On Linear-Quadratic Gaussian Dynamic Games

Abstract

Stochastic dynamic games with partial information are considered. Because the LQG hypothesis is common in control theory for its analytic convenience, we exclusively focus on linear-quadratic Gaussian dynamic games (LQGDGs) – we confine our attention to “zero-sum” LQGDGs where the players have partial information. However, LQGDGs with a nonclassical information pattern can be problematic, as Witsenhausen’s counterexample illustrates. The state of affairs concerning dynamic games and dynamic team problems with partial information is not satisfactory, and the solution of “zero-sum” LQGDGs where the players have partial information has been the Holy Grail/long-standing goal of the controls and games communities. Delayed commitment strategies as opposed to prior commitment strategies are required. The goal is to obtain a Nash equilibrium in delayed commitment strategies such that the optimal solution is time consistent/subgame perfect. In this article the current literature is discussed, and informational aspects are emphasized. Information patterns which render the game amenable to solution by the method of dynamic programming are of interest, so that the correct solution of LQGDGs with partial information can be obtained in closed-form.

The views expressed in this article are those of the author and do not reflect the official policy or position of the United States Air Force, Department of Defense, or the US Government.