Toward the Nash Equilibrium Solutions for Large-Scale Pentagonal Fuzzy Continuous Static Games

Abstract

This study aims to characterize and clarify a pentagonal fuzzy continuous static game (PF-CSG) that constraints and cost functions are fuzzy numbers. Pentagonal fuzzy numbers characterize their fuzzy parameters. The α − Pareto optimal solution concept has specified. The decomposition approach has applied to decompose the problem into subproblems each of them having smaller and independent subproblems. In addition, the Nash equilibrium solution concept was used to obtain the solutions of these subproblems. The advantages of this study are the players independently without collaboration with any of the others and that each player seeks to minimize the cost function. Also, the information available to each player consists of the cost function and constraints. An illustrated numerical example has discussed for proper understanding and interpretation of the proposed concept.