Information Technology Reference
In-Depth Information
16.1.Introduction
From human societies to the simplest biological systems, cooperative interactions
thrive at all levels of organization. A cooperative act typically involves a cost (c) to
the provider while conferring a benet (b) to the recipient (with b > c) [Hamilton
(1996); Trivers (1985); Wilson (1975); Axelrod and Hamilton (1981)]. Individuals
try to maximize their own resources and are therefore expected to avoid paying
any costs while gladly accepting all the benets oered by others. This ubiquitous
paradox is often analyzed in the framework of (evolutionary) game theory. Game
theory describes systems in which the success of an individual depends on the ac-
tion of others. The classical approach focused on the determination of optimal
strategic behavior of rational individuals in such a static setting [von Neumann and
Morgenstern (1944)]. Evolutionary game theory places this framework into a dy-
namical context by looking at the evolutionary dynamics in populations of players
[Maynard Smith (1982)]. The expected payo from the game is a function of the fre-
quencies of all strategies. Successful behaviors spread in such a population. There
are two interpretations of evolutionary game theory: In the conventional setting,
the payo is interpreted as biological tness. Individuals reproduce proportional
to their tness and successful strategies spread by genetic reproduction. A second
interpretation is the basis for cultural evolution in social systems: Successful behav-
iors are imitated with a higher probability. They spread by social learning instead
of genetic reproduction. Both frameworks are captured by the same mathematical
approach: The generic mathematical description of evolutionary game dynamics is
the replicator equation [Taylor and Jonker (1978); Hofbauer and Sigmund (1998);
Zeeman (1980)]. This system of nonlinear ordinary dierential equations describes
how the relative abundances (frequencies) of strategies change over time.
The assumption underlying the replicator equation is that individuals meet each
other at random in innitely large, well-mixed populations. But it also emerges in
other cases, e.g. if the interaction rates between individuals are not random [Taylor
and Nowak (2006)] or from a large-population approximation of evolutionary game
dynamics in nite populations [Traulsen et al. (2005)].
However, in reality the probability to interact with someone else is not the
same across a population or social community. Interactions occur on social net-
works which dene the underlying topology of such cooperation dynamics. Ini-
tially, this line of research has focused on regular lattices [Nowak and May (1992);
Herz (1994); Lindgren and Nordahl (1994); Szabo and Toke (1998); Hauert (2002)].
More recently, more complex topologies and general networks have been considered
in great detail [Vainstein and Arenzon (2001); Abramson and Kuperman (2001);
Ebel and Bornholdt (2002a); Holme et al. (2003); Szabo and Vukov (2004); Santos
and Pacheco (2005); Ohtsuki et al. (2006); Santos et al. (2006b, 2008)]. While the
theoretical advances in this eld are tremendous, there is so far a lack of exper-
imental data.
Designing and implementing such experiments has proven dicult
