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      Spontaneous Symmetry Breaking in Interdependent Networked Game

      1 , 2 , a , 3 , b , 4 , c , 2 , 5 , 6

      Scientific Reports

      Nature Publishing Group

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          Abstract

          Spatial evolution game has traditionally assumed that players interact with direct neighbors on a single network, which is isolated and not influenced by other systems. However, this is not fully consistent with recent research identification that interactions between networks play a crucial rule for the outcome of evolutionary games taking place on them. In this work, we introduce the simple game model into the interdependent networks composed of two networks. By means of imitation dynamics, we display that when the interdependent factor α is smaller than a threshold value α C , the symmetry of cooperation can be guaranteed. Interestingly, as interdependent factor exceeds α C , spontaneous symmetry breaking of fraction of cooperators presents itself between different networks. With respect to the breakage of symmetry, it is induced by asynchronous expansion between heterogeneous strategy couples of both networks, which further enriches the content of spatial reciprocity. Moreover, our results can be well predicted by the strategy-couple pair approximation method.

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          Most cited references 27

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          Emergence of scaling in random networks

          Systems as diverse as genetic networks or the world wide web are best described as networks with complex topology. A common property of many large networks is that the vertex connectivities follow a scale-free power-law distribution. This feature is found to be a consequence of the two generic mechanisms that networks expand continuously by the addition of new vertices, and new vertices attach preferentially to already well connected sites. A model based on these two ingredients reproduces the observed stationary scale-free distributions, indicating that the development of large networks is governed by robust self-organizing phenomena that go beyond the particulars of the individual systems.
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            Community Structure in Time-Dependent, Multiscale, and Multiplex Networks

            Network science is an interdisciplinary endeavor, with methods and applications drawn from across the natural, social, and information sciences. A prominent problem in network science is the algorithmic detection of tightly-connected groups of nodes known as communities. We developed a generalized framework of network quality functions that allowed us to study the community structure of arbitrary multislice networks, which are combinations of individual networks coupled through links that connect each node in one network slice to itself in other slices. This framework allows one to study community structure in a very general setting encompassing networks that evolve over time, have multiple types of links (multiplexity), and have multiple scales.
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              Evolutionary dynamics of social dilemmas in structured heterogeneous populations.

              Real populations have been shown to be heterogeneous, in which some individuals have many more contacts than others. This fact contrasts with the traditional homogeneous setting used in studies of evolutionary game dynamics. We incorporate heterogeneity in the population by studying games on graphs, in which the variability in connectivity ranges from single-scale graphs, for which heterogeneity is small and associated degree distributions exhibit a Gaussian tale, to scale-free graphs, for which heterogeneity is large with degree distributions exhibiting a power-law behavior. We study the evolution of cooperation, modeled in terms of the most popular dilemmas of cooperation. We show that, for all dilemmas, increasing heterogeneity favors the emergence of cooperation, such that long-term cooperative behavior easily resists short-term noncooperative behavior. Moreover, we show how cooperation depends on the intricate ties between individuals in scale-free populations.
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                Author and article information

                Journal
                Sci Rep
                Sci Rep
                Scientific Reports
                Nature Publishing Group
                2045-2322
                14 February 2014
                2014
                : 4
                Affiliations
                [1 ]Center for Complex Network Research and Department of Physics, Northeastern University , Boston, MA 02115, USA
                [2 ]School of Physics, Nankai University , Tianjin 300071, China
                [3 ]Centre for Chaos and Complex Networks, Department of Electronic Engineering, City University of Hong Kong , Kowloon, Hong Kong
                [4 ]Key Laboratory of Computer Vision and System (Ministry of Education) and Tianjin Key Laboratory of Intelligence Computing and Novel Software Technology, Tianjin University of Technology , Tianjin 300384, China
                [5 ]Department of Physics, Hong Kong Baptist University , Kowloon Tong, Hong Kong
                [6 ]Center for Nonlinear Studies, Beijing-Hong Kong-Singapore Joint Center for Nonlinear and Complex systems (Hong Kong), and Institute of Computational and Theoretical Studies, Hong Kong Baptist University , Kowloon Tong, Hong Kong
                Author notes
                Article
                srep04095
                10.1038/srep04095
                3924213
                Copyright © 2014, Macmillan Publishers Limited. All rights reserved

                This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License. To view a copy of this license, visit http://creativecommons.org/licenses/by-nc-nd/3.0/

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