  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.
