The outbreak of cooperation among success-driven individuals under noisy conditions

Edited by Robert May, University of Oxford, Oxford, United Kingdom, and approved January 16, 2009
March 10, 2009
106 (10) 3680-3685

Abstract

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 control. The self-organization of cooperative behavior is particularly puzzling for social dilemmas related to sharing natural resources or creating common goods. Such situations are often described by the prisoner's dilemma. Here, we report the sudden outbreak of predominant cooperation in a noisy world dominated by selfishness and defection, when individuals imitate superior strategies and show success-driven migration. In our model, individuals are unrelated, and do not inherit behavioral traits. They defect or cooperate selfishly when the opportunity arises, and they do not know how often they will interact or have interacted with someone else. Moreover, our individuals have no reputation mechanism to form friendship networks, nor do they have the option of voluntary interaction or costly punishment. Therefore, the outbreak of prevailing cooperation, when directed motion is integrated in a game-theoretical model, is remarkable, particularly when random strategy mutations and random relocations challenge the formation and survival of cooperative clusters. Our results suggest that mobility is significant for the evolution of social order, and essential for its stabilization and maintenance.

Continue Reading

Acknowledgments.

We thank Christoph Hauert, Heiko Rauhut, Sergi Lozano, Michael Maes, Carlos P. Roca, and Didier Sornette for their comments.

Supporting Information

Supporting Information (PDF)
Supporting Information
SM1.avi

References

1
MC Gonzáles, CA Hidalgo, AL Barabási, Understanding individual human mobility patterns. Nature 453, 779–782 (2008).
2
L Hufnagel, D Brockmann, T Geisel, The scaling laws of human travel. Nature 439, 462–465 (2006).
3
M Batty Cities and Complexity (MIT Press, Cambridge, MA, 2005).
4
W Weidlich Sociodynamics. A Systematic Approach to Mathematical Modelling in the Social Sciences (Harwood Academic, Amsterdam, The Netherlands, 2000).
5
, ed D Pumain (John Libbey Eurotext, Montrouge, France Spatial Analysis and Population Dynamics, 1991).
6
JV Neumann, O Morgenstern Theory of Games and Economic Behavior (Princeton University, Princeton, NJ, 1944).
7
R Axelrod The Evolution of Cooperation (Basic Books, New York, 1984).
8
B Skyrms Evolution of the Social Contract (Cambridge Univ Press, New York, 1996).
9
A Flache, R Hegselmann, Do irregular grids make a difference? Relaxing the spatial regularity assumption in cellular models of social dynamics. J Artif Soc Soc Simul 4, Available at: http://www.soc.surrey.ac.uk/JASSS/4/4/6.html. (2001).
10
JM Epstein, Zones of cooperation in demographic prisoner's dilemma. Complexity 4, 36–48 (1998).
11
LA Dugatkin, DS Wilson, ROVER: A strategy for exploiting cooperators in a patchy environment. Am Nat 138, 687–701 (1991).
12
M Enquist, O Leimar, The evolution of cooperation in mobile organisms. Anim Behav 45, 747–757 (1993).
13
J-F Le Galliard, R Ferrière, U Dieckmann, Adaptive evolution of social traits: Origin, trajectories, and correlations of altruism and mobility. Am Nat 165, 206–224 (2005).
14
T Reichenbach, M Mobilia, E Frey, Mobility promotes and jeopardizes biodiversity in rock-paper-scissors games. Nature 448, 1046–1049 (2007).
15
CA Aktipis, Know when to walk away: Contingent movement and the evolution of cooperation. J Theor Biol 231, 249–260 (2004).
16
MH Vainstein, ATC Silva, JJ Arenzon, Does mobility decrease cooperation? J Theor Biol 244, 722–728 (2007).
17
MA Nowak, Five rules for the evolution of cooperation. Science 314, 1560–1563 (2006).
18
A Traulsen, MA Nowak, Evolution of cooperation by multilevel selection. Proc Natl Acad Sci USA 103, 10952–10955 (2006).
19
E Fehr, S Gächter, Altruistic punishment in humans. Nature 415, 137–140 (2002).
20
R Boyd, H Gintis, S Bowles, PJ Richerson, The evolution of altruistic punishment. Proc Natl Acad Sci USA 100, 3531–3535 (2003).
21
MA Nowak, RM May, Evolutionary games and spatial chaos. Nature 359, 826–829 (1992).
22
G Szabó, C Hauert, Phase transitions and volunteering in spatial public goods games. Phys Rev Lett 89, 118101 (2002).
23
C Hauert, M Doebeli, Spatial structure often inhibits the evolution of cooperation in the snowdrift game. Nature 428, 643–646 (2004).
24
MH Vainstein, JJ Arenzon, Disordered environments in spatial games. Phys Rev E 64, 051905. (2001).
25
D Helbing, W Yu, Migration as a mechanism to promote cooperation. Adv Complex Syst 11, 641–652 (2008).
26
HP Young Individual Strategy and Social Structure: An Evolutionary Theory of Institutions (Princeton Univ Press, Princeton, NJ, 1998).
27
NS Glance, BA Huberman, The outbreak of cooperation. J Math Soc 17, 281–302 (1993).
28
C Hauert, Fundamental clusters in spatial 2× 2 games. Proc R Soc Lond B 268, 761–769 (2000).
29
TC Schelling, Dynamic models of segregation. J Math Sociol 1, 143–186 (1971).
30
JL Deneubourg, A Lioni, C Detrain, Dynamics of aggregation and emergence of cooperation. Biol Bull 202, 262–267 (2002).
31
MA Nowak, K Sigmund, Evolution of indirect reciprocity by image scoring. Nature 393, 573–577 (1998).
32
M Milinski, D Semmann, HJ Krambeck, Reputation helps solve the “tragedy of the commons”. Nature 415, 424–426 (2002).
33
B Rockenbach, M Milinski, The efficient interaction of indirect reciprocity and costly punishment. Nature 444, 718–723 (2006).

