In this note we generalize a numerical algorithm presented in [9] to calculate all solutions of the scalar algebraic Riccati equations that play an important role in finding feedback Nash equilibria of the scalar N-player linear affine-quadratic differential game. The algorithm is based on...

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

This paper presents a complete survey of the use of homotopy methods in game theory. Homotopies allow for a robust computation of game-theoretic equilibria and their refinements. Homotopies are also suitable to compute equilibria that are selected by various selection theories. We present all...

In part I of this paper, we proposed a Mixed-Integer Linear Program (MILP) to analyze imperfect competition of oligopoly producers in two-stage zonal power markets. In part II of this paper, we propose a solution algorithm which decomposes the proposed MILP model into several subproblems and...

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 one of the most influential existence theorems in mathematics, John F. Nash proved in 1950 that any normal form game has an equilibrium. More than five decades later, it was shown that the computational task of finding such an equilibrium is intractable, that is, unlikely to be carried out...

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...