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The four volumes of Game Equilibrium Models present applications of
non-cooperative game theory. Problems of strategic interaction
arising in biology, economics, political science and the social
sciences in general are treated in 42 papers on a wide variety of
subjects. Internationally known authors with backgrounds in various
disciplines have contributed original research. The reader finds
innovative modelling combined with advanced methods of analysis.
The four volumes are the outcome of a research year at the Center
for Interdisciplinary Studies of the University of Bielefeld. The
close interaction of an international interdisciplinary group of
researchers has produced an unusual collection of remarkable
results of great interes for everybody who wants to be informed on
the scope, potential, and future direction of work in applied game
theory. Volume I Evolution and Game Dynamics mainly deals with
dynamic stability with respect to evolutionary processes. The book
offers not only theoretical classification of the foundations of
evolutionary game theory, but also exciting new biological
applications. Volume II Methods, Morals and Markets contains areas
of research which will attract the interest of economists,
political scientists, mathematicians and philosophers. The papers
deal with the methodology of analysis of games, game theoretic
contributions to fundamental ethical questions facing societies and
game-theoretic analyses of market environments. Volume III
Strategic Bargaining contains ten papers on game equilibrium models
of bargaining. All these contributions look at bargaining
situations as non-cooperative games. General models of two-person
and n-person bargaining areexplored. Volume IV Social and Political
Interaction contains game equilibrium models focussing on social
and political interaction within communities or states or between
states, i.e. national and international social and political
interaction. Specific aspects of those interactions are modelled as
non-cooperative games and their equilibria are analysed.
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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