Private Provision of a Discrete Public Good : Continuous-Strategy Equilibria in the Private-Information Subscription Game

We reconsider Laussel and Palfrey's (2003) analysis of private provision of a discrete public good via the subscription game. We show that the equilibria they define as semi-regular do not exist. Taking players' values for the public good as uniformly distributed on [vl, vh] with vl > 0, we exhibit a previously unrecognized class of continuous equilibria - those in which contribution strategies are strictly increasing up to their maximum values, not necessarily equal to the full cost of provision, at which point they may have a flat spot. Laussel and Palfrey claimed that if players' values are uniformly distributed on [0, 1] and the cost of the good is sufficiently small, then there exist interim incentive efficient semi-regular equilibria. Our showing that semi-regular equilibria do not exist casts doubt on this efficiency result. Indeed, we show that if players' values are uniformly distributed on [0, 1] and the cost of the good is less than 1, then all symmetric equilibria of the subscription game are interim incentive inefficient