Environmental feedback drives cooperation in spatial social dilemmas

by   Attila Szolnoki, et al.

Exploiting others is beneficial individually but it could also be detrimental globally. The reverse is also true: a higher cooperation level may change the environment in a way that is beneficial for all competitors. To explore the possible consequence of this feedback we consider a coevolutionary model where the local cooperation level determines the payoff values of the applied prisoner's dilemma game. We observe that the coevolutionary rule provides a significantly higher cooperation level comparing to the traditional setup independently of the topology of the applied interaction graph. Interestingly, this cooperation supporting mechanism offers lonely defectors a high surviving chance for a long period hence the relaxation to the final cooperating state happens logarithmically slow. As a consequence, the extension of the traditional evolutionary game by considering interactions with the environment provides a good opportunity for cooperators, but their reward may arrive with some delay.



There are no comments yet.


page 3

page 4


Cooperator driven oscillation in a time-delayed feedback-evolving game

Considering feedback of collective actions of cooperation on common reso...

Reciprocity-based cooperative phalanx maintained by overconfident players

According to the evolutionary game theory principle, a strategy represen...

Cooperation in the spatial prisoner's dilemma game with probabilistic abstention

Research has shown that the addition of abstention as an option transfor...

Signed Networks, Triadic Interactions and the Evolution of Cooperation

We outline a model to study the evolution of cooperation in a population...

Effects of Dynamic-Win-Stay-Lose-Learn model with voluntary participation in social dilemma

In recent years, Win-Stay-Lose-Learn rule has attracted wide attention a...

Knowing the past improves cooperation in the future

Cooperation is the cornerstone of human evolutionary success. Like no ot...

Mobility restores the mechanism which supports cooperation in the voluntary prisoner's dilemma game

It is generally believed that in a situation where individual and collec...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.


