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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 pandemic.
Introduction
What is a Game?
Two Approaches to Game Analysis.
Some Classical Games
The Underlying Biology
Matrix Games
Nonlinear Games
Asymmetric Games
Multi-player Games
Extensive Form Games and other Concepts in Game Theory
State-based Games
Games in Finite Populations and on Graphs
Evolution in Structured Populations
Adaptive Dynamics
The Evolution of Cooperation
Group Living
Mating Games
Food Competition
Predator-prey and host-Parasite Interactions
Epidemic models
Evolutionary Cancer Modelling
Conclusions