Title: Evolutionary games and population dynamics /
Authors: Hofbauer, Josef, 1956-; Sigmund, Karl, 1945-
Publisher: Cambridge University Press,
Year: 1998
Subjects: Population Dynamics; Models, Theoretical; Game Theory; Biological Evolution; Evolution (Biology) Mathematical models; Population biology Mathematical models.; Game theory.; Volterra equations.
Abstract: 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, id est 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.
Contents: Introduction for game theorists -- Introduction for biologists -- Pt. 1. Dynamical Systems and Lotka-Volterra Equations. 1. Logistic growth. 2. Lotka-Volterra equations for predator-prey systems. 3. The Lotka-Volterra equations for two competing species. 4. Ecological equations for two species. 5. Lotka-Volterra equations for more than two populations -- Pt. 2. Game Dynamics and Replicator Equations. 6. Evolutionarily stable strategies. 7. Replicator dynamics. 8. Other game dynamics. 9. Adaptive dynamics. 10. Asymmetric games. 11. More on bimatrix games -- Pt. 3. Permanence and Stability. 12. Catalytic hypercycles. 13. Criteria for permanence. 14. Replicator networks. 15. Stability of n-species communities. 16. Some low-dimensional ecological systems. 17. Heteroclinic cycles: Poincare maps and characteristic matrices -- Pt. 4. Population Genetics and Game Dynamics. 18. Discrete dynamical systems in population genetics. 19. Continuous selection dynamics.