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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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    6. 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.
    7. Wu, Bin, 2022. "On pure-strategy Nash equilibria in large games," Games and Economic Behavior, Elsevier, vol. 132(C), pages 305-315.
    8. He, Wei & Sun, Yeneng, 2022. "Conditional expectation of Banach valued correspondences and economic applications," Journal of Mathematical Economics, Elsevier, vol. 101(C).
    9. 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.
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    11. Staab, Manuel, 2019. "The Formation of Social Groups under Status Concern," MPRA Paper 97114, University Library of Munich, Germany.
    12. Garnier, J. & Cotto, O. & Bouin, E. & Bourgeron, T. & Lepoutre, T. & Ronce, O. & Calvez, V., 2023. "Adaptation of a quantitative trait to a changing environment: New analytical insights on the asexual and infinitesimal sexual models," Theoretical Population Biology, Elsevier, vol. 152(C), pages 1-22.
    13. 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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    15. 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.
    16. Fang, Chuyi & Wu, Bin, 2019. "Socially-maximal Nash equilibrium distributions in large distributional games," Economics Letters, Elsevier, vol. 175(C), pages 40-42.
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    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.
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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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