# Two-Person Zero-Sum Stochastic Linear-Quadratic Differential Games

arXiv: https://arxiv.org/abs/2005.11701 · HTML: https://mlsanity.com/paper/2005.11701/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 May 2020.

## Built on by (most cited first, 3 of 3)

- [A Survey of Decision Making in Adversarial Games](https://mlsanity.com/paper/2207.07971/) (2022)
- [Adversary agent reinforcement learning for pursuit-evasion](https://mlsanity.com/paper/2108.11010/) (2021)
- [Reinforcement Learning Method for Zero-Sum Linear-Quadratic Stochastic Differential Games in Infinite Horizons](https://mlsanity.com/paper/2602.08075/) (2026)

## Abstract (arXiv)

The paper studies the open-loop saddle point and the open-loop lower and upper values, as well as their relationship for two-person zero-sum stochastic linear-quadratic (LQ, for short) differential games with deterministic coefficients. It derives a necessary condition for the finiteness of the open-loop lower and upper values and a sufficient condition for the existence of an open-loop saddle point. It turns out that under the sufficient condition, a strongly regular solution to the associated Riccati equation uniquely exists, in terms of which a closed-loop representation is further established for the open-loop saddle point. Examples are presented to show that the finiteness of the open-loop lower and upper values does not ensure the existence of an open-loop saddle point in general. But for the classical deterministic LQ game, these two issues are equivalent and both imply the solvability of the Riccati equation, for which an explicit representation of the solution is obtained.