Fuzzy Games in Single and Multiple Objective Systems

In this thesis, game theory has been applied for resolution of conflict in competitive systems. We must recognize the existence of ambiguity in decision makers' judgements as well as the imprecision that exists in information in such systems; moreover, decision makers need to be able to accommodate multiple objectives in the solution of the conflict problems. It follows that new solution concepts which take the ambiguity and the multiplicity of the objectives into consideration should be introduced for implementation of game theoretic approach. We present several game representations for the resolution of conflict in competitive systems and demonstrate our computational methods for the proposed solutions. For noncooperative games, two-person games are dealt with and max-min solutions and equilibrium solutions are considered. For cooperative games, lexicographical solutions and a solution based on fuzzy decision rule are examined. The computational methods are based mainly on linear programming techniques, and therefore they have useful practical applications for decision making problems regarding public conflict.Contents / p1 Abstract 1.Introduction / p1 1.1 Introduction and Historical Remarks / p1 1.2 Outline of the Thesis / p6 2.Two-Person Zero-Sum Multiobjective Matrix Games with Fuzzy Goals / p10 2.1 Introduction / p10 2.2 Conventional Two-Person Zero-Sum Matrix Games / p11 2.3 Problem Formulation and Solution Concepts / p14 2.4 Computational Methods / p16 2.5 Conclusion / p32 3.Two-Person Zero-Sum Multiobjective Fuzzy Matrix Games with Fuzzy Goals / p33 3.1 Introduction / p33 3.2 Problem Formulation and Solution Concepts / p34 3.3 Computational Methods / p38 3.4 Conclusion / p52 4.Two-Person Non-Zero-Sum Multiobjective Bimatrix Games with Fuzzy Goals / p54 4.1 Introduction / p54 4.2 Problem Formulation and Solution Concepts / p55 4.3 Computational Methods / p58 4.4 Related Properties for Pareto Equilibrium Solutions / p71 4.5 Conclusion / p75 5.n-Person Cooperative Games with Fuzzy Coalitions / p77 5.1 Introduction / p77 5.2 n-Person Cooperative Games / p78 5.3 n-Person Cooperative Games with Fuzzy Coalitions / p90 5.4 Conclusion / p102 6.n-Person Cooperative Games with Fuzzy Goals / p104 6.1 Introduction / p104 6.2 Problem Formulation and Solution Concepts / p105 6.3 Computational Methods / p111 6.4 Conclusion / p117 7.Conclusion / p118 References / p122 Appendix / p129 Acknowledgments / p133博士(工学)Engineering広島大