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Covering the major topics of evolutionary game theory, Game-Theoretical Models in Biology, second edition presents both abstract and practical mathematical models of real biological situations. It discusses the static aspects of game theory in a mathematically rigorous way that is appealing to mathematicians. In addition, the authors explore many applications of game theory to biology, making the text useful to biologists as well.
The book describes a wide range of topics in evolutionary games, including matrix games, replicator dynamics, the hawk-dove game, and the prisoner's dilemma. It covers the evolutionarily stable strategy, a key concept in biological games, and offers in-depth details of the mathematical models. Most chapters illustrate how to use Python to solve various games.
Important biological phenomena, such as the sex ratio of so many species being close to a half, the evolution of cooperative behaviour, and the existence of adornments (for example, the peacock's tail), have been explained using ideas underpinned by game theoretical modelling. Suitable for readers studying and working at the interface of mathematics and the life sciences, this book shows how evolutionary game theory is used in the modelling of these diverse biological phenomena.
In this thoroughly revised new edition, the authors have added three new chapters on the evolution of structured populations, biological signalling games, and a topical new chapter on evolutionary models of cancer. There are also new sections on games with time constraints that convert simple games to potentially complex nonlinear ones; new models on extortion strategies for the Iterated Prisoner's Dilemma and on social dilemmas; and on evolutionary models of vaccination, a timely section given the current COVID-19 pandemic.
Features:
- Presents a wide range of biological applications of game theory.
- Suitable for researchers and professionals in mathematical biology and the life sciences, and as a text for postgraduate courses in mathematical biology.
- Provides numerous examples, exercises, and Python code.
1. Introduction
2. What is a Game?
3. Two Approaches to Game Analysis
4. Some Classical Games
5. The Underlying Biology
6. Matrix Games
7. Nonlinear Games
8. Asymmetric Games
9. Multi-player Games
10. Extensive Form Games and other Concepts in Game Theory
11. State-based Games
12. Games in Finite Populations and on Graphs
13. Evolution in Structured Populations
14. Adaptive Dynamics
15. The Evolution of Cooperation
16. Group Living
17. Mating Games
18. Signalling Games
19. Food Competition
20. Predator-prey and host-Parasite Interactions
21. Epidemic models
22. Evolutionary Cancer Modelling
23. Conclusions
Appendix: Python
Mark Broom is a professor of mathematics at City, University of London. For over 30 years, he has carried out mathematical research in game theory applied to biology. His major research themes include multi-player games, patterns of evolutionarily stable strategies, models of parasitic behaviour (especially kleptoparasitism), the evolution of defence and signalling, and evolutionary processes in structured populations. He earned his PhD in mathematics from the University of Sheffield.
Jan Rychtář is a professor of mathematics at Virginia Commonwealth University. Prior to joining VCU, he was a Professor at UNC Greensboro. He works on game theoretical models and mathematical models of kleptoparasitism. His recent research interests include mathematical biology and game theory. He earned his PhD in mathematics from the University of Alberta.
"It is hard to imagine that the book by Broom & Rychtář is already a decade old, it stills feels fresh! However, in a second edition, the authors have now successfully addressed several novel topics that have developed rapidly in these past 10 years, such as the evolution of cancer or vaccination games. On top of the excellent structure of the original edition of this book, including great exercises, the authors have now included python code and pointers to relevant packages. This is an excellent way to make a new generation of game theorists familiar with the field and at the same time allow them a much more interactive experience! The new edition of this wonderful book proves that evolutionary game theory is alive and kicking!"
– Arne Traulsen, Director, Max Planck Institute for Evolutionary Biology, Germany
"The second edition of Game-Theoretical Models in Biology shows the tremendous development and applications that this theory has undergone since its inception fifty years ago. That fact that this theory is still undergoing development and finding new applications is evidenced by the fact that the authors have included completely new chapters reflecting, for example, recent applications in the study of cancer evolution or evolution on graphs in the second edition. The book is suitable both for students of mathematical disciplines, to whom it will show the strong application of mathematics in biology, and for students of biological disciplines, who want to gain a solid theoretical basis for the description of eco-evolutionary laws. It is the most comprehensive treatise on the applications of evolutionary game theory in evolutionary and population biology."
– Vlastimil Krivan, University of South Bohemia, Czech Republic
"If you want a solid foundation in the topic of game theory in biology, then work your way through this book. It is an authoritative account of the basics, introduces many important biological applications, and has a plethora of insights. Really excellent."
– John McNamara, Emeritus Professor at University of Bristol, United Kingdom
"In this update of their 2013 book, Broom and Rychtář continue to provide a valuable resource to any researcher interested in evolutionary games. Readers of the original book will especially appreciate the new chapters/sections on recent developments and applications in the field as well as the expanded bibliography. The book will also serve as an excellent self-contained text, with an extensive set of exercises in each chapter, for students at a graduate or senior undergraduate level studying game-theoretic applications to biology"
– Ross Cressman, Wilfrid Laurier University, Canada
