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Evolutionary Games and Population Dynamics - Josef Hofbauer

Evolutionary Games and Population Dynamics

Paperback

Published: 27th July 1998
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Every form of behavior is shaped by trial and error. Such stepwise adaptation can occur through individual learning or through natural selection, the basis of evolution. Since the work of Maynard Smith and others, it has been realized how game theory can model this process. Evolutionary game theory replaces the static solutions of classical game theory by a dynamical approach centered not on the concept of rational players but on the population dynamics of behavioral programs. In this book the authors investigate the nonlinear dynamics of the self-regulation of social and economic behavior, and of the closely related interactions among species in ecological communities. Replicator equations describe how successful strategies spread and thereby create new conditions that can alter the basis of their success, i.e., to enable us to understand the strategic and genetic foundations of the endless chronicle of invasions and extinctions that punctuate evolution. In short, evolutionary game theory describes when to escalate a conflict, how to elicit cooperation, why to expect a balance of the sexes, and how to understand natural selection in mathematical terms.

'... as a mathematical text on an important set of topics in theoretical biology, the book is superb. It is well organised and beautifully written. In choosing from the rich menu of mathematical topics broadly relevant to ecology, behaviour, evolution, and even theoretical immunology, it shows good taste.' The Times Higher Education Supplement '... [has] something for anyone interested in game models in organismal biology.' Marc Mangel, Nature 'The book is a must for any mathematician economist, or biologist working in Evolutionary Game Theory.' C. Alos-Ferrer, International Mathematical News 'This book can highly be recommended to mathematicians interested in applications in social sciences, biology, and population genetics.' Ethology '... an excellent publication that helps to bridge one of the gaps between biologists and mathematicians.' David Boukai, Folia Geobotanica

Introduction for game theorists
Introduction for biologists
Dynamical Systems And Lotka-Volterra Equations
The logistic equation
Lotka-Volterra for predator-prey systems
Lotka-Volterra for two competitors
Ecological equations for two species
Lotka-Volterra for more than two populations
Game Dynamics And Replicator Equations
Evolutionarily stable strategies
Replicator equations
Other game dynamics
Adaptive dynamics
Asymmetric conflicts
More on bimatrix games
More On Lotka-Volterra And Replicator Dynamics
Hypercircles and permanence
Criteria for permanence
Replicator networks
Stability in n-species communities
Some low-dimensional ecological systems
Heteroclinic cycles and C-matrices
Population Genetics
Discrete dynamical systems in population genetics
Continuous selection dynamics
Mutation and recombination
Fertility selection
Game dynamics for Mendelian populations
Bibliography
Index
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9780521625708
ISBN-10: 052162570X
Audience: Professional
Format: Paperback
Language: English
Number Of Pages: 352
Published: 27th July 1998
Publisher: CAMBRIDGE UNIV PR
Country of Publication: GB
Dimensions (cm): 24.2 x 18.8  x 1.7
Weight (kg): 0.76