Finite Horizon Game for Voluntary Provision of a Discrete Public Good

This paper analyzes a dynamic game for the provision of a discrete public good that will be provided only when a certain number of contributions are made. In each period players are randomly ordered and each player decides whether to contribute or not to the provision of the public good. If not enough contributions are made to provide the public good, the game goes to the next period and continue until the public good is either provided or the game ends at the final period. The paper first assumes symmetric players and shows that the exact period in which the public good will be provided is determined under subgame-perfect equilibria and that for some cost structures there will be a delay in provision of the public good. Counterintuitively, in some cases the public good is provided earlier at higher costs than at lower costs. The paper then introduces a partial public good, which requires fewer contributions to be provided but has a smaller value. We show that for some costs, introducing the partial public good eliminates the possibility of providing any kind of public good. For other cost structures, introducing the partial public good may improve social welfare. At last, asymmetric costs are introduced. The results are similar to the symmetric case.