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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 replicator dynamics as an update rule.Strategy update dynamics is asynchronous and the initial BA graph is rewired as explained in the text. Initial density of cooperators is 0.5 uniformly distributed at random in all cases. Leftmost image: the static case. Middle image: frequency  of network rewiring is 0.1; rightmost image: . Values are averages over 100 independent runs.
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pone-0025555-g003: Asymptotic distribution of strategies in the TS plane in static and dynamic BA networks using replicator dynamics as an update rule.Strategy update dynamics is asynchronous and the initial BA graph is rewired as explained in the text. Initial density of cooperators is 0.5 uniformly distributed at random in all cases. Leftmost image: the static case. Middle image: frequency of network rewiring is 0.1; rightmost image: . Values are averages over 100 independent runs.

Mentions: The independent sequence of BA graphs used above constitutes an ideal situation that can be considered as a baseline case, but it is quite far from a realistic link evolution in a given single network. To do a step towards more realism, we shall now assume that the sequence of graphs is generated by successively rewiring an initial given graph as suggested in [17]. We begin with G(0) being a Barabási–Albert network; then, starting at time t = 1, each successive graph G(t) in the sequence is generated by swapping two randomly chosen non-adjacent pair of edges in the previous graph G(t−1). In contrast to the previous case, where the sequence of graphs was an i.i.d. one, this process is a Markov chain since each new graph in the sequence depends on the previous one. The edge swap preserves the degree distribution P(k) of G and obviously the node's degree and the mean degree as well. The graphs, however, become more and more randomized as time goes by, as they tend to loose the historical degree correlations between hubs that arise in the original BA construction. Note that in this case we assume an asynchronous dynamics since it is, in our opinion, qualitatively more adapted to the new situation. Results are almost the same with either synchronous or asynchronous dynamics as shown in [3]. For the BA networks and replicator dynamics, this is also clear from the leftmost images in Figs. 1 and 3. Thus, instead of updating all the players' strategies at once in each time step as before, we randomly choose a player to update (with replacement). This is called an elementary time step. The period of network rewiring in this case is the number of elementary steps before an edge swap takes place, and the frequency ω is just the reciprocal of this number.


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 replicator dynamics as an update rule.Strategy update dynamics is asynchronous and the initial BA graph is rewired as explained in the text. Initial density of cooperators is 0.5 uniformly distributed at random in all cases. Leftmost image: the static case. Middle image: frequency  of network rewiring is 0.1; rightmost image: . Values are averages over 100 independent runs.
© Copyright Policy
Related In: Results  -  Collection

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

pone-0025555-g003: Asymptotic distribution of strategies in the TS plane in static and dynamic BA networks using replicator dynamics as an update rule.Strategy update dynamics is asynchronous and the initial BA graph is rewired as explained in the text. Initial density of cooperators is 0.5 uniformly distributed at random in all cases. Leftmost image: the static case. Middle image: frequency of network rewiring is 0.1; rightmost image: . Values are averages over 100 independent runs.
Mentions: The independent sequence of BA graphs used above constitutes an ideal situation that can be considered as a baseline case, but it is quite far from a realistic link evolution in a given single network. To do a step towards more realism, we shall now assume that the sequence of graphs is generated by successively rewiring an initial given graph as suggested in [17]. We begin with G(0) being a Barabási–Albert network; then, starting at time t = 1, each successive graph G(t) in the sequence is generated by swapping two randomly chosen non-adjacent pair of edges in the previous graph G(t−1). In contrast to the previous case, where the sequence of graphs was an i.i.d. one, this process is a Markov chain since each new graph in the sequence depends on the previous one. The edge swap preserves the degree distribution P(k) of G and obviously the node's degree and the mean degree as well. The graphs, however, become more and more randomized as time goes by, as they tend to loose the historical degree correlations between hubs that arise in the original BA construction. Note that in this case we assume an asynchronous dynamics since it is, in our opinion, qualitatively more adapted to the new situation. Results are almost the same with either synchronous or asynchronous dynamics as shown in [3]. For the BA networks and replicator dynamics, this is also clear from the leftmost images in Figs. 1 and 3. Thus, instead of updating all the players' strategies at once in each time step as before, we randomly choose a player to update (with replacement). This is called an elementary time step. The period of network rewiring in this case is the number of elementary steps before an edge swap takes place, and the frequency ω is just the reciprocal of this number.

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