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Beyond pairwise strategy updating in the prisoner's dilemma game.

Wang X, Perc M, Liu Y, Chen X, Wang L - Sci Rep (2012)

Bottom Line: In spatial games players typically alter their strategy by imitating the most successful or one randomly selected neighbor.This leads to phase diagrams that differ significantly from those obtained by means of pairwise strategy updating.In particular, the survivability of cooperators is possible even by high temptations to defect and over a much wider uncertainty range.

View Article: PubMed Central - PubMed

Affiliation: Center for Complex Systems, Xidian University, Xi'an 710071, China.

ABSTRACT
In spatial games players typically alter their strategy by imitating the most successful or one randomly selected neighbor. Since a single neighbor is taken as reference, the information stemming from other neighbors is neglected, which begets the consideration of alternative, possibly more realistic approaches. Here we show that strategy changes inspired not only by the performance of individual neighbors but rather by entire neighborhoods introduce a qualitatively different evolutionary dynamics that is able to support the stable existence of very small cooperative clusters. This leads to phase diagrams that differ significantly from those obtained by means of pairwise strategy updating. In particular, the survivability of cooperators is possible even by high temptations to defect and over a much wider uncertainty range. We support the simulation results by means of pair approximations and analysis of spatial patterns, which jointly highlight the importance of local information for the resolution of social dilemmas.

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Related in: MedlinePlus

Macroscopic properties of cooperative clusters in the dependence on the cost-to-benefit ratio r.Cluster size (a) and cluster count (b) are depicted for pairwise and locally influenced strategy updating. In both cases the cluster size decreases as r increases, while the cluster count reaches a maximum at a certain value of r and then decreases. Note that for pairwise imitation a minimum cluster size of about 76.18 is required for cooperators to survive. Taking into account the local influence of the neighbors reduces this to 6.61. The depicted results were determined in the stationary state on 100 × 100 square lattices and by using K = 0.83. Error bars indicate the standard deviation.
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f4: Macroscopic properties of cooperative clusters in the dependence on the cost-to-benefit ratio r.Cluster size (a) and cluster count (b) are depicted for pairwise and locally influenced strategy updating. In both cases the cluster size decreases as r increases, while the cluster count reaches a maximum at a certain value of r and then decreases. Note that for pairwise imitation a minimum cluster size of about 76.18 is required for cooperators to survive. Taking into account the local influence of the neighbors reduces this to 6.61. The depicted results were determined in the stationary state on 100 × 100 square lattices and by using K = 0.83. Error bars indicate the standard deviation.

Mentions: The visual inspection of the characteristic spatial patterns invites a quantitative analysis of the exposed differences, the results of which are presented in Fig. 4 separately for both updating rules. It can be observed that, in general, as r increases, the cluster size decreases. The number of clusters, on the other hand, is maximal at an intermediate value of r. Concrete r values, however, differ significantly for the two considered strategy updating rules. In particular, by pairwise strategy updating both the clusters size and the number of clusters are shifted significantly towards lower values of r. One reason is obviously that pairwise strategy updating simply does not support the survivability of cooperators by as high values of r as locally influenced strategy updating. Nonetheless, the fact that for any given value of r, where comparisons are possible, the typical cluster size obtained with pairwise strategy updating is much larger than the one obtained with locally influenced strategy updating begets the conclusion that there are significant differences in the way cooperators cluster to withstand being wiped out by defectors. Note that for cooperators to survive under pairwise updating the minimally required cluster size is ≈ 76.18, while for locally influenced updating it is only 6.61. Moreover, for pairwise strategy updating the cluster size decreases much faster, which speaks in favor of the increased stability of the clusters under locally influenced strategy updating.


Beyond pairwise strategy updating in the prisoner's dilemma game.

Wang X, Perc M, Liu Y, Chen X, Wang L - Sci Rep (2012)

Macroscopic properties of cooperative clusters in the dependence on the cost-to-benefit ratio r.Cluster size (a) and cluster count (b) are depicted for pairwise and locally influenced strategy updating. In both cases the cluster size decreases as r increases, while the cluster count reaches a maximum at a certain value of r and then decreases. Note that for pairwise imitation a minimum cluster size of about 76.18 is required for cooperators to survive. Taking into account the local influence of the neighbors reduces this to 6.61. The depicted results were determined in the stationary state on 100 × 100 square lattices and by using K = 0.83. Error bars indicate the standard deviation.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC3472391&req=5

f4: Macroscopic properties of cooperative clusters in the dependence on the cost-to-benefit ratio r.Cluster size (a) and cluster count (b) are depicted for pairwise and locally influenced strategy updating. In both cases the cluster size decreases as r increases, while the cluster count reaches a maximum at a certain value of r and then decreases. Note that for pairwise imitation a minimum cluster size of about 76.18 is required for cooperators to survive. Taking into account the local influence of the neighbors reduces this to 6.61. The depicted results were determined in the stationary state on 100 × 100 square lattices and by using K = 0.83. Error bars indicate the standard deviation.
Mentions: The visual inspection of the characteristic spatial patterns invites a quantitative analysis of the exposed differences, the results of which are presented in Fig. 4 separately for both updating rules. It can be observed that, in general, as r increases, the cluster size decreases. The number of clusters, on the other hand, is maximal at an intermediate value of r. Concrete r values, however, differ significantly for the two considered strategy updating rules. In particular, by pairwise strategy updating both the clusters size and the number of clusters are shifted significantly towards lower values of r. One reason is obviously that pairwise strategy updating simply does not support the survivability of cooperators by as high values of r as locally influenced strategy updating. Nonetheless, the fact that for any given value of r, where comparisons are possible, the typical cluster size obtained with pairwise strategy updating is much larger than the one obtained with locally influenced strategy updating begets the conclusion that there are significant differences in the way cooperators cluster to withstand being wiped out by defectors. Note that for cooperators to survive under pairwise updating the minimally required cluster size is ≈ 76.18, while for locally influenced updating it is only 6.61. Moreover, for pairwise strategy updating the cluster size decreases much faster, which speaks in favor of the increased stability of the clusters under locally influenced strategy updating.

Bottom Line: In spatial games players typically alter their strategy by imitating the most successful or one randomly selected neighbor.This leads to phase diagrams that differ significantly from those obtained by means of pairwise strategy updating.In particular, the survivability of cooperators is possible even by high temptations to defect and over a much wider uncertainty range.

View Article: PubMed Central - PubMed

Affiliation: Center for Complex Systems, Xidian University, Xi'an 710071, China.

ABSTRACT
In spatial games players typically alter their strategy by imitating the most successful or one randomly selected neighbor. Since a single neighbor is taken as reference, the information stemming from other neighbors is neglected, which begets the consideration of alternative, possibly more realistic approaches. Here we show that strategy changes inspired not only by the performance of individual neighbors but rather by entire neighborhoods introduce a qualitatively different evolutionary dynamics that is able to support the stable existence of very small cooperative clusters. This leads to phase diagrams that differ significantly from those obtained by means of pairwise strategy updating. In particular, the survivability of cooperators is possible even by high temptations to defect and over a much wider uncertainty range. We support the simulation results by means of pair approximations and analysis of spatial patterns, which jointly highlight the importance of local information for the resolution of social dilemmas.

Show MeSH
Related in: MedlinePlus