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Nash equilibrium under Knightian uncertainty: Breaking down backward induction. (English) Zbl 0813.90132
Summary: We define Nash equilibrium for two-person normal-form games in the presence of Knightian uncertainty. Using the formalization of Schmeidler and Gilboa, we show that Nash equilibrium exists for any degree of uncertainty aversion, that maxmin behaviour can occur even when it is not rationalizable in the usual sense, and that backward induction breaks down in the twice repeated prisoners’ dilemma. We relate these results to the literature on cooperation in the finitely repeated prisoners’ dilemma, and the literature on epistemological conditions underlying Nash equilibrium. The knowledge notion implicit in this model of equilibrium does not display logical omniscience.

MSC:
91A05 2-person games
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