Fuzzy and Multiobjective Games for Conflict Resolution

by Nishizaki, Ichiro; Sakawa, Masatoshi

• ISBN13: 9783790813609
• ISBN10: 3790813605
• Format: Hardcover
• Copyright: 2001-02-01
• Publisher: Physica Verlag

Summary

This book presents some of the most important concepts in noncooperative games and cooperative games and introduces as well the latest advances in the new field of game theory in fuzzy and multiobjective environments. Several game representations and solution concepts are introduced which take the amgiguity and the multiplicity of objectives into consideration. The book also demonstrates the computational methods applied for obtaining the solutions. The reader can learn much about fuzzy and multiobjective games for conflict resolution in most realistic settings without prior mathematical sophistication.

Table of Contents

Introduction	1	(10)
Introduction and historical remarks	1	(5)
Outline of the book	6	(5)
Fundamentals of two-person noncooperative games and n-person cooperative games	11	(22)
Introduction	11	(1)
Two-person noncooperative games	12	(9)
Zero-sum games	12	(3)
Non-zero-sum games	15	(6)
n-person cooperative games	21	(12)
Preliminaries	21	(1)
The core	22	(4)
The nucleolus and its related solutions	26	(7)
Multiobjective fuzzy two-person zero-sum games	33	(42)
Introduction	33	(2)
Multiobjective two-person zero-sum games with fuzzy goals	35	(17)
Problem formulation and solution concept	35	(2)
Computational methods	37	(15)
Multiobjective two-person zero-sum games with fuzzy payoffs and fuzzy goals	52	(19)
Problem formulation and solution concepts	52	(4)
Computational methods	56	(15)
Conclusions	71	(4)
Multiobjective fuzzy two-person non-zero-sum games	75	(46)
Introduction	75	(2)
Multiobjective two-person non-zero-sum games with fuzzy goals	77	(22)
Problem formulation and solution concepts	77	(2)
Computational methods	79	(16)
Related properties for Pareto equilibrium solutions	95	(4)
Multiobjective two-person non-zero-sum games with fuzzy payoffs and fuzzy goals	99	(19)
Problem formulation and solution concepts	99	(4)
Mathematical programming problems and the equilibrium solutions	103	(15)
Conclusions	118	(3)
Fuzzy n-person cooperative games	121	(74)
Introduction	121	(5)
The least core and the nucleolus in games with fuzzy coalitions	126	(11)
Preliminaries and the least core in games with fuzzy coalitions	126	(8)
The nucleolus in n-person cooperative games with fuzzy coalitions	134	(3)
Lexicographical solutions in games with fuzzy coalitions	137	(13)
Solution concepts and definitions	137	(2)
Computational method and extension of games	139	(11)
n-Person cooperative games with fuzzy goals	150	(12)
Fuzzy goals and solution concepts	150	(6)
Computational methods	156	(6)
n-Person cooperative games with fuzzy coalition values	162	(4)
Fuzzy linear programming games	166	(24)
A cooperative game arising from a production programming problem	166	(4)
The core of a fuzzy linear production programming game	170	(9)
Solution concepts in fuzzy linear programming games with fuzzy goals	179	(11)
Conclusions	190	(5)
Multiobjective n-person cooperative games	195	(52)
Introduction	195	(3)
Cooperative games with multiple scenarios	198	(10)
Cooperative games incorporating fuzziness, uncertainty or risk	198	(4)
Computational methods for obtaining the solutions	202	(4)
Cooperative games with fuzzy coalitions and multiple scenarios	206	(2)
Multiobjective n-person cooperative games	208	(16)
Multiobjective payoff sets	208	(1)
Reduction to single-objective games	209	(2)
The core, the least core and the nucleolus in multiobjective n-person cooperative games	211	(13)
Multiobjective linear production programming games	224	(20)
Multiobjective games arising from multiobjective linear production programming problems	224	(3)
The core of the multiobjective linear production programming game	227	(8)
The least core and the nucleolus of the multiobjective linear production programming game	235	(9)
Conclusions	244	(3)
References	247	(10)
Index	257