Evolutionary Games and Population Dynamics

How to understand evolution in mathematical terms, i.e. how to model natural selection by game theory.

Josef Hofbauer (Author), Karl Sigmund (Author)

9780521625708, Cambridge University Press

Paperback, published 28 May 1998

352 pages, 20 b/w illus.
24.6 x 18.9 x 1.9 cm, 0.63 kg

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

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.

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.

Subject Areas: Evolution [PSAJ], Applied mathematics [PBW], Game theory [PBUD]