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
Complexity of (iterated) dominance
Proceedings of the 6th ACM conference on Electronic commerce
Online ascending auctions for gradually expiring items
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
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
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
Perspectives on multiagent learning
Artificial Intelligence
Factoring games to isolate strategic interactions
Proceedings of the 6th international joint conference on Autonomous agents and multiagent systems
Computational aspects of Shapley's saddles
Proceedings of The 8th International Conference on Autonomous Agents and Multiagent Systems - Volume 1
Computational aspects of covering in dominance graphs
AAAI'07 Proceedings of the 22nd national conference on Artificial intelligence - Volume 1
Iterated weaker-than-weak dominance
IJCAI'07 Proceedings of the 20th international joint conference on Artifical intelligence
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Significant work has been done on computational aspects of solving games under various solution concepts, such as Nash equilibrium, subgame perfect Nash equilibrium, correlated equilibrium, and (iterated) dominance. However, the fundamental concepts of rationalizability and CURB (Closed Under Rational Behavior sets have not, to our knowledge, been studied from a computational perspective. First, for rationalizability we describe an LP-based polynomial algorithm that finds all strategies that are rationalizable against a mixture over a given set of opponent strategies. Then, we describe a series of increasingly sophisticated polynomial algorithms for finding all minimal CURB sets, one minimal CURB set, and the smallest minimal CURB set. Finally, we give theoretical results regarding the relationships between CURB sets and Nash equilibria, showing that finding a Nash equilibrium can be exponential only in the size of the smallest CURB set. We show that this can lead to an arbitrarily large reduction in the complexity of finding a Nash equilibrium. On the downside, we also show that the smallest CURB set can be arbitrarily larger than the supports of the enclosed Nash equilibrium.