In this paper, the Nash equilibrium strategy of two-person zero-sum games with heptagonal fuzzy payoffs is considered and the existence of Nash equilibrium strategy is studied. Also, based on the fuzzy max order several models in heptagonal fuzzy environment is constructed and the existence of their equilibrium strategies is proposed. In the sequel, the existence of Pareto Nash equilibrium strategies and weak Pareto Nash equilibrium strategies is investigated for fuzzy matrix games. Finally, the relation between Pareto Nash equilibrium strategy and parametric bi-matrix games is established.

Here, the concept of continuous s-point space is introduced in b-metric spaces. Under suitable assumptions, these spaces are absolute retracts and a generalization of the continuous midpoint spaces. Moreover, an important fixed point theorem is proved for nonexpansive mappings in continuous s-point spaces.