The Computational Complexity of Iterated Elimination of Dominated Strategies

The computational complexity of a variety of problems from algorithmic game theory is investigated. These are variations on the question whether a strategy in a normal form game survives iterated elimination of dominated strategies. The difficulty of the computational task depends on the notion of dominance involved, on the number of distinct payoffs and whether the game is constant-sum. Most of the open cases are fully classified, and the remaining cases are shown to be equivalent to certain questions regarding elimination orders on graphs. The classifications may serve as the basis for a discussion to what extent iterated dominance could be useful to restrict rationality for computationally bounded agents.