A Nonlinear Programming Approach to Determine a Generalized Equilibrium for N-Person Normal Form Games

Abstract

A generalized equilibrium (GE) for finite [Formula: see text]-person normal form games is defined as a collection of mixed strategies with the following property: no player in some subset [Formula: see text] of the players can achieve a better expected payoff if players in an associated set [Formula: see text] change strategies unilaterally. A GE is proved to exist for a game if and only if the maximum objective function value of a certain nonlinear programming problem is zero, in which case the solution to the nonlinear program yields a GE.