Participation and the Provision of Discrete Public Goods: A Strategic Analysis

This paper considers the Nash equilibria to a game where a discrete public good is to be provided. Each individual may participate by making a fixed contribution. If a sufficient number of contributions are made, the good is provided. Otherwise, the good is not provided. One variant of the rules allows for contributions to be refunded when the good is not provided, For pure strategies, we find that the Nash equilibria with a refund are a superset of those without a refund, For both rules, the efficient number of players contributing is an equilibrium, For mixed strategies, to every equilibrium without a refund, there is a corresponding equilibrium with a refund with a higher number of expected contributors. Mixed strategy equilibria "disappear" as the number of players grows large. Some results reported in the experimental literature are discussed in light of these theoretical results.