Dynamic Voluntary Provision of Public Goods with Uncertainty: A Stochastic Differential Game Model

Abstract

Fershtman and Nitzan (1991) presented a continuous dynamic public good game model and solved the model for feedback Nash-equilibria. Wirl (1996) extended the model and considered nonlinear strategies. Both models do not include uncertainty and hence neglect an important factor in the theory of public goods. We extend the framework of Nitzan and Fershtman and include a diffusion term. We consider two cases. In the first case the volatility of the diffusion term is dependent on the current level of the public good. This setup will in principle lead to the same feedback strategies computed under certainty. In the second case the volatility is dependent on the current rate of public good provision by the agents. The result in this case is qualitatively different from the first one. We provide a detailed discussion of our results as well as numerical examples.

Keywords: Stochastic differential games, Public goods, Hamilton-Jacobi-Bellman equations

JEL Classification: C61, C73, D21, D62