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Network fluctuations hinder cooperation in evolutionary games.

Antonioni A, Tomassini M - PLoS ONE (2011)

Bottom Line: The results we obtain show that even a moderate amount of random noise on the network links causes a significant loss of cooperation, to the point that cooperation vanishes altogether in the Prisoner's Dilemma when the noise rate is the same as the agents' strategy revision rate.The results appear to be robust since they are essentially the same whatever the type of the exogenous noise.Besides, it turns out that random network noise is more important than strategy noise in suppressing cooperation.

View Article: PubMed Central - PubMed

Affiliation: Information Systems Department, Faculty of Business and Economics, University of Lausanne, Lausanne, Switzerland. alberto.antonioni@unil.ch

ABSTRACT
In this paper we study the influence of random network fluctuations on the behavior of evolutionary games on Barabási-Albert networks. This network class has been shown to promote cooperation on social dilemmas such as the Prisoner's Dilemma and the Snowdrift games when the population network is fixed. Here we introduce exogenous random fluctuations of the network links through several noise models, and we investigate the evolutionary dynamics comparing them with the known static network case. The results we obtain show that even a moderate amount of random noise on the network links causes a significant loss of cooperation, to the point that cooperation vanishes altogether in the Prisoner's Dilemma when the noise rate is the same as the agents' strategy revision rate. The results appear to be robust since they are essentially the same whatever the type of the exogenous noise. Besides, it turns out that random network noise is more important than strategy noise in suppressing cooperation. Thus, even in the more favorable situation of accumulated payoff in which links have no cost, the mere presence of random external network fluctuations act as a powerful limitation to the attainment of high levels of cooperation.

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Empirical degree distribution functions for the original BA networks and for the final rewired ones.Left image: lin-log scales; right image: log-log scales. The distributions for the rewired graphs are shown for two levels of network noise. For high levels of noise, distributions tend to the exponential type, otherwise they are closer to the original power-law. Values are averages over 1000 graph realizations for each curve.
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pone-0025555-g004: Empirical degree distribution functions for the original BA networks and for the final rewired ones.Left image: lin-log scales; right image: log-log scales. The distributions for the rewired graphs are shown for two levels of network noise. For high levels of noise, distributions tend to the exponential type, otherwise they are closer to the original power-law. Values are averages over 1000 graph realizations for each curve.

Mentions: This process makes highly connected nodes more likely to loose a link but, on the other hand, it also gives them more probability of being chosen for a new connection. The network statistics do change but they remain relatively close to the starting BA graph. In our simulations, after many rewirings, the network degree distribution function does remain broad-scale in average, but the tail tends to fall off faster than the original power-law. Figure 4 shows the degree distribution functions for the original and the rewired networks for two levels of noise averaged over 1000 graph realizations. For the rewired networks, the graphs refer to the final configurations. From the curves, one can see that for low noise () the rewired networks have almost the same distribution as the original BA ones. On the other hand, when the noise is high () the networks undergo a more marked change and the resulting degree distributions are closer to an exponential, as seen in the left image of Fig. 4 where the scales on the axes are lin-log. Indeed, most empirical degree distributions sampled on actual static social networks do give results that are between these two limit cases, i.e. a power-law and an exponential distribution [24], [25].


Network fluctuations hinder cooperation in evolutionary games.

Antonioni A, Tomassini M - PLoS ONE (2011)

Empirical degree distribution functions for the original BA networks and for the final rewired ones.Left image: lin-log scales; right image: log-log scales. The distributions for the rewired graphs are shown for two levels of network noise. For high levels of noise, distributions tend to the exponential type, otherwise they are closer to the original power-law. Values are averages over 1000 graph realizations for each curve.
© Copyright Policy
Related In: Results  -  Collection

Show All Figures
getmorefigures.php?uid=PMC3198448&req=5

pone-0025555-g004: Empirical degree distribution functions for the original BA networks and for the final rewired ones.Left image: lin-log scales; right image: log-log scales. The distributions for the rewired graphs are shown for two levels of network noise. For high levels of noise, distributions tend to the exponential type, otherwise they are closer to the original power-law. Values are averages over 1000 graph realizations for each curve.
Mentions: This process makes highly connected nodes more likely to loose a link but, on the other hand, it also gives them more probability of being chosen for a new connection. The network statistics do change but they remain relatively close to the starting BA graph. In our simulations, after many rewirings, the network degree distribution function does remain broad-scale in average, but the tail tends to fall off faster than the original power-law. Figure 4 shows the degree distribution functions for the original and the rewired networks for two levels of noise averaged over 1000 graph realizations. For the rewired networks, the graphs refer to the final configurations. From the curves, one can see that for low noise () the rewired networks have almost the same distribution as the original BA ones. On the other hand, when the noise is high () the networks undergo a more marked change and the resulting degree distributions are closer to an exponential, as seen in the left image of Fig. 4 where the scales on the axes are lin-log. Indeed, most empirical degree distributions sampled on actual static social networks do give results that are between these two limit cases, i.e. a power-law and an exponential distribution [24], [25].

Bottom Line: The results we obtain show that even a moderate amount of random noise on the network links causes a significant loss of cooperation, to the point that cooperation vanishes altogether in the Prisoner's Dilemma when the noise rate is the same as the agents' strategy revision rate.The results appear to be robust since they are essentially the same whatever the type of the exogenous noise.Besides, it turns out that random network noise is more important than strategy noise in suppressing cooperation.

View Article: PubMed Central - PubMed

Affiliation: Information Systems Department, Faculty of Business and Economics, University of Lausanne, Lausanne, Switzerland. alberto.antonioni@unil.ch

ABSTRACT
In this paper we study the influence of random network fluctuations on the behavior of evolutionary games on Barabási-Albert networks. This network class has been shown to promote cooperation on social dilemmas such as the Prisoner's Dilemma and the Snowdrift games when the population network is fixed. Here we introduce exogenous random fluctuations of the network links through several noise models, and we investigate the evolutionary dynamics comparing them with the known static network case. The results we obtain show that even a moderate amount of random noise on the network links causes a significant loss of cooperation, to the point that cooperation vanishes altogether in the Prisoner's Dilemma when the noise rate is the same as the agents' strategy revision rate. The results appear to be robust since they are essentially the same whatever the type of the exogenous noise. Besides, it turns out that random network noise is more important than strategy noise in suppressing cooperation. Thus, even in the more favorable situation of accumulated payoff in which links have no cost, the mere presence of random external network fluctuations act as a powerful limitation to the attainment of high levels of cooperation.

Show MeSH
Related in: MedlinePlus