Open Access
Research articles
Research articlesStable leaders pave the way for cooperation under time-dependent exploration rates
Published:03 February 2021https://doi.org/10.1098/rsos.200910
Abstract
The exploration of different behaviours is part of the adaptation repertoire of individuals to new environments. Here, we explore how the evolution of cooperative behaviour is affected by the interplay between exploration dynamics and social learning, in particular when individuals engage on prisoner’s dilemma along the edges of a social network. We show that when the population undergoes a transition from strong to weak exploration rates a decline in the overall levels of cooperation is observed. However, if the rate of decay is lower in highly connected individuals (Leaders) than for the less connected individuals (Followers) then the population is able to achieve higher levels of cooperation. Finally, we show that minor differences in selection intensities (the degree of determinism in social learning) and individual exploration rates, can translate into major differences in the observed collective dynamics.
References
- 1.
Fowler JH, Christakis NA . 2010Cooperative behavior cascades in human social networks. Proc. Natl Acad. Sci. USA 107, 5334-5338. (doi:10.1073/pnas.0913149107) Crossref, PubMed, ISI, Google Scholar - 2.
Christakis NA, Fowler JH . 2008The collective dynamics of smoking in a large social network. N. Engl. J. Med. 358, 2249-2258. (doi:10.1056/NEJMsa0706154) Crossref, PubMed, ISI, Google Scholar - 3.
Pinheiro FL, Santos MD, Santos FC, Pacheco JM . 2014Origin of peer influence in social networks. Phys. Rev. Lett. 112, 098702. (doi:10.1103/PhysRevLett.112.098702) Crossref, PubMed, ISI, Google Scholar - 4.
Traulsen A, Hauert C, De Silva H, Nowak MA, Sigmund K . 2009Exploration dynamics in evolutionary games. Proc. Natl Acad. Sci. USA 106, 709-712. (doi:10.1073/pnas.0808450106) Crossref, PubMed, ISI, Google Scholar - 5.
Santos FP, Pacheco JM, Santos FC . 2016Evolution of cooperation under indirect reciprocity and arbitrary exploration rates. Sci. Rep. 6, 37517. (doi:10.1038/srep37517) Crossref, PubMed, ISI, Google Scholar - 6.
Nowak MA . 2006Evolutionary dynamics. Cambridge, MA: Harvard University Press. Crossref, Google Scholar - 7.
May RM, Levin SA, Sugihara G . 2008Complex systems: ecology for bankers. Nature 451, 893-895. (doi:10.1038/451893a) Crossref, PubMed, ISI, Google Scholar - 8.
Levin S et al.2013Social-ecological systems as complex adaptive systems: modeling and policy implications. Environ. Dev. Econ. 18, 111-132. (doi:10.1017/S1355770X12000460) Crossref, ISI, Google Scholar - 9.
Hamilton WD . 1964The genetical evolution of social behaviour. II. J. Theor. Biol. 7, 17-52. (doi:10.1016/0022-5193(64)90039-6) Crossref, PubMed, ISI, Google Scholar - 10.
Santos FC, Pinheiro FL, Lenaerts T, Pacheco JM . 2012The role of diversity in the evolution of cooperation. J. Theor. Biol. 299, 88-96. (doi:10.1016/j.jtbi.2011.09.003) Crossref, PubMed, ISI, Google Scholar - 11.
Pinheiro FL, Pacheco JM, Santos FC . 2012From local to global dilemmas in social networks. PLoS ONE 7, e32114. (doi:10.1371/journal.pone.0032114) Crossref, PubMed, ISI, Google Scholar - 12.
Szabó G, Fath G . 2007Evolutionary games on graphs. Phys. Rep. 446, 97-216. (doi:10.1016/j.physrep.2007.04.004) Crossref, ISI, Google Scholar - 13.
Traulsen A, Pacheco JM, Nowak MA . 2007Pairwise comparison and selection temperature in evolutionary game dynamics. J. Theor. Biol. 246, 522-529. (doi:10.1016/j.jtbi.2007.01.002) Crossref, PubMed, ISI, Google Scholar - 14.
