Letter | Published:

A strategy of win-stay, lose-shift that outperforms tit-for-tat in the Prisoner's Dilemma game

Naturevolume 364pages5658 (1993) | Download Citation

Subjects

Abstract

THE Prisoner's Dilemma is the leading metaphor for the evolution of cooperative behaviour in populations of selfish agents, especially since the well-known computer tournaments of Axelrod1 and their application to biological communities2,3. In Axelrod's simulations, the simple strategy tit-for-tat did outstandingly well and subsequently became the major paradigm for reciprocal altruism4 12. Here we present extended evolutionary simulations of heterogeneous ensembles of probabilistic strategies including mutation and selection, and report the unexpected success of another protagonist: Pavlov. This strategy is as simple as tit-for-tat and embodies the fundamental behavioural mechanism win-stay, lose-shift, which seems to be a widespread rule13. Pavlov's success is based on two important advantages over tit-for-tat: it can correct occasional mistakes and exploit unconditional cooperators. This second feature prevents Pavlov populations from being undermined by unconditional cooperators, which in turn invite defectors. Pavlov seems to be more robust than tit-for-tat, suggesting that cooperative behaviour in natural situations may often be based on win-stay, lose-shift.

Access optionsAccess options

Rent or Buy article

Get time limited or full article access on ReadCube.

from$8.99

All prices are NET prices.

References

  1. 1

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

  2. 2

    Axelrod, R. & Hamilton, W. D. Science 211, 1390–1396 (1981).

  3. 3

    Axelrod, R. & Dion, D. Science 242, 1385–1390 (1988).

  4. 4

    Wilkinson, G. Nature 308, 181–184 (1984).

  5. 5

    Lombardo, M. P. Science 227, 1363–1365 (1985).

  6. 6

    Milinski, M. Nature 325, 433–435 (1987).

  7. 7

    May, R. M. Nature 327, 15–17 (1987).

  8. 8

    Dugatkin, L. A. Behav. Ecol. Sociobiol. 25, 395–397 (1988).

  9. 9

    Nowak, M. & Sigmund, K. Nature 355, 250–253 (1992).

  10. 10

    Krebs, J. R. & Davies N. B. An Introduction to Behavioural Ecology (Sinauer, MA, 1981).

  11. 11

    Dawkins, R. The Selfish Gene (Oxford Univ. Press, Oxford, 1988).

  12. 12

    Sigmund, K. Games of Life (Oxford Univ. Press, Oxford, 1993).

  13. 13

    Domjan, M. & Burkhard, B. The Principles of Learning and Behaviour (Brooks/Cole, Monterey, 1986).

  14. 14

    Nowak, M. A. & May, R. M. Nature 359, 826–829 (1992).

  15. 15

    Selten, R. & Hammerstein, P. Th. Behav. Brain Sci. 7, 115–142 (1984).

  16. 16

    Boyd, R. & Lorberbaum, J. P. Nature 327, 58–59 (1987).

  17. 17

    Nowak, M. & Sigmund, K. Proc. natn. Acad. Sci. U.S.A. 90, 5091–5094 (1993).

  18. 18

    Kraines, D. & Kraines, V. Theory and Decision 26, 47–63 (1988).

  19. 19

    Rapoport, A. & Chammah, A. M. Prisoner's Dilemma (Univ. of Michigan Press, Ann Arbor, 1965).

  20. 20

    Nowak, M. & Sigmund, K. Acta appl. Math. 20, 247–265 (1990).

  21. 21

    Boyd, R. J. theor. Biol. 136, 47–56 (1989).

  22. 22

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

  23. 23

    Hofbauer, J. & Sigmund, K. The Theory of Evolution and Dynamical Systems (Cambridge Univ. Press, Cambridge, 1988).

  24. 24

    Maynard Smith, J. Th. Behav. Brain Sci. 7, 95–101 (1984).

  25. 25

    Axelrod, R. in Genetic Algorithms and Simulated Annealing (ed. Davis, D.) (Pitman, London, 1987).

  26. 26

    Lindgren, K. in Artificial Life II (eds Farmer, D. et al.) (Proc. Santa Fe Inst. Stud., Addison Welsey, 1991).

  27. 27

    Reboreda, J. C. & Kacelnik, A. J. exp. Animal Behav. 60, 176–193 (1993).

Download references

Author information

Author notes

  1. Martin Nowak: Department of Zoology, University of Oxford, South Parks Road, Oxford 0X1 3PS, UK

Affiliations

  1. †Institut für Mathematik, Universit † Wien, Strudlhofgasse 4, A-1090, Vienna, Austria

    • Karl Sigmund

Authors

  1. Search for Martin Nowak in:

  2. Search for Karl Sigmund in:

About this article

Publication history

Received

Accepted

Issue Date

DOI

https://doi.org/10.1038/364056a0

Further reading

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.