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Iterated Weaker-Than-Weak Dominance, Shih-Fen Cheng, Michael P. Wellman

Shih-Fen CHENG

We introduce a weakening of standard gametheoretic δ-dominance conditions, called dominance, which enables more aggressive pruning of candidate strategies at the cost of solution accuracy. Equilibria of a game obtained by eliminating a δ-dominated strategy are guaranteed to be approximate equilibria of the original game, with degree of approximation bounded by the dominance parameter. We can apply elimination of δ-dominated strategies iteratively, but the for which a strategy may be eliminated depends on prior eliminations. We discuss implications of this order independence, and propose greedy heuristics for determining a sequence of eliminations to reduce the game as far as possible …