Interval Fuzzy Linear Programming Models to Solve Interval-valued Fuzzy Zero-Sum Games

In Game theory, there are situations in which it is very difficult to characterize the private information of each player. In this case, the payoffs can be given by approximate values, represented by fuzzy numbers. Whenever there is uncertainty in the modeling of those fuzzy numbers, interval fuzzy numbers may be used. This paper introduces two approaches for the solution of interval-valued fuzzy zero-sum games. First, we extend the CamposVerdegay model, which uses triangular fuzzy numbers for the modeling of uncertain payoffs, to consider interval-valued fuzzy payoffs. Then, defining a ranking method for interval fuzzy numbers that induces a total order, we generalize the intervalvalued Campos-Verdegay model to consider payoffs modeled as any type of interval fuzzy numbers. In both models, we establish an Interval Fuzzy Linear Programming problem for each player, which are reduced to classical Linear Programming problems, used in the solution of classical zero-sum games. We show that the solutions are of the same nature of the parameters defining the game, corresponding to an uncertain predicate of type: “the value of the game is in the interval θ”.