We introduce threshold uncertainty,à la Nitzan and Romano (1990), into a private-values model of voluntary provision of a discrete public good. Players are allowed to make any level of contribution toward funding the good, which is provided only if the cost threshold is reached. Otherwise, contributions are refunded. Conditions ensuring existence and uniqueness of a Bayesian equilibrium are established. Further restricting the threshold uncertainty to a uniform distribution, we show the equilibrium strategies are very simple, even allowing for any number of players with asymmetric distributions of values. Comparative statics with respect to changes in players' distributions are derived, allowing changes in both the intensity and the dispersion of values. Finally, we show the equilibrium is interim incentive inefficient. The sharpness of our results greatly contrasts with the more qualified insights of earlier private-values models with known cost threshold, which relied on there being two symmetric players and generally exhibited multiple equilibria.JEL Codes: H41, D61, D82

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We reconsider Laussel and Palfrey's analysis of private provision of discrete public goods via the subscription game. We show their semi-regular equilibria do not exist, casting doubt on their efficiency analysis. Taking players' values for the public good as uniformly distributed on , we exhibit previously unrecognized continuous equilibria-those with contribution strategies strictly increasing up to their maximum values, not necessarily equal to the provision cost, c, at which point they become flat. We show piecewise-linear equilibria are not incentive efficient; and if and , then all symmetric equilibria are interim incentive inefficient. Copyright � 2008 Wiley Periodicals, Inc..

Suggested contributions, membership categories, and discrete, incremental thank-you gifts are devices often used by benevolent associations that provide public goods. Such devices focus donations into discrete levels, thereby effectively limiting the donors' freedom to give. We study the effects on overall donations of the tradeoff between rigid schemes that severely restrict the choices of contribution on the one hand, and flexible membership contracts on the other, taking into account the strategic response of contributors whose values for the public good are private information. We show flexibility dominates when i) the dispersion of donors taste for the public good increases, ii) the number of potential donors increases, and iii) there is greater funding by an external authority. Using the number of default membership categories that National Public Radio stations offer as proxy for flexibility, we document the existence of empirical correlations consistent with our predictions: stations offer a larger number of suggested contribution levels as i) the incomes of the population served become more diverse, ii) the population of the coverage area increases, and iii) there is greater external support from the Corporation for Public Broadcasting.