Skip to main content
SpringerLink
Log in

Dominance Hierarchies Induce a Population’s Full Cooperation

  • Published:
Dynamic Games and Applications Aims and scope Submit manuscript

Abstract

Evolution of cooperation is still a puzzle in evolutionary and socio biology. Based on the asymmetric interactions in a dominance hierarchy system, a simple theoretical framework is developed to reveal the effect of “induced cooperation” (i.e., the cooperative behavior of subordinate individuals to dominant individuals) on the evolution of cooperation. Extending the classic Prisoner’s Dilemma (PD) game, we define the concept of the defection cost of subordinate individuals to measure the effect of induced cooperation, i.e., a subordinate defector will incur a cost when it plays against a dominant defector. The analysis of the repeated PD game with linear dominance hierarchy and with cyclic dominance hierarchy shows clearly that induced cooperation of subordinate individuals may lead to a population’s full cooperation, and that the coexistence of cooperation and defection in a population with hierarchy dominance is possible. Our results are the first step to develop a new theoretical approach for understanding the emergence of cooperation; namely, that induced cooperation is one of the most important forces driving the evolution of cooperation as pointed out by May (in May R, McLean A (eds) Theoretical ecology 3rd edn., (2007)).

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4

Similar content being viewed by others

References

  1. Akcay E, Meirowitz A, Ramsay KW, Levin SA (2012) Evolution of cooperation and skew under imperfect information. Proc Natl Acad Sci USA 109:14936–14941

    Article  Google Scholar 

  2. Amman E, Possajennikov A (2009) On the stability of evolutionary dynamics dynamics in games with incomplete information. Math Soc Sci 58:310–321

    Article  Google Scholar 

  3. Axelrod RM, Hamilton WD (1981) The evolution of cooperaton. Science 1981(211):1390–1396

    Article  MathSciNet  Google Scholar 

  4. Axelrod RM (1984) The evolution of cooperation. Basic Books, New York

    Google Scholar 

  5. Bernestein IS, Sharpe LG (1966) Social roles in a rhesus monkey group. Behaviour 26:91–105

    Article  Google Scholar 

  6. Cressman R (2003) Evolutionary dynamics and extensive form games. MIT Press, Cambridge

    MATH  Google Scholar 

  7. Eisenberg JE, Kuehn RE (1966) The behavior of Ateles geoffroyi and related species. Smithsonian Misc Collect 151, pp. iv + 188

  8. Frank SA (1998) Foundations of social evolution. Princeton University Press, Princeton

    Google Scholar 

  9. Gaunersdorfer A, Hofbauer J (1995) Fictitious play, shapley polygons, and the replicator equation. Games Econ Behav 11:279–303

    Article  MATH  MathSciNet  Google Scholar 

  10. Hamilton WD (1964) The genetic evolution of social behaviour I. J Theor Biol 7:1–16

    Article  Google Scholar 

  11. Hamilton WD (1964) The genetic evolution of social behaviour II. J Theor Biol 7:17–32

    Article  Google Scholar 

  12. Hamilton WD (1988) Narrow Roads of Gene Land: the collected papers of W.D. Hamilton, Volume 1: Evolution of Social Behaviour. Oxford University Press, New York

    Google Scholar 

  13. Hammerstein P (1981) The role of asymmetries in animal contests. Anim Behav 29:578–581

    Article  Google Scholar 

  14. Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge University Press, Cambridge

    Book  MATH  Google Scholar 

  15. Jordan JS (1993) Three problems in learning mixed-strategy Nash equilibrium. Games Econ Behav 5:368–386

    Article  MATH  Google Scholar 

  16. Krebs JR, Davies NB (1993) An introduction to behaviour ecology. Blackwell Publishing, Oxford

    Google Scholar 

  17. May R (2007) Unanswered questions and why they matter. In: May R, McLean A (eds) Theoretical ecology, 3rd edn. Oxford Press, New York, pp 214–215

    Google Scholar 

  18. McNamara JM, Wilson EMT, Houston AI (2006) Is it better to give information, receive it, or be ignorant in a two-player game? Behav Ecol 17:441–451

    Article  Google Scholar 

  19. Mesterton-Gibbons M, Sherratt TN (2011) Information, variance and cooperation: minimal models. Dyn Games Appl 1:419–439

    Article  MATH  MathSciNet  Google Scholar 

  20. Nonacs P, Hager R (2011) The past, present and future of reproductive skew theory. Biol Rev Camb Philos Soc 86:271–298

