We analyze a zero-sum stochastic differential game between two competing players who can choose unbounded controls. The payoffs of the game are defined through backward stochastic differential equations. We prove that each player's priority value satisfies a weak dynamic programming principle...

We analyze a robust version of the Dynkin game over a set P of mutually singular probabilities. We first prove that conservative player's lower and upper value coincide (Let us denote the value by $V$). Such a result connects the robust Dynkin game with second-order doubly reflected backward...

We study a doubly reflected backward stochastic differential equation (BSDE) with integrable parameters and the related Dynkin game. When the lower obstacle $L$ and the upper obstacle $U$ of the equation are completely separated, we construct a unique solution of the doubly reflected BSDE by...

We discuss a natural game of competition and solve the corresponding mean field game with common noise when agents' rewards are rank-dependent. We use this solution to provide an approximate Nash equilibrium for the finite player game and obtain the rate of convergence

We consider a zero-sum optimal stopping game in which the value of the reward is revealed when the second player stops, instead of it being revealed after the first player's stopping time. Such problems appear in the context of financial mathematics when one sells and buys two different American...

We consider a zero-sum stochastic differential controller-and-stopper game in which the state process is a controlled diffusion evolving in a multidimensional Euclidean space. In this game, the controller affects both the drift and diffusion terms of the state process, and the diffusion term can...