Evolutionary games on scale-free networks with a preferential selection mechanism

Considering the heterogeneity of individuals’ influence in the real world, we introduce a preferential selection mechanism to evolutionary games (the Prisoner’s Dilemma Game and the Snowdrift Game) on scale-free networks and focus on the cooperative behavior of the system. In every step, each agent chooses an individual from all its neighbors with a probability proportional to kα indicating the influence of the neighbor, where k is the degree. Simulation results show that the cooperation level has a non-trivial dependence on α. To understand the effect of preferential selection mechanism on the evolution of the system, we investigate the time series of the cooperator frequency in detail. It is found that the cooperator frequency is greatly influenced by the initial strategy of hub nodes when α>0. This observation is confirmed by investigating the system behavior when some hub nodes’ strategies are fixed.

[1]  Wen-Xu Wang,et al.  Effects of average degree on cooperation in networked evolutionary game , 2006 .

[2]  M. Perc.  Coherence resonance in a spatial prisoner's dilemma game , 2006 .

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

[4]  F. C. Santos,et al.  Graph topology plays a determinant role in the evolution of cooperation , 2006, Proceedings of the Royal Society B: Biological Sciences.

[5]  M. Nowak,et al.  Tit for tat in heterogeneous populations , 1992, Nature.

[6]  Beom Jun Kim,et al.  Dynamic instabilities induced by asymmetric influence: prisoners' dilemma game in small-world networks. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

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

[8]  G. Szabo,et al.  Diversity of reproduction rate supports cooperation in the prisoner's dilemma game on complex networks , 2008, 0802.2807.

[9]  C. Hauert,et al.  Game theory and physics , 2005 .

[10]  M. Perc,et al.  Towards effective payoffs in the prisoner’s dilemma game on scale-free networks , 2007, 0711.4028.

[11]  Albert,et al.  Topology of evolving networks: local events and universality , 2000, Physical review letters.

[12]  Dla Polski,et al.  EURO , 2004 .

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

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

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

[16]  G. Szabó,et al.  Evolutionary prisoner's dilemma game on a square lattice , 1997, cond-mat/9710096.

[17]  Wang Ying-Hai,et al.  Prisoner's Dilemma Game with Nonlinear Attractive Effect on Regular Small-World Networks , 2006 .

[18]  Guanrong Chen,et al.  Phase transition and hysteresis loop in structured games with global updating. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

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

[20]  Feng Qi,et al.  Randomness enhances cooperation: a resonance-type phenomenon in evolutionary games. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[21]  Zhi-Xi Wu,et al.  Spatial prisoner's dilemma game with volunteering in Newman-Watts small-world networks. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[22]  Long Wang,et al.  Promotion of cooperation induced by appropriate payoff aspirations in a small-world networked game. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[23]  M. Nowak,et al.  A strategy of win-stay, lose-shift that outperforms tit-for-tat in the Prisoner's Dilemma game , 1993, Nature.

[24]  Wenxu Wang,et al.  Memory-based snowdrift game on networks. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[25]  Long Wang,et al.  Interaction stochasticity supports cooperation in spatial Prisoner's dilemma. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[26]  Zhi-Xi Wu,et al.  Cooperation enhanced by the difference between interaction and learning neighborhoods for evolutionary spatial prisoner's dilemma games. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[27]  M. Perc,et al.  Promoting cooperation in social dilemmas via simple coevolutionary rules , 2008, 0812.1122.

[28]  Xin-Jian Xu,et al.  Promotion of cooperation induced by nonlinear attractive effect in spatial Prisoner's Dilemma game , 2006 .

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

[30]  György Szabó,et al.  Phase transitions and volunteering in spatial public goods games. , 2002, Physical review letters.

[31]  G. Szabó,et al.  Phase diagrams for an evolutionary prisoner's dilemma game on two-dimensional lattices. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[32]  J. Neumann,et al.  Theory of games and economic behavior , 1945, 100 Years of Math Milestones.

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

[34]  M. Doebeli,et al.  The evolution of interspecific mutualisms. , 1998, Proceedings of the National Academy of Sciences of the United States of America.

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

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

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

[38]  Zhi-Xi Wu,et al.  Evolutionary prisoner's dilemma game with dynamic preferential selection. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[39]  A. Barabasi,et al.  Evolution of the social network of scientific collaborations , 2001, cond-mat/0104162.