**Student Mathematical Library**

Volume: 11;
2001;
368 pp;
Softcover

MSC: Primary 91;
Secondary 92

Print ISBN: 978-0-8218-1929-6

Product Code: STML/11

List Price: $48.00

Individual Price: $38.40

**Electronic ISBN: 978-1-4704-2128-1
Product Code: STML/11.E**

List Price: $48.00

Individual Price: $38.40

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#### Supplemental Materials

# An Introduction to Game-Theoretic Modelling: Second Edition

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*Mike Mesterton-Gibbons*

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.

#### Table of Contents

# Table of Contents

## An Introduction to Game-Theoretic Modelling: Second Edition

- Cover Cover11 free
- Title v6 free
- Copyright vi7 free
- Contents ix10 free
- Preface xiii14 free
- Acknowledgements xv16 free
- Agenda xvii18 free
- Chapter 1. Noncooperative Games 126 free
- §1.1. Crossroads: a motorist's dilemma 126
- §1.2. The Hawk-Dove game 631
- §1.3. Rational reaction sets and Nash equilibria 833
- §1.4. Four Ways: a motorist's trilemma 1843
- §1.5. Store Wars: a continuous game of prices 2449
- §1.6. Store Wars II: a three-player game 3459
- §1.7. Max-min strategies 4368
- §1.8. Commentary 4570
- Exercises 1 4671

- Chapter 2. Evolutionary Stability and Other Selection Criteria 5176
- §2.1. Harsanyi and Selten's criterion 5176
- §2.2. Kalai and Samet's criterion 5580
- §2.3. Maynard Smith's criterion 5782
- §2.4. Crossroads as a continuous population game 6691
- §2.5. An example of population dynamics 7297
- §2.6. Discrete population games. Multiple ESSes 7499
- §2.7. Asymmetry of role: Owners and Intruders 80105
- §2.8. Spiders in a spin—a case of anti-Bourgeois? 92117
- §2.9. Commentary 94119
- Exercises 2 96121

- Chapter 3. Cooperative Games in Strategic Form 101126
- Chapter 4. Characteristic Function Games 127152
- §4.1. Characteristic functions and reasonable sets 128153
- §4.2. Core-related concepts 135160
- §4.3. A four-person car pool 140165
- §4.4. Log hauling: a coreless game 144169
- §4.5. Antique dealing. The nucleolus 147172
- §4.6. Team long-jumping. An improper game 157182
- §4.7. The Shapley value 160185
- §4.8. Simple games. The Shapley-Shubik index 165190
- §4.9. Commentary 167192
- Exercises 4 167192

- Chapter 5. Cooperation and the Prisoner's Dilemma 173198
- §5.1. A laboratory prisoner's dilemma 175200
- §5.2. A game of foraging among oviposition sites 178203
- §5.3. Tit for tat: champion reciprocative strategy 182207
- §5.4. Other reciprocative strategies 186211
- §5.5. Dynamic versus static interaction 200225
- §5.6. Stability of a nice population: static case 205230
- §5.7. Stability of a nice population: dynamic case 207232
- §5.8. Mutualism: common ends or enemies 211236
- §5.9. Much ado about scorekeeping 216241
- §5.10. The comedy of errors 218243
- §5.11. Commentary 221246
- Exercises 5 225250

- Chapter 6. More Population Games 229254
- §6.1. Sex allocation: a game with a weak ESS 230255
- §6.2. Damselfly duels: a war of attrition 231256
- §6.3. Games among kin versus games between kin 240265
- §6.4. Information and strategy: a mating game 245270
- §6.5. Roving ravens: a recruitment game 251276
- §6.6. Cooperative wildlife management 261286
- §6.7. Winner and loser effect 271296
- §6.8. Stomatopod strife: a threat game 286311
- §6.9. Commentary 298323
- Exercises 6 302327

- Chapter 7. Appraisal 307332
- Appendix A. The Tracing Procedure 315340
- Appendix B. Solutions to Selected Exercises 319344
- Bibliography 347372
- Index 363388
- Back Cover Back Cover1394

#### Readership

Advanced undergraduates, graduate students, and research mathematicians interested in mathematical modelling; applied mathematicians; biologists, social scientists, and management scientists.

#### Reviews

This book helps not only to make game theory accessible, but also to convey both its power and scope in a variety of applications. The books deals in a unified manner with the central ideas of both classical and evolutionary game theory. The key ideas are illustrated by a variety of well-chosen examples.

-- Zentralblatt MATH

Mesterton-Gibbons' book deals with mathematical modelling, not by an abstract discussion of how modelling should be done, but rather by presenting many concrete examples … The mathematics described [in the book] is fascinating and well worth studying … The examples are great, and the author has clearly put enormous effort into building this collection … a perfect source of problems for a Moore method course … a valuable contribution to the literature … Everyone interested in game theory or mathematical modelling should take a look at it.

-- MAA Online

Readers will be hard-pressed to find a general introduction to game theory that blends biological and mathematical approaches more expertly. It is both a well-rounded survey and a reference work of lasting value.

-- Behavioral Ecology

This book is an introduction to game theory with two specific features: it is written by a mathematician … and it is written from the perspective of a mathematical modeller. This last characteristic implies that all chapters start with examples and the general concepts are only presented once the specific examples have been carefully developed … I find this book excellent and … worth considering when teaching an undergraduate course in game theory to students having some mathematical maturity (some calculus, some knowledge of matrix analysis and probability).

-- Zentralblatt MATH