Biased imitation in coupled evolutionary games in interdependent networks

We explore the evolutionary dynamics of two games—the Prisoner's Dilemma and the Snowdrift Game—played within distinct networks (layers) of interdependent networks. In these networks imitation and interaction between individuals of opposite layers is established through interlinks. We explore an update rule in which revision of strategies is a biased imitation process: individuals imitate neighbors from the same layer with probability p, and neighbors from the second layer with complementary probability 1 − p. We demonstrate that a small decrease of p from p = 1 (which corresponds to forbidding strategy transfer between layers) is sufficient to promote cooperation in the Prisoner's Dilemma subpopulation. This, on the other hand, is detrimental for cooperation in the Snowdrift Game subpopulation. We provide results of extensive computer simulations for the case in which layers are modelled as regular random networks, and support this study with analytical results for coupled well-mixed populations.

[1]  Yamir Moreno,et al.  Contact-based Social Contagion in Multiplex Networks , 2013, Physical review. E, Statistical, nonlinear, and soft matter physics.

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

[3]  Marc Barthelemy,et al.  Growing multiplex networks , 2013, Physical review letters.

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

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

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

[7]  A. Rapoport,et al.  Prisoner's Dilemma: A Study in Conflict and Co-operation , 1970 .

[8]  P. Taylor,et al.  Evolutionarily Stable Strategies and Game Dynamics , 1978 .

[9]  Alessandro Vespignani,et al.  Complex networks: The fragility of interdependency , 2010, Nature.

[10]  Peter Grassberger,et al.  Percolation theory on interdependent networks based on epidemic spreading , 2011, 1109.4447.

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

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

[13]  Arne Traulsen,et al.  Pairwise comparison and selection temperature in evolutionary game dynamics. , 2007, Journal of theoretical biology.

[14]  S. N. Dorogovtsev,et al.  Evolution of networks , 2001, cond-mat/0106144.

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

[16]  博 太郎丸.  ＜書評＞ Robert Sugden, "The economics of rights, co-operation and welfare", Oxford : Basil Blackwell, 1986 , 1992 .

[17]  Michael Doebeli,et al.  Spatial structure often inhibits the evolution of cooperation in the snowdrift game , 2004, Nature.

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

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

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

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

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

[23]  Martin A Nowak,et al.  Evolutionary graph theory: breaking the symmetry between interaction and replacement. , 2007, Journal of theoretical biology.

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

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

[26]  Harry Eugene Stanley,et al.  Robustness of a Network of Networks , 2010, Physical review letters.

[27]  S. N. Dorogovtsev,et al.  Avalanche collapse of interdependent networks. , 2012, Physical review letters.

[28]  P. Kollock.  SOCIAL DILEMMAS: The Anatomy of Cooperation , 1998 .

[29]  R. Sugden.  The Economics of Rights, Co-Operation, and Welfare , 1986 .

[30]  P. Csermely.  The Appearance and Promotion of Creativity by Various Levels of Interdependent Networks , 2013 .

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

[32]  H. Ohtsuki,et al.  A simple rule for the evolution of cooperation on graphs and social networks , 2006, Nature.

[33]  Eugenio Gutiérrez,et al.  Seismic risk assessment of interdependent critical infrastructure systems: The case of European gas and electricity networks , 2012 .

[34]  Barry J. Goodno,et al.  Seismic response of critical interdependent networks , 2007 .

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

[36]  R. Radlow,et al.  An experimental study of "cooperation" in the Prisoner's Dilemma game , 1965 .

[37]  Robert van Rooij,et al.  The Stag Hunt and the Evolution of Social Structure , 2007, Stud Logica.

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

[39]  Ángel Sánchez,et al.  Effect of spatial structure on the evolution of cooperation , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[40]  M. Nowak.  Five Rules for the Evolution of Cooperation , 2006, Science.

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

[42]  Albert,et al.  Emergence of scaling in random networks , 1999, Science.

[43]  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.

[44]  A. Arenas,et al.  Abrupt transition in the structural formation of interconnected networks , 2013, Nature Physics.

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

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

[47]  H. Ohtsuki,et al.  Breaking the symmetry between interaction and replacement in evolutionary dynamics on graphs. , 2007, Physical review letters.

[48]  Arne Traulsen,et al.  Stochastic payoff evaluation increases the temperature of selection. , 2007, Journal of theoretical biology.

[49]  Albert-László Barabási,et al.  Evolution of Networks: From Biological Nets to the Internet and WWW , 2004 .

[50]  Sergey N. Dorogovtsev,et al.  Evolution of Networks: From Biological Nets to the Internet and WWW (Physics) , 2003 .