Categorizing others in a large game

We study the efficiency of categorization of other agents as a way of saving cognitive resources in the settings of a large normal-form game. We assume that, when an agent categorizes (partitions) her opponents, she only has information about 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 result demonstrates the potential of categorization as an efficient way to store information in complex environments. Although possessing a coarse description of their opponents' strategies, agents behave as if they see the full picture.