If players are sparse social dilemmas are too: Importance of percolation for evolution of cooperation

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Abstract

Spatial reciprocity is a well known tour de force of cooperation promotion. A thorough understanding of the effects of different population densities is therefore crucial. Here we study the evolution of cooperation in social dilemmas on different interaction graphs with a certain fraction of vacant nodes. We find that sparsity may favor the resolution of social dilemmas, especially if the population density is close to the percolation threshold of the underlying graph. Regardless of the type of the governing social dilemma as well as particularities of the interaction graph, we show that under pairwise imitation the percolation threshold is a universal indicator of how dense the occupancy ought to be for cooperation to be optimally promoted. We also demonstrate that myopic updating, due to the lack of efficient spread of information via imitation, renders the reported mechanism dysfunctional, which in turn further strengthens its foundations.

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Social diversity promotes the emergence of cooperation in public goods games.

Francisco C. Santos, Marta D. Santos, Jorge M Pacheco (2008)

Humans often cooperate in public goods games and situations ranging from family issues to global warming. However, evolutionary game theory predicts that the temptation to forgo the public good mostly wins over collective cooperative action, and this is often also seen in economic experiments. Here we show how social diversity provides an escape from this apparent paradox. Up to now, individuals have been treated as equivalent in all respects, in sharp contrast with real-life situations, where diversity is ubiquitous. We introduce social diversity by means of heterogeneous graphs and show that cooperation is promoted by the diversity associated with the number and size of the public goods game in which each individual participates and with the individual contribution to each such game. When social ties follow a scale-free distribution, cooperation is enhanced whenever all individuals are expected to contribute a fixed amount irrespective of the plethora of public goods games in which they engage. Our results may help to explain the emergence of cooperation in the absence of mechanisms based on individual reputation and punishment. Combining social diversity with reputation and punishment will provide instrumental clues on the self-organization of social communities and their economical implications.

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Evolutionary dynamics of social dilemmas in structured heterogeneous populations.

F. C. Santos, J M Pacheco, Tom Lenaerts (2006)

Real populations have been shown to be heterogeneous, in which some individuals have many more contacts than others. This fact contrasts with the traditional homogeneous setting used in studies of evolutionary game dynamics. We incorporate heterogeneity in the population by studying games on graphs, in which the variability in connectivity ranges from single-scale graphs, for which heterogeneity is small and associated degree distributions exhibit a Gaussian tale, to scale-free graphs, for which heterogeneity is large with degree distributions exhibiting a power-law behavior. We study the evolution of cooperation, modeled in terms of the most popular dilemmas of cooperation. We show that, for all dilemmas, increasing heterogeneity favors the emergence of cooperation, such that long-term cooperative behavior easily resists short-term noncooperative behavior. Moreover, we show how cooperation depends on the intricate ties between individuals in scale-free populations.

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Coevolutionary games - a mini review

, (2010)

Prevalence of cooperation within groups of selfish individuals is puzzling in that it contradicts with the basic premise of natural selection. Favoring players with higher fitness, the latter is key for understanding the challenges faced by cooperators when competing with defectors. Evolutionary game theory provides a competent theoretical framework for addressing the subtleties of cooperation in such situations, which are known as social dilemmas. Recent advances point towards the fact that the evolution of strategies alone may be insufficient to fully exploit the benefits offered by cooperative behavior. Indeed, while spatial structure and heterogeneity, for example, have been recognized as potent promoters of cooperation, coevolutionary rules can extend the potentials of such entities further, and even more importantly, lead to the understanding of their emergence. The introduction of coevolutionary rules to evolutionary games implies, that besides the evolution of strategies, another property may simultaneously be subject to evolution as well. Coevolutionary rules may affect the interaction network, the reproduction capability of players, their reputation, mobility or age. Here we review recent works on evolutionary games incorporating coevolutionary rules, as well as give a didactic description of potential pitfalls and misconceptions associated with the subject. In addition, we briefly outline directions for future research that we feel are promising, thereby particularly focusing on dynamical effects of coevolutionary rules on the evolution of cooperation, which are still widely open to research and thus hold promise of exciting new discoveries.

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Journal ID (nlm-ta): Sci Rep

Journal ID (iso-abbrev): Sci Rep

Title: Scientific Reports

Publisher: Nature Publishing Group

ISSN (Electronic): 2045-2322

Publication date (Electronic): 17 April 2012

Publication date Collection: 2012

Volume: 2

Electronic Location Identifier: 369

Affiliations

[1 ]simpleSchool of Physics, Nankai University , Tianjin 300071, China

[2 ]simpleDepartment of Physics, Hong Kong Baptist University , Kowloon Tong, Hong Kong

[3 ]simpleInstitute of Technical Physics and Materials Science, Research Centre for Natural Sciences , Hungarian Academy of SciencesP.O. Box 49, H-1525 Budapest, Hungary

[4 ]simpleFaculty of Natural Sciences and Mathematics, University of Maribor , Koroška cesta 160, SI-2000 Maribor, Slovenia

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[a ] matjaz.perc@ 123456uni-mb.si

Article

Publisher Item ID: srep00369

DOI: 10.1038/srep00369

PMC ID: 3328045

PubMed ID: 22511999

SO-VID: b05b5e9b-1979-40a2-acd5-16a7ee0964b5

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This work is licensed under a Creative Commons Attribution-NonCommercial-ShareALike 3.0 Unported License. To view a copy of this license, visit http://creativecommons.org/licenses/by-nc-sa/3.0/

If players are sparse social dilemmas are too: Importance of percolation for evolution of cooperation

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Most cited references 20

Social diversity promotes the emergence of cooperation in public goods games.

Evolutionary dynamics of social dilemmas in structured heterogeneous populations.

Coevolutionary games - a mini review

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