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Optimal interdependence between networks for the evolution of cooperation
Open accessAbstract
Recent research has identified interactions between networks as crucial for the outcome of evolutionary games taking place on them. While the consensus is that interdependence does promote cooperation by means of organizational complexity and enhanced reciprocity that is out of reach on isolated networks, we here address the question just how much interdependence there should be. Intuitively, one might assume the more the better. However, we show that in fact only an intermediate density of sufficiently strong interactions between networks warrants an optimal resolution of social dilemmas. This is due to an intricate interplay between the heterogeneity that causes an asymmetric strategy flow because of the additional links between the networks and the independent formation of cooperative patterns on each individual network. Presented results are robust to variations of the strategy updating rule, the topology of interdependent networks and the governing social dilemma, thus suggesting a high degree of universality.
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Cites
Five Rules for the Evolution of Cooperation
Nowak, M. A. (2006) · Science · doi:10.1126/science.1133755 · Cited by 5,894
Catastrophic cascade of failures in interdependent networks
Buldyrev, S. V., Parshani, R., Paul, G., Stanley, H. E., & Havlin, S. (2010) · Nature · doi:10.1038/nature08932 · Cited by 4,513
Evolutionary games and spatial chaos
Nowak, M. A., & May, R. M. (1992) · Nature · doi:10.1038/359826a0 · Cited by 4,463
Szabó, G., & Fáth, G. (2007) · Physics Reports · doi:10.1016/j.physrep.2007.04.004 · Cited by 2,974
Coevolutionary games—A mini review
Perc, M., & Szolnoki, A. (2010) · Biosystems · doi:10.1016/j.biosystems.2009.10.003 · Cited by 1,971
Self-citationScale-Free Networks Provide a Unifying Framework for the Emergence of Cooperation
Santos, F. C., & Pacheco, J. M. (2005) · Physical Review Letters · doi:10.1103/physrevlett.95.098104 · Cited by 1,804
Spatial structure often inhibits the evolution of cooperation in the snowdrift game
Hauert, C., & Doebeli, M. (2004) · Nature · doi:10.1038/nature02360 · Cited by 1,582
Social diversity promotes the emergence of cooperation in public goods games
Santos, F. C., Santos, M. D., & Pacheco, J. M. (2008) · Nature · doi:10.1038/nature06940 · Cited by 1,442
The Statistical Mechanics of Strategic Interaction
Blume, L. E. (1993) · Games and Economic Behavior · doi:10.1006/game.1993.1023 · Cited by 1,402
Evolutionary dynamics of group interactions on structured populations: a review
Perc, M., Gómez-Gardeñes, J., Szolnoki, A., Floría, L. M., & Moreno, Y. (2013) · Journal of The Royal Society Interface · doi:10.1098/rsif.2012.0997 · Cited by 1,340
Self-citationNetworks formed from interdependent networks
Gao, J., Buldyrev, S. V., Stanley, H. E., & Havlin, S. (2012) · Nature Physics · doi:10.1038/nphys2180 · Cited by 1,216
Evolutionary dynamics of social dilemmas in structured heterogeneous populations
Santos, F. C., Pacheco, J. M., & Lenaerts, T. (2006) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.0508201103 · Cited by 1,011
Diffusion Dynamics on Multiplex Networks
Gómez, S., Díaz-Guilera, A., Gómez-Gardeñes, J., Pérez-Vicente, C. J., Moreno, Y., & Arenas, A. (2013) · Physical Review Letters · doi:10.1103/physrevlett.110.028701 · Cited by 1,003
Evolutionary dynamics of group interactions on structured populations: a review
Perz, M., Gómez‐Gardeñes, J., Szolnoki, A., Florı́a, L. M., & Moreno, Y. (2013) · Repository of the Academy's Library (Library of the Hungarian Academy of Sciences) · Cited by 883
Self-citationSchlag, K. H. (1998) · Journal of Economic Theory · doi:10.1006/jeth.1997.2347 · Cited by 820
