Before revision:  We characterize the optimal investment policies by a set of necessary and sufficient stochastic Kuhn-Tucker conditions , which in turn allow to identify a universal signal process that triggers the public good investments. Further we show that our model exhibits a dynamic free rider effect. We explicitly evaluate it in a symmetric Black-Scholes setting with Cobb-Douglas utilities and we show that uncertainty and irreversibility of public good provisions need not affect the degree of free-riding .
After revision:  We characterize the optimal investment policies by a set of necessary and sufficient stochastic Kuhn-Tucker conditions , which in turn allow to identify a universal signal process that triggers the public good contribution game. In the symmetric case they allow us to prove (qualitative) uniqueness of the Nash equilibrium, which we again construct as the unique optional solution of a stochastic backward equation, although the latter is not related to a meaningful control problem. We finally also provide a detailed analysis of the so-called free rider effect .