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Cooperation in the Finitely Repeated Prisoner’s Dilemma

Author

Listed:
  • Matthew Embrey
  • Guillaume R Fréchette
  • Sevgi Yuksel
Abstract
More than half a century after the first experiment on the finitely repeated prisoner’s dilemma, evidence on whether cooperation decreases with experience—as suggested by backward induction—remains inconclusive. This article provides a meta-analysis of prior experimental research and reports the results of a new experiment to elucidate how cooperation varies with the environment in this canonical game. We describe forces that affect initial play (formation of cooperation) and unraveling (breakdown of cooperation). First, contrary to the backward induction prediction, the parameters of the repeated game have a significant effect on initial cooperation. We identify how these parameters impact the value of cooperation—as captured by the size of the basin of attraction of always defect—to account for an important part of this effect. Second, despite these initial differences, the evolution of behavior is consistent with the unraveling logic of backward induction for all parameter combinations. Importantly, despite the seemingly contradictory results across studies, this article establishes a systematic pattern of behavior: subjects converge to use threshold strategies that conditionally cooperate until a threshold round; conditional on establishing cooperation, the first defection round moves earlier with experience. Simulation results generated from a learning model estimated at the subject level provide insights into the long-term dynamics and the forces that slow down the unraveling of cooperation.

Suggested Citation

  • Matthew Embrey & Guillaume R Fréchette & Sevgi Yuksel, 2018. "Cooperation in the Finitely Repeated Prisoner’s Dilemma," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 133(1), pages 509-551.
  • Handle: RePEc:oup:qjecon:v:133:y:2018:i:1:p:509-551.
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    1. 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.
    2. Larbi Alaoui & Antonio Penta, 2016. "Endogenous Depth of Reasoning," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 83(4), pages 1297-1333.
    3. McKelvey, Richard D & Palfrey, Thomas R, 1992. "An Experimental Study of the Centipede Game," Econometrica, Econometric Society, vol. 60(4), pages 803-836, July.
    4. Fudenberg, Drew & Levine, David, 1998. "Learning in games," European Economic Review, Elsevier, vol. 42(3-5), pages 631-639, May.
    5. Cooper, Russell & DeJong, Douglas V. & Forsythe, Robert & Ross, Thomas W., 1996. "Cooperation without Reputation: Experimental Evidence from Prisoner's Dilemma Games," Games and Economic Behavior, Elsevier, vol. 12(2), pages 187-218, February.
    6. Crawford, Vincent P, 1995. "Adaptive Dynamics in Coordination Games," Econometrica, Econometric Society, vol. 63(1), pages 103-143, January.
    7. Evan Calford & Ryan Oprea, 2017. "Continuity, Inertia, and Strategic Uncertainty: A Test of the Theory of Continuous Time Games," Econometrica, Econometric Society, vol. 85, pages 915-935, May.
    8. Kahn, Lawrence M & Munighan, J Keith, 1993. "A General Experiment on Bargaining in Demand Games with Outside Options," American Economic Review, American Economic Association, vol. 83(5), pages 1260-1280, December.
    9. Kenju Kamei & Louis Putterman, 2013. "Play it Again: Partner Choice, Reputation Building and Learning in Restarting, Finitely-Repeated Dilemma Games," Working Papers 2013-8, Brown University, Department of Economics.
    10. García-Pola, Bernardo & Iriberri, Nagore & Kovářík, Jaromír, 2020. "Non-equilibrium play in centipede games," Games and Economic Behavior, Elsevier, vol. 120(C), pages 391-433.
    11. 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.
    12. Marco Mantovani, 2015. "Limited backward induction: foresight and behavior in sequential games," Working Papers 289, University of Milano-Bicocca, Department of Economics, revised Jan 2015.
    13. Fey, Mark & McKelvey, Richard D & Palfrey, Thomas R, 1996. "An Experimental Study of Constant-Sum Centipede Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 25(3), pages 269-287.
    14. Zauner, Klaus G., 1999. "A Payoff Uncertainty Explanation of Results in Experimental Centipede Games," Games and Economic Behavior, Elsevier, vol. 26(1), pages 157-185, January.
    15. Yoella Bereby-Meyer & Alvin E. Roth, 2006. "The Speed of Learning in Noisy Games: Partial Reinforcement and the Sustainability of Cooperation," American Economic Review, American Economic Association, vol. 96(4), pages 1029-1042, September.
    16. Cheung, Yin-Wong & Friedman, Daniel, 1997. "Individual Learning in Normal Form Games: Some Laboratory Results," Games and Economic Behavior, Elsevier, vol. 19(1), pages 46-76, April.
    17. Daniel Friedman & Ryan Oprea, 2012. "A Continuous Dilemma," American Economic Review, American Economic Association, vol. 102(1), pages 337-363, February.
    18. 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.
    19. Roth, Alvin E. & Erev, Ido, 1995. "Learning in extensive-form games: Experimental data and simple dynamic models in the intermediate term," Games and Economic Behavior, Elsevier, vol. 8(1), pages 164-212.
    20. Roth,Alvin E. (ed.), 1988. "Laboratory Experimentation in Economics," Cambridge Books, Cambridge University Press, number 9780521333924, September.
    21. Matthias Blonski & Peter Ockenfels & Giancarlo Spagnolo, 2011. "Equilibrium Selection in the Repeated Prisoner's Dilemma: Axiomatic Approach and Experimental Evidence," American Economic Journal: Microeconomics, American Economic Association, vol. 3(3), pages 164-192, August.
    22. Hans-Theo Normann & Brian Wallace, 2012. "The impact of the termination rule on cooperation in a prisoner’s dilemma experiment," International Journal of Game Theory, Springer;Game Theory Society, vol. 41(3), pages 707-718, August.
    23. John H. Kagel & Peter McGee, 2016. "Team versus Individual Play in Finitely Repeated Prisoner Dilemma Games," American Economic Journal: Microeconomics, American Economic Association, vol. 8(2), pages 253-276, May.
    24. Frédéric Schneider & Roberto A. Weber, 2013. "Long-term commitment and cooperation," ECON - Working Papers 130, Department of Economics - University of Zurich.
    25. Teck-Hua Ho & Xuanming Su, 2013. "A Dynamic Level-k Model in Sequential Games," Management Science, INFORMS, vol. 59(2), pages 452-469, March.
    26. Drew Fudenberg & David K. Levine, 1998. "The Theory of Learning in Games," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262061945, April.
    27. Rapoport, Amnon & Stein, William E. & Parco, James E. & Nicholas, Thomas E., 2003. "Equilibrium play and adaptive learning in a three-person centipede game," Games and Economic Behavior, Elsevier, vol. 43(2), pages 239-265, May.
    28. Friedman, Daniel & Sinervo, Barry, 2016. "Evolutionary Games in Natural, Social, and Virtual Worlds," OUP Catalogue, Oxford University Press, number 9780199981151.
    29. Sophie Moinas & Sebastien Pouget, 2013. "The Bubble Game: An Experimental Study of Speculation," Econometrica, Econometric Society, vol. 81(4), pages 1507-1539, July.
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    More about this item

    JEL classification:

    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • C92 - Mathematical and Quantitative Methods - - Design of Experiments - - - Laboratory, Group Behavior

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