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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

Fraction of cooperators ρC as a function of the cost-to-benefit ratio r, as obtained for K = 0.1 [panels (a) and (b)] and K = 0.83 [panels (c) and (d)].Results presented in panels (a) and (c) were obtained by means of Monte Carlo simulations, while those presented in panels (b) and (d) were obtained by means of pair approximation (see Methods section for details). Figure legend indicates whether pairwise or locally influenced strategy updating was used.
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f1: Fraction of cooperators ρC as a function of the cost-to-benefit ratio r, as obtained for K = 0.1 [panels (a) and (b)] and K = 0.83 [panels (c) and (d)].Results presented in panels (a) and (c) were obtained by means of Monte Carlo simulations, while those presented in panels (b) and (d) were obtained by means of pair approximation (see Methods section for details). Figure legend indicates whether pairwise or locally influenced strategy updating was used.

Mentions: We begin by presenting the fraction of cooperators ρC as a function of the cost-to-benefit ratio r = c/b at two temperatures, namely at K = 0.1 and K = 0.83. The usage of the latter value is motivated by recent empirical research from behavioral science61, although essentially, as we will show in what follows, the temperature, i.e., the level of uncertainty by strategy adoptions, does not play a decisive role. Results for both the pairwise and locally influenced strategy updating are presented in Fig. 1(a,c). It can be observed that for K = 0.1 the evolution of cooperation is promoted across the whole applicable span of r if the traditionally used pairwise strategy updating is replaced by the proposed local influence based strategy updating. For K = 0.83, however, the outcome is a bit less clear-cut. While pairwise imitation fails to sustain cooperative behavior at such high values of r as locally influenced strategy updating, it is nevertheless more apt for achieving complete cooperator dominance. As we will show in what follows, it is indeed the case that locally influenced strategy updating often fails to completely eliminate defectors at small values of r, yet it opens up the possibility of survival of cooperators even under harsh defector-friendly conditions.


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

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

Fraction of cooperators ρC as a function of the cost-to-benefit ratio r, as obtained for K = 0.1 [panels (a) and (b)] and K = 0.83 [panels (c) and (d)].Results presented in panels (a) and (c) were obtained by means of Monte Carlo simulations, while those presented in panels (b) and (d) were obtained by means of pair approximation (see Methods section for details). Figure legend indicates whether pairwise or locally influenced strategy updating was used.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

f1: Fraction of cooperators ρC as a function of the cost-to-benefit ratio r, as obtained for K = 0.1 [panels (a) and (b)] and K = 0.83 [panels (c) and (d)].Results presented in panels (a) and (c) were obtained by means of Monte Carlo simulations, while those presented in panels (b) and (d) were obtained by means of pair approximation (see Methods section for details). Figure legend indicates whether pairwise or locally influenced strategy updating was used.
Mentions: We begin by presenting the fraction of cooperators ρC as a function of the cost-to-benefit ratio r = c/b at two temperatures, namely at K = 0.1 and K = 0.83. The usage of the latter value is motivated by recent empirical research from behavioral science61, although essentially, as we will show in what follows, the temperature, i.e., the level of uncertainty by strategy adoptions, does not play a decisive role. Results for both the pairwise and locally influenced strategy updating are presented in Fig. 1(a,c). It can be observed that for K = 0.1 the evolution of cooperation is promoted across the whole applicable span of r if the traditionally used pairwise strategy updating is replaced by the proposed local influence based strategy updating. For K = 0.83, however, the outcome is a bit less clear-cut. While pairwise imitation fails to sustain cooperative behavior at such high values of r as locally influenced strategy updating, it is nevertheless more apt for achieving complete cooperator dominance. As we will show in what follows, it is indeed the case that locally influenced strategy updating often fails to completely eliminate defectors at small values of r, yet it opens up the possibility of survival of cooperators even under harsh defector-friendly conditions.

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