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Game - Theoretical Models in Biology

Mark Broom and Jan Rychtář
Chapman & Hall/CRC
Publication Date: 
Number of Pages: 
Chapman & Hall/CRC Mathematical and Computational Biology Series
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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
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
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
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

Types of evolutionary games used in biology
What makes a good mathematical model?
Future developments

Appendix: Intro to MATLAB