Gokhale CS, Iwasa Y, Nowak MA, Traulsen A . 2009The pace of evolution across fitness valleys. J. Theor. Biol. 259, 613-620. (doi:10.1016/j.jtbi.2009.04.011) Crossref, PubMed, ISI, Google Scholar - 15.
Van Segbroeck S, Santos FC, Lenaerts T, Pacheco JM . 2011Selection pressure transforms the nature of social dilemmas in adaptive networks. New J. Phys. 13, 013007. (doi:10.1088/1367-2630/13/1/013007) Crossref, ISI, Google Scholar - 16.
Perc M, Szolnoki A . 2010Coevolutionary games—a mini review. BioSystems 99, 109-125. (doi:10.1016/j.biosystems.2009.10.003) Crossref, PubMed, ISI, Google Scholar - 17.
Allen B, Traulsen A, Tarnita CE, Nowak MA . 2012How mutation affects evolutionary games on graphs. J. Theor. Biol. 299, 97-105. (doi:10.1016/j.jtbi.2011.03.034) Crossref, PubMed, ISI, Google Scholar - 18.
Szolnoki A, Vukov J, Szabó G . 2009Selection of noise level in strategy adoption for spatial social dilemmas. Phys. Rev. E 80, 056112. (doi:10.1103/PhysRevE.80.056112) Crossref, ISI, Google Scholar - 19.
Szolnoki A, Perc M . 2016Leaders should not be conformists in evolutionary social dilemmas. Sci. Rep. 6, 23633. (doi:10.1038/srep23633) Crossref, PubMed, ISI, Google Scholar - 20.
Alam M, Nagashima K, Tanimoto J . 2018Various error settings bring different noise-driven effects on network reciprocity in spatial prisoner’s dilemma. Chaos, Solitons Fractals 114, 338-346. (doi:10.1016/j.chaos.2018.07.014) Crossref, ISI, Google Scholar - 21.
Wilson RC, Geana A, White JM, Ludvig EA, Cohen JD . 2014Humans use directed and random exploration to solve the explore–exploit dilemma. J. Exp. Psychol.: General 143, 2074. (doi:10.1037/a0038199) Crossref, PubMed, ISI, Google Scholar - 22.
Kirkpatrick S, Gelatt CD, Vecchi MP . 1983Optimization by simulated annealing. Science 220, 671-680. (doi:10.1126/science.220.4598.671) Crossref, PubMed, ISI, Google Scholar - 23.
Corne D, Dorigo M, Glover F, Dasgupta D, Moscato P, Poli R, Price KV . 1999New ideas in optimization. Maidenhead, UK: McGraw-Hill Ltd. Google Scholar - 24.
Sutton RS, Barto AG . 1998Introduction to reinforcement learning, vol. 135. Cambridge, UK: MIT Press. Crossref, Google Scholar - 25.
Toyokawa W, Saito Y, Kameda T . 2017Individual differences in learning behaviours in humans: asocial exploration tendency does not predict reliance on social learning. Evol. Hum. Behav. 38, 325-333. (doi:10.1016/j.evolhumbehav.2016.11.001) Crossref, ISI, Google Scholar - 26.
Torkelson J, Harris RS, Lombardo MJ, Nagendran J, Thulin C, Rosenberg SM . 1997Genome-wide hypermutation in a subpopulation of stationary-phase cells underlies recombination-dependent adaptive mutation. EMBO J. 16, 3303-3311. (doi:10.1093/emboj/16.11.3303) Crossref, PubMed, ISI, Google Scholar - 27.
Denamur E, Matic I . 2006Evolution of mutation rates in bacteria. Mol. Microbiol. 60, 820-827. (doi:10.1111/j.1365-2958.2006.05150.x) Crossref, PubMed, ISI, Google Scholar - 28.
