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Game Equilibrium Models I - Evolution and Game Dynamics (Paperback, Softcover reprint of the original 1st ed. 1991)
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Game Equilibrium Models I - Evolution and Game Dynamics (Paperback, Softcover reprint of the original 1st ed. 1991)
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There are two main approaches towards the phenotypic analysis of
frequency dependent natural selection. First, there is the approach
of evolutionary game theory, which was introduced in 1973 by John
Maynard Smith and George R. Price. In this theory, the dynamical
process of natural selection is not modeled explicitly. Instead,
the selective forces acting within a population are represented by
a fitness function, which is then analysed according to the concept
of an evolutionarily stable strategy or ESS. Later on, the static
approach of evolutionary game theory has been complemented by a
dynamic stability analysis of the replicator equations. Introduced
by Peter D. Taylor and Leo B. Jonker in 1978, these equations
specify a class of dynamical systems, which provide a simple
dynamic description of a selection process. Usually, the
investigation of the replicator dynamics centers around a stability
analysis of their stationary solutions. Although evolutionary
stability and dynamic stability both intend to characterize the
long-term outcome of frequency dependent selection, these concepts
differ considerably in the 'philosophies' on which they are based.
It is therefore not too surprising that they often lead to quite
different evolutionary predictions (see, e. g. , Weissing 1983).
The present paper intends to illustrate the incongruities between
the two approaches towards a phenotypic theory of natural
selection. A detailed game theoretical and dynamical analysis is
given for a generic class of evolutionary normal form games.
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