The complexity of eliminating dominated strategies
Mathematics of Operations Research
Complexity of (iterated) dominance
Proceedings of the 6th ACM conference on Electronic commerce
Artificial Intelligence
Multiagent Systems: Algorithmic, Game-Theoretic, and Logical Foundations
Multiagent Systems: Algorithmic, Game-Theoretic, and Logical Foundations
Computational aspects of Shapley's saddles
Proceedings of The 8th International Conference on Autonomous Agents and Multiagent Systems - Volume 1
The Computational Complexity of Weak Saddles
SAGT '09 Proceedings of the 2nd International Symposium on Algorithmic Game Theory
On the parameterized complexity of dominant strategies
ACSC '12 Proceedings of the Thirty-fifth Australasian Computer Science Conference - Volume 122
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In game theory, a player's action is said to be weakly dominated if there exists another action that, with respect to what the other players do, is never worse and sometimes strictly better. We investigate the computational complexity of the process of iteratively eliminating weakly dominated actions (IWD) in two-player constant-sum games, i.e., games in which the interests of both players are diametrically opposed. It turns out that deciding whether an action is eliminable via IWD is feasible in polynomial time whereas deciding whether a given subgame is reachable via IWD is NP-complete. The latter result is quite surprising as we are not aware of other natural computational problems that are intractable in constant-sum games. Furthermore, we slightly improve a result by Conitzer and Sandholm [6] by showing that typical problems associated with IWD in win-lose games with at most one winner are NP-complete.