Computing equilibria for integer programming games

Computing Equilibria for Two-person Games

Computing Nash Equilibria for Stochastic Games

We present two new algorithms for computing Nash equilibria of stochastic games. One is a global random start algorithm based on nonlinear programming, while the other combines a dynamical system with nonlinear programming to find stable equilibria. Promising numerical results are presented.

Computing Equilibria for Two-Person Games

This paper is a self-contained survey of algorithms for computing Nash equilibria of two-person games given in normal form or extensive form. The classical Lemke{Howson algorithm for nding one equilibrium of a bimatrix game is presented graph-theoretically as well as algebraically in terms of complementary pivoting. Common deenitions of degenerate games are shown as equivalent. Enumeration of a...

Computing Strong Nash Equilibria for Multiplayer Games

A new method for computing strong Nash equilibria in multiplayer games that uses the theoretical framework of generative relations combined with a stochastic search method is presented. Generative relations provide a mean to compare two strategy profiles and to assess their relative quality with respect to an equilibria type. The stochastic method used, called Aumann Crowding Based Differential...

Computing the integer programming gap

We determine the maximal gap between the optimal values of an integer program and its linear programming relaxation, where the matrix and cost function are fixed but the right hand side is unspecified. Our formula involves irreducible decomposition of monomial ideals. The gap can be computed in polynomial time when the dimension is fixed.