Information & Authors

Information

Published in

Go to Proceedings of the National Academy of Sciences
Go to Proceedings of the National Academy of Sciences
Proceedings of the National Academy of Sciences
Vol. 106 | No. 10
March 10, 2009
PubMed: 19237576

Classifications

Submission history

Received: November 13, 2008
Published online: March 10, 2009
Published in issue: March 10, 2009

Keywords

  1. evolution
  2. pattern formation
  3. spatial games
  4. mobility
  5. migration

Acknowledgments

We thank Christoph Hauert, Heiko Rauhut, Sergi Lozano, Michael Maes, Carlos P. Roca, and Didier Sornette for their comments.

Notes

This article is a PNAS Direct Submission.
This article contains supporting information online at www.pnas.org/cgi/content/full/0811503106/DCSupplemental.

Authors

Affiliations

Dirk Helbing1 [email protected]
Department of Humanities, Social and Political Sciences, ETH Zurich, Swiss Federal Institute of Technology, UNO D11, Universitätstrasse 41, 8092 Zurich, Switzerland
Wenjian Yu
Department of Humanities, Social and Political Sciences, ETH Zurich, Swiss Federal Institute of Technology, UNO D11, Universitätstrasse 41, 8092 Zurich, Switzerland

Notes

1
To whom correspondence should be addressed. E-mail: [email protected]
Author contributions: D.H. designed research; D.H. performed research; W.Y. performed computer simulations; W.Y. analyzed data; and D.H. wrote the paper.

Competing Interests

The authors declare no conflict of interest.

Metrics & Citations

Metrics

Note: The article usage is presented with a three- to four-day delay and will update daily once available. Due to ths delay, usage data will not appear immediately following publication. Citation information is sourced from Crossref Cited-by service.


Citation statements

Altmetrics

Citations

If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.

Cited by

    Loading...

    View Options

    View options

    PDF format

    Download this article as a PDF file

    DOWNLOAD PDF

    Get Access

    Login options

    Check if you have access through your login credentials or your institution to get full access on this article.

    Personal login Institutional Login

    Recommend to a librarian

    Recommend PNAS to a Librarian

    Purchase options

    Purchase this article to get full access to it.

    Single Article Purchase

    The outbreak of cooperation among success-driven individuals under noisy conditions
    Proceedings of the National Academy of Sciences
    • Vol. 106
    • No. 10
    • pp. 3641-4061

    Media

    Figures

    Tables

    Other

    Share

    Share

    Share article link

    Share on social media