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.
After revision:  We characterize the optimal investment policies by a set of necessary and sufficient stochastic Kuhn-Tucker conditions and we provide its expression in terms of the unique optional solution of a stochastic backward equation. Similar stochastic first order conditions prove to be very useful for studying any Nash equilibria of the public good investments.