On the Robust Dynkin Game

We study a robust Dynkin game over a set of mutually singular probabilities. We first prove that for the conservative player of the game, her lower and upper value processes coincide (i.e. She has a value process $V $ in the game). Such a result helps people connect the robust Dynkin game with second-order doubly reflected backward stochastic differential equations. Also, we show that the value process $V$ is a submartingale under an appropriately defined nonlinear expectations up to the first t...