1,643 research outputs found
Distinguishing the opponents in the prisoner dilemma in well-mixed populations
Here we study the effects of adopting different strategies against different
opponent instead of adopting the same strategy against all of them in the
prisoner dilemma structured in well-mixed populations. We consider an
evolutionary process in which strategies that provide reproductive success are
imitated and players replace one of their worst interactions by the new one. We
set individuals in a well-mixed population so that network reciprocity effect
is excluded and we analyze both synchronous and asynchronous updates. As a
consequence of the replacement rule, we show that mutual cooperation is never
destroyed and the initial fraction of mutual cooperation is a lower bound for
the level of cooperation. We show by simulation and mean-field analysis that
for synchronous update cooperation dominates while for asynchronous update only
cooperations associated to the initial mutual cooperations are maintained. As a
side effect of the replacement rule, an "implicit punishment" mechanism comes
up in a way that exploitations are always neutralized providing evolutionary
stability for cooperation
Weibull-type limiting distribution for replicative systems
The Weibull function is widely used to describe skew distributions observed
in nature. However, the origin of this ubiquity is not always obvious to
explain. In the present paper, we consider the well-known Galton-Watson
branching process describing simple replicative systems. The shape of the
resulting distribution, about which little has been known, is found essentially
indistinguishable from the Weibull form in a wide range of the branching
parameter; this can be seen from the exact series expansion for the cumulative
distribution, which takes a universal form. We also find that the branching
process can be mapped into a process of aggregation of clusters. In the
branching and aggregation process, the number of events considered for
branching and aggregation grows cumulatively in time, whereas, for the binomial
distribution, an independent event occurs at each time with a given success
probability.Comment: 6 pages and 5 figure
Altruistic Contents of Quantum Prisoner's Dilemma
We examine the classical contents of quantum games. It is shown that a
quantum strategy can be interpreted as a classical strategies with effective
density-dependent game matrices composed of transposed matrix elements. In
particular, successful quantum strategies in dilemma games are interpreted in
terms of a symmetrized game matrix that corresponds to an altruistic game plan.Comment: Revised according to publisher's request: 4 pgs, 2 fgs, ReVTeX4. For
more info, go to http://www.mech.kochi-tech.ac.jp/cheon
On the micro mechanics of one-dimensional normal compression
Discrete-element modelling has been used to investigate the micro mechanics of one-dimensional compression. One-dimensional compression is modelled in three dimensions using an oedometer and a large number of particles, and without the use of agglomerates. The fracture of a particle is governed by the octahedral shear stress within the particle due to the multiple contacts and a Weibull distribution of strengths. Different fracture mechanisms are considered, and the influence of the distribution of fragments produced for each fracture on the global particle size distribution and the slope of the normal compression line is investigated. Using the discrete-element method, compression is related to the evolution of a fractal distribution of particles. The compression index is found to be solely a function of the strengths of the particles as a function of size
Nucleation of cracks in a brittle sheet
We use molecular dynamics to study the nucleation of cracks in a two
dimensional material without pre-existing cracks. We study models with zero and
non-zero shear modulus. In both situations the time required for crack
formation obeys an Arrhenius law, from which the energy barrier and pre-factor
are extracted for different system sizes. For large systems, the characteristic
time of rupture is found to decrease with system size, in agreement with
classical Weibull theory. In the case of zero shear modulus, the energy
opposing rupture is identified with the breakage of a single atomic layer. In
the case of non-zero shear modulus, thermally activated fracture can only be
studied within a reasonable time at very high strains. In this case the energy
barrier involves the stretching of bonds within several layers, accounting for
a much higher barrier compared to the zero shear modulus case. This barrier is
understood within adiabatic simulations
Noise-guided evolution within cyclical interactions
We study a stochastic predator-prey model on a square lattice, where each of
the six species has two superior and two inferior partners. The invasion
probabilities between species depend on the predator-prey pair and are
supplemented by Gaussian noise. Conditions are identified that warrant the
largest impact of noise on the evolutionary process, and the results of Monte
Carlo simulations are qualitatively reproduced by a four-point cluster
dynamical mean-field approximation. The observed noise-guided evolution is
deeply routed in short-range spatial correlations, which is supported by
simulations on other host lattice topologies. Our findings are conceptually
