The Open-Loop Discounted Linear Quadratic Differential Game for Regular Higher Order Index Descriptor Systems

Abstract

In this paper we consider the discounted linear quadratic differential game for descriptor systems that have an index larger than one. We derive both necessary and sufficient conditions for existence of an open-loop Nash (OLN) equilibrium. In a small macro-economic stabilization game we illustrate that the corresponding optimal response is generically cyclic.linear quadratic differential games;open-loop information structure;descriptor systems