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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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    Cited by:

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    2. Mohlin, Erik, 2014. "Optimal categorization," Journal of Economic Theory, Elsevier, vol. 152(C), pages 356-381.
    3. Yuval Heller & Eyal Winter, 2016. "Rule Rationality," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 57(3), pages 997-1026, August.
    4. Berman, Ron & Heller, Yuval, 2020. "Naive Analytics Equilibrium," MPRA Paper 103824, University Library of Munich, Germany.
    5. Deb, Joyee & Kalai, Ehud, 2015. "Stability in large Bayesian games with heterogeneous players," Journal of Economic Theory, Elsevier, vol. 157(C), pages 1041-1055.
    6. Daskalova, Vessela & Vriend, Nicolaas J., 2020. "Categorization and coordination," European Economic Review, Elsevier, vol. 129(C).
    7. 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.
    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. Gradwohl, Ronen & Reingold, Omer, 2010. "Partial exposure in large games," Games and Economic Behavior, Elsevier, vol. 68(2), pages 602-613, March.
    10. Azrieli, Yaron, 2010. "Categorization and correlation in a random-matching game," Journal of Mathematical Economics, Elsevier, vol. 46(3), pages 303-310, May.
    11. Daskalova, Vessela & Vriend, Nicolaas J., 2021. "Learning frames," Journal of Economic Behavior & Organization, Elsevier, vol. 191(C), pages 78-96.
    12. Daskalova, Vessela & Vriend, Nicolaas J., 2020. "Categorization and coordination," European Economic Review, Elsevier, vol. 129(C).
    13. Philippe Jehiel & Erik Mohlin, 2023. "Categorization in Games: A Bias-Variance Perspective," Working Papers halshs-04154272, HAL.
    14. Yasar, Alperen, 2023. "Power struggles and gender discrimination in the workplace," SocArXiv t4g83, Center for Open Science.

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