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Socially-maximal Nash equilibrium distributions in large distributional games

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  • Fang, Chuyi
  • Wu, Bin

Abstract

We formulate the notion of a socially-maximal Nash equilibrium distribution in a large distributionalized game with traits, and show that a socially-maximal Nash equilibrium distribution exists. We also show that no-where equivalence condition is not only sufficient but also necessary to the existence of a socially-maximal Nash equilibrium in a class of large individualized games with traits.

Suggested Citation

  • Fang, Chuyi & Wu, Bin, 2019. "Socially-maximal Nash equilibrium distributions in large distributional games," Economics Letters, Elsevier, vol. 175(C), pages 40-42.
    • Handle: RePEc:eee:ecolet:v:175:y:2019:i:c:p:40-42
    DOI: 10.1016/j.econlet.2018.12.007
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    References listed on IDEAS

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    1. R.J. Aumann & S. Hart (ed.), 2002. "Handbook of Game Theory with Economic Applications," Handbook of Game Theory with Economic Applications, Elsevier, edition 1, volume 3, number 3.
    2. Noguchi, Mitsunori, 2009. "Existence of Nash equilibria in large games," Journal of Mathematical Economics, Elsevier, vol. 45(1-2), pages 168-184, January.
    3. Khan, M. Ali & Rath, Kali P. & Sun, Yeneng & Yu, Haomiao, 2013. "Large games with a bio-social typology," Journal of Economic Theory, Elsevier, vol. 148(3), pages 1122-1149.
    4. Rath, Kali P. & Yeneng Sun & Shinji Yamashige, 1995. "The nonexistence of symmetric equilibria in anonymous games with compact action spaces," Journal of Mathematical Economics, Elsevier, vol. 24(4), pages 331-346.
    5. 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.
    6. Khan, M. Ali & Sun, Yeneng, 2002. "Non-cooperative games with many players," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 3, chapter 46, pages 1761-1808, Elsevier.
    7. Mas-Colell, Andreu, 1984. "On a theorem of Schmeidler," Journal of Mathematical Economics, Elsevier, vol. 13(3), pages 201-206, December.
    8. He, Wei & Sun, Xiang & Sun, Yeneng, 2017. "Modeling infinitely many agents," Theoretical Economics, Econometric Society, vol. 12(2), May.
    9. Fu, Haifeng & Yu, Haomiao, 2015. "Pareto-undominated and socially-maximal equilibria in non-atomic games," Journal of Mathematical Economics, Elsevier, vol. 58(C), pages 7-15.
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    Cited by:

    1. Wu, Bin & Xu, Hanping, 2022. "Pareto-undominated and socially-maximal Nash equilibria with coarser traits," Economics Letters, Elsevier, vol. 215(C).

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    More about this item

    Keywords

    Large distributionalized games; Nash equilibrium distribution; Socially-maximal Nash equilibrium distribution;
    All these keywords.

    JEL classification:

    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • D6 - Microeconomics - - Welfare Economics

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