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Game Theory and Its Applications

:	Akio Matsumoto, Ferenc Szidarovszky
:	Game Theory and Its Applications
:	Springer-Verlag
:	9784431547860
:	1
:	CHF 94.90
:

:	Wahrscheinlichkeitstheorie, Stochastik, Mathematische Statistik
:	English

:	265
:	Wasserzeichen/DRM
:	PC/MAC/eReader/Tablet
:	PDF

This book integrates the fundamentals, methodology, and major application fields of noncooperative and cooperative games including conflict resolution. The topics addressed in the book are discrete and continuous games including games represented by finite trees; matrix and bimatrix games as well as oligopolies; cooperative solution concepts; games under uncertainty; dynamic games and conflict resolution. The methodology is illustrated by carefully chosen examples, applications and case studies which are selected from economics, social sciences, engineering, the military and homeland security. This book is highly recommended to readers who are interested in the in-depth and up-to-date integration of the theory and ever-expanding application areas of game theory.

	Preface	5
	Contents	7
	List of Figures	10
	List of Tables	12
	1 Introduction	14
	Part I Noncooperative Games	17
	2 Discrete Static Games	18
	2.1 Examples of Two-Person Finite Games	18
	2.2 General Description of Two-Person Finite Games	25
	2.3 N-person Finite Games	30
	3 Continuous Static Games	31
	3.1 Examples of Two-Person Continuous Games	32
	3.2 Examples of N-Person Continuous Games	51
	4 Relation to Other Mathematical Problems	58
	4.1 Nonlinear Optimization	58
	4.2 Fixed Point Problems	59
	5 Existence of Equilibria	62
	5.1 General Existence Conditions	62
	5.2 Bimatrix and Matrix Games	66
	5.3 Mixed Extensions of N-person Finite Games	70
	5.4 Multiproduct Oligopolies	71
	6 Computation of Equilibria	74
	6.1 Application of the Kuhn--Tucker Conditions	74
	6.2 Reduction to an Optimization Problem	77
	6.3 Solution of Bimatrix Games	79
	6.4 Solution of Matrix Games	83
	6.5 Solution of Oligopolies	86
	7 Special Matrix Games	89
	7.1 Matrix with Identical Elements	89
	7.2 The Case of Diagonal Matrix	89
	7.3 Symmetric Matrix Games	91
	7.4 Relation Between Matrix Games and Linear Programming	92
	7.5 Method of Fictitious Play	97
	7.6 Method of von Neumann	100
	8 Uniqueness of Equilibria	105
	9 Repeated and Dynamic Games	112
	9.1 Leader-Follower Games	112
	9.2 Dynamic Games with Simultaneous Moves	117
	9.3 Dynamic Games with Sequential Moves	122
	9.4 Extensive Forms of Dynamic Games	130
	9.5 Subgames and Subgame-Perfect Nash Equilibria	132
	10 Games Under Uncertainty	134
	10.1 Static Bayesian Games	138
	10.2 Dynamic Bayesian Games	141
	Part II Cooperative Games	147
	11 Solutions Based on Characteristic Functions	148
	11.1 The Core	155
	11.2 Stable Sets	160
	11.3 The Nucleolus	161
	11.4 The Shapley Values	165
	11.5 The Kernel and the Bargaining Set	169
	12 Conflict Resolution	174
	12.1 The Nash Bargaining Solution	176
	12.2 Alternative Solution Concepts	180
	12.3 N-person Conflicts	187
	13 Multiobjective Optimization	189
	13.1 Lexicographic Method	192
	13.2 The ?-constraint Method	194
	13.3 The Weighting Method	195
	13.4 Distance-Based Methods	198
	13.5 Direction-Based Methods	200
	14 Social Choice	203
	14.1 Methods with Symmetric Players	203
	14.2 Methods with Powers of Players	207
	15 Case Studies and Applications	212
	15.1 A Salesman's Dilemma	212
	15.2 Oligopoly in Water Management	216
	15.3 A Forestry Management Problem	217
	15.4 International Fishing	219
	15.5 A Water Distribution Problem	222
	15.6 Control in Oligopolies	226
	15.7 Effect of Information Lag in Oligopoly	229
	Appendix A Vector and Matrix Norms	233
	Appendix B Convexity, Concavity	237
	Appendix C Optimum Conditions	240
	Appendix D Fixed Point Theorems	243
	Appendix E Monotonic Mappings	247
	Appendix F Duality in Linear Programming	250
	Appendix G Multiobjective Optimization	252
	Appendix H Stability and Controllability	255
	References	259
	Index	262