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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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Related in: MedlinePlus

Asymptotic distribution of strategies in the TS plane in rewired networks using replicator dynamics.Strategy update dynamics is asynchronous. Leftmost image: static rewired network (see text). Middle and rightmost images refer to dynamic graphs with frequency  of network rewiring of 0.1 and 1, respectively. Initial density of cooperators is 0.5 uniformly distributed at random in all cases. Values are averages over 100 independent runs.
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pone-0025555-g005: Asymptotic distribution of strategies in the TS plane in rewired networks using replicator dynamics.Strategy update dynamics is asynchronous. Leftmost image: static rewired network (see text). Middle and rightmost images refer to dynamic graphs with frequency of network rewiring of 0.1 and 1, respectively. Initial density of cooperators is 0.5 uniformly distributed at random in all cases. Values are averages over 100 independent runs.

Mentions: The simulations proceed in an asynchronous manner, as explained in the edge swap case above. Figure 5 depicts the behavior of the four game classes on networks undergoing the above link fluctuations. The leftmost image is given for comparison; it refers to a static graph that has been first rewired so as to randomize the links as explained above, before being used as a fixed population topology. The middle and rightmost images depict the noisy cases with a frequency of rewiring of 0.1 (middle) and 1 (right). It is to be remarked that the static rewired network does not become an Erdös-Rényi random graph, and still allows for a fair amount of cooperation with respect to the pure BA case reported in the leftmost image of Fig. 3. Thus, the loss of cooperation observed as the network fluctuates is significant and can lead to full defection for the PD when rewiring and revising strategy have the same time scale (rightmost image). Snowdrift and SH are less negatively affected. The average final values for the three games are reported in Table 4. The conclusion that we can draw from the results obtained with the three network fluctuation models is the following: whatever the source of random link fluctuations, as soon as the amount of noise becomes non-negligible i.e., as soon as network changes are at least ten times slower than strategy revision, the cooperation levels observed on static networks become weaker and they are completely lost when link noise and strategy update occur at the same rate. This conclusion is valid for all the non-trivial games studied, but it is particularly visible in the PD quadrant where defection becomes complete for .


Network fluctuations hinder cooperation in evolutionary games.

Antonioni A, Tomassini M - PLoS ONE (2011)

Asymptotic distribution of strategies in the TS plane in rewired networks using replicator dynamics.Strategy update dynamics is asynchronous. Leftmost image: static rewired network (see text). Middle and rightmost images refer to dynamic graphs with frequency  of network rewiring of 0.1 and 1, respectively. Initial density of cooperators is 0.5 uniformly distributed at random in all cases. Values are averages over 100 independent runs.
© Copyright Policy
Related In: Results  -  Collection

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

pone-0025555-g005: Asymptotic distribution of strategies in the TS plane in rewired networks using replicator dynamics.Strategy update dynamics is asynchronous. Leftmost image: static rewired network (see text). Middle and rightmost images refer to dynamic graphs with frequency of network rewiring of 0.1 and 1, respectively. Initial density of cooperators is 0.5 uniformly distributed at random in all cases. Values are averages over 100 independent runs.
Mentions: The simulations proceed in an asynchronous manner, as explained in the edge swap case above. Figure 5 depicts the behavior of the four game classes on networks undergoing the above link fluctuations. The leftmost image is given for comparison; it refers to a static graph that has been first rewired so as to randomize the links as explained above, before being used as a fixed population topology. The middle and rightmost images depict the noisy cases with a frequency of rewiring of 0.1 (middle) and 1 (right). It is to be remarked that the static rewired network does not become an Erdös-Rényi random graph, and still allows for a fair amount of cooperation with respect to the pure BA case reported in the leftmost image of Fig. 3. Thus, the loss of cooperation observed as the network fluctuates is significant and can lead to full defection for the PD when rewiring and revising strategy have the same time scale (rightmost image). Snowdrift and SH are less negatively affected. The average final values for the three games are reported in Table 4. The conclusion that we can draw from the results obtained with the three network fluctuation models is the following: whatever the source of random link fluctuations, as soon as the amount of noise becomes non-negligible i.e., as soon as network changes are at least ten times slower than strategy revision, the cooperation levels observed on static networks become weaker and they are completely lost when link noise and strategy update occur at the same rate. This conclusion is valid for all the non-trivial games studied, but it is particularly visible in the PD quadrant where defection becomes complete for .

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