Covering the major topics of evolutionary game theory, Game-Theoretical Models in Biology 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 MATLAB® 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 behavior, and the existence of adornments (for example, the peacock’s tail), have been explained using ideas underpinned by game theoretical modeling. 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 modeling of these diverse biological phenomena.

Introduction The history of evolutionary games The key mathematical developments The range of applications Reading this book What Is a Game? Key game elements Games in biological settings Two Approaches to Game Analysis The dynamical approach The static approach—evolutionarily stable strategies (ESSs) Dynamics versus statics Some Classical Games The hawk-dove game The prisoner’s dilemma The war of attrition The sex ratio game The Underlying Biology Darwin and natural selection Genetics Games involving genetics Fitness, strategies and players Selfish genes: how can non-beneficial genes propagate? The role of simple mathematical models Matrix Games Properties of ESSs ESSs in a 2 × 2 matrix game Haigh’s procedure to locate all ESSs ESSs in a 3 × 3 matrix game Patterns of ESSs Extensions to the hawk-dove game Nonlinear Games Overview and general theory Linearity in the focal player strategy and playing the field Nonlinearity due to non-constant interaction rates Nonlinearity in the strategy of the focal player Some differences between linear and nonlinear theory Asymmetric Games Selten’s theorem for games with two roles Bimatrix games Uncorrelated asymmetry—the owner-intruder game Correlated asymmetry Multi-Player Games Multi-player matrix games The multi-player war of attrition Structures of dependent pairwise games Extensive Form Games and Other Concepts in Game Theory Games in extensive form Perfect, imperfect and incomplete information Repeated games State-Based Games State-based games A question of size Life history theory Games in Finite and Structured Populations Finite populations and stochastic games Evolution on graphs Spatial games and cellular automata Adaptive Dynamics Introduction and philosophy Fitness functions and the fitness landscape Pairwise invasibility and evolutionarily singular strategies Adaptive dynamics with multiple traits The assumptions of adaptive dynamics The Evolution of Cooperation Kin selection and inclusive fitness Greenbeard genes Direct reciprocity: developments of the prisoner’s dilemma Punishment Indirect reciprocity and reputation dynamics The evolution of cooperation on graphs Multi-level selection Group Living The costs and benefits of group living Dominance hierarchies: formation and maintenance The enemy without: responses to predators The enemy within: infanticide and other anti-social behavior Mating Games Introduction and overview Direct conflict Indirect conflict and sperm competition The battle of the sexes Selecting mates: signaling and the handicap principle Other signaling scenarios Food Competition Introduction Ideal free distribution for a single species Ideal free distribution for multiple species Distributions at and deviations from the ideal free distribution Compartmental models of kleptoparasitism Compartmental models of interference Producer-scrounger models Predator-Prey and Host-Parasite Interactions Game-theoretical predator-prey models The evolution of defense and signaling Brood parasitism Parasitic wasps and the asymmetric war of attrition Complex parasite lifecycles Epidemic Models SIS and SIR models The evolution of virulence Viruses and the prisoner's dilemma Conclusions Types of evolutionary games used in biology What makes a good mathematical model? Future developments Appendix: Intro to MATLAB Bibliography Index