Efficient Equilibria in the Voluntary Contributions Mechanism with Private Information

We characterize generally the Bayesian Nash equilibria of a voluntary contributions public goods game for two consumers with private information.The two consumers simultaneously make voluntary contributions to the public good, and the contributions are refunded if the total falls short of the cost of the public good. Several families of equilibria (step-function, regular and semi-regular) are studied. Necessary and sufficient conditions for regular and semi-regular equilibrium allocations to be interim incentive efficient are derived. In the uniform distribution case we prove (i) the existence of an open set of incentive efficient regular equilibria when the cost of production is large enough and (ii) the existence of an open set of incentive efficient semi-regular equilibria when the cost of production is low enough. Step-function equilibra are proved to be interim incentive inefficient. Copyright 2003 Blackwell Publishing Inc..