Neutrosophic Games Applied to Political Situations

Abstract

Abstract. Game theory is the branch of applied mathematics dedicated to modeling and resolve conflict situations. This has great application in other sciences such as economics, military sciences, biology, sociology, cybernetics, and political sciences. Conflict situations in politics are common and may reach high degrees of complexity. Opponents tend to change strategies during the course of time; they can cooperate with each other at a certain moment and suddenly take totally opposite positions. In addition, the actions they take at each step can be confusing and ambiguous for the adversary. That is why Neutrosophy can be an adequate theory to model this type of situation. In this paper, we propose a neutrosophic model for non-cooperative games in matrix form that generalizes a previous solution where triangular intuitionistic fuzzy payoffs were used. This generalization allows us to define the indeterminacy membership function, which is not restricted to any condition of dependency between the membership and non-membership functions. Specifically, the elements of the matrix are payoffs of single-valued triangular neutrosophic numbers. The advantage of the neutrosophic solution is that the ambiguity that is typical in political conflicts can be expressed more precisely. The use of the proposed solution is illustrated with two examples.