Incomplete Information and Timing in the Volunteer's Dilemma

We analyze the supply of a public good that can be privately produced at costs smaller than the benefits. Without a coordinating mechanism, the selection of a volunteer poses a social dilemma. By varying two conditions, we obtain four scenarios. First, we distinguish whether or not players observe each other's behavior. Under the condition that behavior is observed, strategies involve timing decisions, namely how long to wait before volunteering, hoping that someone else volunteers first, but incurring costs for delayed production. If behavior cannot be observed, players effectively choose simultaneously, and rational players will either volunteer immediately or not at all. Second, we distinguish complete information with respect to the costs and benefits of the other players from incomplete information. For each of the four scenarios, we discuss a game theoretic model that assumes (ex ante) symmetrical costs and benefits. Remarkably, the probability that a player volunteers may increase with the degree of uncertainty. Moreover, in contrast with the complete information models, if uncertainty is sufficiently high, the probability that the collective good is produced may actually increase with group size. Finally, the four scenarios are ranked by the extent to which they generate favorable incentives for the production of the public good.