Optimal Provision of a Discrete Public Good: Linear Equilibria in the Private-Information Subscription Game

Abstract

We analyze a symmetric Bayesian game in which two players individually contribute to fund a discrete public good; contributions are refunded if they do not meet a threshold set by the seller of the good. We provide a general characterization of symmetric equilibrium strategies that are continuous and nonconstant over the set of values for which the good has a positive chance of provision. Piecewise-linear strategies are our special focus. We characterize the distributions of players' private values that can support a continuous piecewise-linear symmetric equilibrium, and we calculate such equilibria for these distributions. Allowing the seller to charge a nonrefundable entry fee before players make their private contributions, we show these piecewise-linear equilibria can maximize the seller's expected utility, which may include an altruistic component, over all incentive compatible selling mechanisms. Complementing the possible optimality of the subscription game, we show that the mechanism in which players' contributions are not refunded is generically suboptimal.

Keywords: discrete public good, subscription game, Revelation Principle

JEL Classification: H41, D61, D82