Swings T, Van den Bergh B, Wuyts S, Oeyen E, Voordeckers K, Verstrepen KJ, Fauvart M, Verstraeten N, Michiels J . 2017Adaptive tuning of mutation rates allows fast response to lethal stress in Escherichia coli. eLife 6, e22939. (doi:10.7554/eLife.22939) Crossref, PubMed, ISI, Google Scholar - 29.
Santos FC, Pacheco JM, Lenaerts T . 2006Evolutionary dynamics of social dilemmas in structured heterogeneous populations. Proc. Natl Acad. Sci. USA 103, 3490-3494. (doi:10.1073/pnas.0508201103) Crossref, PubMed, ISI, Google Scholar - 30.
Barabási A-L, Albert R . 1999Emergence of scaling in random networks. Science 286, 509-512. (doi:10.1126/science.286.5439.509) Crossref, PubMed, ISI, Google Scholar - 31.
Sigmund K . 2010The calculus of selfishness. Princeton, NJ: Princeton University Press. Crossref, Google Scholar - 32.
Pinheiro FL, Santos FC, Pacheco JM . 2012How selection pressure changes the nature of social dilemmas in structured populations. New J. Phys. 14, 073035. (doi:10.1088/1367-2630/14/7/073035) Crossref, ISI, Google Scholar - 33.
Nowak MA . 2006Five rules for the evolution of cooperation. Science 314, 1560-1563. (doi:10.1126/science.1133755) Crossref, PubMed, ISI, Google Scholar - 34.
Pinheiro FLP . 2016Evolution of cooperation under variable mutation rates. In Characterization of self-organization processes in complex networks, ch. 5, pp. 109–118. Braga, Portugal: Universidade do Minho. Google Scholar - 35.
Ichinose G, Satotani Y, Sayama H . 2018How mutation alters the evolutionary dynamics of cooperation on networks. New J. Phys. 20, 053049. (doi:10.1088/1367-2630/aac2a7) Crossref, ISI, Google Scholar - 36.
Szolnoki A, Perc M, Szabó G, Stark HU . 2009Impact of aging on the evolution of cooperation in the spatial prisoner’s dilemma game. Phys. Rev. E 80, 021901. (doi:10.1103/PhysRevE.80.021901) Crossref, ISI, Google Scholar - 37.
Apicella CL, Marlowe FW, Fowler JH, Christakis NA . 2012Social networks and cooperation in hunter-gatherers. Nature 481, 497. (doi:10.1038/nature10736) Crossref, PubMed, ISI, Google Scholar - 38.
Rand DG, Nowak MA, Fowler JH, Christakis NA . 2014Static network structure can stabilize human cooperation. Proc. Natl Acad. Sci. USA 111, 17 093-17 098. (doi:10.1073/pnas.1400406111) Crossref, ISI, Google Scholar - 39.
Li X, Jusup M, Wang Z, Li H, Shi L, Podobnik B, Stanley HE, Havlin S, Boccaletti S . 2018Punishment diminishes the benefits of network reciprocity in social dilemma experiments. Proc. Natl Acad. Sci. USA 115, 30-35. (doi:10.1073/pnas.1707505115) Crossref, PubMed, ISI, Google Scholar - 40.
Traulsen A, Semmann D, Sommerfeld RD, Krambeck H-J, Milinski M . 2010Human strategy updating in evolutionary games. Proc. Natl Acad. Sci. USA 107, 2962-2966. (doi:10.1073/pnas.0912515107) Crossref, PubMed, ISI, Google Scholar - 41.
Grujic J, Gracia-Lázaro C, Milinski M, Semmann D, Traulsen A, Cuesta JA, Moreno Y, Sánchez A . 2014A comparative analysis of spatial prisoner’s dilemma experiments: conditional cooperation and pay-off irrelevance. Sci. Rep. 4, 4615. (doi:10.1038/srep04615) Crossref, PubMed, ISI, Google Scholar - 42.
Shirado H, Christakis NA . 2017Locally noisy autonomous agents improve global human coordination in network experiments. Nature 545, 370. (doi:10.1038/nature22332) Crossref, PubMed, ISI, Google Scholar - 43.
