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Pure strategy dominance. (English) Zbl 0768.90103
The paper re-investigates the characterization of expected utility maximizing strategies as undominated strategies. The class of games considered is that of finite normal-form games. The traditional result in this field takes the players’ von Neumann-Morgenstern utility functions as exogeneously given. It is then shown that a strategy maximizes expected utility for some subjective belief if and only if it is not dominated. The notion of dominance that is used in this result is “strong dominance”. For the traditional result to be true, this notion must be applied to an extended strategy space which includes not only the players’ pure strategies but also their mixed strategies. In this paper, an alternative approach is presented. Only the player’s preferences over pure strategy outcomes are taken as exogeneously given. All utility functions which are compatible with these preferences are admitted. Like the traditional result, the main result of this paper says that a strategy maximizes expected utility for some compatible utility function and some subjective belief if and only if it is not dominated. The notion of dominance that is used in this result is, however, a modification of “strong dominance”. This notion needs to be applied to pure strategies, only. Mixed strategies need not be considered.

MSC:
91A35 Decision theory for games
91B06 Decision theory
91A10 Noncooperative games
91E99 Mathematical psychology
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