Parshani, R., Buldyrev, S. V., & Havlin, S. (2010) · Physical Review Letters · doi:10.1103/physrevlett.105.048701 · Cited by 788
Evolutionary game theory: Temporal and spatial effects beyond replicator dynamics
Roca, C. P., Cuesta, J. A., & Sánchez, A. (2009) · Physics of Life Reviews · doi:10.1016/j.plrev.2009.08.001 · Cited by 766
Coevolution of Strategy and Structure in Complex Networks with Dynamical Linking
Pacheco, J. M., Traulsen, A., & Nowak, M. A. (2006) · Physical Review Letters · doi:10.1103/physrevlett.97.258103 · Cited by 697
Cooperation Prevails When Individuals Adjust Their Social Ties
Santos, F. C., Pacheco, J. M., & Lenaerts, T. (2006) · PLoS Computational Biology · doi:10.1371/journal.pcbi.0020140 · Cited by 556
Dynamical Organization of Cooperation in Complex Topologies
Gómez-Gardeñes, J., Campillo, M., Floría, L. M., & Moreno, Y. (2007) · Physical Review Letters · doi:10.1103/physrevlett.98.108103 · Cited by 555
Social games in a social network
Abramson, G., & Kuperman, M. (2001) · Physical Review E · doi:10.1103/physreve.63.030901 · Cited by 535
Phase diagrams for an evolutionary prisoner’s dilemma game on two-dimensional lattices
Szabó, G., Vukov, J., & Szolnoki, A. (2005) · Physical Review E · doi:10.1103/physreve.72.047107 · Cited by 529
Self-citationRobustness of interdependent networks under targeted attack
Huang, X., Gao, J., Buldyrev, S. V., Havlin, S., & Stanley, H. E. (2011) · Physical Review E · doi:10.1103/physreve.83.065101 · Cited by 527
Coevolution of dynamical states and interactions in dynamic networks
Zimmermann, M. G., Eguíluz, V. M., & San Miguel, M. (2004) · Physical Review E · doi:10.1103/physreve.69.065102 · Cited by 504
Interdependent network reciprocity in evolutionary games
Wang, Z., Szolnoki, A., & Perc, M. (2013) · Scientific Reports · doi:10.1038/srep01183 · Cited by 485
Self-citationEvolution of Cooperation in Multiplex Networks
Gómez-Gardeñes, J., Reinares, I., Arenas, A., & Floría, L. M. (2012) · Scientific Reports · doi:10.1038/srep00620 · Cited by 462
Topology-independent impact of noise on cooperation in spatial public goods games
Szolnoki, A., Perc, M., & Szabó, G. (2009) · Physical Review E · doi:10.1103/physreve.80.056109 · Cited by 458
Self-citationCooperation enhanced by inhomogeneous activity of teaching for evolutionary Prisoner's Dilemma games
Szolnoki, A., & Szabó, G. (2007) · Europhysics Letters (EPL) · doi:10.1209/0295-5075/77/30004 · Cited by 443
Self-citationAvalanche Collapse of Interdependent Networks
Baxter, G. J., Dorogovtsev, S. N., Goltsev, A. V., & Mendes, J. F. F. (2012) · Physical Review Letters · doi:10.1103/physrevlett.109.248701 · Cited by 376
Evolution of public cooperation on interdependent networks: The impact of biased utility functions
Wang, Z., Szolnoki, A., & Perc, M. (2012) · EPL (Europhysics Letters) · doi:10.1209/0295-5075/97/48001 · Cited by 354
Self-citationHeterogeneous networks do not promote cooperation when humans play a Prisoner’s Dilemma
Gracia-Lázaro, C., Ferrer, A., Ruiz, G., Tarancón, A., Cuesta, J. A., Sánchez, A., & Moreno, Y. (2012) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.1206681109 · Cited by 343
Roles of mixing patterns in cooperation on a scale-free networked game
Rong, Z., Li, X., & Wang, X. (2007) · Physical Review E · doi:10.1103/physreve.76.027101 · Cited by 338
Coevolution of teaching activity promotes cooperation
Szolnoki, A., & Perc, M. (2008) · New Journal of Physics · doi:10.1088/1367-2630/10/4/043036 · Cited by 337
Self-citationTowards effective payoffs in the prisoner’s dilemma game on scale-free networks
Szolnoki, A., Perc, M., & Danku, Z. (2008) · Physica A: Statistical Mechanics and its Applications · doi:10.1016/j.physa.2007.11.021 · Cited by 297
Self-citationCoevolutionary games on networks
Ebel, H., & Bornholdt, S. (2002) · Physical Review E · doi:10.1103/physreve.66.056118 · Cited by 267
