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A Continuous Dilemma

Author

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  • Daniel Friedman
  • Ryan Oprea

Abstract

We study prisoners' dilemmas played in continuous time with flow payoffs accumulated over 60 seconds. In most cases, the median rate of mutual cooperation is about 90 percent. Control sessions with repeated matchings over eight subperiods achieve less than half as much cooperation, and cooperation rates approach zero in one-shot sessions. In follow-up sessions with a variable number of subperiods, cooperation rates increase nearly linearly as the grid size decreases, and, with one-second subperiods, they approach continuous levels. Our data support a strand of theory that explains how capacity to respond rapidly stabilizes cooperation and destabilizes defection in the prisoner's dilemma. (JEL C72, C78, C91)

Suggested Citation

  • Daniel Friedman & Ryan Oprea, 2012. "A Continuous Dilemma," American Economic Review, American Economic Association, vol. 102(1), pages 337-363, February.
  • Handle: RePEc:aea:aecrev:v:102:y:2012:i:1:p:337-63
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    References listed on IDEAS

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    1. Jim Engle-Warnick & Robert Slonim, 2006. "Inferring repeated-game strategies from actions: evidence from trust game experiments," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 28(3), pages 603-632, August.
    2. Selten, Reinhard & Stoecker, Rolf, 1986. "End behavior in sequences of finite Prisoner's Dilemma supergames A learning theory approach," Journal of Economic Behavior & Organization, Elsevier, vol. 7(1), pages 47-70, March.
    3. 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.
    4. Aoyagi, Masaki & Fréchette, Guillaume, 2009. "Collusion as public monitoring becomes noisy: Experimental evidence," Journal of Economic Theory, Elsevier, vol. 144(3), pages 1135-1165, May.
    5. Esther Hauk & Rosemarie Nagel, 2000. "Choice of partners in multiple two-person prisoner's dilemma games: An experimental study," Economics Working Papers 487, Department of Economics and Business, Universitat Pompeu Fabra.
    6. Simon, Leo K & Stinchcombe, Maxwell B, 1989. "Extensive Form Games in Continuous Time: Pure Strategies," Econometrica, Econometric Society, vol. 57(5), pages 1171-1214, September.
    7. Fudenberg, Drew & Maskin, Eric, 1986. "The Folk Theorem in Repeated Games with Discounting or with Incomplete Information," Econometrica, Econometric Society, vol. 54(3), pages 533-554, May.
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    Citations

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    Cited by:

