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Thinking categorically about others: A conjectural equilibrium approach

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  • Azrieli, Yaron

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.

Suggested Citation

  • Azrieli, Yaron, 2007. "Thinking categorically about others: A conjectural equilibrium approach," MPRA Paper 3843, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:3843
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    File URL: https://mpra.ub.uni-muenchen.de/4742/1/MPRA_paper_4742.pdf
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    References listed on IDEAS

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    1. Rubinstein Ariel & Wolinsky Asher, 1994. "Rationalizable Conjectural Equilibrium: Between Nash and Rationalizability," Games and Economic Behavior, Elsevier, vol. 6(2), pages 299-311, March.
    2. Dekel, Eddie & Fudenberg, Drew & Levine, David K., 1999. "Payoff Information and Self-Confirming Equilibrium," Journal of Economic Theory, Elsevier, vol. 89(2), pages 165-185, December.
    3. Kalai, Ehud & Lehrer, Ehud, 1993. "Rational Learning Leads to Nash Equilibrium," Econometrica, Econometric Society, vol. 61(5), pages 1019-1045, September.
    4. Pearce, David G, 1984. "Rationalizable Strategic Behavior and the Problem of Perfection," Econometrica, Econometric Society, vol. 52(4), pages 1029-1050, July.
    5. Jehiel, Philippe, 2005. "Analogy-based expectation equilibrium," Journal of Economic Theory, Elsevier, vol. 123(2), pages 81-104, August.
    6. Ehud Kalai, 2005. "Partially-Specified Large Games," Levine's Bibliography 784828000000000565, UCLA Department of Economics.
    7. Bernheim, B Douglas, 1984. "Rationalizable Strategic Behavior," Econometrica, Econometric Society, vol. 52(4), pages 1007-1028, July.
    8. Khan, M. Ali & Sun, Yeneng, 2002. "Non-cooperative games with many players," Handbook of Game Theory with Economic Applications,in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 3, chapter 46, pages 1761-1808 Elsevier.
    9. Fudenberg, Drew & Levine, David K, 1993. "Self-Confirming Equilibrium," Econometrica, Econometric Society, vol. 61(3), pages 523-545, May.
    10. Ehud Kalai, 2004. "Large Robust Games," Econometrica, Econometric Society, vol. 72(6), pages 1631-1665, November.
    11. Kalai, Ehud & Lehrer, Ehud, 1993. "Subjective Equilibrium in Repeated Games," Econometrica, Econometric Society, vol. 61(5), pages 1231-1240, September.
    12. Rath, Kali P, 1992. "A Direct Proof of the Existence of Pure Strategy Equilibria in Games with a Continuum of Players," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 2(3), pages 427-433, July.
    13. Spiegler, Ran, 2004. "Simplicity of beliefs and delay tactics in a concession game," Games and Economic Behavior, Elsevier, vol. 47(1), pages 200-220, April.
    14. Eliaz, Kfir, 2003. "Nash equilibrium when players account for the complexity of their forecasts," Games and Economic Behavior, Elsevier, vol. 44(2), pages 286-310, August.
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    Cited by:

    1. Azrieli, Yaron, 2010. "Categorization and correlation in a random-matching game," Journal of Mathematical Economics, Elsevier, vol. 46(3), pages 303-310, May.

    More about this item

    Keywords

    Categorization; Conjectural equilibrium; Large games;

    JEL classification:

    • D84 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Expectations; Speculations
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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