IDEAS home Printed from https://ideas.repec.org/p/zbw/dicedp/19.html
   My bibliography  Save this paper

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

Author

Listed:
  • Normann, Hans-Theo
  • Wallace, Brian

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 vs. 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.

Suggested Citation

  • Normann, Hans-Theo & Wallace, Brian, 2011. "The impact of the termination rule on cooperation in a prisoner's dilemma experiment," DICE Discussion Papers 19, Heinrich Heine University Düsseldorf, Düsseldorf Institute for Competition Economics (DICE).
    • Handle: RePEc:zbw:dicedp:19
    as

    Download full text from publisher

    File URL: https://www.econstor.eu/bitstream/10419/45614/1/659004682.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Kreps, David M. & Milgrom, Paul & Roberts, John & Wilson, Robert, 1982. "Rational cooperation in the finitely repeated prisoners' dilemma," Journal of Economic Theory, Elsevier, vol. 27(2), pages 245-252, August.
    2. Ernst Fehr & Klaus M. Schmidt, 1999. "A Theory of Fairness, Competition, and Cooperation," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 114(3), pages 817-868.
    3. Urs Fischbacher, 2007. "z-Tree: Zurich toolbox for ready-made economic experiments," Experimental Economics, Springer;Economic Science Association, vol. 10(2), pages 171-178, June.
    4. Lisa Bruttel & Werner Güth & Ulrich Kamecke, 2012. "Finitely repeated prisoners’ dilemma experiments without a commonly known end," International Journal of Game Theory, Springer;Game Theory Society, vol. 41(1), pages 23-47, February.
    5. Todd R. Kaplan & Bradley J. Ruffle, 2012. "Which Way to Cooperate," Economic Journal, Royal Economic Society, vol. 122(563), pages 1042-1068, September.
    6. Lisa Bruttel & Ulrich Kamecke, 2012. "Infinity in the lab. How do people play repeated games?," Theory and Decision, Springer, vol. 72(2), pages 205-219, February.
    7. Stahl, Dale II, 1991. "The graph of Prisoners' Dilemma supergame payoffs as a function of the discount factor," Games and Economic Behavior, Elsevier, vol. 3(3), pages 368-384, August.
    8. Andreoni, James A & Miller, John H, 1993. "Rational Cooperation in the Finitely Repeated Prisoner's Dilemma: Experimental Evidence," Economic Journal, Royal Economic Society, vol. 103(418), pages 570-585, May.
    9. Henrik Orzen, 2008. "Counterintuitive number effects in experimental oligopolies," Experimental Economics, Springer;Economic Science Association, vol. 11(4), pages 390-401, December.
    10. Sigrid Suetens & Jan Potters, 2007. "Bertrand colludes more than Cournot," Experimental Economics, Springer;Economic Science Association, vol. 10(1), pages 71-77, March.
    11. Engle-Warnick, Jim & Slonim, Robert L., 2004. "The evolution of strategies in a repeated trust game," Journal of Economic Behavior & Organization, Elsevier, vol. 55(4), pages 553-573, December.
    12. Pedro Dal Bó, 2005. "Cooperation under the Shadow of the Future: Experimental Evidence from Infinitely Repeated Games," American Economic Review, American Economic Association, vol. 95(5), pages 1591-1604, December.
    13. Vera Angelova & Lisa V. Bruttel & Werner Güth & Ulrich Kamecke, 2013. "Can Subgame Perfect Equilibrium Threats Foster Cooperation? An Experimental Test Of Finite-Horizon Folk Theorems," Economic Inquiry, Western Economic Association International, vol. 51(2), pages 1345-1356, April.
    14. Axel Ockenfels & Gary E. Bolton, 2000. "ERC: A Theory of Equity, Reciprocity, and Competition," American Economic Review, American Economic Association, vol. 90(1), pages 166-193, March.
    15. Holt, Charles A, 1985. "An Experimental Test of the Consistent-Conjectures Hypothesis," American Economic Review, American Economic Association, vol. 75(3), pages 314-325, June.
    16. Gonzalez, Luis G. & Guth, Werner & Levati, M. Vittoria, 2005. "When does the game end? Public goods experiments with non-definite and non-commonly known time horizons," Economics Letters, Elsevier, vol. 88(2), pages 221-226, August.
    17. Abraham Neyman, 1999. "Cooperation in Repeated Games when the Number of Stages is Not Commonly Known," Econometrica, Econometric Society, vol. 67(1), pages 45-64, January.
    18. Reinhard Selten & Michael Mitzkewitz & Gerald R. Uhlich, 1997. "Duopoly Strategies Programmed by Experienced Players," Econometrica, Econometric Society, vol. 65(3), pages 517-556, May.
    19. Benoit, Jean-Pierre & Krishna, Vijay, 1985. "Finitely Repeated Games," Econometrica, Econometric Society, vol. 53(4), pages 905-922, July.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. repec:tiu:tiucen:200922 is not listed on IDEAS
    2. Ernesto Reuben & Sigrid Suetens, 2012. "Revisiting strategic versus non-strategic cooperation," Experimental Economics, Springer;Economic Science Association, vol. 15(1), pages 24-43, March.
