On the value of stochastic differential games

Relative Value Iteration for Stochastic Differential Games

Abstract. We study zero-sum stochastic differential games with player dynamics governed by a nondegenerate controlled diffusion process. Under the assumption of uniform stability, we establish the existence of a solution to the Isaac’s equation for the ergodic game and characterize the optimal stationary strategies. The data is not assumed to be bounded, nor do we assume geometric ergodicity. T...

Linear Quadratic Stochastic Differential Games under Asymmetric Value of Information

This paper considers a variant of two-player linear quadratic stochastic differential games. In this framework, none of the players has access to the state observations for all the time, which restricts the possibility of continuous feedback strategies. However, they can observe the state intermittently at discrete time instances by paying some finite cost. Having on demand costly measurements ...

Stochastic Differential Portfolio Games

We study stochastic dynamic investment games in continuous time between two investors (players) who have available two different, but possibly correlated, investment opportunities. There is a single payoff function which depends on both investors’ wealth processes. One player chooses a dynamic portfolio strategy in order to maximize this expected payoff while his opponent is simultaneously choo...

Continuity of the Value in Stochastic Games

We prove that the undiscounted value of a stochastic game, as a function of the transition, is continuous in the relative interior of the set of transition functions. ∗I thank Ehud Lehrer for raising the question and commenting on an earlier version of the paper, and Ron, who had an inactive yet an important role in the solution. †Department of Managerial Economics and Decision Sciences, Kellog...

The NTU-Value of Stochastic Games