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Free keywords:
multi-player games; finite population; fixation probability; fixation time;
average abundance
Abstract:
William D. Hamilton famously stated that “human life is a many person game
and not just a disjoined collection of two person games”. However, most of the theoretical
results in evolutionary game theory have been developed for two player games. In spite of
a multitude of examples ranging from humans to bacteria, multi-player games have received
less attention than pairwise games due to their inherent complexity. Such complexities arise
from the fact that group interactions cannot always be considered as a sum of multiple
pairwise interactions. Mathematically, multi-player games provide a natural way to introduce
non-linear, polynomial fitness functions into evolutionary game theory, whereas pairwise
games lead to linear fitness functions. Similarly, studying finite populations is a natural
way of introducing intrinsic stochasticity into population dynamics. While these topics have
been dealt with individually, few have addressed the combination of finite populations and
multi-player games so far. We are investigating the dynamical properties of evolutionary
multi-player games in finite populations. Properties of the fixation probability and fixation
time, which are relevant for rare mutations, are addressed in well mixed populations. For
more frequent mutations, the average abundance is investigated in well mixed as well as in
structured populations. While the fixation properties are generalizations of the results from
two player scenarios, addressing the average abundance in multi-player games gives rise to
novel outcomes not possible in pairwise games.
