Nash equilibrium strategy for non-cooperative games with interval type-2 fuzzy payoffs

Abstract

This paper is the first to attempt the characterization of Nash equilibrium strategy in interval type-2 fuzzy environment. The payoffs of the matrix games are considered to be interval type-2 triangular fuzzy numbers. An ordering for interval type-2 fuzzy numbers is introduced and a model to investigate equilibrium strategies in this environment is proposed. Due to the uncertainty in payoffs, three types of equilibriums are given those are natural extensions of the Nash equilibrium from crisp games. The existence of these equilibrium strategies is studied and a method to obtain the equilibrium strategy by means of parametric bimatrix crisp game is also given. Finally, solutions to a few numerical examples of matrix games are explored using this new interval-valued fuzzy game framework. © 2018 IEEE.