Dynamic voluntary provision of public goods with uncertainty: a stochastic differential game model. (English) Zbl 1198.91073
Summary: C. Fershtman and S. Nitzan [“Dynamic voluntary provision of public goods”, Eur. Econ. Rev. 35, 1057–1067 (1991)] presented a continuous dynamic public good game and solved the model for feedback Nash equilibria. F. Wirl [“Dynamic voluntary provision of public goods: extension to nonlinear strategies”, Eur. J. Polit. Econ. 12, 555–560 (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 set-up will in principle lead to the same type of 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 results are qualitatively different. We provide a detailed discussion as well as numerical examples. In particular, we show that in both cases uncertainty signifies the free rider effect.
MSC:
| 91B18 | Public goods |
| 91A15 | Stochastic games, stochastic differential games |
| 49L20 | Dynamic programming in optimal control and differential games |
Keywords:
stochastic differential games; public goods; Hamilton-Jacobi-Bellman equations; dynamic programmingReferences:
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