    1. Crosetto, P. & Filippin, A., 2015. "The sound of others: suprising evidence of conformist behavior," Working Papers 2015-07, Grenoble Applied Economics Laboratory (GAEL).
    2. Oprea, Ryan & Charness, Gary & Friedman, Daniel, 2014. "Continuous time and communication in a public-goods experiment," Journal of Economic Behavior & Organization, Elsevier, vol. 108(C), pages 212-223.
    3. Tremewan, James & Vanberg, Christoph, 2016. "The dynamics of coalition formation – A multilateral bargaining experiment with free timing of moves," Journal of Economic Behavior & Organization, Elsevier, vol. 130(C), pages 33-46.
    4. Tasneem, Dina & Engle-Warnick, Jim & Benchekroun, Hassan, 2017. "An experimental study of a common property renewable resource game in continuous time," Journal of Economic Behavior & Organization, Elsevier, vol. 140(C), pages 91-119.
    5. Brocas, Isabelle & Carrillo, Juan D & Giga, Aleksandar & Zapatero, Fernando, 2015. "Risk Aversion in a Dynamic Asset Allocation Experiment," CEPR Discussion Papers 10332, C.E.P.R. Discussion Papers.
    6. Luhan, Wolfgang J. & Poulsen, Anders U. & Roos, Michael W.M., 2017. "Real-time tacit bargaining, payoff focality, and coordination complexity: Experimental evidence," Games and Economic Behavior, Elsevier, vol. 102(C), pages 687-699.
    7. Oprea, Ryan & Henwood, Keith & Friedman, Daniel, 2011. "Separating the Hawks from the Doves: Evidence from continuous time laboratory games," Journal of Economic Theory, Elsevier, vol. 146(6), pages 2206-2225.
    8. Hans-Theo Normann & Till Requate & Israel Waichman, 2014. "Do short-term laboratory experiments provide valid descriptions of long-term economic interactions? A study of Cournot markets," Experimental Economics, Springer;Economic Science Association, vol. 17(3), pages 371-390, September.
    9. Cary Deck & Nikos Nikiforakis, 2012. "Perfect and imperfect real-time monitoring in a minimum-effort game," Experimental Economics, Springer;Economic Science Association, vol. 15(1), pages 71-88, March.
    10. Friedman, Daniel & Huck, Steffen & Oprea, Ryan & Weidenholzer, Simon, 2015. "From imitation to collusion: Long-run learning in a low-information environment," Journal of Economic Theory, Elsevier, vol. 155(C), pages 185-205.
    11. Jensen, Martin Kaae & Kozlovskaya, Maria, 2016. "A representation theorem for guilt aversion," Journal of Economic Behavior & Organization, Elsevier, vol. 125(C), pages 148-161.
    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. Eugenio Proto & Aldo Rustichini & Andis Sofianos, 2016. "Intelligence, Personality and Gains from Cooperation in Repeated Interactions," CESifo Working Paper Series 6121, CESifo Group Munich.
    14. Christoph Engel & Michael Kurschilgen, 2015. "The Jurisdiction of the Man Within – Introspection, Identity, and Cooperation in a Public Good Experiment," Discussion Paper Series of the Max Planck Institute for Research on Collective Goods 2015_01, Max Planck Institute for Research on Collective Goods.
    15. Camerer, Colin & Dreber, Anna & Forsell, Eskil & Ho, Teck-Hua & Huber, Jurgen & Johannesson, Magnus & Kirchler, Michael & Almenberg, Johan & Altmejd, Adam & Chan, Taizan & Heikensten, Emma & Holzmeist, 2016. "Evaluating replicability of laboratory experiments in Economics," MPRA Paper 75461, University Library of Munich, Germany.
    16. Bigoni, Maria & Potters, Jan & Spagnolo, Giancarlo, 2012. "Flexibility and Collusion with Imperfect Monitoring," CEPR Discussion Papers 8877, C.E.P.R. Discussion Papers.
    17. repec:eee:gamebe:v:105:y:2017:i:c:p:276-296 is not listed on IDEAS
    18. Horstmann, Niklas & Krämer, Jan & Schnurr, Daniel, 2015. "Upstream Competition and Open Access Regimes: Experimental Evidence," 26th European Regional ITS Conference, Madrid 2015 127149, International Telecommunications Society (ITS).
    19. Ioannou, Christos A. & Romero, Julian, 2014. "A generalized approach to belief learning in repeated games," Games and Economic Behavior, Elsevier, vol. 87(C), pages 178-203.
    20. James Pettit & Daniel Friedman & Curtis Kephart & Ryan Oprea, 2014. "Software for continuous game experiments," Experimental Economics, Springer;Economic Science Association, vol. 17(4), pages 631-648, December.
    21. Di Guida, Sibilla & Marchiori, Davide & Erev, Ido, 2012. "Decisions among defaults and the effect of the option to do nothing," Economics Letters, Elsevier, vol. 117(3), pages 790-793.
    22. Schüssler, Katharina & Schüssler, Michael & Mühlbauer, Daniel, 2018. "Individual Differences and Contribution Sequences in Threshold Public Goods," Rationality and Competition Discussion Paper Series 88, CRC TRR 190 Rationality and Competition.
    23. repec:eee:jeborg:v:145:y:2018:i:c:p:495-510 is not listed on IDEAS
    24. Matthew Embrey & Guillaume R. Frechette & Sevgi Yuksel, 2016. "Cooperation in the Finitely Repeated Prisoner's Dilemma," Working Paper Series 08616, Department of Economics, University of Sussex.

    More about this item

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • C91 - Mathematical and Quantitative Methods - - Design of Experiments - - - Laboratory, Individual Behavior

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    1. A Continous Dilemma (AER 2012) in ReplicationWiki

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