Complexity of (iterated) dominance
Proceedings of the 6th ACM conference on Electronic commerce
The complexity of computing a Nash equilibrium
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Settling the Complexity of Two-Player Nash Equilibrium
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
Artificial Intelligence
Algorithms for rationalizability and CURB sets
AAAI'06 Proceedings of the 21st national conference on Artificial intelligence - Volume 1
A generalized strategy eliminability criterion and computational methods for applying it
AAAI'05 Proceedings of the 20th national conference on Artificial intelligence - Volume 2
The Computational Complexity of Weak Saddles
SAGT '09 Proceedings of the 2nd International Symposium on Algorithmic Game Theory
On the Complexity of Iterated Weak Dominance in Constant-Sum Games
SAGT '09 Proceedings of the 2nd International Symposium on Algorithmic Game Theory
Algorithms for closed under rational behavior (CURB) sets
Journal of Artificial Intelligence Research
ACM SIGecom Exchanges
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Game-theoretic solution concepts, such as Nash equilibrium, are playing an ever increasing role in the study of systems of autonomous computational agents. A common criticism of Nash equilibrium is that its existence relies on the possibility of randomizing over actions, which in many cases is deemed unsuitable, impractical, or even infeasible. In work dating back to the early 1950s Lloyd Shapley proposed ordinal set-valued solution concepts for zero-sum games that he refers to as strict and weak saddles. These concepts are intuitively appealing, they always exist, and are unique in important subclasses of games. We initiate the study of computational aspects of Shapley's saddles and provide polynomial-time algorithms for computing strict saddles in normal-form games and weak saddles in a subclass of symmetric zero-sum games. On the other hand, we show that certain problems associated with weak saddles in bimatrix games are NP-hard. Finally, we extend our results to mixed refinements of Shapley's saddles introduced by Duggan and Le Breton.