×

Co-evolution of strategies and update rules in the prisoner’s dilemma game on complex networks. (English) Zbl 1448.91062

Summary: In this paper, we study a weak prisoner’s dilemma (PD) game in which both strategies and update rules are subjected to evolutionary pressure. Interactions among agents are specified by complex topologies, and we consider both homogeneous and heterogeneous situations. We consider deterministic and stochastic update rules for the strategies, which in turn may consider single links or the full context when selecting agents to copy from. Our results indicate that the co-evolutionary process preserves heterogeneous networks as a suitable framework for the emergence of cooperation. Furthermore, on those networks the update rule leading to a larger fraction, which we call replicator dynamics, is selected during co-evolution. On homogeneous networks, we observe that even if the replicator dynamics again turns out to be the selected update rule, the cooperation level is greater than on a fixed update rule framework. We conclude that for a variety of topologies, the fact that the dynamics co-evolves with the strategies leads, in general, to more cooperation in the weak PD game.

MSC:

91A43 Games involving graphs
91A22 Evolutionary games
91A06 \(n\)-person games, \(n>2\)
PDFBibTeX XMLCite
Full Text: DOI arXiv

References:

[1] Szabó G and Fáth G 2007 Phys. Rep.446 97-216 · doi:10.1016/j.physrep.2007.04.004
[2] Roca C P, Cuesta J and Sánchez A 2009 Phys. Life Rev.6 208-49 · doi:10.1016/j.plrev.2009.08.001
[3] Hofbauer J and Sigmund K 1998 Evolutionary Games and Population Dynamics (Cambridge: Cambridge University Press) · Zbl 0914.90287 · doi:10.1017/CBO9781139173179
[4] Nowak M A 2006 Evolutionary Dynamics: Exploring the Equations of Life (Cambridge, MA: Belknap Press) · Zbl 1115.92047
[5] Gintis H 2009 Game Theory Evolving 2nd edn (Princeton, NJ: Princeton University Press) · Zbl 1161.91005
[6] Pennisi E 2009 Science325 1196 · doi:10.1126/science.325_1196
[7] Nowak M A 2006 Science314 1560-3 · doi:10.1126/science.1133755
[8] Gómez-Gardeñes J, Campillo M, Floría L M and Moreno Y 2007 Phys. Rev. Lett.98 108103 · doi:10.1103/PhysRevLett.98.108103
[9] Fletcher J A and Doebeli M 2009 Proc. R. Soc. B 276 13-9 · doi:10.1098/rspb.2008.0829
[10] Roca C P, Cuesta J A and Sánchez A 2009 Phys. Rev. E 80 046106 · doi:10.1103/PhysRevE.80.046106
[11] Traulsen A, Semmann D, Sommerfeld R D, Krambeck H J and Milinski M 2010 Proc. Natl Acad. Sci. USA107 2962-6 · doi:10.1073/pnas.0912515107
[12] Grujić J, Fosco C, Araújo L, Cuesta J A and Sánchez A 2010 PLoS One at press
[13] Gross T and Blasius B 2008 J. R. Soc. Inter.5 259-71 · doi:10.1098/rsif.2007.1229
[14] Perc M and Szolnoki A 2010 Biosystems99 109-25 · doi:10.1016/j.biosystems.2009.10.003
[15] Ebel H, Mielsch L I and Bornholdt S 2002 Phys. Rev. E 66 056118 · doi:10.1103/PhysRevE.66.056118