Percolation theory on interdependent networks based on epidemic spreading
Son, S.-W., Bizhani, G., Christensen, C., Grassberger, P., & Paczuski, M. (2012) · EPL (Europhysics Letters) · doi:10.1209/0295-5075/97/16006 · Cited by 251
Gao, J., Buldyrev, S. V., Havlin, S., & Stanley, H. E. (2012) · Physical Review E · doi:10.1103/physreve.85.066134 · Cited by 237
Kim, B. J., Trusina, A., Holme, P., Minnhagen, P., Chung, J. S., & Choi, M. Y. (2002) · Physical Review E · doi:10.1103/physreve.66.021907 · Cited by 230
Enhancement of cooperation in highly clustered scale-free networks
Assenza, S., Gómez-Gardeñes, J., & Latora, V. (2008) · Physical Review E · doi:10.1103/physreve.78.017101 · Cited by 228
Spatial prisoner's dilemma optimally played in small-world networks
Masuda, N., & Aihara, K. (2003) · Physics Letters A · doi:10.1016/s0375-9601(03)00693-5 · Cited by 217
Assortativity decreases the robustness of interdependent networks
Zhou, D., Stanley, H. E., D’Agostino, G., & Scala, A. (2012) · Physical Review E · doi:10.1103/physreve.86.066103 · Cited by 217
Complex Cooperative Networks from Evolutionary Preferential Attachment
Poncela, J., Gómez-Gardeñes, J., Floría, L. M., Sánchez, A., & Moreno, Y. (2008) · PLoS ONE · doi:10.1371/journal.pone.0002449 · Cited by 212
Five Rules for the Evolution of Cooperation
Nowak, M. A. (2013) · Evolution, Games, and God · doi:10.2307/j.ctvjnrscp.8 · Cited by 204
The role of diversity in the evolution of cooperation
Santos, F. C., Pinheiro, F. L., Lenaerts, T., & Pacheco, J. M. (2012) · Journal of Theoretical Biology · doi:10.1016/j.jtbi.2011.09.003 · Cited by 197
Participation costs dismiss the advantage of heterogeneous networks in evolution of cooperation
Masuda, N. (2007) · Proceedings of the Royal Society B: Biological Sciences · doi:10.1098/rspb.2007.0294 · Cited by 188
Wang, Z., Szolnoki, A., & Perc, M. (2012) · Scientific Reports · doi:10.1038/srep00369 · Cited by 188
Self-citationHavlin, S., Kenett, D. Y., Ben-Jacob, E., Bunde, A., Cohen, R., Hermann, H., Kantelhardt, J. W., Kertész, J., Kirkpatrick, S., Kurths, J., et al. (2012) · The European Physical Journal Special Topics · doi:10.1140/epjst/e2012-01695-x · Cited by 187
Evolutionary Prisoner's Dilemma on heterogeneous Newman-Watts small-world network
Fu, F., Liu, L.-H., & Wang, L. (2007) · The European Physical Journal B · doi:10.1140/epjb/e2007-00124-5 · Cited by 179
Evolutionary game dynamics in a growing structured population
Poncela, J., Gómez-Gardeñes, J., Traulsen, A., & Moreno, Y. (2009) · New Journal of Physics · doi:10.1088/1367-2630/11/8/083031 · Cited by 162
Hawks and Doves on small-world networks
Tomassini, M., Luthi, L., & Giacobini, M. (2006) · Physical Review E · doi:10.1103/physreve.73.016132 · Cited by 148
Percolation threshold determines the optimal population density for public cooperation
Wang, Z., Szolnoki, A., & Perc, M. (2012) · Physical Review E · doi:10.1103/physreve.85.037101 · Cited by 140
Self-citationEvolutionary games defined at the network mesoscale: The Public Goods game
Gómez‐Gardeñes, J., Romance, M., Criado, R., Vilone, D., & Sánchez, A. (2011) · Chaos An Interdisciplinary Journal of Nonlinear Science · doi:10.1063/1.3535579 · Cited by 132
SOCIAL DILEMMAS AND COOPERATION IN COMPLEX NETWORKS
Tomassini, M., Pestelacci, E., & Luthi, L. (2007) · International Journal of Modern Physics C · doi:10.1142/s0129183107011212 · Cited by 128
Evolutionary dynamics on interdependent populations
Gómez‐Gardeñes, J., Gracia-Lázaro, C., Florı́a, L. M., & Moreno, Y. (2012) · Physical Review E · doi:10.1103/physreve.86.056113 · Cited by 116
Emergent Hierarchical Structures in Multiadaptive Games
Lee, S., Holme, P., & Wu, Z.-X. (2011) · Physical Review Letters · doi:10.1103/physrevlett.106.028702 · Cited by 114
