International Journal of Game Theory

, Volume 16, Issue 3, pp 187–195 | Cite as

A note on uncertainty and cooperation in a finitely repeated prisoner's dilemma

  • L. Samuelson


An intuitive expectation is that in a finitely repeated prisoner's dilemma, the players will achieve mutual cooperation in at least some periods. Existing explanations for equilibrium cooperation (with agents perfectly informed of one another's characteristics) require that the number of repetitions be unknown, which is in many cases an uncomfortably strong uncertainty assertion. This paper demonstrates that if agents have private information concerning the number of repetitions (as opposed to being completely uninformed), equilibrium mutual cooperation can occur in a finitely repeated game. This appears to be a weaker and more palatable assumption then that of complete uncertainty, and hence provides a natural and useful alternative foundation for mutual cooperation.


Economic Theory Game Theory Private Information Mutual Cooperation Intuitive Expectation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Aumann R (1959) Acceptable points in general cooperativen-person games. In: Tucker AW, Luce RD (eds) Contributions to the theory of games IV. Annuals of Mathematics Studies 40, Princeton University Press, pp 287–324Google Scholar
  2. Benoit J-P, Krishna V (1985) Finitely repeated games. Econometrica 53:905–922Google Scholar
  3. Friedman J (1971) A non-cooperative equilibrium for supergames. Review of Economic Studies 38(1):1–12Google Scholar
  4. Kreps D, Milgrom P, Roberts J, Wilson R (1982) Rational cooperation in the finitely repeated prisoner's dilemma. Journal of Economic Theory 27:245–252Google Scholar
  5. Kreps D, Wilson R (1982) Sequential equilibria. Econometrica 50:863–894Google Scholar
  6. Kurz M (1978) Altruism as an outcome of social iteration. American Economic Review 68(2): 216–222Google Scholar
  7. Luce R, Raiffa H (1957) Games and decisions. John Wiley & Sons, NYGoogle Scholar
  8. Milgrom P (1981) An axiomatic characterization of common knowledge. Econometrica 51:219–222Google Scholar
  9. Owen G (1982) Game theory second ed. Saunders, PhiladelphiaGoogle Scholar
  10. Porter R (1983) Optimal cartel trigger price strategies. Journal of Economic Theory 29:313–338Google Scholar
  11. Radner R (1980) Collusive behavior in noncooperative epsilon-equilibria of oligopolies with long but finite lives. Journal of Economic Theory 22(2):136–154Google Scholar
  12. Rosenthal R (1980) New equilibria for noncooperative two-person games. Journal of Mathematical Sociology 7(1):15–26Google Scholar
  13. Rubinstein A (1979) Equilibrium in supergames with the overtaking criterion. Journal of Economic Theory 21:1–9Google Scholar
  14. Rubinstein A (1980) Strong perfect equilibrium. International Journal of Game Theory 9:1–12Google Scholar
  15. Sanghvi A, Sobel M (1976) Bayesian games as stochastic processes. International Journal of Game Theory 5(1):l-22Google Scholar
  16. Selten R (1975) Reexamination of the perfectness concept for equilibrium points in extensive games. International Journal of Game Theory 4:22–55Google Scholar
  17. Selten R (1978) The chain store paradox. Theory and Decision 9(1):127–159Google Scholar
  18. Smale S (1980) The prisoner's dilemma and dynamical systems associated to non-cooperative games. Econometrica 48(7): 1617–1634Google Scholar

Copyright information

© Physica-Verlag 1987

Authors and Affiliations

  • L. Samuelson
    • 1
  1. 1.Department of EconomicsThe Pennsylvania State UniversityUniversity ParkUSA

Personalised recommendations