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Categorizing others in a large game

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  • Azrieli, Yaron

Abstract

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.

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  • Azrieli, Yaron, 2009. "Categorizing others in a large game," Games and Economic Behavior, Elsevier, vol. 67(2), pages 351-362, November.
    • Handle: RePEc:eee:gamebe:v:67:y:2009:i:2:p:351-362
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    3. Yasar, Alperen, 2023. "Power struggles and gender discrimination in the workplace," SocArXiv t4g83, Center for Open Science.
    4. Pierpaolo Battigalli & Simone Cerreia-Vioglio & Fabio Maccheroni & Massimo Marinacci, 2015. "Self-Confirming Equilibrium and Model Uncertainty," American Economic Review, American Economic Association, vol. 105(2), pages 646-677, February.
    5. Azrieli, Yaron, 2010. "Categorization and correlation in a random-matching game," Journal of Mathematical Economics, Elsevier, vol. 46(3), pages 303-310, May.
    6. Mohlin, Erik, 2014. "Optimal categorization," Journal of Economic Theory, Elsevier, vol. 152(C), pages 356-381.
    7. Philippe Jehiel & Erik Mohlin, 2023. "Categorization in Games: A Bias-Variance Perspective," Working Papers halshs-04154272, HAL.
    8. Pierpaolo Battigalli & Simone Cerreia-Vioglio & Fabio Maccheroni & Massimo Marinacci, 2011. "Selfconfirming Equilibrium and Uncertainty," Working Papers 428, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
    9. Daskalova, Vessela & Vriend, Nicolaas J., 2021. "Learning frames," Journal of Economic Behavior & Organization, Elsevier, vol. 191(C), pages 78-96.
    10. Halpern, Joe & Heller, Yuval & Winter, Eyal, 2022. "The Benefits of Coarse Preferences," MPRA Paper 111670, University Library of Munich, Germany.
    11. Deb, Joyee & Kalai, Ehud, 2015. "Stability in large Bayesian games with heterogeneous players," Journal of Economic Theory, Elsevier, vol. 157(C), pages 1041-1055.
    12. Daskalova, Vessela & Vriend, Nicolaas J., 2020. "Categorization and coordination," European Economic Review, Elsevier, vol. 129(C).
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    14. Daskalova, Vessela & Vriend, Nicolaas J., 2020. "Categorization and coordination," European Economic Review, Elsevier, vol. 129(C).

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