Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

  • Letter
  • Published:

Development of cooperative relationships through increasing investment

Abstract

Reciprocal altruism1 can become established among selfish, unrelated individuals if they use responsive strategies such as ‘tit-for-tat’2,3,4. This result raises the fundamental question: how altruistic should one be? The problem is difficult to solve using current ‘prisoner's dilemma’ based models because they allow only the discrete choice of cooperating or defecting. In reality, however, cooperation is rarely all-or-nothing. Furthermore, if cooperative investment is variable, a new and more subtle kind of cheating becomes possible: individuals may invest slightly less than their partner. A concern is that this ‘short-changing’ will erode cooperative ventures. Here we show that cooperation can thrive despite variable investment through the new strategy of ‘raise-the-stakes’. This strategy offers a small amount on first meeting and then, if matched, raises its investment, something that no strategy in the discrete model can do. We show that such behaviour can readily invade a population of non-altruists and cannot be effectively exploited. The practice of ‘testing the water’ rather than making sudden cooperative ‘leaps of faith’ powerfully reinforces the stability and effectiveness of reciprocity.

This is a preview of subscription content, access via your institution

Access options

Rent or buy this article

Prices vary by article type

from$1.95

to$39.95

Prices may be subject to local taxes which are calculated during checkout

Figure 1: Here we illustrate how a strategy of increasing cooperative investment fares in competition with less altruistic strategies.
Figure 2: Profits obtained by each strategy in turn when playing against each other strategy in each round.
Figure 3: Here we illustrate how a strategy of increasing investment fares against strategies that invest at some average level, in competition with less altruistic strategies.

Similar content being viewed by others

References

  1. Trivers, R. L. The evolution of reciprocal altruism. Q. Rev. Biol. 46, 35–57 (1971).

    Article  Google Scholar 

  2. Axelrod, R. & Hamilton, W. D. The evolution of cooperation. Science 211, 1390–1396 (1981).

    Article  ADS  MathSciNet  CAS  Google Scholar 

  3. Nowak, M. & Sigmund, K. Tit-for-tat in heterogeneous populations. Nature 355, 250–253 (1992).

    Article  ADS  Google Scholar 

  4. Nowak, M. A. & Sigmund, K. Astrategy of win–stay, lose–shift that outperforms tit-for-tat in the Prisoner's Dilemma game. Nature 364, 56–58 (1993).

    Article  ADS  CAS  Google Scholar 

  5. Wilkinson, G. S. Reciprocal food sharing in vampire bats. Nature 308, 181–184 (1984).

    Article  ADS  Google Scholar 

  6. Milinski, M. Tit for Tat and the evolution of cooperation in sticklebacks. Nature 325, 433–435 (1987).

    Article  ADS  CAS  Google Scholar 

  7. Hart, B. L. & Hart, L. Reciprocal allogrooming in impala, Aepyceros melampus. Anim. Behav. 44, 1073–1083 (1992).

    Article  Google Scholar 

  8. Frean, M. R. The evolution of degrees of cooperation. J. Theor. Biol. 182, 549–559 (1996).

    Article  CAS  Google Scholar 

  9. Mesterton-Gibbons, M. On the iterated prisoner's dilemma in a finite population. Bull. Math. Biol. 54, 423–443 (1992).

    Article  Google Scholar 

  10. Maynard Smith, J. Evolution and the Theory of Games (Cambridge Univ. Press, Cambridge, (1982)).

    Book  Google Scholar 

  11. Axelrod, R. M. The Evolution of Cooperation (Basic Books, New York, (1984)).

    MATH  Google Scholar 

  12. Halpern, J. J. Elements of a script for friendship in transactions. J. Conflict Res. 41, 835–868 (1997).

    Article  Google Scholar 

  13. Benedict, R. Patterns of Culture (Routledge and Kegan Paul, London, (1935)).

    Google Scholar 

  14. Heinsohn, R. & Packer, C. Complex cooperative strategies in group-territorial African lions. Science 269, 1260–1263 (1995).

    Article  ADS  CAS  Google Scholar 

  15. de Waal, F. B. M. The chimpanzee's service economy: food for grooming. Evol. Hum. Behav. 18, 375–386 (1997).

    Article  Google Scholar 

  16. Seyfarth, R. M. & Cheney, D. L. Grooming alliances and reciprocal altruism in vervet monkeys. Nature 308, 541–543 (1984).

    Article  ADS  CAS  Google Scholar 

  17. Roberts, G. Competitive altruism: from reciprocity to the handicap principle. Proc. R. Soc. Lond. B 265, 427–431 (1998).

    Article  Google Scholar 

  18. Sherratt, T. N. & Roberts, G. The evolution of generosity and choosiness in co-operative exchanges. J. Theor. Biol. (in the press).

  19. Peck, J. R. Friendship and the evolution of co-operation. J. Theor. Biol. 162, 195–228 (1993).

    Article  CAS  Google Scholar 

  20. Connor, R. C. Impala allogrooming and the parcelling model of reciprocity. Anim. Behav. 49, 528–530 (1995).

    Article  Google Scholar 

  21. Clements, R. & Stephens, D. C. Testing models of non-kin cooperation: mutualism and the Prisoner's Dilemma. Anim. Behav. 50, 527–535 (1995).

    Article  Google Scholar 

  22. Frean, M. R. The prisoner's dilemma without synchrony. Proc. R. Soc. Lond. B 257, 75–79 (1994).

    Article  ADS  CAS  Google Scholar 

  23. Nowak, M. A. & Sigmund, K. The alternating Prisoner's Dilemma. J. Theor. Biol. 168, 219–226 (1994).

    Article  Google Scholar 

Download references

Acknowledgements

We thank J. Lazarus, B. Charlton, R. Barton and M. Petrie for discussion and comments. G.R. is supported by a Lord Adams Fellowship.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Gilbert Roberts.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Roberts, G., Sherratt, T. Development of cooperative relationships through increasing investment. Nature 394, 175–179 (1998). https://doi.org/10.1038/28160

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/28160

This article is cited by

Comments

By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.

Search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing