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Cooperation in the Finitely Repeated Prisoner's Dilemma

Author

Listed:
  • Matthew Embrey

    () (University of Sussex)

  • Guillaume R. Frechette

    (NYU)

  • Sevgi Yuksel

    (UCSB)

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 paper 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 paper establishes a systematic pattern of behavior: subjects converge to use threshold strategies that conditionally cooperate until a threshold round; and 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. Frechette & Sevgi Yuksel, 2016. "Cooperation in the Finitely Repeated Prisoner's Dilemma," Working Paper Series 08616, Department of Economics, University of Sussex.
  • Handle: RePEc:sus:susewp:08616
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    File URL: http://www.sussex.ac.uk/economics/documents/wps-86-2016.pdf
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    References listed on IDEAS

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    1. Larbi Alaoui & Antonio Penta, 2016. "Endogenous Depth of Reasoning," Review of Economic Studies, Oxford University Press, vol. 83(4), pages 1297-1333.
    2. 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.
    3. repec:wly:emetrp:v:85:y:2017:i::p:915-935 is not listed on IDEAS
    4. 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.
    5. 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.
    6. Garcia-Pola, Bernardo & Iriberri, Nagore & Kovarik, Jaromir, 2016. "Non-equilibrium Play in Centipede Games," CEPR Discussion Papers 11477, C.E.P.R. Discussion Papers.
    7. 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.
    8. 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.
    9. Crawford, Vincent P, 1995. "Adaptive Dynamics in Coordination Games," Econometrica, Econometric Society, vol. 63(1), pages 103-143, January.
    10. 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.
    11. McKelvey, Richard D & Palfrey, Thomas R, 1992. "An Experimental Study of the Centipede Game," Econometrica, Econometric Society, vol. 60(4), pages 803-836, July.
    12. 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.
    13. 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.
    14. Drew Fudenberg & David K. Levine, 1998. "The Theory of Learning in Games," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262061945, November.
    15. 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.
    16. Friedman, Daniel & Sinervo, Barry, 2016. "Evolutionary Games in Natural, Social, and Virtual Worlds," OUP Catalogue, Oxford University Press, number 9780199981151.
    17. Sophie Moinas & Sebastien Pouget, 2013. "The Bubble Game: An Experimental Study of Speculation," Econometrica, Econometric Society, vol. 81(4), pages 1507-1539, July.
    18. 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.
    19. 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.
    20. 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.
    21. 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.
    22. 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.
    23. Daniel Friedman & Ryan Oprea, 2012. "A Continuous Dilemma," American Economic Review, American Economic Association, vol. 102(1), pages 337-363, February.
    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.
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    Cited by:

    1. repec:eee:jeborg:v:147:y:2018:i:c:p:76-94 is not listed on IDEAS
    2. Lugovskyy, Volodymyr & Puzzello, Daniela & Sorensen, Andrea & Walker, James & Williams, Arlington, 2017. "An experimental study of finitely and infinitely repeated linear public goods games," Games and Economic Behavior, Elsevier, vol. 102(C), pages 286-302.
    3. repec:wly:emetrp:v:85:y:2017:i::p:915-935 is not listed on IDEAS
    4. Andrea Gallice & Ignacio Monzon, 2016. "Cooperation in Social Dilemmas through Position Uncertainty," Carlo Alberto Notebooks 493, Collegio Carlo Alberto.
    5. Bernergård, Axel & Mohlin, Erik, 2017. "Evolutionary Selection against Iteratively Weakly Dominated Strategies," Working Papers 2017:18, Lund University, Department of Economics.
    6. He, Simin & Wu, Jiabin, 2018. "Compromise and Coordination: An Experimental Study," MPRA Paper 84713, University Library of Munich, Germany.
    7. T.K Ahn & Loukas Balafoutas & Mongoljin Batsaikhan & Francisco Campos Ortiz & Louis Putterman & Matthias Sutter, 2016. "Trust and Communication in a Property Rights Dilemma," Working Papers 2016-5, Brown University, Department of Economics.
    8. Caleb Cox & Matthew Jones & Kevin Pflum & Paul Healy, 2015. "Revealed reputations in the finitely repeated prisoners’ dilemma," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 58(3), pages 441-484, April.
    9. repec:kap:expeco:v:20:y:2017:i:2:d:10.1007_s10683-016-9494-z is not listed on IDEAS
    10. Drew Fudenberg & David K Levine, 2016. "Whither Game Theory?," Levine's Working Paper Archive 786969000000001307, David K. Levine.

    More about this item

    Keywords

    repeated games; prisoners dilemma; threshold strategies; basin of attraction;

    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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