    3. repec:tiu:tiucen:200833 is not listed on IDEAS
    4. Lisa Bruttel & Werner Güth & Ulrich Kamecke, 2012. "Finitely repeated prisoners’ dilemma experiments without a commonly known end," International Journal of Game Theory, Springer;Game Theory Society, vol. 41(1), pages 23-47, February.
    5. Ernesto Reuben & Sigrid Suetens, 2018. "Instrumental Reciprocity as an Error," Games, MDPI, vol. 9(3), pages 1-9, September.
    6. Ralph-C Bayer, 2014. "On the Credibility of Punishment in Repeated Social Dilemma Games," School of Economics and Public Policy Working Papers 2014-08, University of Adelaide, School of Economics and Public Policy.
    7. Müller, Wieland & Tan, Fangfang, 2013. "Who acts more like a game theorist? Group and individual play in a sequential market game and the effect of the time horizon," Games and Economic Behavior, Elsevier, vol. 82(C), pages 658-674.
    8. Ramón Cobo-Reyes & Natalia Jiménez, 2012. "The dark side of friendship: ‘envy’," Experimental Economics, Springer;Economic Science Association, vol. 15(4), pages 547-570, December.
    9. Tóbiás, Áron, 2023. "Rational Altruism," Journal of Economic Behavior & Organization, Elsevier, vol. 207(C), pages 50-80.
    10. Eugenio Proto & Aldo Rustichini & Andis Sofianos, 2019. "Intelligence, Personality, and Gains from Cooperation in Repeated Interactions," Journal of Political Economy, University of Chicago Press, vol. 127(3), pages 1351-1390.
    11. Engel, Christoph & Zhurakhovska, Lilia, 2014. "Conditional cooperation with negative externalities – An experiment," Journal of Economic Behavior & Organization, Elsevier, vol. 108(C), pages 252-260.
    12. Maria Bigoni & Marco Casari & Andrzej Skrzypacz & Giancarlo Spagnolo, 2015. "Time Horizon and Cooperation in Continuous Time," Econometrica, Econometric Society, vol. 83, pages 587-616, March.
    13. John Duffy & Felix Munoz-Garcia, 2009. "Patience or Fairness? Analyzing Social Preferences in Repeated Games," Working Paper 383, Department of Economics, University of Pittsburgh, revised Nov 2009.
    14. Marlats, Chantal, 2019. "Perturbed finitely repeated games," Mathematical Social Sciences, Elsevier, vol. 98(C), pages 39-46.
    15. Jeannette Brosig & Joachim Weimann & Axel Ockenfels, 2003. "The Effect of Communication Media on Cooperation," German Economic Review, Verein für Socialpolitik, vol. 4(2), pages 217-241, May.
    16. Robert S. Gibbons & Manuel Grieder & Holger Herz & Christian Zehnder, 2019. "Building an Equilibrium: Rules Versus Principles in Relational Contracts," CESifo Working Paper Series 7871, CESifo.
    17. Ambrus, Attila & Pathak, Parag A., 2011. "Cooperation over finite horizons: A theory and experiments," Journal of Public Economics, Elsevier, vol. 95(7), pages 500-512.
    18. Lisa Bruttel & Ulrich Kamecke, 2012. "Infinity in the lab. How do people play repeated games?," Theory and Decision, Springer, vol. 72(2), pages 205-219, February.
    19. Ubeda, Paloma, 2014. "The consistency of fairness rules: An experimental study," Journal of Economic Psychology, Elsevier, vol. 41(C), pages 88-100.
    20. Johnsen, Åshild A. & Kvaløy, Ola, 2021. "Conspiracy against the public - An experiment on collusion11“People of the same trade seldom meet together, even for merriment and diversion, but the conversation ends in a conspiracy against the publ," Journal of Behavioral and Experimental Economics (formerly The Journal of Socio-Economics), Elsevier, vol. 94(C).
    21. Attanasi, Giuseppe & Battigalli, Pierpaolo & Manzoni, Elena & Nagel, Rosemarie, 2019. "Belief-dependent preferences and reputation: Experimental analysis of a repeated trust game," Journal of Economic Behavior & Organization, Elsevier, vol. 167(C), pages 341-360.
    22. Doğan, Gönül, 2018. "Collusion in a buyer–seller network formation game," Journal of Economic Behavior & Organization, Elsevier, vol. 155(C), pages 445-457.

    More about this item

    Keywords

    Prisoner's dilemma; Repeated games; Infinite-horizon games; Experimental economics;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C92 - Mathematical and Quantitative Methods - - Design of Experiments - - - Laboratory, Group Behavior
    • D21 - Microeconomics - - Production and Organizations - - - Firm Behavior: Theory
    • D43 - Microeconomics - - Market Structure, Pricing, and Design - - - Oligopoly and Other Forms of Market Imperfection

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:zbw:dicedp:19. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: ZBW - Leibniz Information Centre for Economics (email available below). General contact details of provider: https://edirc.repec.org/data/diduede.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.