SPA-Seminar: A controller-stopper game with hidden controller type

Abstract: We consider a game between a controller (Player 1) and a stopper (Player 2), where the stopper is uncertain if the controller is active. In this game both players seek to maximize their payoff, which is based on a drift of a stochastic process. The controller (if he is active) can choose a control taking two different values to control the drift of the process, while the stopper can choose a stopping time, where the game ends.

This non-zero sum game combines elements of filtering theory, optimal control/stopping and game theory to find a Nash equilibrium. This Nash equilibrium is based on the conditional probability of the controller being active and is of double threshold type.

This is a seminar in our seminar series on Stochastic Pocesses and Applications (SPA).