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On the space of players in idealized limit games

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  • Qiao, Lei
  • Yu, Haomiao

Abstract

This paper demonstrates the class of atomless spaces that accurately models the space of players in a large game which represents an idealized limit of a sequence of finite-player games. Through two examples, we show that arbitrary atomless probability spaces, in particular, the Lebesgue unit interval, may not be appropriate to model the space of players of an idealized limit. This inappropriateness hinges on the fact there is a convergent sequence of exact pure-strategy Nash equilibria in the sequence of finite-player games, while the idealized limit game of the sequence does not have any equilibrium. Instead, a saturated probability space is shown to be not only sufficient but also necessary, to model the space of players in any proper idealized limit. This complements the study of large games with a bio-social typology in Khan et al. [10] as such a connection between finite-limiting and idealized continuum-limit games was not able to be obtained in their framework.

Suggested Citation

  • Qiao, Lei & Yu, Haomiao, 2014. "On the space of players in idealized limit games," Journal of Economic Theory, Elsevier, vol. 153(C), pages 177-190.
    • Handle: RePEc:eee:jetheo:v:153:y:2014:i:c:p:177-190
    DOI: 10.1016/j.jet.2014.06.009
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    Cited by:

    1. 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.
    2. Wu, Bin, 2022. "On pure-strategy Nash equilibria in large games," Games and Economic Behavior, Elsevier, vol. 132(C), pages 305-315.
    3. 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.
    4. 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.
    5. Carmona, Guilherme & Podczeck, Konrad, 2020. "Pure strategy Nash equilibria of large finite-player games and their relationship to non-atomic games," Journal of Economic Theory, Elsevier, vol. 187(C).
    6. 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.
    7. Sun, Xiang & Zeng, Yishu, 2020. "Perfect and proper equilibria in large games," Games and Economic Behavior, Elsevier, vol. 119(C), pages 288-308.
    8. Fu, Haifeng & Wu, Bin, 2019. "Characterization of Nash equilibria of large games," Journal of Mathematical Economics, Elsevier, vol. 85(C), pages 46-51.
    9. He, Wei & Sun, Xiang & Sun, Yeneng, 2017. "Modeling infinitely many agents," Theoretical Economics, Econometric Society, vol. 12(2), May.
    10. 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

    Large games; Games with traits; Idealized limit; Saturated probability space; Pure-strategy Nash equilibrium; Weak closed-graph property;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D50 - Microeconomics - - General Equilibrium and Disequilibrium - - - General
    • C65 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Miscellaneous Mathematical Tools

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