Private provision of discrete public goods

We investigate private provision of discrete public goods under refund and cost-sharing. If it is commonly believed that individuals may be warm-glow altruists and the group-size is a Poisson random variable, then the equilibrium distribution of collected contributions is uniquely determined. If composition uncertainty is very small and the expected group-size sufficiently large, the distribution of contributions can be described by concentrating in a symmetric mixed-strategy equilibrium. As the expected group-size increases, the probability a randomly selected player contributes and the associated expected number of contributions converge to the corresponding ones in the symmetric mixed-strategy equilibrium of the game with no uncertainty.