A novel equilibrium solution concept for intuitionistic fuzzy bi-matrix games considering proportion mix of possibility and necessity expectations

Abstract

This paper considers a class of bi-matrix games involving two players with their payoffs matrices having entries from the set of trapezoidal intuitionistic fuzzy numbers. We generalize the notion of Nash equilibrium for such a class of games by modeling the variations in the proportion of the actual realization of the expected values from the game by the two players in terms of the two matrices $${\varvec{\alpha }}$$ and $${\varvec{\beta }}$$ depending upon the subjectivity of the respective players. Using the intuitionistic fuzzy measure approach, a convex combination of the possibility and the necessity measures, we introduce the notion of $$({\varvec{\alpha }},{\varvec{\beta }})$$ -intuitionistic fuzzy measure equilibrium solutions for games in this class. A methodology is developed to extract the proposed equilibrium solution of an intuitionistic fuzzy bi-matrix game by solving an equivalent quadratic programming problem with linear constraints. The viability of the proposed concept is depicted through two real-life examples of decision-making on marketing strategies to magnetize the preference degrees of the customers. Conclusively, a comparison is drawn between the proposed solution concept with a few of the proximate equilibrium solutions concepts existing for such a class of games.