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...

In this paper we try to quantify/measure the main factors that influence the equilibrium outcome and pursued strategies in a simplistic model for the use of fossil versus green energy over time. The model is derived using the standard Solow macro-economic growth model in a two-country setting...

In this paper we review a number of algorithms to compute Nash equilibria in deterministic linear quadratic differential games. We will review the open-loop and feedback information case. In both cases we address both the finite and the infinite-planning horizon

In this note we present both necessary and sufficient conditions for the existence of a linear static state feedback controller if the system is described by an index one descriptor system. A priori no definiteness restrictions are made w.r.t. the quadratic performance criterium. It is shown...

This note analyzes in a fishery management problem the effects of relaxing one of the usual assumptions in the literature of dynamic games. Specifically, the assumption that players restrict to strategies that stabilize the system. Previous works in the literature have shown that feedback Nash...

In this paper we consider the linear quadratic differential game for descriptor systems that have index one. We derive both necessary and sufficient conditions for existence of an open-loop Nash equilibrium

In this paper, we analyze the consequences of taking noise into account in a simple two person fishery management game. Both a stochastic and deterministic formulation are considered. Compared to the noise-free model it is shown that the used stochastic framework has no implications for the...

In this note, we reconsider the indefinite open-loop Nash linear quadratic differential game with an infinite planning horizon. In particular, we derive both necessary and sufficient conditions under which the game will have a unique equilibrium

In this paper, we provide a numerical algorithm to calculate all soft-constrained Nash equilibria in a regular scalar indefinite linear-quadratic game. The algorithm is based on the calculation of the eigenstructure of a certain matrix. The analysis follows the lines of the approach taken by...

In this note, we consider the open-loop Nash linear quadratic differential game with an infinite planning horizon. The performance function is assumed to be indefinite and the underlying system affine. We derive both necessary and sufficient conditions under which this game has a unique Nash...