Dilemma solving by the coevolution of networks and strategy in a 2×2 game
Tanimoto, J. (2007) · Physical Review E · doi:10.1103/physreve.76.021126 · Cited by 113
Connect and win: The role of social networks in political elections
Halu, A., Zhao, K., Baronchelli, A., & Bianconi, G. (2013) · Europhysics Letters (EPL) · doi:10.1209/0295-5075/102/16002 · Cited by 103
Network reciprocity by coexisting learning and teaching strategies
Tanimoto, J., Brede, M., & Yamauchi, A. (2012) · Physical Review E · doi:10.1103/physreve.85.032101 · Cited by 98
Human behavior in Prisoner's Dilemma experiments suppresses network reciprocity
Gracia-Lázaro, C., Cuesta, J. A., Sánchez, Á., & Moreno, Y. (2012) · Scientific Reports · doi:10.1038/srep00325 · Cited by 92
Baokui, W., Chen, X., & Wang, L. (2012) · Journal of Statistical Mechanics Theory and Experiment · doi:10.1088/1742-5468/2012/11/p11017 · Cited by 90
Evolution of Robust Network Topologies: Emergence of Central Backbones
Peixoto, T. P., & Bornholdt, S. (2012) · Physical Review Letters · doi:10.1103/physrevlett.109.118703 · Cited by 83
Conformity hinders the evolution of cooperation on scale-free networks
Peña, J., Volken, H., Pestelacci, E., & Tomassini, M. (2009) · Physical Review E · doi:10.1103/physreve.80.016110 · Cited by 78
Percolation on interacting, antagonistic networks
Zhao, K., & Bianconi, G. (2013) · Journal of Statistical Mechanics Theory and Experiment · doi:10.1088/1742-5468/2013/05/p05005 · Cited by 73
Promotion of cooperation induced by the interplay between structure and game dynamics
Fu, F., Chen, X., Liu, L., & Wang, L. (2007) · Physica A Statistical Mechanics and its Applications · doi:10.1016/j.physa.2007.04.099 · Cited by 63
From Local to Global Dilemmas in Social Networks
Pinheiro, F. L., Pacheco, J. M., & Santos, F. C. (2012) · PLoS ONE · doi:10.1371/journal.pone.0032114 · Cited by 63
Cooperation in scale-free networks with limited associative capacities
Poncela-Casasnovas, J., Gómez‐Gardeñes, J., & Moreno, Y. (2011) · Physical Review E · doi:10.1103/physreve.83.057101 · Cited by 59
Algorithm to determine the percolation largest component in interconnected networks
Schneider, C. M., Araújo, N. A. M., & Herrmann, H. J. (2013) · Physical Review E · doi:10.1103/physreve.87.043302 · Cited by 33
Evolution of Cooperation in Spatial Traveler's Dilemma Game
Li, R.-H., Yu, J. X., & Lin, J. (2013) · PLoS ONE · doi:10.1371/journal.pone.0058597 · Cited by 32
Short Versus Long Term Benefits and the Evolution of Cooperation in the Prisoner's Dilemma Game
Brede, M. (2013) · PLoS ONE · doi:10.1371/journal.pone.0056016 · Cited by 31
Playing against the fittest: A simple strategy that promotes the emergence of cooperation
Brede, M. (2011) · Europhysics Letters (EPL) · doi:10.1209/0295-5075/94/30003 · Cited by 31
Relationship between clustering coefficient and the success of cooperation in networks
Kuperman, M. N., & Risau-Gusman, S. (2012) · Physical Review E · doi:10.1103/physreve.86.016104 · Cited by 24
Simko, G. I., & Csermely, P. (2013) · PLoS ONE · doi:10.1371/journal.pone.0067159 · Cited by 23
The Appearance and Promotion of Creativity by Various Levels of Interdependent Networks
Csermely, P. (2013) · Cited by 11
Portillo, I. G. (2012) · Physical Review E · doi:10.1103/physreve.86.051108 · Cited by 7
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Self-citationUniversal scaling for the dilemma strength in evolutionary games
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Metadata
- Authors
- Wang, Z., Szolnoki, A., & Perc, M.
- Venue
- Scientific Reports
- Published
- 2013-08-20
- Volume
- 3
- Issue
- 1
- Pages
- 2470-2470
- ISSN
- 2045-2322 (ISSN-L)
- OpenAlex
- W2041584829
- Cited by
- 311
- References
- 74
- FWCI
- 154.56
- Type
- journal article
- Language
- en
- Open access
- gold
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