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Evolutionary Games and Population Dynamics

By Josef Hofbauer and Karl Sigmund
Cambridge University Press (1998).

From the Back Cover
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 centered not on the concept of rational players but on the population dynamics of behavioural programs.

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, 6 pages, PDF.Introduction
"Evolutionary game theory has been a latecomer in the evolution of game theory. The initial aim of game theorists was to find principles of rational behaviour, by means of thought experiments involving fictitious players who were assumed to know such a theory, and to know that their equally fictitious co-players would use it. At the same time, it was expected that rational behaviour would prove to be optimal against irrational behaviour too. It turned out that this was asking for too much."
Table of Contents
Part one - Dynamical Systems and Lotka-Volterra Equations
Part two - Game Dynamics and Replicator Equations
Part three - Permanence and Stability
Part four - Population Genetics and Game Dynamics

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Book Review in Journal of Ecology
"This an excellent book, worthy sucessor to their "Theory of Evolution and Dynamical Systems; [...]"

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