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Equivalence between best responses and undominated strategies: a generalization from finite to compact strategy sets.
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Abstract
For games with expected utility maximizing players whose strategy sets are finite, Pearce (1984) shows that a strategy is strictly dominated by some mixed strategy, if and only if, this strategy is not a best response to some belief about opponents' strategy choice. This note generalizes Pearce''s (1984) equivalence result to games with expected utility maximizing players whose strategy sets are arbitrary compact sets.