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Cooperation Prevails When Individuals Adjust Their Social Ties

DOI: 10.1371/journal.pcbi.0020140

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Conventional evolutionary game theory predicts that natural selection favours the selfish and strong even though cooperative interactions thrive at all levels of organization in living systems. Recent investigations demonstrated that a limiting factor for the evolution of cooperative interactions is the way in which they are organized, cooperators becoming evolutionarily competitive whenever individuals are constrained to interact with few others along the edges of networks with low average connectivity. Despite this insight, the conundrum of cooperation remains since recent empirical data shows that real networks exhibit typically high average connectivity and associated single-to-broad–scale heterogeneity. Here, a computational model is constructed in which individuals are able to self-organize both their strategy and their social ties throughout evolution, based exclusively on their self-interest. We show that the entangled evolution of individual strategy and network structure constitutes a key mechanism for the sustainability of cooperation in social networks. For a given average connectivity of the population, there is a critical value for the ratio W between the time scales associated with the evolution of strategy and of structure above which cooperators wipe out defectors. Moreover, the emerging social networks exhibit an overall heterogeneity that accounts very well for the diversity of patterns recently found in acquired data on social networks. Finally, heterogeneity is found to become maximal when W reaches its critical value. These results show that simple topological dynamics reflecting the individual capacity for self-organization of social ties can produce realistic networks of high average connectivity with associated single-to-broad–scale heterogeneity. On the other hand, they show that cooperation cannot evolve as a result of “social viscosity” alone in heterogeneous networks with high average connectivity, requiring the additional mechanism of topological co-evolution to ensure the survival of cooperative behaviour.


[1]  Nowak M, Sigmund K (2005) Evolution of indirect reciprocity. Nature 437: 1291–1298.
[2]  Smith JM, Szathmáry E (1995) The major transitions in evolution. Oxford: Freeman. 346 p.
[3]  Rapoport A, Chamah AM (1965) The prisoner's dilemma. Ann Arbor (Michigan): University of Michigan Press. 270 p.
[4]  Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge (United Kingdom): Cambridge University Press. 351 p.
[5]  Gintis H (2000) Game theory evolving. Cambridge (United Kingdom): Cambridge University Press. 528 p.
[6]  Nowak MA, Sigmund K (2004) Evolutionary dynamics of biological games. Science 303: 793–799.
[7]  Santos FC, Pacheco JM, Lenaerts T (2006) Evolutionary dynamics of social dilemmas in structured heterogeneous populations. Proc Natl Acad Sci U S A 103: 3490–3494.
[8]  Ohtsuki H, Hauert C, Lieberman E, Nowak MA (2006) A simple rule for evolution of cooperation on graphs and social networks. Nature 441: 502–505.
[9]  Macy MW, Flache A (2002) Learning dynamics in social dilemmas. Proc Natl Acad Sci U S A 99: 7229–7236.
[10]  Watts DJ (1999) Small worlds: The dynamics of networks between order and randomness. Princeton (New Jersey): Princeton University Press. 262 p.
[11]  Amaral LA, Scala A, Barthelemy M, Stanley HE (2000) Classes of small-world networks. Proc Natl Acad Sci U S A 97: 11149–11152.
[12]  Albert R, Barabási AL (2002) Statistical mechanics of complex networks. Rev Mod Phys 74: 47–98.
[13]  Dorogotsev SN, Mendes JFF (2003) Evolution of networks: From biological nets to the Internet and WWW. Oxford: Oxford University Press. 264 p.
[14]  Newman MEJ (2003) The structure and function of complex networks. SIAM 45: 167–256.
[15]  Watts DJ (2004) The “new” science of networks. Ann Rev Sociobiol 30: 243–270.
[16]  Guimerá R, Amaral LAN (2005) Functional cartography of complex metabolic networks. Nature 433: 895.
[17]  Albert R, Barabasi AL (2000) Topology of evolving networks: Local events and universality. Phys Rev Lett 85: 5234–5237.
[18]  Kossinets G, Watts DJ (2006) Empirical analysis of an evolving social network. Science 311: 88–90.
[19]  Eguiluz VM, Zimmerman M, Cela-Conte C, San-Miguel M (2005) Cooperation and the emergence of role differentiation in the dynamics of social networks. Am J Soc 110: 977–1008.
[20]  Bala V, Goyal S (2000) A noncooperative model of network formation. Econometrica 68: 1181–1229.
[21]  Ebel H, Bornholdt S (2002) Coevolutionary games on networks. Phys Rev E 66: 056118.
[22]  Hanaki N, Peterhansl A, Dodds PS, Watts DJ (2006) Cooperation in evolving social networks. Manage Sci. In press.
[23]  Skyrms B, Pemantle R (2000) A dynamic model of social network formation. Proc Natl Acad Sci U S A 97: 9340–9346.
[24]  Santos FC, Rodrigues JF, Pacheco JM (2006) Graph topology plays a determinant role in the evolution of cooperation. Proc Biol Sci 273: 51–55.
[25]  Eshel I, Cavalli-Sforza LL (1982) Assortment of encounters and evolution of cooperativeness. Proc Natl Acad Sci U S A 79: 1331–1335.
[26]  Santos FC, Pacheco JM (2006) A new route to the evolution of cooperation. J Evol Biol 19: 726–733.
[27]  Traulsen A, Nowak MA, Pacheco JM (2006) Stochastic dynamics of invasion and fixation. Phys Rev E. 74.
[28]  Santos FC, Rodrigues JF, Pacheco JM (2005) Epidemic spreading and cooperation dynamics on homogeneous small-world networks. Phys Rev E 72: 056128.


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