. In this paper we (1) extend the sequence-form double-oracle method to be applicable on non-deterministic extensive-form games, (2) present more efficient methods for maintaining valid restricted game and computing best-response sequences, and finally we (3) provide theoretical guarantees of the convergence of the algorithm to a Nash equilibrium. We experimentally evaluate our algorithm on two types of games: a search game on a graph and simplified variants of Poker. The results show significant running-time improvements compared to the previous variant of the double-oracle algorithm, and demonstrate the ability to find an exact solution of much larger games compared to solving full linear program for the complete game.