The authors consider a zero-sum stochastic game on linear diffusion processes with two players, one called controller and the other called stopper. Let with the state space , which is a nonempty bounded open interval, be the diffusion process governed by the equation
on a filtered probability space , where is a standard Brownian motion. The first player chooses a pair from some given class and the second player selects a stopping time , in which the first (second) player minimizes (resp. maximizes) an expectation , where is a discount factor and is a real-valued continuous function on . They then give a saddle-point and show the game has a value, that is,
for an undiscounted case and a discounted case under some assumptions.