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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易碎的多CPR游戏

易碎的CPR游戏是资源共享游戏的一个实例，在该资源共享游戏中，多个玩家共享一个公共池资源，该资源由于过度使用而容易发生故障。每个参与者都有固定的初始end赋，并且面临着在不迫使其失败的情况下投资于公共池资源的任务。公用池资源的收益存在不确定性，并且参与者会以前景理论的方式来感知收益。在[A.〜R.〜Hota，S.〜Garg，S.〜Sundaram，\ textit {在前景理论风险态度下的公地脆弱性}，博弈与经济行为\ textbf {98}（2016）中显示135--164。]，在一些温和的假设下，脆弱的CPR游戏承认唯一的纳什均衡。在本文中，我们研究了易碎CPR游戏的扩展版本，其中允许玩家共享多个公共池资源，这些资源也可能因过度使用而失败。我们将此游戏称为易碎的多CPR游戏。我们的主要结果表明，在一些温和的假设下，脆弱的多CPR博弈承认广义Nash均衡。此外，我们证明，当玩家数量超过公共池资源时，由脆弱多CPR游戏的所有广义Nash均衡组成的集合的Lebesgue度量为零。