A fragile multi-CPR game

Christos Pelekis, Panagiotis Promponas, Juan Alvarado (), Eirini Eleni Tsiropoulou () and Symeon Papavassiliou ()
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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

Mathematical Methods of Operations Research, 2021, vol. 94, issue 3, No 5, 492 pages

Abstract: 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.

Keywords: CPR games; prospect theory; Generalized Nash equilibrium; 91A06; 90C25 (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s00186-021-00766-6

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