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Nash’s demand game and resource-allocation

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  • Shiran Rachmilevitch

    (University of Haifa)

Abstract

I consider Nash’s demand game (NDG) in the context of resource-allocation, rather than in the abstract utility space. If the resource is one-dimensional, the known results from the NDG literature are recovered: either the Nash solution is uniquely supported at the perturbations’ limit, or the entire (relative interior of the) Pareto frontier is supported; which case obtains depends on the type of perturbation. I show that, contrary to the prominence of the Nash solution under smoothing in the utility space, the entire frontier can be supported under a variety of economically-plausible perturbations. The case where the resource is multi-dimensional is qualitatively different.

Suggested Citation

  • Shiran Rachmilevitch, 2025. "Nash’s demand game and resource-allocation," International Journal of Game Theory, Springer;Game Theory Society, vol. 54(1), pages 1-14, June.
    • Handle: RePEc:spr:jogath:v:54:y:2025:i:1:d:10.1007_s00182-025-00941-7
    DOI: 10.1007/s00182-025-00941-7
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    References listed on IDEAS

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    6. Emin Karagözoğlu & Shiran Rachmilevitch, 2018. "Implementing egalitarianism in a class of Nash demand games," Theory and Decision, Springer, vol. 85(3), pages 495-508, October.
    7. Andersson, Ola & Argenton, Cédric & Weibull, Jörgen W., 2018. "Robustness to strategic uncertainty in the Nash demand game," Mathematical Social Sciences, Elsevier, vol. 91(C), pages 1-5.
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    Keywords

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    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory

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