Nash equilibrium strategy for fuzzy non-cooperative games

Abstract

In this article, two-person zero-sum games are investigated in the fuzzy environment. Several models constructed by Maeda in the symmetrical fuzzy environment are extended to the models in the asymmetric fuzzy environment. The existence of equilibrium strategies for these extended models is proposed in the asymmetric fuzzy environment. However, in some cases, Nash equilibrium strategies may not exist. Therefore, two special cases are presented for which Nash equilibrium strategies do exist. In order to investigate the existence of (weak) Pareto Nash equilibrium strategies for fuzzy matrix games, we introduce the concept of crisp bi-matrix games with parameters. By solving the parametric bi-matrix games, we obtain the (weak) Pareto Nash equilibrium strategies for the fuzzy matrix games.