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

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  • Wooders, Myrna
  • Selten, Reinhard
  • Cartwright, Edward

Abstract

We introduce the framework of noncooperative pregames and demonstrate that for all games with sufficiently many players, there exist approximate (ε) Nash equilibria in pure strategies. In fact, every mixed strategy equilibrium can be used to construct an ε-equilibrium in pure strategies — ours is an ‘ε-purification’ result. Our main result is that there exists an ε- equilibrium in pure strategies with the property that most players choose the same strategies as all other players with similar attributes. More precisely, there is an integer L, depending on ε but not on the number of players, so that any sufficiently large society can be partitioned into fewer than L 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. We would be grateful for any comments that might help us improve the paper.

Suggested Citation

  • Wooders, Myrna & Selten, Reinhard & Cartwright, Edward, 2001. "Some First Results for Noncooperative Pregames: Social Conformity and Equilibrium in Pure Strategies," Economic Research Papers 269360, University of Warwick - Department of Economics.
    • Handle: RePEc:ags:uwarer:269360
    DOI: 10.22004/ag.econ.269360
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    13. SCHMEIDLER, David, 1973. "Equilibrium points of nonatomic games," LIDAM Reprints CORE 146, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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    Cited by:

    1. 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.
    2. 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.
    3. 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.
    4. Guilherme Carmona, 2003. "Nash and Limit Equilibria of Games with a Continuum of Players," Game Theory and Information 0311004, University Library of Munich, Germany.

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    Keywords

    Agricultural and Food Policy; Research Methods/ Statistical Methods;

    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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