This paper is a self-contained survey of algorithms for computing Nash equilibria of two-person games. The games may be given in strategic form or extensive form. The classical Lemke-Howson algorithm finds one equilibrium of a bimatrix game, and provides an elementary proof that a Nash...

In this note we reconsider Nash equilibria for the linear quadratic differential game for an infinite planning horizon. We consider an open-loop information structure. In the standard literature this problem is solved under the assumption that every player can stabilize the system on his own. In...

In this note we consider the non-cooperative linear feedback Nash quadratic differential game with an infinite planning horizon for descriptor systems of index one. The performance function is assumed to be indefinite. We derive both necessary and sufficient conditions under which this game has...

In this note we consider the non-cooperative linear feedback Nash 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...

The main objects here are Nash equilibria in spatial Cournot oligopolies when profits depend on coordinated distribution. Production is non-cooperative, but the subsequent transportation must be performed jointly to minimize costs. Cournot-Nash equilibria for this two-stage game with partial...

Relaxation algorithms provide a powerful method of finding noncooperative equilibria in general synchronous games. Through use of the Nikaido-Isoda function, the Nash solution to a broad category of constrained, multiplayer, non-zerosum games can easily be found. We provide solutions to some...

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