Game Theory under MCDM and Fuzzy Set Theory

In this thesis, several methodologies have been proposed to solve the different types of game theory problems under fuzzy environment. Analytic Hierarchy process has been applied to find out the weights to solve the two-person zero-sum games with multiple payoffs. Considering the triangular and trapezoidal fuzzy numbers for the payoff matrix in two-person zero-game, the formulated models have been solved by parametric programming approach. Co- operative game theoretic approach has been applied to solve some multi-objective linear and non- linear programming problems. In non co-operative games, Nash equilibrium solutions have been calculated for multi-objective bimatrix games in fuzzy environment. Fuzzy programming has been applied to find out the Stackelberg equilibrium solution for bimatrix games and for bi-level programming problem. By considering the elements of the payoffs matrix as crisp and fuzzy numbers, two different ways have been applied to analyze two- person multicriteria bimatrix games. Finally, an overall concluding remarks has been made and scopes of future directions of investigation have been highlighted.

Dr. Sankar Kr. Roy, received M.Sc. from Vidyasagar University, Midnapur and Ph.D from IIT, Kharagpur, India. He is Reader in Mathematics, Vidyasagar University. He has to his credit several research papers published in international journals. His research areas are O. R., Game Theory, Discrete Mathematics, Fuzzy and Rough Set Theory.