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Behavioral Conformity in Games with Many Players

Author

Listed:
  • Myrna Wooders

    () (Department of Economics, Vanderbilt University)

  • Edward Cartwright

    () (Department of Economics, Keynes College, University of Kent)

  • Reinhard Selten

    (Department of Economics, University of Bonn)

Abstract

In the literature of psychology and economics it is frequently observed that individuals tend to conform in their behavior to the behavior of similar individuals. A fundamental question is whether the outcome of such behavior can be consistent with self-interest. We propose that this consistency requires the existence of a Nash or approximate Nash equilibrium that induces a partition of the player set into relatively few societies, each consisting of similar individuals playing the same or similar strategies. In this paper we introduce a notion of a society and characterize a family of games admitting the existence of such an equilibrium. We also introduce the concept of 'crowding types' into our description of players and distinguish between the crowding type of a player -- those characteristics of a player that have direct effects on others -- and his tastes, taken to directly affect only that player. With the assumptions of 'within crowding type anonymity' and 'linearity of taste-types' we show that the number of groups can be uniformly bounded.

Suggested Citation

  • Myrna Wooders & Edward Cartwright & Reinhard Selten, 2005. "Behavioral Conformity in Games with Many Players," Vanderbilt University Department of Economics Working Papers 0513, Vanderbilt University Department of Economics.
  • Handle: RePEc:van:wpaper:0513
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    References listed on IDEAS

    as
    1. Grandmont, Jean-Michel, 1978. "Intermediate Preferences and the Majority Rule," Econometrica, Econometric Society, vol. 46(2), pages 317-330, March.
    2. Conley, John P. & Wooders, Myrna H., 2001. "Tiebout Economies with Differential Genetic Types and Endogenously Chosen Crowding Characteristics," Journal of Economic Theory, Elsevier, vol. 98(2), pages 261-294, June.
    3. Edward Cartwright, 2002. "Learning to play approximate Nash equilibria in games with many players," Levine's Working Paper Archive 506439000000000070, David K. Levine.
    4. 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.
    5. Mas-Colell, Andreu, 1984. "On a theorem of Schmeidler," Journal of Mathematical Economics, Elsevier, vol. 13(3), pages 201-206, December.
    6. Wooders, Myrna Holtz, 1994. "Equivalence of Games and Markets," Econometrica, Econometric Society, vol. 62(5), pages 1141-1160, September.
    7. Edward Cartwright & Myrna Wooders, 2003. "Social Conformity and Bounded Rationality in Arbitrary Games with Incomplete Information: Some First Results," Working Papers 2003.119, Fondazione Eni Enrico Mattei.
    8. Bernheim, B Douglas, 1994. "A Theory of Conformity," Journal of Political Economy, University of Chicago Press, vol. 102(5), pages 841-877, October.
    9. Ehud Kalai, 2000. "Private Information in Large Games," Discussion Papers 1312, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    10. Ehud Kalai, 2004. "Large Robust Games," Econometrica, Econometric Society, vol. 72(6), pages 1631-1665, November.
    11. Rui Pascoa, Mario, 1993. "Approximate equilibrium in pure strategies for non-atomic games," Journal of Mathematical Economics, Elsevier, vol. 22(3), pages 223-241.
    12. Wooders, M. & Selten, R. & Cartwright, E., 2001. "Some First Results for Noncooperative Pregames : Social Conformity and Equilibrium in Pure Strategies," The Warwick Economics Research Paper Series (TWERPS) 589, University of Warwick, Department of Economics.
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    Citations

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    Cited by:

    1. Edward Cartwright & Myrna Wooders, 2009. "On equilibrium in pure strategies in games with many players," International Journal of Game Theory, Springer;Game Theory Society, vol. 38(1), pages 137-153, March.
    2. Chaitanya Gokhale & Arne Traulsen, 2014. "Evolutionary Multiplayer Games," Dynamic Games and Applications, Springer, vol. 4(4), pages 468-488, December.
    3. Cartwright, Edward, 2009. "Social norms: Does it matter whether agents are rational or boundedly rational?," Journal of Behavioral and Experimental Economics (formerly The Journal of Socio-Economics), Elsevier, vol. 38(3), pages 403-410, June.
    4. Carmona, Guilherme, 2008. "Purification of Bayesian-Nash equilibria in large games with compact type and action spaces," Journal of Mathematical Economics, Elsevier, vol. 44(12), pages 1302-1311, December.
    5. Edward Cartwright & Myrna Wooders, 2014. "Correlated Equilibrium, Conformity, and Stereotyping in Social Groups," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 16(5), pages 743-766, October.
    6. Edward Cartwright, 2007. "On the Emergence of Social Norms," Studies in Economics 0704, School of Economics, University of Kent.
    7. Carmona, Guilherme & Podczeck, Konrad, 2009. "On the existence of pure-strategy equilibria in large games," Journal of Economic Theory, Elsevier, vol. 144(3), pages 1300-1319, May.
    8. Grajzl, Peter & Baniak, Andrzej, 2012. "Mandating behavioral conformity in social groups with conformist members," Journal of Economic Behavior & Organization, Elsevier, vol. 82(2), pages 479-493.
    9. Edward Cartwright & Myrna Wooders, 2008. "Behavioral Properties of Correlated Equilibrium; Social Group Structures with Conformity and Stereotyping," Vanderbilt University Department of Economics Working Papers 0814, Vanderbilt University Department of Economics.
    10. Gradwohl, Ronen & Reingold, Omer, 2010. "Partial exposure in large games," Games and Economic Behavior, Elsevier, vol. 68(2), pages 602-613, March.
    11. Daniel S. Hamermesh & Michael C Burda & Philippe Weil, 2008. "Different but Equal: Total Work, Gender and Social Norms in EU and US Time Use," Sciences Po publications info:hdl:2441/8642, Sciences Po.
    12. Guilherme Carmona, 2009. "Intermediate Preferences and Behavioral Conformity in Large Games," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 11(1), pages 9-25, February.
    13. Michael C Burda & Daniel S Hamermesh & Philippe Weil, 2008. "Total Work, Gender and Social Norms in EU and US Time Use," Post-Print hal-00972821, HAL.
    14. Azrieli, Yaron, 2009. "Categorizing others in a large game," Games and Economic Behavior, Elsevier, vol. 67(2), pages 351-362, November.

    More about this item

    Keywords

    Behavioral conformity; noncooperative games; pregames; Nash equilibrium; purification; social norms; behavioral norms;

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • Z13 - Other Special Topics - - Cultural Economics - - - Economic Sociology; Economic Anthropology; Language; Social and Economic Stratification

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