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Representative simulation results for the spatial prisoner's dilemma with payoffs T = 1.3, R = 1, P = 0.1, and S = 0 after t = 200 

Representative simulation results for the spatial prisoner's dilemma with payoffs T = 1.3, R = 1, P = 0.1, and S = 0 after t = 200 

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According to Thomas Hobbes' Leviathan [1651; 2008 (Touchstone, New York), English Ed], "the life of man [is] solitary, poor, nasty, brutish, and short," and it would need powerful social institutions to establish social order. In reality, however, social cooperation can also arise spontaneously, based on local interactions rather than centralized c...

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... range [16]. However, strategy mutations, random relocations, and other sources of stochas- ticity ("noise") can significantly challenge the formation and survival of cooperative clusters. When no mobility or undi- rected, random mobility are considered, the level of cooper- ation in the spatial games studied by us is sensitive to noise (see Figs. 1d and 3c), as favorable correlations between co- operative neighbors are destroyed. Success-driven migration, in contrast, is a robust mechanism: By leaving unfavorable neighborhoods, seeking more favorable ones, and remaining in cooperative neighborhoods, it supports cooperative clus- ters very efficiently against the destructive effects of ...
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... may be considered to reflect deficient imitation attempts or trial- and-error behavior. As a side effect, such noise leads to an independence of the finally resulting level of cooperation from the initial one at t = 0, and a qualitatively different pattern formation dynamics for the same payoff values, update rules, and initial conditions (see Fig. 1). Using the alternative Fermi update rule [22] would have been possible as well. However, re- setting strategies rather than inverting them, combined with values q much smaller than 1/2, has here the advantage of creating particularly adverse conditions for cooperation, inde- pendently of what strategy prevails. Below, we want to ...
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... case of classical spatial games with noise 1, but without a migration step, the resulting fraction of coop- erators in the PD tends to be very low. It basically reflects the fraction rq of cooperators due to strategy mutations. For r = q = 0.05, we find almost frozen configurations, in which only a small number of cooperators survive (see Fig. 1d). In the migration-only case without an imitation step, the frac- tion of cooperators changes only by strategy mutations. Even when the initial strategy distribution is uniform, one observes the formation of spatio-temporal patterns, but the patterns get almost frozen after some time (see Fig. ...
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... only a small number of cooperators survive (see Fig. 1d). In the migration-only case without an imitation step, the frac- tion of cooperators changes only by strategy mutations. Even when the initial strategy distribution is uniform, one observes the formation of spatio-temporal patterns, but the patterns get almost frozen after some time (see Fig. ...
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... is interesting that, although for the connectivity struc- ture of our PD model neither imitation only ( Fig. 1d) nor mi- gration only (Fig. 1e) can promote cooperation under noisy conditions, their combination does: Computer simulations show the formation of cooperative clusters with a few de- fectors at their boundaries (see Fig. 1f). Once cooperators are organized in clusters, they tend to have more neighbors and to reach higher payoffs on ...
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... is interesting that, although for the connectivity struc- ture of our PD model neither imitation only ( Fig. 1d) nor mi- gration only (Fig. 1e) can promote cooperation under noisy conditions, their combination does: Computer simulations show the formation of cooperative clusters with a few de- fectors at their boundaries (see Fig. 1f). Once cooperators are organized in clusters, they tend to have more neighbors and to reach higher payoffs on average, which allows them to ...
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... is interesting that, although for the connectivity struc- ture of our PD model neither imitation only ( Fig. 1d) nor mi- gration only (Fig. 1e) can promote cooperation under noisy conditions, their combination does: Computer simulations show the formation of cooperative clusters with a few de- fectors at their boundaries (see Fig. 1f). Once cooperators are organized in clusters, they tend to have more neighbors and to reach higher payoffs on average, which allows them to survive [9,10,25]. It will now have to be revealed, how success-driven migration causes the formation of clusters at all, considering the opposing noise effects. In particular, we will study, why ...
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... conditions for the spreading of cooperators from a supercritical cluster ("nucleus") can be understood by con- figurational analysis [26,28] (see Fig. S1), but the underlying argument can be both, simplified and extended: According to Fig. 6a, the level of cooperation changes when certain lines (or, more generally, certain hyperplanes) in the payoff-parameter space are crossed. These hyperplanes are all of the linear ...
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... above features-the survival of cooperation in a large parameter area of the PD, spatio- temporal pattern formation, noise-resistance, and the out- break of predominant cooperation-can be captured by con- sidering a mechanism as simple as success-driven migration: Success-driven migration destabilizes a homogeneous strategy distribution (compare Fig. 1c with 1a and Fig. 1f with 1d). This triggers the spontaneous formation of agglomeration and segregation patterns [29], where noise or diffusion would cause dispersal in the imitation-only case. The self-organized pat- terns create self-reinforcing social environments characterized by behavioral correlations, and imitation promotes the fur- ther ...
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... survival of cooperation in a large parameter area of the PD, spatio- temporal pattern formation, noise-resistance, and the out- break of predominant cooperation-can be captured by con- sidering a mechanism as simple as success-driven migration: Success-driven migration destabilizes a homogeneous strategy distribution (compare Fig. 1c with 1a and Fig. 1f with 1d). This triggers the spontaneous formation of agglomeration and segregation patterns [29], where noise or diffusion would cause dispersal in the imitation-only case. The self-organized pat- terns create self-reinforcing social environments characterized by behavioral correlations, and imitation promotes the fur- ther growth of ...
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... self-organized pat- terns create self-reinforcing social environments characterized by behavioral correlations, and imitation promotes the fur- ther growth of supercritical cooperation clusters. While each mechanism by itself tends to produce frozen spatial struc- tures, the combination of imitation and migration supports adaptive patterns (see Fig. 1f). This facilitates, for example, the regrouping of a cluster of cooperators upon invasion by a defector, which is crucial for the survival and success of coop- erators (see Fig. ...

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... Remarkably, as an important reference and an enlightening attempt, Helbing et al. soon conceive an elaborate model embedded with profit-maximization-driven migration [22]. By means of the so-called cost-free fictitious interaction, for the first time, they spark an explosion of cooperation by deterministic migration in a noisy environment where defection completely dominates. ...
... By comparison, so far, it is not difficult to find that Helbing et al. mainly focus on where to move [22], nevertheless others give more weight to when to leave [24][25][26][27][28][29][30], resulting in the biggest gap between them. In either case, however, existing literatures have more or less imposed an aversion to defection during migration. ...
... Compared with existing work, this operation seems to be more strategy-neutral. Therefore, migration in this article is often risky due to the absence of optimal relocation as generated by the success-driven migration [22], which constitutes the most striking feature of this design. n s i denotes the number of strategy s i , n i the size of i's neighborhood excluding unoccupied vacancies, and π a the average payoff of i's neighborhood before the current iteration. ...
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