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Evolutionary Games and Population Dynamics

Evolutionary Games and Population Dynamics

AUD$103.95 inc GST

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  • Date Published: July 1998
  • availability: Available
  • format: Paperback
  • isbn: 9780521625708

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  • Every form of behaviour 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 realised how game theory can model this process. Evolutionary game theory replaces the static solutions of classical game theory by a dynamical approach centred not on the concept of rational players but on the population dynamics of behavioural programmes. In this book the authors investigate the nonlinear dynamics of the self-regulation of social and economic behaviour, and of the closely related interactions between species in ecological communities. Replicator equations describe how successful strategies spread and thereby create new conditions which 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 which 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.

    • Comprehensive treatment of ecological and game theoretic dynamics
    • Invasion dynamics and permanence as key concepts
    • Explanation in terms of games of things like competition between species
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    Reviews & endorsements

    '… 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

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    Product details

    • Date Published: July 1998
    • format: Paperback
    • isbn: 9780521625708
    • length: 352 pages
    • dimensions: 246 x 189 x 19 mm
    • weight: 0.63kg
    • contains: 20 b/w illus.
    • availability: Available
  • Table of Contents

    Introduction for game theorists
    Introduction for biologists
    Part I. Dynamical Systems And Lotka-Volterra Equations:
    1. The logistic equation
    2. Lotka-Volterra for predator-prey systems
    3. Lotka-Volterra for two competitors
    4. Ecological equations for two species
    5. Lotka-Volterra for more than two populations
    Part II. Game Dynamics And Replicator Equations:
    6. Evolutionarily stable strategies
    7. Replicator equations
    8. Other game dynamics
    9. Adaptive dynamics
    10. Asymmetric conflicts
    11. More on bimatrix games
    Part III. More On Lotka-Volterra And Replicator Dynamics:
    12. Hypercircles and permanence
    13. Criteria for permanence
    14. Replicator networks
    15. Stability in n-species communities
    16. Some low-dimensional ecological systems
    17. Heteroclinic cycles and C-matrices
    Part IV. Population Genetics:
    18. Discrete dynamical systems in population genetics
    19. Continuous selection dynamics
    20. Mutation and recombination
    21. Fertility selection
    22. Game dynamics for Mendelian populations
    Bibliography
    Index.

  • Authors

    Josef Hofbauer, Universität Wien, Austria

    Karl Sigmund, Universität Wien, Austria

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