IDEAS home Printed from https://ideas.repec.org/p/eie/wpaper/1116.html
   My bibliography  Save this paper

Time Horizon and Cooperation in Continuous Time

Author

Listed:
  • Maria Bigoni

    (Department of Economics, University of Bologna)

  • Marco Casari

    (Department of Economics, University of Bologna)

  • Andrzej Skrzypacz

    (Graduate School of Business, Stanford University)

  • Giancarlo Spagnolo

    (SITE, Tor Vergata, EIEF and CEPR)

Abstract

We study interactions with different durations and termination rules in a (quasi) continuous-time prisoner’s dilemma experiment. We find that cooperation is easier to achieve and sustain with deterministic horizons than with stochastic ones; end-game effects emerge, but subjects postpone them with experience; longer duration helps cooperation. Static theories for continuous-time games cannot simultaneously account for these findings and miss the evolution of behavior across supergames. We propose a simple model – based on the replicator dynamics – that proves consistent with this evidence. The analysis of strategies and an additional treatment lend further support to the proposed explanation.

Suggested Citation

  • Maria Bigoni & Marco Casari & Andrzej Skrzypacz & Giancarlo Spagnolo, 2011. "Time Horizon and Cooperation in Continuous Time," EIEF Working Papers Series 1116, Einaudi Institute for Economics and Finance (EIEF), revised Jan 2013.
    • Handle: RePEc:eie:wpaper:1116
    as

