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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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Asymptotic distribution of strategies in the TS plane in static and dynamic BA networks using the Fermi rule (see text).Initial density of cooperators is 0.5 uniformly distributed at random in all cases. In all cases β = 0.1. Leftmost image: the static case. Middle image: frequency of graph renewal . Right image: . Values are averages over 100 independent runs.
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pone-0025555-g006: Asymptotic distribution of strategies in the TS plane in static and dynamic BA networks using the Fermi rule (see text).Initial density of cooperators is 0.5 uniformly distributed at random in all cases. In all cases β = 0.1. Leftmost image: the static case. Middle image: frequency of graph renewal . Right image: . Values are averages over 100 independent runs.

Mentions: Until now, we have studied the impact of network fluctuations on typical evolutionary games. Another common source of noise in games arises from strategy errors. These are meant to capture various sources of uncertainty such as deliberate and involuntary decision errors which might play the role of experimentation in the environment, or be related to insufficient familiarity with the game. One easy way to include strategy noise is to use the Fermi function [2] as an update rule (see the Methods section for definitions). The parameter β in the function gives the amount of noise: a low β corresponds to high probability of error and, conversely, high β means that errors will be rare. One may ask how much these errors influence cooperation in networks of contacts, and whether they combine positively or negatively with network noise. As for their influence on static BA networks, the answer has been given in [3], where it is shown that for low noise (β = 10) the equilibrium behavior is similar to the one seen with replicator dynamics, while values of β close to 0.01 are enough to suppress all residual cooperation in the PD. In this case selection is weak, payoffs and network structure play a less important role. In other words, only comparatively high rates of strategy errors are really detrimental to cooperation. But when network fluctuations are present, cooperation is quickly lost, even for values of β that still allow for a fair amount of cooperation in the static case. Figure 6 shows this for a static network (leftmost image) as well as for two levels of network noise (central and right image) for β = 0.1. Network noise has been created as in our first model, i.e. by generating a sequence of independent BA networks with frequency .


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 the Fermi rule (see text).Initial density of cooperators is 0.5 uniformly distributed at random in all cases. In all cases β = 0.1. Leftmost image: the static case. Middle image: frequency of graph renewal . Right image: . Values are averages over 100 independent runs.
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Related In: Results  -  Collection

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getmorefigures.php?uid=PMC3198448&req=5

pone-0025555-g006: Asymptotic distribution of strategies in the TS plane in static and dynamic BA networks using the Fermi rule (see text).Initial density of cooperators is 0.5 uniformly distributed at random in all cases. In all cases β = 0.1. Leftmost image: the static case. Middle image: frequency of graph renewal . Right image: . Values are averages over 100 independent runs.
Mentions: Until now, we have studied the impact of network fluctuations on typical evolutionary games. Another common source of noise in games arises from strategy errors. These are meant to capture various sources of uncertainty such as deliberate and involuntary decision errors which might play the role of experimentation in the environment, or be related to insufficient familiarity with the game. One easy way to include strategy noise is to use the Fermi function [2] as an update rule (see the Methods section for definitions). The parameter β in the function gives the amount of noise: a low β corresponds to high probability of error and, conversely, high β means that errors will be rare. One may ask how much these errors influence cooperation in networks of contacts, and whether they combine positively or negatively with network noise. As for their influence on static BA networks, the answer has been given in [3], where it is shown that for low noise (β = 10) the equilibrium behavior is similar to the one seen with replicator dynamics, while values of β close to 0.01 are enough to suppress all residual cooperation in the PD. In this case selection is weak, payoffs and network structure play a less important role. In other words, only comparatively high rates of strategy errors are really detrimental to cooperation. But when network fluctuations are present, cooperation is quickly lost, even for values of β that still allow for a fair amount of cooperation in the static case. Figure 6 shows this for a static network (leftmost image) as well as for two levels of network noise (central and right image) for β = 0.1. Network noise has been created as in our first model, i.e. by generating a sequence of independent BA networks with frequency .

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