We show that whenever a decision maker reasons about an optimal decision he is able to find one, even with non-transitive preferences. The existence of a reasoning process allows him to strategically manipulate how he reasons. A reasoning strategy that is robust against (finite) deviations is captured by the notion of cognitive equilibrum. We show that a cognitive equilibrium exists under all complete preferences, and characterize outcomes that can be implemented within it. Cognitive equilibria employ complex cognitive strategies. Simple strategies suffice only under transitive preferences. Robustness of the model is evaluated in the language of von Neumann-Morgenstern stable sets.
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