738 research outputs found
Metastability of Asymptotically Well-Behaved Potential Games
One of the main criticisms to game theory concerns the assumption of full
rationality. Logit dynamics is a decentralized algorithm in which a level of
irrationality (a.k.a. "noise") is introduced in players' behavior. In this
context, the solution concept of interest becomes the logit equilibrium, as
opposed to Nash equilibria. Logit equilibria are distributions over strategy
profiles that possess several nice properties, including existence and
uniqueness. However, there are games in which their computation may take time
exponential in the number of players. We therefore look at an approximate
version of logit equilibria, called metastable distributions, introduced by
Auletta et al. [SODA 2012]. These are distributions that remain stable (i.e.,
players do not go too far from it) for a super-polynomial number of steps
(rather than forever, as for logit equilibria). The hope is that these
distributions exist and can be reached quickly by logit dynamics.
We identify a class of potential games, called asymptotically well-behaved,
for which the behavior of the logit dynamics is not chaotic as the number of
players increases so to guarantee meaningful asymptotic results. We prove that
any such game admits distributions which are metastable no matter the level of
noise present in the system, and the starting profile of the dynamics. These
distributions can be quickly reached if the rationality level is not too big
when compared to the inverse of the maximum difference in potential. Our proofs
build on results which may be of independent interest, including some spectral
characterizations of the transition matrix defined by logit dynamics for
generic games and the relationship of several convergence measures for Markov
chains
Entanglement Entropy, decoherence, and quantum phase transition of a dissipative two-level system
The concept of entanglement entropy appears in multiple contexts, from black
hole physics to quantum information theory, where it measures the entanglement
of quantum states. We investigate the entanglement entropy in a simple model,
the spin-boson model, which describes a qubit (two-level system) interacting
with a collection of harmonic oscillators that models the environment
responsible for decoherence and dissipation. The entanglement entropy allows to
make a precise unification between entanglement of the spin with its
environment, decoherence, and quantum phase transitions. We derive exact
analytical results which are confirmed by Numerical Renormalization Group
arguments both for an ohmic and a subohmic bosonic bath. Those demonstrate that
the entanglement entropy obeys universal scalings. We make comparisons with
entanglement properties in the quantum Ising model and in the Dicke model. We
also emphasize the possibility of measuring this entanglement entropy using
charge qubits subject to electromagnetic noise; such measurements would provide
an empirical proof of the existence of entanglement entropy.Comment: 38 pages, 8 figures, related to cond-mat/0612095 and arXiv:0705.0957;
final version to appear in Annals of Physic
Spin density wave dislocation in chromium probed by coherent x-ray diffraction
We report on the study of a magnetic dislocation in pure chromium. Coherent
x-ray diffraction profiles obtained on the incommensurate Spin Density Wave
(SDW) reflection are consistent with the presence of a dislocation of the
magnetic order, embedded at a few micrometers from the surface of the sample.
Beyond the specific case of magnetic dislocations in chromium, this work may
open up a new method for the study of magnetic defects embedded in the bulk.Comment: 8 pages, 7 figure
A numerical study on the evolution of portfolio rules
In this paper we test computationally the performance of CAPM in an evolutionary setting. In particular we study the stability of distribution of wealth in a financial market where some traders invest as prescribed by CAPM and others behave according to different portfolio rules. Our study is motivated by recent analytical results that show that, whenever a logarithmic utility maximiser enters the market, CAPM traders vanish in the long run. Our analysis provides further insights and extends these results. We simulate a sequence of trades in a financial market and: first, we address the issue of how long is the long run in different parametric settings; second, we study the effect of heterogeneous savings behaviour on asymptotic wealth shares. We find that CAPM is particularly “unfit” for highly risky environments
A measure of individual role in collective dynamics
Identifying key players in collective dynamics remains a challenge in several
research fields, from the efficient dissemination of ideas to drug target
discovery in biomedical problems. The difficulty lies at several levels: how to
single out the role of individual elements in such intermingled systems, or
which is the best way to quantify their importance. Centrality measures
describe a node's importance by its position in a network. The key issue
obviated is that the contribution of a node to the collective behavior is not
uniquely determined by the structure of the system but it is a result of the
interplay between dynamics and network structure. We show that dynamical
influence measures explicitly how strongly a node's dynamical state affects
collective behavior. For critical spreading, dynamical influence targets nodes
according to their spreading capabilities. For diffusive processes it
quantifies how efficiently real systems may be controlled by manipulating a
single node.Comment: accepted for publication in Scientific Report
Optimal interdependence between networks for the evolution of cooperation
Recent research has identified interactions between networks as crucial for the outcome of evolutionary
games taking place on them. While the consensus is that interdependence does promote cooperation by
means of organizational complexity and enhanced reciprocity that is out of reach on isolated networks, we
here address the question just how much interdependence there should be. Intuitively, one might assume
the more the better. However, we show that in fact only an intermediate density of sufficiently strong
interactions between networks warrants an optimal resolution of social dilemmas. This is due to an intricate
interplay between the heterogeneity that causes an asymmetric strategy flow because of the additional links
between the networks, and the independent formation of cooperative patterns on each individual network.
