Iterated Weak Dominance in Strictly Competitive Games of Perfect Information

Christian Ewerhart

No 01-33, Sonderforschungsbereich 504 Publications from Sonderforschungsbereich 504, Universität Mannheim, Sonderforschungsbereich 504, University of Mannheim

Abstract: We prove that any strictly competitive perfect-information two-person game with n outcomes is solvable in n-1 steps of elimination of weakly dominated strategies - regardless of the length of the game tree. The derivation is based on the fact that if player i does not possess a winning strategy, then any of player j's strategies that enables i to win is eliminated by two steps of iterated dominance. The given bound is shown to be tight using a variant of Rosenthal's centipede game.

Pages: 15 pages
Date: 2001-05-12
Note: Financial support from the Deutsche Forschungsgemeinschaft, SFB 504, at the University of Mannheim, is gratefully acknowledged.
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