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A fragile multi-CPR game

Author

Listed:
  • Christos Pelekis

    (National Technical University of Athens)

  • Panagiotis Promponas

    (National Technical University of Athens)

  • Juan Alvarado

    (KU Leuven)

  • Eirini Eleni Tsiropoulou

    (University of New Mexico)

  • Symeon Papavassiliou

    (National Technical University of Athens)

Abstract

A Fragile CPR Game is an instance of a resource sharing game where a common-pool resource, which is prone to failure due to overuse, is shared among several players. Each player has a fixed initial endowment and is faced with the task of investing in the common-pool resource without forcing it to fail. The return from the common-pool resource is subject to uncertainty and is perceived by the players in a prospect-theoretic manner. It has already been shown in the existing literature that, under some mild assumptions, a Fragile CPR Game admits a unique Nash equilibrium. In this article we investigate an extended version of a Fragile CPR Game, in which players are allowed to share multiple common-pool resources that are also prone to failure due to overuse. We refer to this game as a Fragile multi-CPR Game. Our main result states that, under some mild assumptions, a Fragile multi-CPR Game admits a Generalized Nash equilibrium. Moreover, we show that, when there are more players than common-pool resources, the set consisting of all Generalized Nash equilibria of a Fragile multi-CPR Game is of Lebesgue measure zero.

Suggested Citation

  • Christos Pelekis & Panagiotis Promponas & Juan Alvarado & Eirini Eleni Tsiropoulou & Symeon Papavassiliou, 2021. "A fragile multi-CPR game," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 94(3), pages 461-492, December.
    • Handle: RePEc:spr:mathme:v:94:y:2021:i:3:d:10.1007_s00186-021-00766-6
    DOI: 10.1007/s00186-021-00766-6
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    References listed on IDEAS

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