Stability and perfection of Nash equilibria
Stability and perfection of Nash equilibria
The complexity of computing a Nash equilibrium
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Computing Nash Equilibria: Approximation and Smoothed Complexity
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
Lossless abstraction of imperfect information games
Journal of the ACM (JACM)
A note on approximate Nash equilibria
Theoretical Computer Science
Simple search methods for finding a Nash equilibrium
AAAI'04 Proceedings of the 19th national conference on Artifical intelligence
Mixed-integer programming methods for finding Nash equilibria
AAAI'05 Proceedings of the 20th national conference on Artificial intelligence - Volume 2
AAAI'07 Proceedings of the 22nd national conference on Artificial intelligence - Volume 1
Local search techniques for computing equilibria in two-player general-sum strategic-form games
Proceedings of the 9th International Conference on Autonomous Agents and Multiagent Systems: volume 1 - Volume 1
The computational complexity of trembling hand perfection and other equilibrium refinements
SAGT'10 Proceedings of the Third international conference on Algorithmic game theory
Bilateral bargaining with one-sided uncertain reserve prices
Autonomous Agents and Multi-Agent Systems
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The computational study of strategic interaction situations has recently deserved a lot of attention in multi--agent systems. A number of results on strategic--form games and zero--sum extensive--form games are known in the literature, while general--sum extensive--form games are not studied in depth. We focus on the problem to decide whether or not a solution is a refinement of the Nash equilibrium (NE) for extensive--form games. Refinements are needed because the NE concept is not satisfactory for this game class. While verifying whether a solution is an NE is in P, verifying whether it is a NE refinement may be not (all the results known so far show NP--hardness). In this paper, we provide the first positive result, showing that verifying a sequential equilibrium with any number of agents and a quasi perfect equilibrium with two agents are in P. We show also that when the input is expressed in (non--perturbed) sequence form even the problem to verify a subgame perfect equilibrium is NP--complete and that sequence form, if applicable, must be rethought to verify (and therefore to compute) an extensive--form perfect equilibrium.