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Modeling infinitely many agents

Author

Listed:
  • He, Wei

    (Department of Economics, Chinese University of Hong Kong)

  • Sun, Xiang

    (Economics and Management School, Wuhan University)

  • Sun, Yeneng

    (Department of Economics, National University of Singapore)

Abstract

This paper offers a resolution to an extensively studied question in theoretical economics: which measure spaces are suitable for modeling many economic agents? We propose the condition of ``nowhere equivalence'' to characterize those measure spaces that can be effectively used to model the space of many agents. In particular, this condition is shown to be more general than various approaches that have been proposed to handle the shortcoming of the Lebesgue unit interval as an agent space. We illustrate the minimality of the nowhere equivalence condition by showing its necessity in deriving the determinateness property, the existence of equilibria, and the closed graph property for equilibrium correspondences in general equilibrium theory and game theory.

Suggested Citation

  • He, Wei & Sun, Xiang & Sun, Yeneng, 2017. "Modeling infinitely many agents," Theoretical Economics, Econometric Society, vol. 12(2), May.
    • Handle: RePEc:the:publsh:1647
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    Cited by:

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    4. Chen, Enxian & Qiao, Lei & Sun, Xiang & Sun, Yeneng, 2022. "Robust perfect equilibrium in large games," Journal of Economic Theory, Elsevier, vol. 201(C).
    5. Guilherme Carmona & Konrad Podczeck, 2022. "Approximation and characterization of Nash equilibria of large games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 73(2), pages 679-694, April.
    6. Wei He & Yeneng Sun, 2018. "Conditional expectation of correspondences and economic applications," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 66(2), pages 265-299, August.
    7. Balbus, Lukasz & Dziewulski, Pawel & Reffett, Kevin & Wozny, Lukasz, 2022. "Markov distributional equilibrium dynamics in games with complementarities and no aggregate risk," Theoretical Economics, Econometric Society, vol. 17(2), May.
    8. Wu, Bin, 2022. "On pure-strategy Nash equilibria in large games," Games and Economic Behavior, Elsevier, vol. 132(C), pages 305-315.
    9. He, Wei & Sun, Yeneng, 2022. "Conditional expectation of Banach valued correspondences and economic applications," Journal of Mathematical Economics, Elsevier, vol. 101(C).
    10. Qiao, Lei & Yu, Haomiao & Zhang, Zhixiang, 2016. "On the closed-graph property of the Nash equilibrium correspondence in a large game: A complete characterization," Games and Economic Behavior, Elsevier, vol. 99(C), pages 89-98.
    11. Wu, Bin & Xu, Hanping, 2022. "Pareto-undominated and socially-maximal Nash equilibria with coarser traits," Economics Letters, Elsevier, vol. 215(C).
    12. He, Wei & Sun, Yeneng, 2019. "Pure-strategy equilibria in Bayesian games," Journal of Economic Theory, Elsevier, vol. 180(C), pages 11-49.
    13. Khan, M. Ali & Zhang, Yongchao, 2018. "On pure-strategy equilibria in games with correlated information," Games and Economic Behavior, Elsevier, vol. 111(C), pages 289-304.
    14. Fu, Haifeng & Yu, Haomiao, 2018. "Pareto refinements of pure-strategy equilibria in games with public and private information," Journal of Mathematical Economics, Elsevier, vol. 79(C), pages 18-26.
    15. Fang, Chuyi & Wu, Bin, 2019. "Socially-maximal Nash equilibrium distributions in large distributional games," Economics Letters, Elsevier, vol. 175(C), pages 40-42.
    16. Sebastián Cea-Echenique & Matías Fuentes, 2020. "On the continuity of the walras correspondence for distributional economies with an infinite dimensional commodity space," Working Papers hal-02430960, HAL.
    17. Staab, Manuel, 2019. "The Formation of Social Groups under Status Concern," MPRA Paper 97114, University Library of Munich, Germany.
    18. Sun, Xiang & Zeng, Yishu, 2020. "Perfect and proper equilibria in large games," Games and Economic Behavior, Elsevier, vol. 119(C), pages 288-308.
    19. Fu, Haifeng & Wu, Bin, 2019. "Characterization of Nash equilibria of large games," Journal of Mathematical Economics, Elsevier, vol. 85(C), pages 46-51.
    20. Sun, Xiang & Sun, Yeneng & Yu, Haomiao, 2020. "The individualistic foundation of equilibrium distribution," Journal of Economic Theory, Elsevier, vol. 189(C).

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    More about this item

    Keywords

    Agent space; nowhere equivalence; Nash equilibrium; Walrasian equilibrium; determinateness property; closed graph property; relative saturation; atomless independent supplement; conditional atomlessness;
    All these keywords.

    JEL classification:

    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • D0 - Microeconomics - - General
    • D5 - Microeconomics - - General Equilibrium and Disequilibrium

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