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Existence of Nash equilibria in large games

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  • Noguchi, Mitsunori

Abstract

Podczeck [Podczeck, K., 1997. Markets with infinitely many commodities and a continuum of agents with non-convex preferences. Economic Theory 9, 385-426] provided a mathematical formulation of the notion of "many economic agents of almost every type" and utilized this formulation as a sufficient condition for the existence of Walras equilibria in an exchange economy with a continuum of agents and an infinite dimensional commodity space. The primary objective of this article is to demonstrate that a variant of Podczeck's condition provides a sufficient condition for the existence of pure-strategy Nash equilibria in a large non-anonymous game G when defined on an atomless probability space not necessary rich, and equipped with a common uncountable compact metric space of actions A. We also investigate to see whether the condition can be applied as well to the broader context of Bayesian equilibria and prove an analogue of Yannelis's results [Yannelis, N.C., in press. Debreu's social equilibrium theorem with asymmetric information and a continuum of agents. Economic Theory] on Debreu's social equilibrium theorem with asymmetric information and a continuum of agents.

Suggested Citation

  • Noguchi, Mitsunori, 2009. "Existence of Nash equilibria in large games," Journal of Mathematical Economics, Elsevier, vol. 45(1-2), pages 168-184, January.
  • Handle: RePEc:eee:mateco:v:45:y:2009:i:1-2:p:168-184
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    References listed on IDEAS

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    1. Konard Podczeck, 1997. "Markets with infinitely many commodities and a continuum of agents with non-convex preferences (*)," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 9(3), pages 385-426.
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    Cited by:

    1. Khan, M. Ali & Rath, Kali P. & Yu, Haomiao & Zhang, Yongchao, 2013. "Large distributional games with traits," Economics Letters, Elsevier, vol. 118(3), pages 502-505.
    2. Haomiao Yu, 2014. "Rationalizability in large games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 55(2), pages 457-479, February.
    3. Jianwei Wang & Yongchao Zhang, 2012. "Purification, saturation and the exact law of large numbers," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 50(3), pages 527-545, August.
    4. Barelli, Paulo & Duggan, John, 2015. "Extremal choice equilibrium with applications to large games, stochastic games, & endogenous institutions," Journal of Economic Theory, Elsevier, vol. 155(C), pages 95-130.
    5. Xiang Sun & Yongchao Zhang, 2015. "Pure-strategy Nash equilibria in nonatomic games with infinite-dimensional action spaces," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 58(1), pages 161-182, January.
    6. Noguchi, Mitsunori, 2010. "Large but finite games with asymmetric information," Journal of Mathematical Economics, Elsevier, vol. 46(2), pages 191-213, March.
    7. Khan, Mohammed Ali & Rath, Kali P. & Yu, Haomiao & Zhang, Yongchao, 2017. "On the equivalence of large individualized and distributionalized games," Theoretical Economics, Econometric Society, vol. 12(2), May.
    8. He, Wei & Sun, Xiang & Sun, Yeneng, 2017. "Modeling infinitely many agents," Theoretical Economics, Econometric Society, vol. 12(2), May.
    9. Takashi Suzuki, 2016. "A coalitional production economy with infinitely many indivisible commodities," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 4(1), pages 35-52, April.

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