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The existence of a pure-strategy Nash equilibrium in a discrete ponds dilemma

Author

Listed:
  • Gusev, Vasily
  • Nesterov, Alexander
  • Reshetov, Mikhail
  • Suzdaltsev, Alex

Abstract

In a variety of economic situations discrete agents choose one resource among several available resources and, once admitted to the resource of choice, divide it among fellow agents admitted there. The amount of the resource an agent gets is proportional to her relative ability to acquire this particular resource, what we refer to as an agent's weight at the resource. The relevant applications include students self-selecting into colleges, politicians self-selecting into races, and athletes self-selecting into teams. We find that this game has a pure-strategy Nash equilibrium in at least three special cases: 1) when agents have the same weight at each resource, 2) when all resources are the same, 3) when there are only two resources. We also show that this game always has an approximate Nash equilibrium when the number of players is large. Existence in the general case remains an open problem.

Suggested Citation

  • Gusev, Vasily & Nesterov, Alexander & Reshetov, Mikhail & Suzdaltsev, Alex, 2024. "The existence of a pure-strategy Nash equilibrium in a discrete ponds dilemma," Games and Economic Behavior, Elsevier, vol. 147(C), pages 38-51.
    • Handle: RePEc:eee:gamebe:v:147:y:2024:i:c:p:38-51
    DOI: 10.1016/j.geb.2024.06.001
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    References listed on IDEAS

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    1. Bando, Keisuke, 2012. "Many-to-one matching markets with externalities among firms," Journal of Mathematical Economics, Elsevier, vol. 48(1), pages 14-20.
    2. Harks, Tobias & Klimm, Max, 2015. "Equilibria in a class of aggregative location games," Journal of Mathematical Economics, Elsevier, vol. 61(C), pages 211-220.
    3. Konrad, Kai A. & Kovenock, Dan, 2012. "The lifeboat problem," European Economic Review, Elsevier, vol. 56(3), pages 552-559.
    4. Marek Pycia & M Bumin Yenmez, 2023. "Matching with Externalities," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 90(2), pages 948-974.
    5. Ettore Damiano & Hao Li & Wing Suen, 2010. "First In Village Or Second In Rome?," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 51(1), pages 263-288, February.
    6. Sasaki, Hiroo & Toda, Manabu, 1996. "Two-Sided Matching Problems with Externalities," Journal of Economic Theory, Elsevier, vol. 70(1), pages 93-108, July.
    7. Ghazala Azmat & Marc Möller, 2009. "Competition among contests," RAND Journal of Economics, RAND Corporation, vol. 40(4), pages 743-768, December.
    8. Mumcu, Ayse & Saglam, Ismail, 2010. "Stable one-to-one matchings with externalities," Mathematical Social Sciences, Elsevier, vol. 60(2), pages 154-159, September.
    9. Milchtaich, Igal, 1996. "Congestion Games with Player-Specific Payoff Functions," Games and Economic Behavior, Elsevier, vol. 13(1), pages 111-124, March.
    10. John P. Conley & Ali Sina Onder, 2014. "The Research Productivity of New PhDs in Economics: The Surprisingly High Non-success of the Successful," Journal of Economic Perspectives, American Economic Association, vol. 28(3), pages 205-216, Summer.
    11. Milchtaich, Igal, 2009. "Weighted congestion games with separable preferences," Games and Economic Behavior, Elsevier, vol. 67(2), pages 750-757, November.
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    More about this item

    Keywords

    Congestion games; Potential games; Pure Nash equilibrium; Sorting into contests; College admissions;
    All these keywords.

    JEL classification:

    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • D47 - Microeconomics - - Market Structure, Pricing, and Design - - - Market Design
    • D78 - Microeconomics - - Analysis of Collective Decision-Making - - - Positive Analysis of Policy Formulation and Implementation
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design

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