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Evolutionary dynamics of social dilemmas in structured heterogeneous populations - PubMed

  • ️Sun Jan 01 2006

Evolutionary dynamics of social dilemmas in structured heterogeneous populations

F C Santos et al. Proc Natl Acad Sci U S A. 2006.

Abstract

Real populations have been shown to be heterogeneous, in which some individuals have many more contacts than others. This fact contrasts with the traditional homogeneous setting used in studies of evolutionary game dynamics. We incorporate heterogeneity in the population by studying games on graphs, in which the variability in connectivity ranges from single-scale graphs, for which heterogeneity is small and associated degree distributions exhibit a Gaussian tale, to scale-free graphs, for which heterogeneity is large with degree distributions exhibiting a power-law behavior. We study the evolution of cooperation, modeled in terms of the most popular dilemmas of cooperation. We show that, for all dilemmas, increasing heterogeneity favors the emergence of cooperation, such that long-term cooperative behavior easily resists short-term noncooperative behavior. Moreover, we show how cooperation depends on the intricate ties between individuals in scale-free populations.

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Conflict of interest statement

Conflict of interest statement: No conflicts declared.

Figures

Fig. 1.
Fig. 1.

Heterogeneous NoC. Shown is the cumulative degree distribution, D(k) [defined for a graph with N vertices as Σi=kN−1(Ni/N), where Ni gives the number of vertices with i edges], for two types of NoC for which N = 104. The first type of NoC are single-scale heterogeneous NoC, depicted with a dashed line, in which most individuals have a similar number of connections, leading to a narrow degree distribution. The Gaussian tail (20) of such a distribution is responsible for the fast decay exhibited by the cumulative degree distribution depicted. The second type of NoC are scale-free NoC, generated according to the Barabási–Albert model and exhibiting a cumulative degree distribution scaling as D(k) ≈ k−2 (solid line). The tail at the end of the solid line results from the finiteness of the population. For the class of broad-scale networks identified in ref. , the cumulative degree distribution will tail-off at degree values intermediate from those associated with the single-scale and scale-free NoC depicted.

Fig. 2.
Fig. 2.

Evolution of cooperation in different NoC. Results for the fraction of cooperators in the population are plotted as a contour drawn as a function of two parameters: S, the disadvantage of a cooperator being defected (when S < 0), and T, the temptation to defect on a cooperator (when T > 1). In the absence of any of these threats (S ≥ 0 and T ≤ 1; upper-left quadrant) cooperators trivially dominate. The lower-left quadrant (S < 0 and T ≤ 1) corresponds to the Stag-Hunt domain (SH). The lower triangle in the upper-right quadrant (S ≥ 0, T > 1 and (T + S) < 2) corresponds to the Snowdrift game domain (SG). The lower-right quadrant (S < 0 and T > 1) corresponds to the Prisoner’s Dilemma domain (PD). (Left) Results obtained in complete NoC that reproduce in finite populations the analytic solutions known for infinite, well mixed populations. These results provide the reference scenario with which the role of population structure will be subsequently assessed. (Right) Results obtained for single-scale NoC, characterized by a moderate degree of heterogeneity. Comparison with the results for finite, well mixed populations (Left) shows that such small heterogeneity is on the basis of the overall enhancement of cooperation (details provided in main text).

Fig. 3.
Fig. 3.

Evolution of cooperation in scale-free NoC. We use the same notation and scale as Fig. 2. (Left) Random scale-free NoC. The interplay between small-world effects and heterogeneity effects leads to a net overall increase of cooperation for all dilemmas. (Right) Barabási–Albert scale-free NoC. When highly connected individuals are directly interconnected, cooperators dominate defectors for all values of the temptation to defect T > 1, enlarging the range of intensities of S < 0 for which they successfully survive defectors, showing how the intricate ties between individuals affect the evolutionary dynamics of cooperators. Abbreviations are the same as those in Fig. 2.

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References

    1. Sigmund K. Games of Life. Oxford: Oxford Univ. Press; 1993.
    1. Maynard-Smith J., Szathmáry E. The Major Transitions in Evolution. Oxford: Freeman; 1995.
    1. Michod R. E. Darwinian Dynamics: Evolutionary Transitions in Fitness and Individuality. Princeton, NJ: Princeton Univ. Press; 1999.
    1. Hamilton W. D. Am. Nat. 1964;97:354–356.
    1. Hamilton W. D. In: Biophysical Anthropology. Fox R., editor. New York: Wiley; 1975.

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