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.
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'… 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
'… [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
Über das Produkt
It has been realised for some time how game theory can model natural selection. Evolutionary game theory replaces the concept of rational players with the population dynamics of behavioural programmes and can be used to understand the strategic and genetic foundations of the endless chronicle of invasions and extinctions which punctuate evolution.
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"Some of the simplest models for the dynamics of a single population exhibit very complicated behaviour, including bifurcations and chaos." Lesen Sie die erste Seite
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"Some of the simplest models for the dynamics of a single population exhibit very complicated behaviour, including bifurcations and chaos." Lesen Sie die erste Seite
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Die hilfreichsten Kundenrezensionen
12 von 12 Kunden fanden die folgende Rezension hilfreich
Von Herbert Gintis
Format:Taschenbuch
When I was writing the chapter on evolutionary dynamics for my book Game Theory Evolving (Princeton, 2000), I looked at all the books available and found nothing. Then Hofbauer and Sigmund's new book (a totally revised version of their earlier Theory of Evolution and Dynamical Systems) came out, and I knew I had a masterpiece in hand.
The book does not assume the reader knows basic differential equation theory--it presents all the theory necessary. Indeed, it is a wonderful way to learn differential equation theory, since one immediately is faced with meaningful problems to solve. It does assume the reader is familiar with multivariate calculus. The book should be accessible to biologists and game theorists with a minimum understanding of each other's disciplines.
There are four parts. First, HS deal with Lotka-Volterra equations of the type prevalent in predator-prey models, which they extend to ecological models and several populations. Like the rest of the book, there are lots of problems and the presentation is elegant and succinct.
The second part deals with game theory dynamics and replicator equations, including sections on evolutionary games and asymmetric games. This too is extremely nicely presented, and the links to the Lotka-Volterra models are made clear.
Part three is on dynamical systems especially of relevance to biochemistry--catalytic hypercycles--as well as higher dimensional phase space dynamics of ecological models.
Part four deal with population genetic models using a differential equation approach. This section is also excellent, though for serious readers it should be complemented by Karlin and Taylor's Second Course in Stochastic Processes (which is much more mathematically demanding).
The physical production of the book is also first rate--a pleasure to read and use.
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51 von 52 Kunden fanden die folgende Rezension hilfreich
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The Best There Is On Evolutionary Dynamics
13. Juli 2000
Von Herbert Gintis
- Veröffentlicht auf Amazon.com
Format:Taschenbuch|Von Amazon bestätigter Kauf
When I was writing the chapter on evolutionary dynamics for my book Game Theory Evolving (Princeton, 2000), I looked at all the books available and found nothing. Then Hofbauer and Sigmund's new book (a totally revised version of their earlier Theory of Evolution and Dynamical Systems) came out, and I knew I had a masterpiece in hand.
The book does not assume the reader knows basic differential equation theory--it presents all the theory necessary. Indeed, it is a wonderful way to learn differential equation theory, since one immediately is faced with meaningful problems to solve. It does assume the reader is familiar with multivariate calculus. The book should be accessible to biologists and game theorists with a minimum understanding of each other's disciplines.
There are four parts. First, HS deal with Lotka-Volterra equations of the type prevalent in predator-prey models, which they extend to ecological models and several populations. Like the rest of the book, there are lots of problems and the presentation is elegant and succinct.
The second part deals with game theory dynamics and replicator equations, including sections on evolutionary games and asymmetric games. This too is extremely nicely presented, and the links to the Lotka-Volterra models are made clear.
Part three is on dynamical systems especially of relevance to biochemistry--catalytic hypercycles--as well as higher dimensional phase space dynamics of ecological models.
Part four deal with population genetic models using a differential equation approach. This section is also excellent, though for serious readers it should be complemented by Karlin and Taylor's Second Course in Stochastic Processes (which is much more mathematically demanding).
The physical production of the book is also first rate--a pleasure to read and use.
5 von 10 Kunden fanden die folgende Rezension hilfreich
2.0 von 5 Sternen
bring along your math dictionary
23. August 2009
Von frustrated
- Veröffentlicht auf Amazon.com
Format:Taschenbuch
This book covers alot of ground and the table of contents had me really excited. However, one chapter into the book and the authors are using, without explanation, terms and symbols that will be foreign to most biologists. Moreover, they present practice problems for solution that have no analogue in the text. This book is probably great if you already know all the math. But, I respectfully disagree with the previous reviewer that it's a good source from which to learn about dynamical systems for the first time...
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