Private Provision of a Discrete Public Good: Efficient Equilibria in the Private-Information Contribution Game

Abstract

We study the voluntary provision of a discrete public good via the contribution game. Players independently and simultaneously make nonrefundable contributions to fund a discrete public good, which is provided if and only if the contributions are at least as great as the cost of production. We characterize nonconstant continuous symmetric equilibria and give sufficient conditions for their existence. We show the common normalization by which players' values are distributed over [0, 1] is not without loss of generality; for example, if the distribution over this interval has continuous density f with f(0) > 0, then no (nonconstant) continuous symmetric equilibrium exists. We study in detail the case in which players' private values for the good follow a uniform distribution. For this distribution we show that, generically, when one continuous equilibrium exists, a nondegenerate continuum of continuous equilibria exists. For any given cost of the good, multiple continuous equilibria cannot be Pareto ranked. Nevertheless, not all continuous equilibria are interim incentive efficient. The set of interim incentive efficient equilibria is exactly determined. When one interim incentive efficient equilibrium exists, a nondegenerate continuum of interim incentive efficient equilibria exists.

Keywords: discrete public good, contribution game, interim incentive efficiency

JEL Classification: H41, D61, D82