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Thinking categorically about others: A conjectural equilibrium approach

Azrieli, Yaron (2007): Thinking categorically about others: A conjectural equilibrium approach.

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Abstract

Inspired by the social psychology literature, we study the implications of categorical thinking on decision making in the context of a large normal form game. Every agent has a categorization (partition) of her opponents and can only observe the average behavior 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.

We show that, for a wide family of games and for a particular categorization profile, every CCE becomes almost Nash as the number of players grows. An equivalence of CCE and Nash equilibrium is achieved in the settings of a non-atomic game. 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. Some properties of CCE when players categorize `non-optimally' are also considered.

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