Introduction to Game Theoretic Modelling / Edition 1

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Overview

This is an introduction to game theory and applications with an emphasis on self-discovery from the perspective of a mathematical modeller. The book deals in a unified manner with the central concepts of both classical and evolutionary game theory. The key ideas are illustrated throughout by a wide variety of well-chosen examples of both human and non-human behavior, including car pooling, price fixing, food sharing, sex allocation and competition for territories or oviposition sites. There are numerous exercises with solutions.
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Editorial Reviews

Booknews
A textbook for students who are not now nor even intend to be mathematical purists, but may want to use game theory in mathematical modelling in life, social, or management science. Mestert-Gibbons, who is not identified, assumes felicity with calculus, a rudimentary knowledge of matrix algebra and probability, a passing acquaintance with differential equations, and some degree of mathematical maturity. No date is mentioned for the first edition. Annotation c. Book News, Inc., Portland, OR (booknews.com)
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Product Details

  • ISBN-13: 9780201554489
  • Publisher: Addison-Wesley
  • Publication date: 2/28/1992
  • Edition number: 1
  • Pages: 237

Table of Contents

Preface
Acknowledgements
Agenda
Ch. 1 Noncooperative Games 1
1.1 Crossroads: a motorist's dilemma 1
1.2 The Hawk-Dove game 6
1.3 Rational reaction sets and Nash equilibria 8
1.4 Four Ways: a motorist's trilemma 18
1.5 Store Wars: a continuous game of prices 24
1.6 Store Wars II: a three-player game 34
1.7 Max-min strategies 43
Ch. 2 Evolutionary Stability and Other Selection Criteria 51
2.1 Harsanyi and Selten's criterion 51
2.2 Kalai and Samet's criterion 55
2.3 Maynard Smith's criterion 57
2.4 Crossroads as a continuous population game 66
2.5 An example of population dynamics 72
2.6 Discrete population games. Multiple ESSes 74
2.7 Asymmetry of role: Owners and Intruders 80
2.8 Spiders in a spin - a case of anti-Bourgeois? 92
Ch. 3 Cooperative Games in Strategic Form 101
3.1 Unimprovability: group rationality 102
3.2 Necessary conditions for unimprovability 109
3.3 The Nash bargaining solution 115
3.4 Independent versus correlated strategies 120
Ch. 4 Characteristic Function Games 127
4.1 Characteristic functions and reasonable sets 128
4.2 Core-related concepts 135
4.3 A four-person car pool 140
4.4 Log hauling: a coreless game 144
4.5 Antique dealing. The nucleolus 147
4.6 Team long-jumping. An improper game 157
4.7 The Shapley value 160
4.8 Simple games. The Shapley-Shubik index 165
Ch. 5 Cooperation and the Prisoner's Dilemma 173
5.1 A laboratory prisoner's dilemma 175
5.2 A game of foraging among oviposition sites 178
5.3 Tit for tat: champion reciprocative strategy 182
5.4 Other reciprocative strategies 186
5.5 Dynamic versus static interaction 200
5.6 Stability of a nice population: static case 205
5.7 Stability of a nice population: dynamic case 207
5.8 Mutualism: common ends or enemies 211
5.9 Much ado about scorekeeping 216
5.10 The comedy of errors 218
Ch. 6 More Population Games 229
6.1 Sex allocation: a game with a weak ESS 230
6.2 Damselfly duels: a war of attrition 231
6.3 Games among kin versus games between kin 240
6.4 Information and strategy: a mating game 245
6.5 Roving ravens: a recruitment game 251
6.6 Cooperative wildlife management 261
6.7 Winner and loser effects 271
6.8 Stomatopod strife: a threat game 286
Ch. 7 Appraisal 307
App. A The Tracing Procedure 315
App. B Solutions to Selected Exercises 319
Bibliography 347
Index 363
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