Advertisement

International Journal of Game Theory

, Volume 41, Issue 3, pp 707–718 | Cite as

The impact of the termination rule on cooperation in a prisoner’s dilemma experiment

  • Hans-Theo Normann
  • Brian WallaceEmail author
Article

Abstract

Cooperation in prisoner’s dilemma games can usually be sustained only if the game has an infinite horizon. We analyze to what extent the theoretically crucial distinction of finite versus infinite-horizon games is reflected in the outcomes of a prisoner’s dilemma experiment. We compare three different experimental termination rules in four treatments: a known finite end, an unknown end, and two variants with a random termination rule (with a high and with a low continuation probability, where cooperation can occur in a subgame-perfect equilibrium only with the high probability). We find that the termination rules do not significantly affect average cooperation rates. Specifically, employing a random termination rule does not cause significantly more cooperation compared to a known finite horizon, and the continuation probability does not significantly affect average cooperation rates either. However, the termination rules may influence cooperation over time and end-game behavior. Further, the (expected) length of the game significantly increases cooperation rates. The results suggest that subjects may need at least some learning opportunities (like repetitions of the supergame) before significant backward induction arguments in finitely repeated game have force.

Keywords

Prisoner’s dilemma Repeated games Infinite-horizon games Experimental economics 

JEL Classification

C72 C92 D21 D43 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Andreoni J, Miller JH (1993) Rational cooperation in the finitely repeated prisoners’ dilemma: experimental evidence. Econ J 103: 570–585CrossRefGoogle Scholar
  2. Angelova V, Bruttel LV, Güth W, Kamecke U (2011) Can subgame perfect equilibrium threats foster cooperation? An experimental test of finite-horizon folk theorems. Econ Inq (forthcoming)Google Scholar
  3. Axelrod R (1984) The evolution of cooperation. Basic Books, New YorkGoogle Scholar
  4. Axelrod R (1980) More effective choice in the prisoner’s dilemma. J Confl Resolut 24: 379–403CrossRefGoogle Scholar
  5. Benoit J-P, Krishna V (1985) Finitely repeated games. Econometrica 53(4): 905–922CrossRefGoogle Scholar
  6. Benoit J-P, Krishna V (1987) Nash equilibria of finitely repeated games. Int J Game Theory 16(3): 197–204CrossRefGoogle Scholar
  7. Bolton GE, Ockenfels A (2000) ERC: a theory of equity, reciprocity and competition. Am Econ Rev 90: 166–193CrossRefGoogle Scholar
  8. Bruttel L, Kamecke U (2012) Infinity in the lab. How do people play repeated games? Theory Dec 72(2): 205–219Google Scholar
  9. Bruttel LV, Güth W, Kamecke U (2012) Finitely repeated prisoners’ dilemma experiments without a commonly known end. Int J Game Theory 41(1): 23–47CrossRefGoogle Scholar
  10. Dal Bo P (2005) Cooperation under the shadow of the future: experimental evidence from infinitely repeated games. Am Econ Rev 95: 1591–1604CrossRefGoogle Scholar
  11. Engle-Warnick J, Slonim RL (2004) The evolution of strategies in a repeated trust game. J Econ Behav Organ 55: 553–573CrossRefGoogle Scholar
  12. Fehr E, Schmidt KM (1999) A theory of fairness, competition and cooperation. Q J Econ 114: 817–868CrossRefGoogle Scholar
  13. Feinberg RM, Husted TA (1993) An experimental test of discount effects on collusive behavior in dupoly markets. J Ind Econ 41(2): 153–160CrossRefGoogle Scholar
  14. Fischbacher U (2007) Z-Tree, Zurich toolbox for readymade economic experiments. Exp Econ 10(2): 171–178CrossRefGoogle Scholar
  15. Flood MM (1952) Some experimental games. Research Memorandum RM-789. RAND Corporation, Santa Monica, CAGoogle Scholar
  16. Fouraker L, Siegel S (1963) Bargaining behavior. McGraw-Hill, New YorkGoogle Scholar
  17. Gonzales LG, Güth W, Levati V (2005) When does the game end? Public goods experiments with non-definite and non-commonly known time horizons. Econ Lett 88(2): 221–226CrossRefGoogle Scholar
  18. Hollander M, Wolfe DA (1999) Nonparametric statistical methods. Wiley, New YorkGoogle Scholar
  19. Holt CH (1985) An experimental test of the consistent—conjectures hypothesis. Am Econ Rev 75: 314–325Google Scholar
  20. Kaplan T, Ruffle B (2006) Which way to cooperate? Working Paper, Ben-Gurion UniversityGoogle Scholar
  21. Kreps DM, Milgrom P, Roberts J, Wilson R (1982) Rational cooperation in the finitely repeated prisoner’s dilemma. J Econ Theory 27(2): 245–252CrossRefGoogle Scholar
  22. Luce RD, Raiffa H (1957) Games and decisions: introduction and critical survey. Wiley, New YorkGoogle Scholar
  23. Morehous LG (1966) One-play, two-play, five-play, and ten-play runs of prisoner’s dilemma. J Confl Resolut 10: 354–361CrossRefGoogle Scholar
  24. Murnighan JK, Roth AE (1983) Expecting continued play in prisoner’s dilemma games: a test of three models. J Confl Resolut 27: 279–300CrossRefGoogle Scholar
  25. Neyman A (1999) Cooperation in repeated games when the number of stages is not commonly known econometrica. Econometrica 67: 45–64CrossRefGoogle Scholar
  26. Orzen H (2008) Counterintuitive number effects in experimental oligopolies. Exp Econ 11(4): 390–401CrossRefGoogle Scholar
  27. Rapoport A, Cammah AM (1965) Prisoner’s dilemma. A study in conflict and cooperation. University of Michigan Press, Ann ArborGoogle Scholar
  28. Roth AE (1995) Bargaining experiments. In: Kagel J, Roth AE (eds) Handbook of experimental economics. Princeton University Press, Princeton, pp 253–348Google Scholar
  29. Roth AE, Murnighan JK (1978) Equilibrium behavior and repeated play of the prisoners’ dilemma. J Math Psychol 17: 189–198CrossRefGoogle Scholar
  30. Samuelson L (1987) A note on uncertainty and cooperation in a finitely repeated prisoner’s dilemma. International Journal of Game Theory 16(3): 187–195CrossRefGoogle Scholar
  31. Selten R, Stoecker R (1986) End behavior in finite prisoner’s dilemma supergames. J Econ Behav Organ 7: 47–70CrossRefGoogle Scholar
  32. Selten R, Mitzkewitz M, Uhlich GR (1997) Duopoly strategies programmed by experienced players. Econometrica 65: 517–556CrossRefGoogle Scholar
  33. Suetens S, Potters J (2007) Bertrand Colludes more than Cournot. Exp Econ 10(1): 71–77CrossRefGoogle Scholar
  34. Stahl DO (1991) The graph of prisoner’s dilemma supergame payoffs as a function of the discount factor. Games Econ Behav 3: 360–384CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2012

Authors and Affiliations

  1. 1.Duesseldorf Institute for Competition Economics (DICE)University of DuesseldorfDüesseldorfGermany
  2. 2.Department of EconomicsUniversity College LondonLondonUK

Personalised recommendations