731 research outputs found
Social Dilemmas and Cooperation in Complex Networks
In this paper we extend the investigation of cooperation in some classical
evolutionary games on populations were the network of interactions among
individuals is of the scale-free type. We show that the update rule, the payoff
computation and, to some extent the timing of the operations, have a marked
influence on the transient dynamics and on the amount of cooperation that can
be established at equilibrium. We also study the dynamical behavior of the
populations and their evolutionary stability.Comment: 12 pages, 7 figures. to appea
Evolutionary prisoner's dilemma game on hierarchical lattices
An evolutionary prisoner's dilemma (PD) game is studied with players located
on a hierarchical structure of layered square lattices. The players can follow
two strategies [D (defector) and C (cooperator)] and their income comes from PD
games with the ``neighbors.'' The adoption of one of the neighboring strategies
is allowed with a probability dependent on the payoff difference. Monte Carlo
simulations are performed to study how the measure of cooperation is affected
by the number of hierarchical levels (Q) and by the temptation to defect.
According to the simulations the highest frequency of cooperation can be
observed at the top level if the number of hierarchical levels is low (Q<4).
For larger Q, however, the highest frequency of cooperators occurs in the
middle layers. The four-level hierarchical structure provides the highest
average (total) income for the whole community.Comment: appendix adde
Experimental analysis of lateral impact on planar brittle material
The fragmentation of alumina and glass plates due to lateral impact is
studied. A few hundred plates have been fragmented at different impact
velocities and the produced fragments are analyzed. The method employed in this
work allows one to investigate some geometrical properties of the fragments,
besides the traditional size distribution usually studied in former
experiments. We found that, although both materials exhibit qualitative similar
fragment size distribution function, their geometrical properties appear to be
quite different. A schematic model for two-dimensional fragmentation is also
presented and its predictions are compared to our experimental results. The
comparison suggests that the analysis of the fragments' geometrical properties
constitutes a more stringent test of the theoretical models' assumptions than
the size distribution
Extreme value statistics and return intervals in long-range correlated uniform deviates
We study extremal statistics and return intervals in stationary long-range
correlated sequences for which the underlying probability density function is
bounded and uniform. The extremal statistics we consider e.g., maximum relative
to minimum are such that the reference point from which the maximum is measured
is itself a random quantity. We analytically calculate the limiting
distributions for independent and identically distributed random variables, and
use these as a reference point for correlated cases. The distributions are
different from that of the maximum itself i.e., a Weibull distribution,
reflecting the fact that the distribution of the reference point either
dominates over or convolves with the distribution of the maximum. The
functional form of the limiting distributions is unaffected by correlations,
although the convergence is slower. We show that our findings can be directly
generalized to a wide class of stochastic processes. We also analyze return
interval distributions, and compare them to recent conjectures of their
functional form
Renormalization group theory for finite-size scaling in extreme statistics
We present a renormalization group (RG) approach to explain universal
features of extreme statistics, applied here to independent, identically
distributed variables. The outlines of the theory have been described in a
previous Letter, the main result being that finite-size shape corrections to
the limit distribution can be obtained from a linearization of the RG
transformation near a fixed point, leading to the computation of stable
perturbations as eigenfunctions. Here we show details of the RG theory which
exhibit remarkable similarities to the RG known in statistical physics. Besides
the fixed points explaining universality, and the least stable eigendirections
accounting for convergence rates and shape corrections, the similarities
include marginally stable perturbations which turn out to be generic for the
Fisher-Tippett-Gumbel class. Distribution functions containing unstable
perturbations are also considered. We find that, after a transitory divergence,
they return to the universal fixed line at the same or at a different point
depending on the type of perturbation.Comment: 15 pages, 8 figures, to appear in Phys. Rev.
