The de Finetti problem with unknown competition
Abstract
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.
Keywords
Cite
@article{arxiv.2204.07016,
title = {The de Finetti problem with unknown competition},
author = {Erik Ekström and Alessandro Milazzo and Marcus Olofsson},
journal= {arXiv preprint arXiv:2204.07016},
year = {2022}
}