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Evolutionary Games and Population Dynamics

Evolutionary Games and Population Dynamics

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

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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.

    • 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

    "...something for anyone interested in game models in organismal biology." Nature

    "The book under review is a very nice further development of its ten-year-old predecessor...by the authors. Not only has the title been modified, but also the contents have been thoroughly reworked and thus adapted to today's topics of interest in the field of biomathematics. The book is totally restructured and contains much new material, mainly in game theory, especially in its evolutionary and dynamical aspects...the book is written in the well-known authors' usual clear, elegant and motivating style." Mathematical Reviews

    "For the biologist who is mathematically inclined or the mathematician interested in biology...this volume is rich in results and likely to provoke stimulating thought." The Quarterly Review of Biology

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    Product details

    • Date Published: June 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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