Self-organization towards optimally interdependent networks by means of coevolution

Coevolution between strategy and network structure is established as a means to arrive at the optimal conditions needed to resolve social dilemmas. Yet recent research has highlighted that the interdependence between networks may be just as important as the structure of an individual network. We therefore introduce the coevolution of strategy and network interdependence to see whether this can give rise to elevated levels of cooperation in the prisonerʼs dilemma game. We show that the interdependence between networks self-organizes so as to yield optimal conditions for the evolution of cooperation. Even under extremely adverse conditions, cooperators can prevail where on isolated networks they would perish. This is due to the spontaneous emergence of a two-class society, with only the upper class being allowed to control and take advantage of the interdependence. Spatial patterns reveal that cooperators, once arriving at the upper class, are much more competent than defectors in sustaining compact clusters of followers. Indeed, the asymmetric exploitation of interdependence confers to them a strong evolutionary advantage that may resolve even the toughest of social dilemmas.

[1]  M. Tomassini,et al.  Hawks and Doves on small-world networks. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[2]  E A Leicht,et al.  Suppressing cascades of load in interdependent networks , 2011, Proceedings of the National Academy of Sciences.

[3]  Attila Szolnoki,et al.  Resolving social dilemmas on evolving random networks , 2009, 0910.1905.

[4]  Víctor M Eguíluz,et al.  Coevolution of dynamical states and interactions in dynamic networks. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[5]  Andrea Baronchelli,et al.  Connect and win: The role of social networks in political elections , 2012, ArXiv.

[6]  Harry Eugene Stanley,et al.  Assortativity Decreases the Robustness of Interdependent Networks , 2012, Physical review. E, Statistical, nonlinear, and soft matter physics.

[7]  V. Latora,et al.  Complex networks: Structure and dynamics , 2006 .

[8]  Alessandro Vespignani,et al.  Dynamical Processes on Complex Networks , 2008 .

[9]  Yamir Moreno,et al.  Evolutionary dynamics on interdependent populations. , 2012, Physical review. E, Statistical, nonlinear, and soft matter physics.

[10]  Marco Tomassini,et al.  Conformity hinders the evolution of cooperation on scale-free networks. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[11]  Jun Tanimoto,et al.  Network reciprocity by coexisting learning and teaching strategies. , 2012, Physical review. E, Statistical, nonlinear, and soft matter physics.

[12]  G. Bianconi Statistical mechanics of multiplex networks: entropy and overlap. , 2013, Physical review. E, Statistical, nonlinear, and soft matter physics.

[13]  John Pretz,et al.  Detection of atmospheric muon neutrinos with the IceCube 9-string detector , 2007 .

[14]  Yamir Moreno,et al.  Cooperation in scale-free networks with limited associative capacities. , 2011, Physical review. E, Statistical, nonlinear, and soft matter physics.

[15]  J M Smith,et al.  Evolution and the theory of games , 1976 .

[16]  Xiang Li,et al.  Roles of mixing patterns in cooperation on a scale-free networked game. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[17]  S. Assenza,et al.  Enhancement of cooperation in highly clustered scale-free networks. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[18]  Harry Eugene Stanley,et al.  Catastrophic cascade of failures in interdependent networks , 2009, Nature.

[19]  Conrado J. Pérez Vicente,et al.  Diffusion dynamics on multiplex networks , 2012, Physical review letters.

[20]  Arne Traulsen,et al.  Coevolution of strategy and structure in complex networks with dynamical linking. , 2006, Physical review letters.

[21]  W. Hamilton,et al.  The evolution of cooperation. , 1984, Science.

[22]  M. Nowak,et al.  Evolutionary games and spatial chaos , 1992, Nature.

[23]  Harry Eugene Stanley,et al.  Robustness of interdependent networks under targeted attack , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[24]  A. Châtelain,et al.  The European Physical Journal D , 1999 .

