On the Efficiency of Categorization in Large Games

We study the efficiency of categorization of other agents as a way of simplifying the decision problem that agents face when involved in a large game. We assume that, when an agent categorizes (partitions) her opponents, she can only observe the average strategy in each category. A strategy profile is a Conjectural Categorical Equilibrium (CCE) with respect to a given categorization profile if every player’s strategy is a best response to some consistent conjecture about the strategies of her opponents. It is shown that, for a wide family of games and for a particular categorization profile, every CCE is an approximate Nash equilibrium when the number of players is large. This highlights the advantage of categorization as a simplifying mechanism in complex environments. With much less information in their hands agents behave as if they see the full picture. JEL classification: C72, D81, D84.