Multi-objective Bi-matrix Game with Uncertain Payoffs

Abstract

In this paper, uncertain multi-objective bi-matrix games are studied. The uncertainty theory is a new theory to consider the lack of information and knowledge about the parameters and variables of the problem. It has a major role in game theory and model behavior of human in real world. In this paper, we investigate the games which contain multiple objectives and all entries of their payoff matrices are uncertain. A new notion of expected efficient equilibrium points is introduced. Using the concept of expected values, the game is transformed to a crisp multi-objective model. By weighted sum approach, a single objective model is obtained. Then, a quadratic programming is introduced to obtain expected efficient equilibrium points. F