    Article  Google Scholar 

  21. Nowak MA (2006) Evolutionary dynamics. The Belknap Press of Harvard University Press, Cambridge

    MATH  Google Scholar 

  22. Nowak MA (2006) Five rules for the evolution of cooperation. Science 314:1560–1563

    Article  Google Scholar 

  23. Nowak MA (2011) Super cooperators. Free Press, New York

    Google Scholar 

  24. Nowak MA, Sigmund K (1998) Evolution of indirect reciprocity by image scoring. Nature 393:573–577

    Article  Google Scholar 

  25. Nowak MA, Sigmund K (1998) The dynamics of indirect reciprocity. J Theor Biol 194:561–571

    Article  Google Scholar 

  26. Nowak MA, Sigmund K (2007) How populations cohere: five rules for cooperation. In: May R, McLean A (eds) Theoretical ecology, 3rd edn. Oxford Press, Oxford

    Google Scholar 

  27. Ohtsuki H, Hauert C, Liberman E, Nowak M (2006) A simple rule for the evolution of cooperation on graphs and social networks. Nature 441:502–505

    Article  Google Scholar 

  28. Reeve HK, Emlen ST (2000) Reproductive skew and group size: an N-person staying incentive model. Behav Ecol 11:640–647

    Article  Google Scholar 

  29. Sandholm WD (2010) Population games and evolutionary dynamics. MIT Press, Cambridge

    MATH  Google Scholar 

  30. Smith Maynard J (1982) Evolution and the theory of games. Cambridge University Press, Cambridge

    Book  MATH  Google Scholar 

  31. Tokuda K, Jensen GD (1968) The leader’s role in controlling aggressive behavior in a monkey group. Primates 9:319–322

    Article  Google Scholar 

  32. Traulsen A, Nowak MA (2006) Evolution of cooperation by multi-level selection. Proc Natl Acad Sci USA 103:10952–10955

    Article  Google Scholar 

  33. Trivers RL (1971) The evolution of reciprocal altruism. Q Rev Biol 46:35–37

    Article  Google Scholar 

  34. Trubenov B, Hager R (2012) Reproductive skew theory. Wiley, Chichester

    Google Scholar 

  35. Ubeda F, Duenez-Guzman EA (2011) Power and corruption. Evolution 65:1127–1139

    Article  Google Scholar 

  36. van Damme E, Hurkens S (1999) Endogenous Stackelberg leadership. Games Econ Behav 28:105–129

    Article  MATH  Google Scholar 

  37. van Veelen M (2007) Hamilton’s missing link. J Theor Biol 246:551–554

    Article  Google Scholar 

  38. von Stengel B (2010) Follower payoffs in symmetric duopoly games. Games Econ Behav 69:512–516

    Article  MATH  Google Scholar 

  39. Walters JR, Seyfarth RM (1987) Conflict and cooperation. In: Smuts BB, Cheney DL, Seyfarth RM, Wrangham RW, Struhsaker T (eds) Primate societies. University of Chicago Press, Chicago, pp 306–317

    Google Scholar 

  40. Wilson EO (1975) Sociobiology: the new synthesis. Belknap Press, Harvard

    Google Scholar 

Download references

Acknowledgments

Support from the Natural Sciences and Engineering Research Council of Canada and from National Natural Science Foundation of China (Grant No. 31270439) is gratefully acknowledged. Referee suggestions for improvements are also appreciated.

Author information

Authors and Affiliations

  1. Key Lab of Animal Ecology and Conservational Biology, Centre for Computational and Evolutionary Biology, Institute of Zoology, Chinese Academy of Sciences, Beijing, China

    Yi Tao & Cong Li

  2. Department of Applied Mathematics, University of Western Ontario, London, ON, Canada

    Jing-Jing Xu

  3. Department of Mathematics, Wilfrid Laurier University, Waterloo, ON, Canada

    Ross Cressman

Authors
  1. Yi Tao
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jing-Jing Xu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Cong Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Ross Cressman
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ross Cressman.

Electronic supplementary material

Below is the link to the electronic supplementary material.

Supplementary material 1 (pdf 8542 KB)

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Tao, Y., Xu, JJ., Li, C. et al. Dominance Hierarchies Induce a Population’s Full Cooperation. Dyn Games Appl 4, 432–447 (2014). https://doi.org/10.1007/s13235-014-0126-y

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s13235-014-0126-y

Keywords

Search

Navigation