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Social Conformity And Equilibrium In Pure Strategies In Games With Many Players

Author

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  • Wooders, Myrna

    (Department of Economics, University of Warwick)

  • Edward Cartwright

    (Department of Economics, University of Warwick)

  • Selten, Reinhard

    (Department of Economics, University of Bonn)

Abstract

We introduce a framework of noncooperative pregames, in which players are characterized by their attributes, and demonstrate that for all games with sufficiently many players, there exist approximate (e) Nash equilibria in pure strategies. In fact, every mixed strategy equilibrium can be used to construct an e-equilibrium in pure strategies, an ‘e-purification’ result. Our main result is a social conformity theorem. Interpret a set of players, all with attributes in some convex subset of attribute space and all playing the same strategy, as a society. Observe that the number of societies may be as large as the number of players. Our social conformity result dictates that, given e > 0, there is an integer L, depending on e but not on the number of players, such that any sufficiently large game has an e-equilibrium in pure strategies that induces a partition of the player set into fewer than L societies.

Suggested Citation

  • Wooders, Myrna & Edward Cartwright & Selten, Reinhard, 2002. "Social Conformity And Equilibrium In Pure Strategies In Games With Many Players," The Warwick Economics Research Paper Series (TWERPS) 636, University of Warwick, Department of Economics.
  • Handle: RePEc:wrk:warwec:636
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    File URL: https://www2.warwick.ac.uk/fac/soc/economics/research/workingpapers/2008/twerp636.pdf
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    1. Aloisio Araújo & Jaime Orrillo & Mario R. Páscoa, 2000. "Equilibrium with Default and Endogenous Collateral," Mathematical Finance, Wiley Blackwell, vol. 10(1), pages 1-21.
    2. Fudenberg, Drew & Levine, David, 1998. "Learning in games," European Economic Review, Elsevier, vol. 42(3-5), pages 631-639, May.
    3. Ellison, Glenn, 1993. "Learning, Local Interaction, and Coordination," Econometrica, Econometric Society, vol. 61(5), pages 1047-1071, September.
    4. Khan, M. Ali & Rath, Kali P. & Sun, Yeneng, 1997. "On the Existence of Pure Strategy Equilibria in Games with a Continuum of Players," Journal of Economic Theory, Elsevier, vol. 76(1), pages 13-46, September.
    5. Gale, Douglas & Rosenthal, Robert W., 1999. "Experimentation, Imitation, and Stochastic Stability," Journal of Economic Theory, Elsevier, vol. 84(1), pages 1-40, January.
    6. Glenn Ellison & Drew Fudenberg, 1995. "Word-of-Mouth Communication and Social Learning," The Quarterly Journal of Economics, Oxford University Press, vol. 110(1), pages 93-125.
    7. Blume Lawrence E., 1993. "The Statistical Mechanics of Strategic Interaction," Games and Economic Behavior, Elsevier, vol. 5(3), pages 387-424, July.
    8. Wooders, Myrna & Cartwright, Edward & Selten, Reinhard, 2003. "Social Conformity in Games with Many Players," The Warwick Economics Research Paper Series (TWERPS) 682, University of Warwick, Department of Economics.
    9. Rath, Kali P. & Yeneng Sun & Shinji Yamashige, 1995. "The nonexistence of symmetric equilibria in anonymous games with compact action spaces," Journal of Mathematical Economics, Elsevier, vol. 24(4), pages 331-346.
    10. Ellison, Glenn & Fudenberg, Drew, 1993. "Rules of Thumb for Social Learning," Journal of Political Economy, University of Chicago Press, vol. 101(4), pages 612-643, August.
    11. Hildenbrand, Werner, 1971. "Random preferences and equilibrium analysis," Journal of Economic Theory, Elsevier, vol. 3(4), pages 414-429, December.
    12. Scharfstein, David S & Stein, Jeremy C, 1990. "Herd Behavior and Investment," American Economic Review, American Economic Association, vol. 80(3), pages 465-479, June.
    13. Philip J. Reny, 1999. "On the Existence of Pure and Mixed Strategy Nash Equilibria in Discontinuous Games," Econometrica, Econometric Society, vol. 67(5), pages 1029-1056, September.
    14. Khan, M. Ali & Sun, Yeneng, 1999. "Non-cooperative games on hyperfinite Loeb spaces1," Journal of Mathematical Economics, Elsevier, vol. 31(4), pages 455-492, May.
    15. Aumann, Robert J, 1985. "An Axiomatization of the Non-transferable Utility Value," Econometrica, Econometric Society, vol. 53(3), pages 599-612, May.
    16. Mark Walker & John Wooders, 2001. "Minimax Play at Wimbledon," American Economic Review, American Economic Association, vol. 91(5), pages 1521-1538, December.
    17. Follmer, Hans, 1974. "Random economies with many interacting agents," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 51-62, March.
    18. Ehud Kalai, 2000. "Private Information in Large Games," Discussion Papers 1312, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    19. Kandori, Michihiro & Mailath, George J & Rob, Rafael, 1993. "Learning, Mutation, and Long Run Equilibria in Games," Econometrica, Econometric Society, vol. 61(1), pages 29-56, January.
    20. Rui Pascoa, Mario, 1993. "Approximate equilibrium in pure strategies for non-atomic games," Journal of Mathematical Economics, Elsevier, vol. 22(3), pages 223-241.
    21. Wooders, Myrna Holtz, 1983. "The epsilon core of a large replica game," Journal of Mathematical Economics, Elsevier, vol. 11(3), pages 277-300, July.
    22. Wooders, Myrna Holtz, 1994. "Equivalence of Games and Markets," Econometrica, Econometric Society, vol. 62(5), pages 1141-1160, September.
    23. Rashid, Salim, 1983. "Equilibrium points of non-atomic games : Asymptotic results," Economics Letters, Elsevier, vol. 12(1), pages 7-10.
    24. Alan Kirman, 1993. "Ants, Rationality, and Recruitment," The Quarterly Journal of Economics, Oxford University Press, vol. 108(1), pages 137-156.
    25. Green, Edward J, 1984. "Continuum and Finite-Player Noncooperative Models of Competition," Econometrica, Econometric Society, vol. 52(4), pages 975-993, July.
    26. Pascoa Mario Rui, 1993. "Noncooperative Equilibrium and Chamberlinian Monopolistic Competition," Journal of Economic Theory, Elsevier, vol. 60(2), pages 335-353, August.
    27. Binmore, Ken & Samuelson, Larry, 2001. "Evolution and Mixed Strategies," Games and Economic Behavior, Elsevier, vol. 34(2), pages 200-226, February.
    28. Mario Rui Pascoa, 1998. "Nash equilibrium and the law of large numbers," International Journal of Game Theory, Springer;Game Theory Society, vol. 27(1), pages 83-92.
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    Cited by:

    1. Edward Cartwright, 2002. "Learning to play approximate Nash equilibria in games with many players," Levine's Working Paper Archive 506439000000000070, David K. Levine.
    2. Cartwright, Edward & Wooders, Myrna, 2005. "Correlated equilibrium and behavioural conformity," The Warwick Economics Research Paper Series (TWERPS) 732, University of Warwick, Department of Economics.
    3. 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.
    4. 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.

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