Participation and Demand Levels for a Joint Project

We examine a voluntary participation game in public good provision in which each agent has a demand level for the public good. The agent's demand level is the minimum level of the public good from which she can receive a positive benefit. In this game, there exists a subgame perfect Nash equilibrium at which the (Pareto) efficient allocation is achieved. The voluntary participation game may also have a subgame perfect Nash equilibrium with underprovision of the public good. However, some subgame perfect Nash equilibrium with the efficient allocation satisfies strong perfection, introduced by Rubinstein (1980), and strong perfection is satisfied only by the subgame perfect Nash equilibrium with the efficient allocation. Furthermore, all payoffs at strong perfect equilibria belong to the core of the enterprise game. By these results, we conclude that in our case, the voluntary participation problem is not as serious as the earlier studies report. We also discuss the extensibility of these results