[25]  Josef Hofbauer,et al.  Evolutionary Games and Population Dynamics , 1998 .

[26]  Albert-László Barabási,et al.  Statistical mechanics of complex networks , 2001, ArXiv.

[27]  Long Wang,et al.  Evolutionary Prisoner's Dilemma on heterogeneous Newman-Watts small-world network , 2006, math/0609626.

[28]  J. Tanimoto Dilemma solving by the coevolution of networks and strategy in a 2 x 2 game. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[29]  P. Thiran,et al.  Error and attack tolerance of layered complex networks. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[30]  Attila Szolnoki,et al.  Coevolutionary Games - A Mini Review , 2009, Biosyst..

[31]  Wei Li,et al.  Cascading Failures in Interdependent Lattice Networks: The Critical Role of the Length of Dependency Links , 2012, Physical review letters.

[32]  M. Kuperman,et al.  Social games in a social network. , 2000, Physical review. E, Statistical, nonlinear, and soft matter physics.

[33]  Kun Zhao,et al.  Percolation on interacting, antagonistic networks , 2012, ArXiv.

[34]  Attila Szolnoki,et al.  Interdependent network reciprocity in evolutionary games , 2013, Scientific Reports.

[35]  R. Axelrod,et al.  Evolutionary Dynamics , 2004 .

[36]  Attila Szolnoki,et al.  Optimal interdependence between networks for the evolution of cooperation , 2013, Scientific Reports.

[37]  Ángel Sánchez,et al.  Evolutionary game theory: Temporal and spatial effects beyond replicator dynamics , 2009, Physics of life reviews.

[38]  E. Ben-Jacob,et al.  Challenges in network science: Applications to infrastructures, climate, social systems and economics , 2012 .

[39]  Ignacio Gomez Portillo Building Cooperative Networks , 2012, ArXiv.

[40]  Yamir Moreno,et al.  Complex Cooperative Networks from Evolutionary Preferential Attachment , 2008, PloS one.

[41]  Francisco C. Santos,et al.  Cooperation Prevails When Individuals Adjust Their Social Ties , 2006, PLoS Comput. Biol..

[42]  G. Szabó,et al.  Cooperation enhanced by inhomogeneous activity of teaching for evolutionary Prisoner's Dilemma games , 2006, q-bio/0610001.

[43]  Matjaz Perc,et al.  Spreading of cooperative behaviour across interdependent groups , 2013, Scientific Reports.

[44]  Matjaz Perc,et al.  Does strong heterogeneity promote cooperation by group interactions? , 2011, ArXiv.

[45]  L. Wang,et al.  Probabilistic interconnection between interdependent networks promotes cooperation in the public goods game , 2012, ArXiv.

[46]  I. N. A. C. I. J. H. Fowler Book Review: Connected: The surprising power of our social networks and how they shape our lives. , 2009 .

[47]  Attila Szolnoki,et al.  Information sharing promotes prosocial behaviour , 2013, ArXiv.

[48]  Dirk Helbing,et al.  Globally networked risks and how to respond , 2013, Nature.

[49]  Christian M Schneider,et al.  Algorithm to determine the percolation largest component in interconnected networks. , 2013, Physical review. E, Statistical, nonlinear, and soft matter physics.

[50]  Attila Szolnoki,et al.  Evolutionary dynamics of group interactions on structured populations: a review , 2013, Journal of The Royal Society Interface.

[51]  Manfred Milinski,et al.  The Calculus of Selfishness , 2011 .

[52]  H. Stanley,et al.  Networks formed from interdependent networks , 2011, Nature Physics.

[53]  H. Stanley,et al.  Linking agent-based models and stochastic models of financial markets , 2012, Proceedings of the National Academy of Sciences.

[54]  M Barthelemy,et al.  Transport on coupled spatial networks. , 2012, Physical review letters.

[55]  F. C. Santos,et al.  Scale-free networks provide a unifying framework for the emergence of cooperation. , 2005, Physical review letters.

