Limits...
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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Asymptotic distribution of strategies in the TS plane in static and dynamic BA networks using unconditional imitation of the best neighbor as an update rule.Initial density of cooperators is 0.5 uniformly distributed at random in all cases. Leftmost image: the static case. Increasing towards the right: frequency  of network generation is 0.1 and 1. Values are averages over 100 independent runs.
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pone-0025555-g002: Asymptotic distribution of strategies in the TS plane in static and dynamic BA networks using unconditional imitation of the best neighbor as an update rule.Initial density of cooperators is 0.5 uniformly distributed at random in all cases. Leftmost image: the static case. Increasing towards the right: frequency of network generation is 0.1 and 1. Values are averages over 100 independent runs.

Mentions: Figure 2 shows the same dynamics but using unconditional imitation of the best instead of replicator dynamics. Here the focal player imitates the strategy of the neighbor having obtained the highest payoff, including himself (see Methods section). Looking at the static case (leftmost image) it is already clear that there is a lower amount of cooperation to start with in the PD quadrant, as well as in the SH case with respect to random graphs, while cooperation is high for the SD game (see Roca et al. [3] for a detailed discussion of these effects). Adding network noise has little effect but still the tiny amount of cooperation existing is almost completely lost when the noise level reaches the value one. A tentative qualitative explanation of the relative insensitivity to noise in this case is the following. The way in which a new network is generated in the noisy case (see above) tells us that, on the average, a given player will have more or less the same proportion of cooperators and defectors as neighbors in the new network as in the previous one. Since deterministic unconditional imitation rule depends on the global state of the neighborhood, it seems likely that the network dynamics will not have a large effect in this case.


Network fluctuations hinder cooperation in evolutionary games.

Antonioni A, Tomassini M - PLoS ONE (2011)

Asymptotic distribution of strategies in the TS plane in static and dynamic BA networks using unconditional imitation of the best neighbor as an update rule.Initial density of cooperators is 0.5 uniformly distributed at random in all cases. Leftmost image: the static case. Increasing towards the right: frequency  of network generation is 0.1 and 1. Values are averages over 100 independent runs.
© Copyright Policy
Related In: Results  -  Collection

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

pone-0025555-g002: Asymptotic distribution of strategies in the TS plane in static and dynamic BA networks using unconditional imitation of the best neighbor as an update rule.Initial density of cooperators is 0.5 uniformly distributed at random in all cases. Leftmost image: the static case. Increasing towards the right: frequency of network generation is 0.1 and 1. Values are averages over 100 independent runs.
Mentions: Figure 2 shows the same dynamics but using unconditional imitation of the best instead of replicator dynamics. Here the focal player imitates the strategy of the neighbor having obtained the highest payoff, including himself (see Methods section). Looking at the static case (leftmost image) it is already clear that there is a lower amount of cooperation to start with in the PD quadrant, as well as in the SH case with respect to random graphs, while cooperation is high for the SD game (see Roca et al. [3] for a detailed discussion of these effects). Adding network noise has little effect but still the tiny amount of cooperation existing is almost completely lost when the noise level reaches the value one. A tentative qualitative explanation of the relative insensitivity to noise in this case is the following. The way in which a new network is generated in the noisy case (see above) tells us that, on the average, a given player will have more or less the same proportion of cooperators and defectors as neighbors in the new network as in the previous one. Since deterministic unconditional imitation rule depends on the global state of the neighborhood, it seems likely that the network dynamics will not have a large effect in this case.

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