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Intermediate Preferences and Behavioral Conformity in Large Games
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We consider games with a continuum of players and intermediate preferences. We show that any such game has a Nash equilibrium that induces a partition of the set of attributes into a bounded number of convex sets with the following property: all players with an attribute in the interior of the same element of the partition play the same action. Furthermore, if the game induces an absolutely continuous distribution (with respect to the Lebesgue measure) on the attribute space, then we can strengthen the conclusion by showing that all players with an attribute in the same element of the partition play the same action. We then use these results to show that all sufficiently large, equicontinuous games with intermediate preferences have an approximate equilibrium with the same properties in both cases (for the stronger result, we require the attribute space to be a subset of the real line). Our result on behavior conformity for large finite game generalizes Theorem 3 of Wooders, Cartwright, and Selten (2006) by allowing both a wider class of preferences and a more general attribute space.
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Carmona, Guilherme, Intermediate Preferences and Behavioral Conformity in Large Games (November, 2007). FEUNL Working Paper Series No. 523