    Download full text from publisher

    File URL: http://www.eief.it/files/2013/01/wp-16-time-horizon-and-cooperation-in-continuous-time.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. 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. Yuliy Sannikov & Andrzej Skrzypacz, 2007. "Impossibility of Collusion under Imperfect Monitoring with Flexible Production," American Economic Review, American Economic Association, vol. 97(5), pages 1794-1823, December.
    4. 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.
    5. 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.
    6. Siegfried Berninghaus & Karl-Martin Ehrhart & Marion Ott, 2006. "A network experiment in continuous time: The influence of link costs," Experimental Economics, Springer;Economic Science Association, vol. 9(3), pages 237-251, September.
    7. 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.
    8. 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.
    9. 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.
    10. Borgers, Tilman & Sarin, Rajiv, 1997. "Learning Through Reinforcement and Replicator Dynamics," Journal of Economic Theory, Elsevier, vol. 77(1), pages 1-14, November.
    11. Szymanski, Stefan, 1996. "Making Hay While the Sun Shines," Journal of Industrial Economics, Wiley Blackwell, vol. 44(1), pages 1-16, March.
    12. 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.
    13. 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.
    14. 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.
    15. Reinhard Selten & Michael Mitzkewitz & Gerald R. Uhlich, 1997. "Duopoly Strategies Programmed by Experienced Players," Econometrica, Econometric Society, vol. 65(3), pages 517-556, May.
    16. Thomas R. Palfrey & Howard Rosenthal, 1994. "Repeated Play, Cooperation and Coordination: An Experimental Study," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 61(3), pages 545-565.
    17. 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.
    18. Ben Greiner, 2004. "The Online Recruitment System ORSEE 2.0 - A Guide for the Organization of Experiments in Economics," Working Paper Series in Economics 10, University of Cologne, Department of Economics.
    19. Ben Greiner, 2004. "The Online Recruitment System ORSEE - A Guide for the Organization of Experiments in Economics," Papers on Strategic Interaction 2003-10, Max Planck Institute of Economics, Strategic Interaction Group.
    20. 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.
    21. 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.
    22. Daniel Friedman & Ryan Oprea, 2012. "A Continuous Dilemma," American Economic Review, American Economic Association, vol. 102(1), pages 337-363, February.
    23. Bergin, James & MacLeod, W Bentley, 1993. "Continuous Time Repeated Games," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 34(1), pages 21-37, February.
    24. Siegfried Berninghaus & Karl-Martin Ehrhart & Marion Ott & Bodo Vogt, 2007. "Evolution of networks—an experimental analysis," Journal of Evolutionary Economics, Springer, vol. 17(3), pages 317-347, June.
    25. Mailath, George J. & Samuelson, Larry, 2006. "Repeated Games and Reputations: Long-Run Relationships," OUP Catalogue, Oxford University Press, number 9780195300796.
    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. Embrey, Matthew & Seel, Christian & Philipp Reiss, J., 2024. "Gambling in risk-taking contests: Experimental evidence," Journal of Economic Behavior & Organization, Elsevier, vol. 221(C), pages 570-585.
    2. He, Simin & Zhu, Xun, 2023. "Real-time monitoring in a public-goods game," Games and Economic Behavior, Elsevier, vol. 142(C), pages 454-479.
    3. 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.
    4. Ernesto Reuben & Sigrid Suetens, 2012. "Revisiting strategic versus non-strategic cooperation," Experimental Economics, Springer;Economic Science Association, vol. 15(1), pages 24-43, March.
    5. Zhao, Shuchen, 2021. "Taking turns in continuous time," Journal of Economic Behavior & Organization, Elsevier, vol. 191(C), pages 257-279.
    6. Goeschl, Timo & Jarke, Johannes, 2014. "Trust, but verify? When trustworthiness is observable only through (costly) monitoring," WiSo-HH Working Paper Series 20, University of Hamburg, Faculty of Business, Economics and Social Sciences, WISO Research Laboratory.
    7. 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.
    8. repec:tiu:tiucen:200922 is not listed on IDEAS
    9. repec:dgr:kubcen:200922 is not listed on IDEAS
    10. 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.
    11. Ailin Leng & Lana Friesen & Kenan Kalayci & Priscilla Man, 2018. "A minimum effort coordination game experiment in continuous time," Experimental Economics, Springer;Economic Science Association, vol. 21(3), pages 549-572, September.
    12. 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.
    13. Maria Bigoni & Jan Potters & Giancarlo Spagnolo, 2019. "Frequency of interaction, communication and collusion: an experiment," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 68(4), pages 827-844, November.
    14. repec:dgr:kubcen:200833 is not listed on IDEAS
    15. repec:tiu:tiucen:200833 is not listed on IDEAS
    16. Gary Charness & Francesco Feri & Miguel A. Meléndez‐Jiménez & Matthias Sutter, 2014. "Experimental Games on Networks: Underpinnings of Behavior and Equilibrium Selection," Econometrica, Econometric Society, vol. 82(5), pages 1615-1670, September.
    17. Kartal, Melis & Müller, Wieland & Tremewan, James, 2021. "Building trust: The costs and benefits of gradualism," Games and Economic Behavior, Elsevier, vol. 130(C), pages 258-275.
    18. 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.
    19. Juan Lacomba & Francisco Lagos & Tibor Neugebauer, 2011. "Who makes the pie bigger? An experimental study on co-opetition," New Zealand Economic Papers, Taylor & Francis Journals, vol. 45(1-2), pages 59-68.
    20. Pedro Dal Bo & Guillaume R. Frochette, 2011. "The Evolution of Cooperation in Infinitely Repeated Games: Experimental Evidence," American Economic Review, American Economic Association, vol. 101(1), pages 411-429, February.
    21. repec:cup:judgdm:v:4:y:2009:i:5:p:363-384 is not listed on IDEAS
    22. Simon Gächter & Armin Falk, 2002. "Reputation and Reciprocity: Consequences for the Labour Relation," Scandinavian Journal of Economics, Wiley Blackwell, vol. 104(1), pages 1-26, March.
    23. Simon Gaechter & Armin Falk, 2001. "Reputation or Reciprocity? An Experimental Investigation," CESifo Working Paper Series 496, CESifo.
    24. Cox, Caleb A. & Stoddard, Brock, 2018. "Strategic thinking in public goods games with teams," Journal of Public Economics, Elsevier, vol. 161(C), pages 31-43.
    25. Ernesto Reuben & Sigrid Suetens, 2018. "Instrumental Reciprocity as an Error," Games, MDPI, vol. 9(3), pages 1-9, September.

    More about this item

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • C91 - Mathematical and Quantitative Methods - - Design of Experiments - - - Laboratory, Individual Behavior
    • C92 - Mathematical and Quantitative Methods - - Design of Experiments - - - Laboratory, Group Behavior
    • D74 - Microeconomics - - Analysis of Collective Decision-Making - - - Conflict; Conflict Resolution; Alliances; Revolutions

    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:eie:wpaper:1116. 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: Facundo Piguillem (email available below). General contact details of provider: https://edirc.repec.org/data/einauit.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.