Linear quadratic stochastic two-person zero-sum differential games in an infinite horizon

Linear Quadratic Zero-Sum Two-Person Differential Games

As in optimal control theory, linear quadratic (LQ) differential games (DG) can be solved, even in high dimension, via a Riccati equation. However, contrary to the control case, existence of the solution of the Riccati equation is not necessary for the existence of a closed-loop saddle point. One may “survive” a particular, non generic, type of conjugate point. An important application of LQDG’...

Two-person Zero-sum Linear Quadratic Stochastic Differential Games by a Hilbert Space Method

An open-loop two-person zero-sum linear quadratic (LQ for short) stochastic differential game is considered. The controls for both players are allowed to appear in both the drift and diffusion of the state equation, the weighting matrices in the payoff/cost functional are not assumed to be definite/nonsingular, and the cross-terms between two controls are allowed to appear. A forward-backward s...

One-sided adaptation for infinite-horizon linear quadratic N-person non-zero-sum dynamic games and sensitivity analysis

To cite this Article Tan, Xiaohuan and Cruz Jr, Jose B.(2008)'One-sided adaptation for infinite-horizon linear quadratic N-person non-zero-sum dynamic games and sensitivity analysis' This article may be used for research, teaching and private study purposes. Any substantial or systematic reproduction, redistribution , reselling , loan or sub-licensing, systematic supply or distribution in any f...

Zero-Sum Two Person Games

Infinite Horizon LQ Zero-Sum Stochastic Differential Games with Markovian Jumps

This paper studies a class of continuous-time two person zero-sum stochastic differential games characterized by linear Itô’s differential equation with state-dependent noise and Markovian parameter jumps. Under the assumption of stochastic stabilizability, necessary and sufficient condition for the existence of the optimal control strategies is presented by means of a system of coupled algebra...