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The Population Lotto Game: how strategic resource allocation structures non-transitive outcomes in pairwise competitions

Author

Listed:
  • Giovanni Artiglio

    (University of Wisconsin-Madison)

  • Aiden Youkhana

    (Arizona State University: West Valley Campus)

  • Joel Nishimura

    (Arizona State University: West Valley Campus)

Abstract

In order to understand if and how strategic resource allocation can constrain the structure of pair-wise competition outcomes in human competitions we introduce a new multiplayer resource allocation game, the Population Lotto Game. This new game allows agents to allocate their resources across a continuum of possible specializations. While this game allows non-transitive cycles between players, we show that the Nash equilibrium of the game also forms a hierarchical structure between discrete ‘leagues’ based on their different resource budgets, with potential sub-league structure and/or non-transitive cycles inside individual leagues. We provide an algorithm that can find a particular Nash equilibrium for any finite set of discrete sub-population sizes and budgets. Further, our algorithm finds the unique Nash equilibrium that remains stable for the subset of players with budgets below any threshold.

Suggested Citation

  • Giovanni Artiglio & Aiden Youkhana & Joel Nishimura, 2024. "The Population Lotto Game: how strategic resource allocation structures non-transitive outcomes in pairwise competitions," International Journal of Game Theory, Springer;Game Theory Society, vol. 53(3), pages 913-937, September.
    • Handle: RePEc:spr:jogath:v:53:y:2024:i:3:d:10.1007_s00182-024-00891-6
    DOI: 10.1007/s00182-024-00891-6
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    References listed on IDEAS

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    1. Sergiu Hart, 2008. "Discrete Colonel Blotto and General Lotto games," International Journal of Game Theory, Springer;Game Theory Society, vol. 36(3), pages 441-460, March.
    2. Brian Roberson, 2006. "The Colonel Blotto game," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 29(1), pages 1-24, September.
    3. Enric Boix-Adser`a & Benjamin L. Edelman & Siddhartha Jayanti, 2020. "The Multiplayer Colonel Blotto Game," Papers 2002.05240, arXiv.org, revised May 2021.
    4. Nicolas Sahuguet & Nicola Persico, 2006. "Campaign spending regulation in a model of redistributive politics," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 28(1), pages 95-124, May.
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