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. |