Evolution of Coordination in Social Networks: A Numerical Study
Coordination games are important to explain efficient and desirable social
behavior. Here we study these games by extensive numerical simulation on
networked social structures using an evolutionary approach. We show that local
network effects may promote selection of efficient equilibria in both pure and
general coordination games and may explain social polarization. These results
are put into perspective with respect to known theoretical results. The main
insight we obtain is that clustering, and especially community structure in
social networks has a positive role in promoting socially efficient outcomes.Comment: preprint submitted to IJMP
Conditional strategies and the evolution of cooperation in spatial public goods games
The fact that individuals will most likely behave differently in different
situations begets the introduction of conditional strategies. Inspired by this,
we study the evolution of cooperation in the spatial public goods game, where
besides unconditional cooperators and defectors, also different types of
conditional cooperators compete for space. Conditional cooperators will
contribute to the public good only if other players within the group are likely
to cooperate as well, but will withhold their contribution otherwise. Depending
on the number of other cooperators that are required to elicit cooperation of a
conditional cooperator, the latter can be classified in as many types as there
are players within each group. We find that the most cautious cooperators, such
that require all other players within a group to be conditional cooperators,
are the undisputed victors of the evolutionary process, even at very low
synergy factors. We show that the remarkable promotion of cooperation is due
primarily to the spontaneous emergence of quarantining of defectors, which
become surrounded by conditional cooperators and are forced into isolated
convex "bubbles" from where they are unable to exploit the public good. This
phenomenon can be observed only in structured populations, thus adding to the
relevance of pattern formation for the successful evolution of cooperation.Comment: 7 two-column pages, 7 figures; accepted for publication in Physical
Review
Evolutionary Dynamics of Populations with Conflicting Interactions: Classification and Analytical Treatment Considering Asymmetry and Power
Evolutionary game theory has been successfully used to investigate the
dynamics of systems, in which many entities have competitive interactions. From
a physics point of view, it is interesting to study conditions under which a
coordination or cooperation of interacting entities will occur, be it spins,
particles, bacteria, animals, or humans. Here, we analyze the case, where the
entities are heterogeneous, particularly the case of two populations with
conflicting interactions and two possible states. For such systems, explicit
mathematical formulas will be determined for the stationary solutions and the
associated eigenvalues, which determine their stability. In this way, four
different types of system dynamics can be classified, and the various kinds of
phase transitions between them will be discussed. While these results are
interesting from a physics point of view, they are also relevant for social,
economic, and biological systems, as they allow one to understand conditions
for (1) the breakdown of cooperation, (2) the coexistence of different
behaviors ("subcultures"), (2) the evolution of commonly shared behaviors
("norms"), and (4) the occurrence of polarization or conflict. We point out
that norms have a similar function in social systems that forces have in
physics
Extreme value distributions and Renormalization Group
In the classical theorems of extreme value theory the limits of suitably
rescaled maxima of sequences of independent, identically distributed random
variables are studied. So far, only affine rescalings have been considered. We
show, however, that more general rescalings are natural and lead to new limit
distributions, apart from the Gumbel, Weibull, and Fr\'echet families. The
problem is approached using the language of Renormalization Group
transformations in the space of probability densities. The limit distributions
are fixed points of the transformation and the study of the differential around
them allows a local analysis of the domains of attraction and the computation
of finite-size corrections.Comment: 16 pages, 5 figures. Final versio
Social Network Reciprocity as a Phase Transition in Evolutionary Cooperation
In Evolutionary Dynamics the understanding of cooperative phenomena in
natural and social systems has been the subject of intense research during
decades. We focus attention here on the so-called "Lattice Reciprocity"
mechanisms that enhance evolutionary survival of the cooperative phenotype in
the Prisoner's Dilemma game when the population of darwinian replicators
interact through a fixed network of social contacts. Exact results on a "Dipole
Model" are presented, along with a mean-field analysis as well as results from
extensive numerical Monte Carlo simulations. The theoretical framework used is
that of standard Statistical Mechanics of macroscopic systems, but with no
energy considerations. We illustrate the power of this perspective on social
modeling, by consistently interpreting the onset of lattice reciprocity as a
thermodynamical phase transition that, moreover, cannot be captured by a purely
mean-field approach.Comment: 10 pages. APS styl
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