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Asymptotic interpretations for equilibria of nonatomic games

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  • Yang, Jian
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    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.

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    Bibliographic Info

    Article provided by Elsevier in its journal Journal of Mathematical Economics.

    Volume (Year): 47 (2011)
    Issue (Month): 4-5 ()
    Pages: 491-499

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    Handle: RePEc:eee:mateco:v:47:y:2011:i:4:p:491-499

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    Web page: http://www.elsevier.com/locate/jmateco

    Related research

    Keywords: Nonatomic games; Law of large numbers; Empirical distribution;

    References

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    1. Khan, M. Ali & Yeneng, Sun, 1995. "Pure strategies in games with private information," Journal of Mathematical Economics, Elsevier, vol. 24(7), pages 633-653.
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    5. Guilherme Carmona, 2003. "Nash and Limit Equilibria of Games with a Continuum of Players," Game Theory and Information 0311004, EconWPA.
    6. Green, Edward J, 1984. "Continuum and Finite-Player Noncooperative Models of Competition," Econometrica, Econometric Society, vol. 52(4), pages 975-93, July.
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    8. Rashid, Salim, 1983. "Equilibrium points of non-atomic games : Asymptotic results," Economics Letters, Elsevier, vol. 12(1), pages 7-10.
    9. Ehud Kalai, 2002. "Large Robust Games," Discussion Papers 1350, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
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