43,193 research outputs found
Evolutionary games on graphs
Game theory is one of the key paradigms behind many scientific disciplines
from biology to behavioral sciences to economics. In its evolutionary form and
especially when the interacting agents are linked in a specific social network
the underlying solution concepts and methods are very similar to those applied
in non-equilibrium statistical physics. This review gives a tutorial-type
overview of the field for physicists. The first three sections introduce the
necessary background in classical and evolutionary game theory from the basic
definitions to the most important results. The fourth section surveys the
topological complications implied by non-mean-field-type social network
structures in general. The last three sections discuss in detail the dynamic
behavior of three prominent classes of models: the Prisoner's Dilemma, the
Rock-Scissors-Paper game, and Competing Associations. The major theme of the
review is in what sense and how the graph structure of interactions can modify
and enrich the picture of long term behavioral patterns emerging in
evolutionary games.Comment: Review, final version, 133 pages, 65 figure
On scale-free and poly-scale behaviors of random hierarchical network
In this paper the question about statistical properties of
block--hierarchical random matrices is raised for the first time in connection
with structural characteristics of random hierarchical networks obtained by
mipmapping procedure. In particular, we compute numerically the spectral
density of large random adjacency matrices defined by a hierarchy of the
Bernoulli distributions on matrix elements, where
depends on hierarchy level as (). For the spectral density we clearly see the free--scale
behavior. We show also that for the Gaussian distributions on matrix elements
with zero mean and variances , the tail of the
spectral density, , behaves as for and , while for
the power--law behavior is terminated. We also find that the vertex
degree distribution of such hierarchical networks has a poly--scale fractal
behavior extended to a very broad range of scales.Comment: 11 pages, 6 figures (paper is substantially revised
Evolution of cooperation on dynamical graphs
There are two key characteristic of animal and human societies: (1) degree heterogeneity, meaning that not all individual have the same number of associates; and (2) the interaction topology is not static, i.e. either individuals interact with different set of individuals at different times of their life, or at least they have different associations than their parents. Earlier works have shown that population structure is one of the mechanisms promoting cooperation. However, most studies had assumed that the interaction network can be described by a regular graph (homogeneous degree distribution). Recently there are an increasing number of studies employing degree heterogeneous graphs to model interaction topology. But mostly the interaction topology was assumed to be static. Here we investigate the fixation probability of the cooperator strategy in the prisoner’s dilemma, when interaction network is a random regular graph, a random graph or a scale-free graph and the interaction network is allowed to change.
We show that the fixation probability of the cooperator strategy is lower when the interaction topology is described by a dynamical graph compared to a static graph. Even a limited network dynamics significantly decreases the fixation probability of cooperation, an effect that is mitigated stronger by degree heterogeneous networks topology than by a degree homogeneous one. We have also found that from the considered graph topologies the decrease of fixation probabilities due to graph dynamics is the lowest on scale-free graphs
Mutual Trust and Cooperation in the Evolutionary Hawks-Doves Game
Using a new dynamical network model of society in which pairwise interactions
are weighted according to mutual satisfaction, we show that cooperation is the
norm in the Hawks-Doves game when individuals are allowed to break ties with
undesirable neighbors and to make new acquaintances in their extended
neighborhood. Moreover, cooperation is robust with respect to rather strong
strategy perturbations. We also discuss the empirical structure of the emerging
networks, and the reasons that allow cooperators to thrive in the population.
Given the metaphorical importance of this game for social interaction, this is
an encouraging positive result as standard theory for large mixing populations
prescribes that a certain fraction of defectors must always exist at
equilibrium.Comment: 23 pages 12 images, to appea
An analysis of the fixation probability of a mutant on special classes of non-directed graphs
There is a growing interest in the study of evolutionary dynamics on populations with some non-homogeneous structure. In this paper we follow the model of Lieberman et al. (Lieberman et al. 2005 Nature 433, 312–316) of evolutionary dynamics on a graph. We investigate the case of non-directed equally weighted graphs and find solutions for the fixation probability of a single mutant in two classes of simple graphs. We further demonstrate that finding similar solutions on graphs outside these classes is far more complex. Finally, we investigate our chosen classes numerically and discuss a number of features of the graphs; for example, we find the fixation probabilities for different initial starting positions and observe that average fixation probabilities are always increased for advantageous mutants as compared with those of unstructured populations
Information content of colored motifs in complex networks
We study complex networks in which the nodes of the network are tagged with
different colors depending on the functionality of the nodes (colored graphs),
using information theory applied to the distribution of motifs in such
networks. We find that colored motifs can be viewed as the building blocks of
the networks (much more so than the uncolored structural motifs can be) and
that the relative frequency with which these motifs appear in the network can
be used to define the information content of the network. This information is
defined in such a way that a network with random coloration (but keeping the
relative number of nodes with different colors the same) has zero color
information content. Thus, colored motif information captures the
exceptionality of coloring in the motifs that is maintained via selection. We
study the motif information content of the C. elegans brain as well as the
evolution of colored motif information in networks that reflect the interaction
between instructions in genomes of digital life organisms. While we find that
colored motif information appears to capture essential functionality in the C.
elegans brain (where the color assignment of nodes is straightforward) it is
not obvious whether the colored motif information content always increases
during evolution, as would be expected from a measure that captures network
complexity. For a single choice of color assignment of instructions in the
digital life form Avida, we find rather that colored motif information content
increases or decreases during evolution, depending on how the genomes are
organized, and therefore could be an interesting tool to dissect genomic
rearrangements.Comment: 21 pages, 8 figures, to appear in Artificial Lif
- …