Germeier’s Scalarization for Approximating Solution of Multicriteria Matrix Games

In this paper, we study the properties of Germeier’s scalarization applied for solving multicriteria games. The equilibria and equilibrium values such games, as a rule, make sets, problems parametrizing approximating these sets arise. Shapley proved that Nash matrix game can be found by two-parametric family scalar games obtained with help linear criteria vector. We show parametrizes using one-parametric has certain advantages over one, suggest it finite set. For two-criteria 2×2 matrices, examples there is no continuity in scalarizing parameters. prove one-sided (from left or from right) values. As result, come to convergence Hausdorff metric set ϵ-net on simplex parameters value ϵ→0. constructed approximation may helpful practical applications, where players try find compromise an iterative negotiating procedure under multiple criteria.