Before revision:  We study the corresponding social planner problem and the case of strategic interaction between the agents and we characterize the optimal investment policies by a set of necessary and sufficient stochastic Kuhn-Tucker conditions . Suitably combining arguments from Duality Theory and the General Theory of Stochastic Processes, we prove an abstract existence result for a Nash equilibrium of our public good contribution game. Also, we show that our model exhibits a dynamic free rider effect.
After revision:  We study the corresponding social planner problem and the case of strategic interaction between the agents and 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.