[16] Zimmermann M G, Eguíluz V M and San Miguel M 2004 Phys. Rev. E 69 065102 · doi:10.1103/PhysRevE.69.065102
[17] Pacheco J M, Traulsen A and Nowak M A 2006 Phys. Rev. Lett.97 258103 · doi:10.1103/PhysRevLett.97.258103
[18] Pestelacci E, Tomassini M and Luthi L 2008 Biol. Theor.3 139-53 · doi:10.1162/biot.2008.3.2.139
[19] Szolnoki A and Perc M 2009 Eur. Phys. J. B 67 337-42 · Zbl 1188.91161 · doi:10.1140/epjb/e2008-00470-8
[20] Szolnoki A and Perc M 2009 Europhys. Lett.86 30007 · doi:10.1209/0295-5075/86/30007
[21] Szolnoki A and Perc M 2009 New J. Phys.11 093033 · doi:10.1088/1367-2630/11/9/093033
[22] Wu B, Zhou D, Fu F, Luo Q, Wang L and Traulsen A 2010 PLoS One5 e11187 · doi:10.1371/journal.pone.0011187
[23] Poncela J, Gómez-Gardeñes J, Floría L M, Sánchez A and Moreno Y 2008 PLoS One3 e2449 · doi:10.1371/journal.pone.0002449
[24] Poncela J, Gómez-Gardeñes J, Traulsen A and Moreno Y 2009 New J. Phys.11 083031 · doi:10.1088/1367-2630/11/8/083031
[25] Poncela J, Gómez-Gardeñes J, Floría L M, Sánchez A and Moreno Y 2009 Europhys. Lett.88 38003 · doi:10.1209/0295-5075/88/38003
[26] Kirchkamp O 1999 J. Econ. Behav. Org.40 295-312 · doi:10.1016/S0167-2681(99)00069-4
[27] Moyano L G and Sánchez A 2009 J. Theor. Biol.259 84-95 · Zbl 1402.91052 · doi:10.1016/j.jtbi.2009.03.002
[28] Szabó G, Szolnoki A and Vukov J 2009 Europhys. Lett.87 18007 · doi:10.1209/0295-5075/87/18007
[29] Szolnoki A, Vukov J and Szabó G 2009 Phys. Rev. E 80 056112 · doi:10.1103/PhysRevE.80.056112
[30] Gómez-Gardeñes J and Moreno Y 2006 Phys. Rev. E 73 056124 · doi:10.1103/PhysRevE.73.056124
[31] Barabási A L and Albert R 1992 J. Econ. Theory57 407-19 · Zbl 0793.90108 · doi:10.1016/0022-0531(92)90043-H
[32] Erdös P and Rényi A 1959 Publ. Math.6 290-7 · Zbl 0092.15705
[33] Nowak M A and May R M 1992 Nature359 826-9 · doi:10.1038/359826a0
[34] Helbing D 1992 Physica A 181 29-52 · doi:10.1016/0378-4371(92)90195-V
[35] Schlag K H 1998 J. Econ. Theory78 130-56 · Zbl 0895.90003 · doi:10.1006/jeth.1997.2347
[36] Moran P A P 1962 The Statistical Processes of Evolutionary Theory (Oxford: Clarendon) · Zbl 0119.35901
[37] Szabó G and Töke C 1998 Phys. Rev. E 58 69-73 · doi:10.1103/PhysRevE.58.69
[38] Altrock P M and Traulsen A 2009 Phys. Rev. E 80 011909 · doi:10.1103/PhysRevE.80.011909
[39] Huberman B A and Glance N S 1993 Proc. Natl Acad. Sci. USA90 7716-8 · Zbl 0800.92168 · doi:10.1073/pnas.90.16.7716
[40] Nowak M A, Bonhoeffer S and May R M 1994 Proc. Natl Acad. Sci. USA91 4877-81 · Zbl 0799.92010 · doi:10.1073/pnas.91.11.4877
[41] Roca C P, Cuesta J A and Sánchez A 2009 Europhys. Lett.87 48005 · doi:10.1209/0295-5075/87/48005
[42] Santos F C and Pacheco J M 2005 Phys. Rev. Lett.95 98104 · doi:10.1103/PhysRevLett.95.098104
[43] Ellison G 1993 Econometrica61 1047-71 · Zbl 0802.90143 · doi:10.2307/2951493
[44] Roca C P, Cuesta J and Sánchez A 2009 Eur. Phys. J. B 71 587-95 · doi:10.1140/epjb/e2009-00189-0
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.