Equilibrium solutions for resource dilemmas

Considered in this article is a class of resource dilemma games designed to study interactive decision behavior in the face of both strategic and environmental uncertainty. Groups of n members are asked to share a common resource pool whose exact size, x, is not known. Rather, x is sampled randomly from a uniform probability distribution which is common knowledge. Each group member j(j=1,...,n) requests r _j units from the random resource pool. Individual decisions are made independently and anonymously. Preplay communication is prohibited. If (r ₁+r ₂+...+r _n ) x, each member j is granted his/her request; otherwise, group members get nothing. We derive the Nash equilibrium solution for this resource dilemma game, and compare it to an expected utility model originally proposed by Suleiman and Rapoport (1988). We then show that the equilibrium solution accounts for the major qualitative features of experimental results reported in two previous studies.