Lexicographic and Strictly Weighted Equilibrium Strategy Profiles with Applications to Interval-Valued Bi-matrix Games

Abstract

We prove the existence of lexicographic equilibrium strategy profiles for pair-valued bi-matrix games under some conditions, which leads to an existence result for lexicographic mean-standard deviation equilibrium strategy profile in the case of interval-valued bi-matrix games. Our main result in this context is that a strategy profile is a lexicographic equilibrium strategy profile if and only if with some real numbers it solves a bi-linear programming problem and the optimal value pair of the problem is zero. We also provide necessary conditions and sufficient conditions for a strategy profile to be a strictly weighted equilibrium strategy profile with analogous results being applicable for strictly weighted mean-standard deviation equilibrium strategy profiles for interval-valued bi-matrix games.