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arXiv · 2102.12820

A Fragile multi-CPR Game

Christos Pelekis·Panagiotis Promponas·Juan Alvarado·Eirini-Eleni Tsiropoulou·Symeon Papavassiliou
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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 is shown in [A.~R.~Hota, S.~Garg, S.~Sundaram, \textit{Fragility of the commons under prospect-theoretic risk attitudes}, Games and Economic Behavior \textbf{98} (2016) 135--164.] 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.

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Christos Pelekis, Panagiotis Promponas, Juan Alvarado, Eirini-Eleni Tsiropoulou, Symeon Papavassiliou. 2021-02-25. A Fragile multi-CPR Game. https://arxiv.org/abs/2102.12820

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