  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 possibility to extract all the remaining resources in one
piece, may exist; we interpret this unknown competition as the agent being
subject to possible fraud. This situation is modelled as a
controller-and-stopper non-zero-sum stochastic game with incomplete
information. In order to allow the fraudster to hide his existence, we consider
strategies where his action time is randomised. Under these conditions, we
provide a Nash equilibrium which is fully described in terms of the
corresponding single-player de Finetti problem. In this equilibrium, the agent
and the fraudster 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.