[56]  Markus Brede,et al.  Playing against the fittest: A simple strategy that promotes the emergence of cooperation , 2011, ArXiv.

[57]  Mark E. J. Newman,et al.  The Structure and Function of Complex Networks , 2003, SIAM Rev..

[58]  M. Perc,et al.  Social diversity and promotion of cooperation in the spatial prisoner's dilemma game. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[59]  Attila Szolnoki,et al.  Making new connections towards cooperation in the prisoner's dilemma game , 2008, 0811.4372.

[60]  David Bawden,et al.  Book Review: Evolution and Structure of the Internet: A Statistical Physics Approach. , 2006 .

[61]  F. C. Santos,et al.  Social diversity promotes the emergence of cooperation in public goods games , 2008, Nature.

[62]  M. Perc,et al.  Coevolution of teaching activity promotes cooperation , 2008, 0803.4091.

[63]  F. C. Santos,et al.  Evolutionary dynamics of social dilemmas in structured heterogeneous populations. , 2006, Proceedings of the National Academy of Sciences of the United States of America.

[64]  S. Havlin,et al.  Interdependent networks: reducing the coupling strength leads to a change from a first to second order percolation transition. , 2010, Physical review letters.

[65]  Jinzhi Lei,et al.  Burst synchronization transitions in a neuronal network of subnetworks. , 2011, Chaos.

[66]  Daniele Vilone,et al.  Disentangling social and group heterogeneities: Public Goods games on complex networks , 2011, ArXiv.

[67]  J. Gómez-Gardeñes,et al.  Evolutionary game dynamics in a growing structured population , 2009, 0907.2649.

[68]  R. Rosenfeld Nature , 2009, Otolaryngology--head and neck surgery : official journal of American Academy of Otolaryngology-Head and Neck Surgery.

[69]  Marc Timme,et al.  Self-organized adaptation of a simple neural circuit enables complex robot behaviour , 2010, ArXiv.

[70]  Long Wang,et al.  Evolution of Interactions and Cooperation in the Spatial Prisoner's Dilemma Game , 2011, PloS one.

[71]  Long Wang,et al.  Promotion of cooperation induced by the interplay between structure and game dynamics , 2007 .

[72]  Luis Mario Floría,et al.  Evolution of Cooperation in Multiplex Networks , 2012, Scientific Reports.

[73]  Daniele Vilone,et al.  Evolutionary Games defined at the Network Mesoscale: The Public Goods game , 2010, Chaos.

[74]  J Gómez-Gardeñes,et al.  Dynamical organization of cooperation in complex topologies. , 2007, Physical review letters.

[75]  Patrick Thiran,et al.  Layered complex networks. , 2006, Physical review letters.

[76]  Jürgen Kurths,et al.  Investigating the topology of interacting networks , 2011, 1102.3067.

[77]  Peter Csermely,et al.  Nodes Having a Major Influence to Break Cooperation Define a Novel Centrality Measure: Game Centrality , 2013, PloS one.

[78]  F. C. Santos,et al.  From Local to Global Dilemmas in Social Networks , 2012, PloS one.

[79]  G. Szabó,et al.  Evolutionary games on graphs , 2006, cond-mat/0607344.

[80]  S. Bornholdt,et al.  Coevolutionary games on networks. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[81]  J. Rogers Chaos , 1876 .

[82]  Attila Szolnoki,et al.  Evolution of public cooperation on interdependent networks: The impact of biased utility functions , 2012, ArXiv.

[83]  Sergey V. Buldyrev,et al.  Critical effect of dependency groups on the function of networks , 2010, Proceedings of the National Academy of Sciences.

[84]  D. E. Matthews Evolution and the Theory of Games , 1977 .

[85]  F. C. Santos,et al.  The role of diversity in the evolution of cooperation. , 2012, Journal of theoretical biology.