The complexity of eliminating dominated strategies
Mathematics of Operations Research
Run the GAMUT: A Comprehensive Approach to Evaluating Game-Theoretic Algorithms
AAMAS '04 Proceedings of the Third International Joint Conference on Autonomous Agents and Multiagent Systems - Volume 2
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
Complexity of (iterated) dominance
Proceedings of the 6th ACM conference on Electronic commerce
On the Complexity of Two-PlayerWin-Lose Games
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
Improved complexity results on solving real-number linear feasibility problems
Mathematical Programming: Series A and B
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
Settling the Complexity of Two-Player Nash Equilibrium
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
The complexity of computing a Nash equilibrium
Communications of the ACM - Inspiring Women in Computing
Computational aspects of Shapley's saddles
Proceedings of The 8th International Conference on Autonomous Agents and Multiagent Systems - Volume 1
Simple search methods for finding a Nash equilibrium
AAAI'04 Proceedings of the 19th national conference on Artifical intelligence
A generalized strategy eliminability criterion and computational methods for applying it
AAAI'05 Proceedings of the 20th national conference on Artificial intelligence - Volume 2
Mixed-integer programming methods for finding Nash equilibria
AAAI'05 Proceedings of the 20th national conference on Artificial intelligence - Volume 2
The computational complexity of trembling hand perfection and other equilibrium refinements
SAGT'10 Proceedings of the Third international conference on Algorithmic game theory
Extensive--form games with heterogeneous populations
Proceedings of the 2013 international conference on Autonomous agents and multi-agent systems
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We provide a series of algorithms demonstrating that solutions according to the fundamental game-theoretic solution concept of closed under rational behavior (CURB) sets in two-player, normal-form games can be computed in polynomial time (we also discuss extensions to n-player games). First, we describe an algorithm that identifies all of a player's best responses conditioned on the belief that the other player will play from within a given subset of its strategy space. This algorithm serves as a subroutine in a series of polynomial-time algorithms for finding all minimal CURB sets, one minimal CURB set, and the smallest minimal CURB set in a game. We then show that the complexity of finding a Nash equilibrium can be exponential only in the size of a game's smallest CURB set. Related to this, we show that the smallest CURB set can be an arbitrarily small portion of the game, but it can also be arbitrarily larger than the supports of its only enclosed Nash equilibrium. We test our algorithms empirically and find that most commonly studied academic games tend to have either very large or very small minimal CURB sets.