Presented results are robust to variations of the strategy updating rule, the topology of interdependent
networks, and the governing social dilemma, thus suggesting a high degree of universality
Independent Lazy Better-Response Dynamics on Network Games
International audienceWe study an independent best-response dynamics on network games in which the nodes (players) decide to revise their strategies independently with some probability. We provide several bounds on the convergence time to an equilibrium as a function of this probability, the degree of the network, and the potential of the underlying games. These dynamics are somewhat more suitable for distributed environments than the classical better- and best-response dynamics where players revise their strategies "sequentially'", i.e., no two players revise their strategies simultaneously
Influence of opinion dynamics on the evolution of games
Under certain circumstances such as lack of information or bounded
rationality, human players can take decisions on which strategy to choose in a
game on the basis of simple opinions. These opinions can be modified after each
round by observing own or others payoff results but can be also modified after
interchanging impressions with other players. In this way, the update of the
strategies can become a question that goes beyond simple evolutionary rules
based on fitness and become a social issue. In this work, we explore this
scenario by coupling a game with an opinion dynamics model. The opinion is
represented by a continuous variable that corresponds to the certainty of the
agents respect to which strategy is best. The opinions transform into actions
by making the selection of an strategy a stochastic event with a probability
regulated by the opinion. A certain regard for the previous round payoff is
included but the main update rules of the opinion are given by a model inspired
in social interchanges. We find that the dynamics fixed points of the coupled
model is different from those of the evolutionary game or the opinion models
alone. Furthermore, new features emerge such as the resilience of the fraction
of cooperators to the topology of the social interaction network or to the
presence of a small fraction of extremist players.Comment: 7 pages, 5 figure
Illuminating hydrological processes at the soil-vegetation-atmosphere interface with water stable isotopes
Funded by DFG research project “From Catchments as Organised Systems to Models based on Functional Units” (FOR 1Peer reviewedPublisher PDFPublisher PD
On sea surface salinity skin effect iInduced by evaporation and implications for remote sensing of ocean salinity
Author Posting. © American Meteorological Society, 2010. This article is posted here by permission of American Meteorological Society for personal use, not for redistribution. The definitive version was published in Journal of Physical Oceanography 46 (2010): 85-102, doi:10.1175/2009JPO4168.1.The existence of a cool and salty sea surface skin under evaporation was first proposed by Saunders in 1967, but few efforts have since been made to perceive the salt component of the skin layer. With two salinity missions scheduled to launch in the coming years, this study attempted to revisit the Saunders concept and to utilize presently available air–sea forcing datasets to analyze, understand, and interpret the effect of the salty skin and its implication for remote sensing of ocean salinity.
Similar to surface cooling, the skin salinification would occur primarily at low and midlatitudes in regions that are characterized by low winds or high evaporation. On average, the skin is saltier than the interior water by 0.05–0.15 psu and cooler by 0.2°–0.5°C. The cooler and saltier skin at the top is always statically unstable, and the tendency to overturn is controlled by cooling. Once the skin layer overturns, the time to reestablish the full increase of skin salinity was reported to be on the order of 15 min, which is approximately 90 times slower than that for skin temperature. Because the radiation received from a footprint is averaged over an area to give a single pixel value, the slow recovery by the salt diffusion process might cause a slight reduction in area-averaged skin salinity and thus obscure the salty skin effect on radiometer retrievals. In the presence of many geophysical error sources in remote sensing of ocean salinity, the salt enrichment at the surface skin does not appear to be a concern
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