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Iterated admissibility is a well-known and important concept in classicalgame theory, e.g. to determine rational behaviors in multi-player matrix games.As recently shown by Berwanger, this concept can be soundly extended toinfinite games played on graphs with omega-regular objectives. In this paper,we study the algorithmic properties of this concept for such games. We settlethe exact complexity of natural decision problems on the set of strategies thatsurvive iterated elimination of dominated strategies. As a byproduct of ourconstruction, we obtain automata which recognize all the possible outcomes ofsuch strategies.

The Complexity of Admissibility in Omega-Regular Games