Game Theory: An Introduction

Cover......Page 1
Title......Page 4
CONTENTS......Page 8
PREFACE......Page 12
ACKNOWLEDGMENTS......Page 16
INTRODUCTION......Page 18
1.1 THE BASICS......Page 22
1.2 THE VON NEUMANN MINIMAX THEOREM......Page 36
1.3 MIXED STRATEGIES......Page 43
1.4 SOLVING 2x2 GAMES GRAPHICALLY......Page 58
1.5 GRAPHICAL SOLUTION OF 2 m AND 2 GAMES......Page 60
1.6 BEST RESPONSE STRATEGIES......Page 68
2.1 SOLUTION OF SOME SPECIAL GAMES......Page 76
2.2 INVERTIBLE MATRIX GAMES......Page 81
2.3 SYMMETRIC GAMES......Page 89
2.4 MATRIX GAMES AND LINEAR PROGRAMMING......Page 94
2.5 LINEAR PROGRAMMING AND THE SIMPLEX METHOD (OPTIONAL)......Page 111
2.6 A GAME THEORY MODEL OF ECONOMIC GROWTH (OPTIONAL)......Page 122
3.1 THE BASICS......Page 130
3.2 2x2 BIMATRIX GAMES......Page 139
3.3 INTERIOR MIXED NASH POINTS BY CALCULUS......Page 150
3.4 NONLINEAR PROGRAMMING METHOD FOR NONZERO SUM TWO-PERSON GAMES......Page 164
3.5 CHOOSING AMONG SEVERAL NASH EQUILIBRIA (OPTIONAL)......Page 176
4.1 THE BASICS......Page 184
4.2 ECONOMICS APPLICATIONS OF NASH EQUILIBRIA......Page 190
4.3 DUELS (OPTIONAL)......Page 207
4.4 AUCTIONS (OPTIONAL)......Page 216
5.1 COALITIONS AND CHARACTERISTIC FUNCTIONS......Page 240
5.2 THE NUCLEOLUS......Page 270
5.3 THE SHAPLEY VALUE......Page 285
5.4 BARGAINING......Page 298
6 EVOLUTIONARY STABLE STRATEGIES AND POPULATION GAMES......Page 330
6.1 EVOLUTION......Page 331
6.2 POPULATION GAMES......Page 341
APPENDIX A THE ESSENTIALS OF MATRIX ANALYSIS......Page 366
APPENDIX B THE ESSENTIALS OF PROBABILITY......Page 372
APPENDIX C THE ESSENTIALS OF MAPLE......Page 378
APPENDIX D THE MATHEMATICA COMMANDS......Page 384
APPENDIX E BIOGRAPHIES......Page 400
PROBLEM SOLUTIONS......Page 404
REFERENCES......Page 430
INDEX......Page 432