Evolutionary Games and Population Dynamics

ISBN-13: 9780521625708 / Angielski / Miękka / 1998 / 352 str.

Josef Hofbauer

Opis

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.

Recenzje

'… an excellent publication that helps to bridge one of the gaps between biologists and mathematicians.' David Boukai, Folia Geobotanica

Spis treści

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.