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Some First Results for Noncooperative Pregames : Social Conformity and Equilibrium in Pure Strategies

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  • Wooders, M.
  • Selten, R.
  • Cartwright, E.

Abstract

We introduce the framework of noncooperative pregames and demonstrate that for all games with sufficiently many players, there exists approximate (E) Nash equilibria in pure strategies. Moreover, an equilibrium can be selected with the property that most players choose the same strategies as all other players with similar attributes. More precisely, there is an integer K, depending on E but not on the number of players so that any sufficiently large society can be partitioned into fewer than K groups, or cultures, consisting of similar players, and all players in the same group play the same pure strategy. In ongoing research we are extending the model to cover a broader class of situations, including incomplete information.

Suggested Citation

  • 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.
    • Handle: RePEc:wrk:warwec:589
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    References listed on IDEAS

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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, January.
    2. 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.
    3. Kovalenkov, A. & Holtz Wooders, M., 1997. "An Explicit Bound on epsilon for Non-Emptiness of the epsilon-Core of an Arbitrary Game with Side Payments," UFAE and IAE Working Papers 393.97, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
    4. Mas-Colell, Andreu, 1984. "On a theorem of Schmeidler," Journal of Mathematical Economics, Elsevier, vol. 13(3), pages 201-206, December.
    5. Hildenbrand, Werner, 1971. "Random preferences and equilibrium analysis," Journal of Economic Theory, Elsevier, vol. 3(4), pages 414-429, December.
    6. Wooders, Myrna Holtz & Zame, William R, 1984. "Approximate Cores of Large Games," Econometrica, Econometric Society, vol. 52(6), pages 1327-1350, November.
    7. Follmer, Hans, 1974. "Random economies with many interacting agents," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 51-62, March.
    8. Ehud Kalai, 2000. "Private Information in Large Games," Discussion Papers 1312, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    9. Rui Pascoa, Mario, 1993. "Approximate equilibrium in pure strategies for non-atomic games," Journal of Mathematical Economics, Elsevier, vol. 22(3), pages 223-241.
    10. SCHMEIDLER, David, 1973. "Equilibrium points of nonatomic games," LIDAM Reprints CORE 146, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    11. Wooders, Myrna Holtz, 1983. "The epsilon core of a large replica game," Journal of Mathematical Economics, Elsevier, vol. 11(3), pages 277-300, July.
    12. Wooders, Myrna Holtz, 1994. "Equivalence of Games and Markets," Econometrica, Econometric Society, vol. 62(5), pages 1141-1160, September.
    13. Rashid, Salim, 1983. "Equilibrium points of non-atomic games : Asymptotic results," Economics Letters, Elsevier, vol. 12(1), pages 7-10.
    14. Kovalenkov, Alexander & Wooders, Myrna Holtz, 2001. "Epsilon Cores of Games with Limited Side Payments: Nonemptiness and Equal Treatment," Games and Economic Behavior, Elsevier, vol. 36(2), pages 193-218, August.
    15. HILDENBRAND, Werner, 1971. "Random preferences and equilibrium analysis," LIDAM Reprints CORE 100, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    16. R. J. Aumann & Y. Katznelson & R. Radner & R. W. Rosenthal & B. Weiss, 1983. "Approximate Purification of Mixed Strategies," Mathematics of Operations Research, INFORMS, vol. 8(3), pages 327-341, August.
    17. 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. Guilherme Carmona, 2003. "Nash and Limit Equilibria of Games with a Continuum of Players," Game Theory and Information 0311004, University Library of Munich, Germany.
    2. 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.
    3. Wooders, Myrna & Cartwright, Edward & Selten, Reinhard, 2006. "Behavioral conformity in games with many players," Games and Economic Behavior, Elsevier, vol. 57(2), pages 347-360, November.
    4. Guilherme Carmona, 2004. "Nash equilibria of games with a continuum of players," Nova SBE Working Paper Series wp466, Universidade Nova de Lisboa, Nova School of Business and Economics.

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    More about this item

    Keywords

    GAMES ; INFORMATION ; STRATEGIC PLANNING;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General

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