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Asymptotic interpretations for equilibria of nonatomic games

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  • Yang, Jian

Abstract

We show that a mixed equilibrium of a semi-anonymous nonatomic game can be used to generate pure-strategy profiles for finite games randomly generated from the type distribution of the nonatomic game. As the numbers of players involved in the finite games increase, the generated profiles will be asymptotically equilibrium. The converse of this result is also true, i.e., a mixed-strategy profile that is not an equilibrium for the nonatomic game will not be able to achieve the above asymptotic rationality for large finite games. The combined finding can be specialized to situations where the nonatomic game is anonymous and where the given equilibrium is pure. Besides their practical values, these results offer yet one more justification for the study of nonatomic games. They also suggest that efforts may be better spent on searching for mixed rather than pure equilibria of nonatomic games.

Suggested Citation

  • Yang, Jian, 2011. "Asymptotic interpretations for equilibria of nonatomic games," Journal of Mathematical Economics, Elsevier, vol. 47(4-5), pages 491-499.
  • Handle: RePEc:eee:mateco:v:47:y:2011:i:4:p:491-499
    DOI: 10.1016/j.jmateco.2011.06.009
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    References listed on IDEAS

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    8. Guilherme Carmona, 2003. "Nash and Limit Equilibria of Games with a Continuum of Players," Game Theory and Information 0311004, University Library of Munich, Germany.
    9. Balder, Erik J., 2002. "A Unifying Pair of Cournot-Nash Equilibrium Existence Results," Journal of Economic Theory, Elsevier, vol. 102(2), pages 437-470, February.
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    Cited by:

    1. repec:eee:proeco:v:191:y:2017:i:c:p:178-193 is not listed on IDEAS
    2. repec:spr:jogath:v:46:y:2017:i:2:d:10.1007_s00182-016-0539-5 is not listed on IDEAS
    3. Jian Yang, 2015. "A Link between Sequential Semi-anonymous Nonatomic Games and their Large Finite Counterparts," Papers 1510.06809, arXiv.org, revised Jun 2016.
    4. Jian Yang, 2015. "Analysis of Markovian Competitive Situations using Nonatomic Games," Papers 1510.06813, arXiv.org, revised Apr 2017.

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