Intermediate Preferences and Behavioral Conformity in Large Games

Motivated by Wooders, Cartwright, and Selten (2006), 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. We then use this result to show that all sufficiently large, equicontinuous games with intermediate preferences have an approximate equilibrium with the same property. Our result on behavior conformity for large finite game generalizes Theorem 3 of Wooders et al. (2006) by allowing both a wider class of preferences and a more general attribute space.