Macy MW, Flache A . 2002Learning dynamics in social dilemmas. Proc. Natl Acad. Sci. USA 99, 7229-7236. (doi:10.1073/pnas.092080099) Crossref, PubMed, ISI, Google Scholar - 44.
Caldarelli G . 2007Scale-free networks: complex webs in nature and technology. New York, NY: Oxford University Press. Crossref, Google Scholar - 45.
Amaral LA, Ottino JM . 2004Complex networks. Eur. Phys. J. B: Condens. Matter Complex Syst. 38, 147-162. (doi:10.1140/epjb/e2004-00110-5) Crossref, Google Scholar - 46.
Traulsen A, Nowak MA, Pacheco JM . 2006Stochastic dynamics of invasion and fixation. Phys. Rev. E 74, 011909. (doi:10.1103/PhysRevE.74.011909) Crossref, ISI, Google Scholar - 47.
Pacheco JM, Santos FC, Souza MO, Skyrms B . 2009Evolutionary dynamics of collective action in N-person stag hunt dilemmas. Proc. R. Soc. B 276, 315-321. (doi:10.1098/rspb.2008.1126) Link, ISI, Google Scholar - 48.
Santos FC, Pacheco JM . 2011Risk of collective failure provides an escape from the tragedy of the commons. Proc. Natl Acad. Sci. USA 108, 10 421-10 425. (doi:10.1073/pnas.1015648108) Crossref, ISI, Google Scholar - 49.
Chalub FA, Souza MO . 2016Fixation in large populations: a continuous view of a discrete problem. J. Math. Biol. 72, 283-330. (doi:10.1007/s00285-015-0889-9) Crossref, PubMed, ISI, Google Scholar - 50.
Vasconcelos VV, Santos FP, Santos FC, Pacheco JM . 2017Stochastic dynamics through hierarchically embedded Markov chains. Phys. Rev. Lett. 118, 058301. (doi:10.1103/PhysRevLett.118.058301) Crossref, PubMed, ISI, Google Scholar - 51.
Hindersin L, Wu B, Traulsen A, García J . 2019Computation and simulation of evolutionary game dynamics in finite populations. Sci. Rep. 9, 1-21. (doi:10.1038/s41598-019-43102-z) Crossref, PubMed, ISI, Google Scholar - 52.
Pacheco JM, Pinheiro FL, Santos FC . 2009Population structure induces a symmetry breaking favoring the emergence of cooperation. PLoS Comput. Biol. 5, e1000596. (doi:10.1371/journal.pcbi.1000596) Crossref, PubMed, ISI, Google Scholar - 53.
Pinheiro FL, Santos FC, Pacheco JM . 2016Linking individual and collective behavior in adaptive social networks. Phys. Rev. Lett. 116, 128702. (doi:10.1103/PhysRevLett.116.128702) Crossref, PubMed, ISI, Google Scholar - 54.
Scheffer M . 2009Critical transitions in nature and society. Princeton, NJ: Princeton University Press. Crossref, Google Scholar - 55.
Scheffer M, Carpenter S, Foley JA, Folke C, Walker B . 2001Catastrophic shifts in ecosystems. Nature 413, 591-596. (doi:10.1038/35098000) Crossref, PubMed, ISI, Google Scholar - 56.
Scheffer M et al.2012Anticipating critical transitions. Science 338, 344-348. (doi:10.1126/science.1225244) Crossref, PubMed, ISI, Google Scholar - 57.
Lade SJ, Tavoni A, Levin SA, Schlüter M . 2013Regime shifts in a social-ecological system. Theor. Ecol. 6, 359-372. (doi:10.1007/s12080-013-0187-3) Crossref, ISI, Google Scholar - 58.
Pinheiro FL, Pacheco JM, Santos FC . 2021Data from: Stable leaders pave the way for cooperation under time-dependent exploration rates. Dryad Digital Repository. (doi:10.5061/dryad.m0cfxpp15) Google Scholar
