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      Spontaneous symmetry breaking in interdependent networked game.

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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 references27

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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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              Coevolutionary games--a mini review.

              Prevalence of cooperation within groups of selfish individuals is puzzling in that it contradicts with the basic premise of natural selection. Favoring players with higher fitness, the latter is key for understanding the challenges faced by cooperators when competing with defectors. Evolutionary game theory provides a competent theoretical framework for addressing the subtleties of cooperation in such situations, which are known as social dilemmas. Recent advances point towards the fact that the evolution of strategies alone may be insufficient to fully exploit the benefits offered by cooperative behavior. Indeed, while spatial structure and heterogeneity, for example, have been recognized as potent promoters of cooperation, coevolutionary rules can extend the potentials of such entities further, and even more importantly, lead to the understanding of their emergence. The introduction of coevolutionary rules to evolutionary games implies, that besides the evolution of strategies, another property may simultaneously be subject to evolution as well. Coevolutionary rules may affect the interaction network, the reproduction capability of players, their reputation, mobility or age. Here we review recent works on evolutionary games incorporating coevolutionary rules, as well as give a didactic description of potential pitfalls and misconceptions associated with the subject. In addition, we briefly outline directions for future research that we feel are promising, thereby particularly focusing on dynamical effects of coevolutionary rules on the evolution of cooperation, which are still widely open to research and thus hold promise of exciting new discoveries. Copyright (c) 2009 Elsevier Ireland Ltd. All rights reserved.
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                Author and article information

                Journal
                Sci Rep
                Scientific reports
                Springer Science and Business Media LLC
                2045-2322
                2045-2322
                Feb 14 2014
                : 4
                Affiliations
                [1 ] 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.
                [2 ] Centre for Chaos and Complex Networks, Department of Electronic Engineering, City University of Hong Kong, Kowloon, Hong Kong.
                [3 ] 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.
                [4 ] 1] School of Physics, Nankai University, Tianjin 300071, China [2] Department of Physics, Hong Kong Baptist University, Kowloon Tong, Hong Kong [3] 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.
                Article
                srep04095
                10.1038/srep04095
                3924213
                24526076
                1fa3a051-d541-4244-b486-963f19902832
                History

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