  • [1] Nordhaus W. D. Proc. Natl. Acad. Sci. USA107201011721.
  • [2] Hardin G. Science16219681243.
  • [3] Frick T. Schuster S. Naturwissenschaften902003327.
  • [4] Hummert S., Hummert C., Schröter A., Hube B. Schuster S. J. Theor. Biol.2642010312.
  • [5] Weigert M. Kümmerli R. Proc. R. Soc. B284201720170631.
  • [6] Weitz J. S., Eksin C., Paarporn K., Brown S. P. Ratcliff W. C. Proc. Natl. Acad. Sci. USA1132017E7518.
  • [7] Nowak M. A. May R. M. Nature3591992826.
  • [8] Santos F. C. Pacheco J. M. Phys. Rev. Lett.952005098104.
  • [9] Santos F. C., Rodrigues J. F. Pacheco J. M. Proc. R. Soc. B273200651.
  • [10] Szabó G. Fáth G. Phys. Rep.446200797.
  • [11] Perc M., Szolnoki A. Szabó G. Phys. Rev. E782008066101.
  • [12] Floría L. M., Gracia-Lázaro C., Gómez-Gardeñes J. Moreno Y. Phys. Rev. E792009026106.
  • [13] Fu F., Nowak M. A. Hauert C. J. Theor. Biol.2662010358.
  • [14] Roman S. Brede M. Phys. Rev. E952017052310.
  • [15] Hauert C., De Monte S., Hofbauer J. Sigmund K. Science29620021129.
  • [16] Vainstein M. H. Arenzon J. J. Phys. Rev. E642001051905.
  • [17] Press W. Dyson F. Proc. Natl. Acad. Sci. USA109201210409.
  • [18] Yang H.-X., Wang W.-X., Wu Z.-X., Lai Y.-C. Wang B.-H. Phys. Rev. E792009056107.
  • [19] Szolnoki A. Perc M. Phys. Rev. E852012026104.
  • [20] Javarone M. A. Atzeni A. E. Compu. Social Networks2201515.
  • [21] Suzuki R., Kato M. Arita T. Phys. Rev. E772008021911.
  • [22] Sicardi E. A., Fort H., Vainstein M. H. Arenzon J. J. J. Theor. Biol.2562009240.
  • [23] Boyd R., Gintis H., Bowles S. Richerson P. J. Proc. Natl. Acad. Sci. USA10020033531.
  • [24] Brandt H., Hauert C. Sigmund K. Proc. Natl. Acad. Sci. USA1032006495.
  • [25] Helbing D., Szolnoki A., Perc M. Szabó G. PLoS Comput. Biol.62010e1000758.
  • [26] Sigmund K., Hauert C. Nowak M. A. Proc. Natl. Acad. Sci. USA98200110757.
  • [27] Sasaki T. Uchida S. Biol. Lett.10201420130903.
  • [28] Szolnoki A. Perc M. EPL92201038003.
  • [29] Sigmund K. The Calculus of Selfishness (Princeton University Press, Princeton, NJ) 2010.
  • [30] Perc M. Szolnoki A. BioSystems992010109.
  • [31] Perc M., Gómez-Gardeñes J., Szolnoki A. Floría and Y. Moreno L. M. J. R. Soc. Interface10201320120997.
  • [32] Dickman R. Phys. Lett. A1221986463.
  • [33] Gutowitz H. A., Victor J. D. Knight B. W. Physica D28198718.
  • [34] Szabó G., Szolnoki A. Izsák R. J. Phys. A: Math. Gen.3720042599.
  • [35] Vukov J., Szabó G. Szolnoki A. Phys. Rev. E732006067103.
  • [36] Santos F. C., Pacheco J. M. Lenaerts T. Proc. Natl. Acad. Sci. USA10320063490.
  • [37] Tomassini M., Luthi L. Pestelacci E. Int. J. Mod. Phys. C1820071173.
  • [38] Szolnoki A., Perc M. Danku Z. Physica A38720082075.
  • [39] Masuda N. Proc. R. Soc. B27420071815.
  • [40] Pennisi E. Science309200593.
  • [41] Lomborg B. Am. Soc. Rev.611996278.
  • [42] Sober E. Wilson D. S. Unto Others: The Evolution and Psychology of Unselfish Behavior (Harvard University Press, Cambridge, MA) 1998.
  • [43] Wang X., Pan Q., Kang Y. He M. Ecological Complexity262016117.
  • [44] Maynard Smith J. Evolution and the Theory of Games (Cambridge University Press, Cambridge, U.K.) 1982.
  • [45] Ben-Jacob E., Coffey D. S. Levine H. Trends Microbiology122012403.
  • [46] Pacheco J. M., Santos F. C. Dingli D. Interface Focus4201720140019.
  • [47] Archetti M. J. Theor. Biol.3962016191.
  • [48] Nowak M. A. Science31420061560.
  • [49] Szolnoki A. Chen X. Phys. Rev. E922015042813.
  • [50] Hagel K., Chakra M. A., Bauer B. Traulsen A. Sci. Rep.6201619269.
  • [51] Takesue H., Ozawa A. Morikawa S. EPL118201748002.
  • [52] Alonso J., Fernández A. Fort H. J. Stat. Mech. Theor. Exp.20062006P06013.
  • [53] Chen X., Fu F. Wang L. Phys. Rev. E802009051104.
  • [54] Nishi A., Christakis N. A., Evans A. M., O’Malley A. J. Rand D. G. Sci. Rep.6201729622.
  • [55] Gracia-Lázaro C., Floría L. M., Gómez-Gardeñes J. Moreno Y. Chaos Solitons & Fractals562013188.
  • [56] Wu T., Wang L. Fu F. PLoS Comput. Biol.132017e1005363.
  • [57] Richter H. BioSystems153-154201726.
  • [58] Stewart A. J. Plotkin J. B. Proc. Natl. Acad. Sci. USA111201417558.