An Introduction to Game-Theoretic Modelling (Student Mathematical Library, Vol. 11) (Student Mathema pdf epub mobi txt 电子书 下载 2025

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This book is about using game theory in mathematical modelling. It is an introductory text, covering the basic ideas and methods of game theory as well as the necessary ideas from the vast spectrum of scientific study where the methods are applied.

It has by now become generally apparent that game theory is a fascinating branch of mathematics with both serious and recreational applications. Strategic behavior arises whenever the outcome of an individual's action depends on actions to be taken by other individuals—whether human, as in the Prisoners' Dilemma, or otherwise, as in the “duels of damselflies”. As a result, game-theoretic mathematical models are applicable in both the social and natural sciences. In reading this book, you can learn not just about game theory, but also about how to model real situations so that they can be analyzed mathematically.

Mesterton-Gibbons includes the familiar game theory examples where they are needed for explaining the mathematics or when they provide a valuable application. There are also plenty of new examples, in particular from biology, such as competitions for territory or mates, games among kin versus games between kin, and cooperative wildlife management.

Prerequisites are modest. Students should have some mathematical maturity and a familiarity with basic calculus, matrix algebra, probability, and some differential equations. As Mesterton-Gibbons writes, “The recurring theme is that game theory is fun to learn, doesn't require a large amount of mathematical rigor, and has great potential for application.”

This new edition contains a significant amount of updates and new material, particularly on biological games. An important chapter on population games now has virtually all new material. The book is absolutely up-to-date with numerous references to the literature. Each chapter ends with a commentary which surveys current developments.

Mike Mesterton-Gibbons: Florida State University, Tallahassee, FL

Cover 1
Title 6
Copyright 7
Contents 10
Preface 14
Acknowledgements 16
Agenda 18
Chapter 1. Noncooperative Games 26
§1.1. Crossroads: a motorist's dilemma 26
§1.2. The Hawk-Dove game 31
§1.3. Rational reaction sets and Nash equilibria 33
§1.4. Four Ways: a motorist's trilemma 43
§1.5. Store Wars: a continuous game of prices 49
§1.6. Store Wars II: a three-player game 59
§1.7. Max-min strategies 68
§1.8. Commentary 70
Exercises 1 71
Chapter 2. Evolutionary Stability and Other Selection Criteria 76
§2.1. Harsanyi and Selten's criterion 76
§2.2. Kalai and Samet's criterion 80
§2.3. Maynard Smith's criterion 82
§2.4. Crossroads as a continuous population game 91
§2.5. An example of population dynamics 97
§2.6. Discrete population games. Multiple ESSes 99
§2.7. Asymmetry of role: Owners and Intruders 105
§2.8. Spiders in a spin—a case of anti-Bourgeois? 117
§2.9. Commentary 119
Exercises 2 121
Chapter 3. Cooperative Games in Strategic Form 126
§3.1. Unimprovability: group rationality 127
§3.2. Necessary conditions for unimprovability 134
§3.3. The Nash bargaining solution 140
§3.4. Independent versus correlated strategies 145
§3.5. Commentary 149
Exercises 3 149
Chapter 4. Characteristic Function Games 152
§4.1. Characteristic functions and reasonable sets 153
§4.2. Core-related concepts 160
§4.3. A four-person car pool 165
§4.4. Log hauling: a coreless game 169
§4.5. Antique dealing. The nucleolus 172
§4.6. Team long-jumping. An improper game 182
§4.7. The Shapley value 185
§4.8. Simple games. The Shapley-Shubik index 190
§4.9. Commentary 192
Exercises 4 192
Chapter 5. Cooperation and the Prisoner's Dilemma 198
§5.1. A laboratory prisoner's dilemma 200
§5.2. A game of foraging among oviposition sites 203
§5.3. Tit for tat: champion reciprocative strategy 207
§5.4. Other reciprocative strategies 211
§5.5. Dynamic versus static interaction 225
§5.6. Stability of a nice population: static case 230
§5.7. Stability of a nice population: dynamic case 232
§5.8. Mutualism: common ends or enemies 236
§5.9. Much ado about scorekeeping 241
§5.10. The comedy of errors 243
§5.11. Commentary 246
Exercises 5 250
Chapter 6. More Population Games 254
§6.1. Sex allocation: a game with a weak ESS 255
§6.2. Damselfly duels: a war of attrition 256
§6.3. Games among kin versus games between kin 265
§6.4. Information and strategy: a mating game 270
§6.5. Roving ravens: a recruitment game 276
§6.6. Cooperative wildlife management 286
§6.7. Winner and loser effect 296
§6.8. Stomatopod strife: a threat game 311
§6.9. Commentary 323
Exercises 6 327
Chapter 7. Appraisal 332
Appendix A. The Tracing Procedure 340
Appendix B. Solutions to Selected Exercises 344
Bibliography 372
Index 388
A 388
B 388
C 388
D 389
E 389
F 390
G 390
H 390
I 390
J 391
K 391
L 391
M 391
N 391
O 391
P 391
R 392
S 392
T 393
U 393
V 393
W 393
Z 393
Back Cover 394
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