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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

Characteristic snapshots of spatial patterns formed by cooperators (blue) and defectors (red) under pairwise imitation [(a) r = 0.004, (b) r = 0.019] and under strategy updating based on local influence [(c) r = 0.004, (d) r = 0.221].The size of the square lattice was 100 × 100 and K = 0.83. (a) In this snapshot there are 77 clusters, ranging in size from a single cooperator to 3042 cooperators, with a weighted average size of 1925.21. The stationary fraction of cooperators is ρC ≈ 0.52. (b) In this snapshot there are 99 clusters, ranging in size from a single cooperator to 162 cooperators, with a weighted average size of 70.01. The stationary fraction of cooperators is ρC ≈ 0.19. These characteristics are significantly different in the bottom two snapshots. (c) In this snapshot there are 439 clusters, ranging in size from a single cooperator to 427 cooperators, with a weighted average size of 137.69. The stationary fraction of cooperators is ρC ≈ 0.52. (d) In this snapshot there are 164 clusters, ranging in size from a single cooperator to 19 cooperators, with a weighted average size of 6.63. The stationary fraction of cooperators is ρC ≈ 0.05. Note that in snapshots (a) and (c) the densities of cooperators for both update rules are practically identical, while nearer to the extinction thresholds [panels (b) and (d)] they differ quite significantly.
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f3: Characteristic snapshots of spatial patterns formed by cooperators (blue) and defectors (red) under pairwise imitation [(a) r = 0.004, (b) r = 0.019] and under strategy updating based on local influence [(c) r = 0.004, (d) r = 0.221].The size of the square lattice was 100 × 100 and K = 0.83. (a) In this snapshot there are 77 clusters, ranging in size from a single cooperator to 3042 cooperators, with a weighted average size of 1925.21. The stationary fraction of cooperators is ρC ≈ 0.52. (b) In this snapshot there are 99 clusters, ranging in size from a single cooperator to 162 cooperators, with a weighted average size of 70.01. The stationary fraction of cooperators is ρC ≈ 0.19. These characteristics are significantly different in the bottom two snapshots. (c) In this snapshot there are 439 clusters, ranging in size from a single cooperator to 427 cooperators, with a weighted average size of 137.69. The stationary fraction of cooperators is ρC ≈ 0.52. (d) In this snapshot there are 164 clusters, ranging in size from a single cooperator to 19 cooperators, with a weighted average size of 6.63. The stationary fraction of cooperators is ρC ≈ 0.05. Note that in snapshots (a) and (c) the densities of cooperators for both update rules are practically identical, while nearer to the extinction thresholds [panels (b) and (d)] they differ quite significantly.

Mentions: In order to obtain an understanding of the reported observations, we proceed with the presentation of characteristic spatial patterns, as obtained for both pairwise and locally influenced strategy updating, in Fig. 3. Regardless of which update rule is applied, cooperators form compact clusters by means of which they are able to exploit the mechanism of network reciprocity19. If the value of r is small, the clusters are larger and more compact than for higher values of r. On the other hand, the spatial patterns emerging under the two update rules also have noticeable dissimilarities. Foremost, given a value of r, pairwise strategy updating yields larger clusters than locally influenced strategy updating, even if the density of cooperators is approximately the same [compare panels (a) and (c)]. Nearer to the extinction threshold the stationary densities differ, yet the difference in the spatial patterns the two rules generate becomes most apparent [compare panels (b) and (d)].


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

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

Characteristic snapshots of spatial patterns formed by cooperators (blue) and defectors (red) under pairwise imitation [(a) r = 0.004, (b) r = 0.019] and under strategy updating based on local influence [(c) r = 0.004, (d) r = 0.221].The size of the square lattice was 100 × 100 and K = 0.83. (a) In this snapshot there are 77 clusters, ranging in size from a single cooperator to 3042 cooperators, with a weighted average size of 1925.21. The stationary fraction of cooperators is ρC ≈ 0.52. (b) In this snapshot there are 99 clusters, ranging in size from a single cooperator to 162 cooperators, with a weighted average size of 70.01. The stationary fraction of cooperators is ρC ≈ 0.19. These characteristics are significantly different in the bottom two snapshots. (c) In this snapshot there are 439 clusters, ranging in size from a single cooperator to 427 cooperators, with a weighted average size of 137.69. The stationary fraction of cooperators is ρC ≈ 0.52. (d) In this snapshot there are 164 clusters, ranging in size from a single cooperator to 19 cooperators, with a weighted average size of 6.63. The stationary fraction of cooperators is ρC ≈ 0.05. Note that in snapshots (a) and (c) the densities of cooperators for both update rules are practically identical, while nearer to the extinction thresholds [panels (b) and (d)] they differ quite significantly.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

f3: Characteristic snapshots of spatial patterns formed by cooperators (blue) and defectors (red) under pairwise imitation [(a) r = 0.004, (b) r = 0.019] and under strategy updating based on local influence [(c) r = 0.004, (d) r = 0.221].The size of the square lattice was 100 × 100 and K = 0.83. (a) In this snapshot there are 77 clusters, ranging in size from a single cooperator to 3042 cooperators, with a weighted average size of 1925.21. The stationary fraction of cooperators is ρC ≈ 0.52. (b) In this snapshot there are 99 clusters, ranging in size from a single cooperator to 162 cooperators, with a weighted average size of 70.01. The stationary fraction of cooperators is ρC ≈ 0.19. These characteristics are significantly different in the bottom two snapshots. (c) In this snapshot there are 439 clusters, ranging in size from a single cooperator to 427 cooperators, with a weighted average size of 137.69. The stationary fraction of cooperators is ρC ≈ 0.52. (d) In this snapshot there are 164 clusters, ranging in size from a single cooperator to 19 cooperators, with a weighted average size of 6.63. The stationary fraction of cooperators is ρC ≈ 0.05. Note that in snapshots (a) and (c) the densities of cooperators for both update rules are practically identical, while nearer to the extinction thresholds [panels (b) and (d)] they differ quite significantly.
Mentions: In order to obtain an understanding of the reported observations, we proceed with the presentation of characteristic spatial patterns, as obtained for both pairwise and locally influenced strategy updating, in Fig. 3. Regardless of which update rule is applied, cooperators form compact clusters by means of which they are able to exploit the mechanism of network reciprocity19. If the value of r is small, the clusters are larger and more compact than for higher values of r. On the other hand, the spatial patterns emerging under the two update rules also have noticeable dissimilarities. Foremost, given a value of r, pairwise strategy updating yields larger clusters than locally influenced strategy updating, even if the density of cooperators is approximately the same [compare panels (a) and (c)]. Nearer to the extinction threshold the stationary densities differ, yet the difference in the spatial patterns the two rules generate becomes most apparent [compare panels (b) and (d)].

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