related to the coherence resonance phenomenon in dynamical systems via the
mechanism of threshold duality. We also show that the introduced concept of
noise-guided evolution via the exploitation of threshold duality is not limited
to predator-prey cyclical interactions, but may apply to models of evolutionary
game theory as well, thus indicating its applicability in several different
fields of research.Comment: to be published in New J. Phy
Coevolution of dynamical states and interactions in dynamic networks
We explore the coupled dynamics of the internal states of a set of
interacting elements and the network of interactions among them. Interactions
are modeled by a spatial game and the network of interaction links evolves
adapting to the outcome of the game. As an example we consider a model of
cooperation, where the adaptation is shown to facilitate the formation of a
hierarchical interaction network that sustains a highly cooperative stationary
state. The resulting network has the characteristics of a small world network
when a mechanism of local neighbor selection is introduced in the adaptive
network dynamics. The highly connected nodes in the hierarchical structure of
the network play a leading role in the stability of the network. Perturbations
acting on the state of these special nodes trigger global avalanches leading to
complete network reorganization.Comment: 4 pages, 5 figures, for related material visit
http:www.imedea.uib.es/physdept
Aspiring to the fittest and promotion of cooperation in the prisoner's dilemma game
Strategy changes are an essential part of evolutionary games. Here we
introduce a simple rule that, depending on the value of a single parameter ,
influences the selection of players that are considered as potential sources of
the new strategy. For positive players with high payoffs will be considered
more likely, while for negative the opposite holds. Setting equal to
zero returns the frequently adopted random selection of the opponent. We find
that increasing the probability of adopting the strategy from the fittest
player within reach, i.e. setting positive, promotes the evolution of
cooperation. The robustness of this observation is tested against different
levels of uncertainty in the strategy adoption process and for different
interaction network. Since the evolution to widespread defection is tightly
associated with cooperators having a lower fitness than defectors, the fact
that positive values of facilitate cooperation is quite surprising. We show
that the results can be explained by means of a negative feedback effect that
increases the vulnerability of defectors although initially increasing their
survivability. Moreover, we demonstrate that the introduction of
effectively alters the interaction network and thus also the impact of
uncertainty by strategy adoptions on the evolution of cooperation.Comment: 7 two-column pages, 5 figures; accepted for publication in Physical
Review
Restricted connections among distinguished players support cooperation
We study the evolution of cooperation within the spatial prisoner's dilemma
game on a square lattice where a fraction of players can spread their
strategy more easily than the rest due to a predetermined larger teaching
capability. In addition, players characterized with the larger teaching
capability are allowed to temporarily link with distant opponents of the same
kind with probability , thus introducing shortcut connections among the
distinguished. We show that these additional temporary connections are able to
sustain cooperation throughout the whole range of the temptation to defect.
Remarkably, we observe that as the temptation to defect increases the optimal
decreases, and moreover, only minute values of warrant the best
promotion of cooperation. Our study thus indicates that influential individuals
must be few and sparsely connected in order for cooperation to thrive in a
defection prone environment.Comment: 6 two-column pages, 6 figures; accepted for publication in Physical
Review
On Phase Transitions to Cooperation in the Prisoner's Dilemma
Game theory formalizes certain interactions between physical particles or
between living beings in biology, sociology, and economics, and quantifies the
outcomes by payoffs. The prisoner's dilemma (PD) describes situations in which
it is profitable if everybody cooperates rather than defects (free-rides or
cheats), but as cooperation is risky and defection is tempting, the expected
outcome is defection. Nevertheless, some biological and social mechanisms can
support cooperation by effectively transforming the payoffs. Here, we study the
related phase transitions, which can be of first order (discontinous) or of
second order (continuous), implying a variety of different routes to
cooperation. After classifying the transitions into cases of equilibrium
displacement, equilibrium selection, and equilibrium creation, we show that a
transition to cooperation may take place even if the stationary states and the
eigenvalues of the replicator equation for the PD stay unchanged. Our example
is based on adaptive group pressure, which makes the payoffs dependent on the
endogeneous dynamics in the population. The resulting bistability can invert
the expected outcome in favor of cooperation.Comment: For related work see http://www.soms.ethz.ch
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