# On martingale problems with continuous-time mixing and values of zero-sum games without Isaacs condition

arXiv: https://arxiv.org/abs/1307.4686 · HTML: https://mlsanity.com/paper/1307.4686/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Jul 2013.

## Built on by (most cited first, 1 of 1)

- [Convergence of GANs Training: A Game and Stochastic Control Methodology](https://mlsanity.com/paper/2112.00222/) (2021)

## Abstract (arXiv)

We consider a zero-sum stochastic differential game over elementary mixed feed-back strategies. These are strategies based only on the knowledge of the past state, randomized continuously in time from a sampling distribution which is kept constant in between some stopping rules. Once both players choose such strategies, the state equation admits a unique solution in the sense of the martingale problem of Stroock and Varadhan. We show that the game defined over martingale solutions has a value, which is the unique continuous viscosity solution of the randomized Isaacs equation.