Discrete-time stopping games with risk-sensitive discounted cost criterion

In this paper, we focus on the discrete-time stopping games under the risk-sensitive discounted cost criterion. The state space and the action spaces of all the players are assumed to be Borel spaces. The cost functions are allowed to be unbounded from above and from below. At each decision epoch, each player chooses an action to influence the transition laws, and player 1 incurs a running cost. If players 1 or 2 decides to stop the game, player 1 incurs a corresponding terminated cost. Under suitable hypothesis, we show that the game model has a value which is a unique solution of risk-sensitive stopping optimality equation by an approximation technique. Furthermore, we derive the existence of equilibria.