Graph topology plays a determinant role in the evolution of cooperation

We study the evolution of cooperation in communities described in terms of graphs, such that individuals occupy the vertices and engage in single rounds of the Prisoner's Dilemma with those individuals with whom they are connected through the edges of those graphs. We find an overwhelming dominance of cooperation whenever graphs are dynamically generated through the mechanisms of growth and preferential attachment. These mechanisms lead to the appearance of direct links between hubs, which constitute sufficient conditions to sustain cooperation. We show that cooperation dominates from large population sizes down to communities with nearly 100 individuals, even when extrinsic factors set a limit on the number of interactions that each individual may engage in.

[1]  E. M.,et al.  Statistical Mechanics , 2021, Manual for Theoretical Chemistry.

[2]  H. Simon,et al.  ON A CLASS OF SKEW DISTRIBUTION FUNCTIONS , 1955 .

[3]  R. Merton.  The Matthew Effect in Science , 1968, Science.

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

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

[6]  W. Hamilton,et al.  The Evolution of Cooperation , 1984 .

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

[8]  Michael Mesterton-Gibbons,et al.  An introduction to game-theoretic modelling , 2019 .

[9]  Bruce A. Reed,et al.  A Critical Point for Random Graphs with a Given Degree Sequence , 1995, Random Struct. Algorithms.

[10]  D. Rand,et al.  Correlation models for childhood epidemics , 1997, Proceedings of the Royal Society of London. Series B: Biological Sciences.

[11]  M. Baalen,et al.  The Unit of Selection in Viscous Populations and the Evolution of Altruism. , 1998, Journal of theoretical biology.

[12]  Reka Albert,et al.  Mean-field theory for scale-free random networks , 1999 .

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

[14]  H E Stanley,et al.  Classes of small-world networks. , 2000, Proceedings of the National Academy of Sciences of the United States of America.

[15]  S. N. Dorogovtsev,et al.  Size-dependent degree distribution of a scale-free growing network. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

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

[17]  R. May,et al.  Infectious disease dynamics: What characterizes a successful invader? , 2001, Philosophical transactions of the Royal Society of London. Series B, Biological sciences.

[18]  Stefano Mossa,et al.  Truncation of power law behavior in "scale-free" network models due to information filtering. , 2002, Physical review letters.

[19]  M. Feldman,et al.  Local dispersal promotes biodiversity in a real-life game of rock–paper–scissors , 2002, Nature.

[20]  Robert Boyd,et al.  Genetic and Cultural Evolution of Cooperation , 2003 .

[21]  M. Keeling,et al.  Disease evolution on networks: the role of contact structure , 2003, Proceedings of the Royal Society of London. Series B: Biological Sciences.

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

[23]  Francisco C. Santos,et al.  Network Dependence of the Dilemmas Of Cooperation , 2005 .

[24]  Martin A. Nowak,et al.  Spatial structure often inhibits the evolution of cooperation in the snowdrift game , 2022 .