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Thinking categorically about others: A conjectural equilibrium approach

  • Azrieli, Yaron

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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Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 3843.

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Date of creation: 14 May 2007
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Handle: RePEc:pra:mprapa:3843
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  1. Fudenberg, D. & Levine, D.K., 1991. "Self-Confirming Equilibrium ," Working papers 581, Massachusetts Institute of Technology (MIT), Department of Economics.
  2. E. Kalai & E. Lehrer, 2010. "Rational Learning Leads to Nash Equilibrium," Levine's Working Paper Archive 529, David K. Levine.
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  8. Khan, A. & Sun, Y., 2000. "Non-Cooperative Games with Many Players," Papiers d'Economie Mathématique et Applications 2000.80, Université Panthéon-Sorbonne (Paris 1).
  9. Ehud Kalai, 2004. "Large Robust Games," Econometrica, Econometric Society, vol. 72(6), pages 1631-1665, November.
  10. Pearce, David G, 1984. "Rationalizable Strategic Behavior and the Problem of Perfection," Econometrica, Econometric Society, vol. 52(4), pages 1029-50, July.
  11. Rubinstein Ariel & Wolinsky Asher, 1994. "Rationalizable Conjectural Equilibrium: Between Nash and Rationalizability," Games and Economic Behavior, Elsevier, vol. 6(2), pages 299-311, March.
  12. 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.
  13. Rath, Kali P, 1992. "A Direct Proof of the Existence of Pure Strategy Equilibria in Games with a Continuum of Players," Economic Theory, Springer, vol. 2(3), pages 427-33, July.
  14. Eliaz, K., 2001. "Nash Equilibrium When Players Account for the Complexity of their Forecasts," Papers 2001-6, Tel Aviv.
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