A fragile multi-CPR game

• Published in: Mathematical methods of operations research (Heidelberg, Germany) Germany), 2021-12, Vol.94 (3), p.461-492
• Main Authors: Pelekis, Christos, Promponas, Panagiotis, Alvarado, Juan, Tsiropoulou, Eirini Eleni, Papavassiliou, Symeon
• Format: Article
• Language: English
• Subjects: Business and Management; Calculus of Variations and Optimal Control; Optimization; Computer engineering; Equilibrium; Game theory; Games; Mathematics; Mathematics and Statistics; Operations research; Operations Research/Decision Theory; Original Article; Players; Spectrum allocation; Wireless networks
• ISSN: 1432-2994; 1432-5217
• DOI: 10.1007/s00186-021-00766-6

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.