THE DE FINETTI PROBLEM WITH UNCERTAIN COMPETITION

We consider a resource extraction problem which extends the classical de Finetti problem for a Wiener process to include the case when a competitor, who is equipped with the ability to extract all the remaining resources in one piece, may exist. This situation is modeled as a nonzero-sum controller-and-stopper game with incomplete information. For this stochastic game we provide a Nash equilibrium with an explicit structure. In equilibrium, the agent and the competitor use singular strategies in such a way that a two-dimensional process, which represents available resources and the filtering estimate of active competition, reflects in a specific direction along a given boundary.