Participation costs dismiss the advantage of heterogeneous networks in evolution of cooperation - PubMed (original) (raw)

Participation costs dismiss the advantage of heterogeneous networks in evolution of cooperation

Naoki Masuda. Proc Biol Sci. 2007.

Abstract

Real social interactions occur on networks in which each individual is connected to some, but not all, of others. In social dilemma games with a fixed population size, heterogeneity in the number of contacts per player is known to promote evolution of cooperation. Under a common assumption of positively biased pay-off structure, well-connected players earn much by playing frequently, and cooperation once adopted by well-connected players is unbeatable and spreads to others. However, maintaining a social contact can be costly, which would prevent local pay-offs from being positively biased. In replicator-type evolutionary dynamics, it is shown that even a relatively small participation cost extinguishes the merit of heterogeneous networks in terms of cooperation. In this situation, more connected players earn less so that they are no longer spreaders of cooperation. Instead, those with fewer contacts win and guide the evolution. The participation cost, or the baseline pay-off, is irrelevant in homogeneous populations, but is essential for evolutionary games on heterogeneous networks.

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Figures

Figure 1

Figure 1

The Prisoner's Dilemma on the scale-free networks with participation costs. The pay-off matrix is represented by equation (3.2). (a) The final fraction of cooperators _c_f**.** (b) c_f for the scale-free networks shown in (a) −_c_f for the regular random graph shown in the electronic supplementary material figure 1_a.

Figure 2

Figure 2

The effect of the number of neighbours in the Prisoner's Dilemma on the scale-free networks. (a) The average generation pay-off and (b) the average number of flips are plotted in terms of the number of neighbours that a player has. Note that the log scale is used for the abscissa of (b) for clarity. The lines correspond to _h_=0 (thinnest line), 0.2, 0.23, 0.24, 0.25, 0.3 and 0.5 (thickest line). The pay-off matrix is given by equation (3.2) with _T_=1.5.

Figure 3

Figure 3

The snowdrift game on the scale-free networks with participation costs. (a) _c_f and (b) _c_f for the scale-free networks shown in (a) −_c_f for the regular random graph shown in the electronic supplementary material figure 2.

Figure 4

Figure 4

_c_f in the T_–_S space for (a) the regular random graph and the scale-free networks with (b) _h_=0, (c) _h_=0.5, (d) _h_=1 and (e) _h_=2.

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