# Linear Quadratic Stochastic Differential Games: Open-Loop and Closed-Loop Saddle Points

arXiv: https://arxiv.org/abs/1401.4754 · HTML: https://mlsanity.com/paper/1401.4754/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Jan 2014.

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

- [Reinforcement Learning Method for Zero-Sum Linear-Quadratic Stochastic Differential Games in Infinite Horizons](https://mlsanity.com/paper/2602.08075/) (2026)

## Abstract (arXiv)

In this paper, we consider a linear quadratic stochastic two-person zero-sum differential game. The controls for both players are allowed to appear in both drift and diffusion of the state equation. The weighting matrices in the performance functional are not assumed to be definite/non-singular. A necessary and sufficient condition for the existence of a closed-loop saddle point is established in terms of the solvability of a Riccati differential equation with certain regularity. It is possible that the closed-loop saddle point fails to exist, and at the same time, the corresponding Riccati equation admits a solution (which does not have needed regularity). Also, we will indicate that the solution of the Riccati equation may be non-unique.