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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
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    References listed on IDEAS

    as
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    Citations

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    Cited by:

    1. Jörg Oechssler & Alex Roomets & Stefan Roth, 2016. "From imitation to collusion: a replication," Journal of the Economic Science Association, Springer;Economic Science Association, vol. 2(1), pages 13-21, May.
    2. 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.
    3. Crosetto, P. & Filippin, A., 2015. "The sound of others: suprising evidence of conformist behavior," Working Papers 2015-07, Grenoble Applied Economics Laboratory (GAEL).
    4. 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.
    5. repec:eee:jeborg:v:140:y:2017:i:c:p:91-119 is not listed on IDEAS
    6. 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.
    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:wly:emetrp:v:85:y:2017:i::p:915-935 is not listed on IDEAS
    9. 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.
    10. 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.
    11. Oechssler, Jörg & Roomets, Alex & Roth, Stefan, 2015. "From Imitation to Collusion - A Comment," Working Papers 0588, University of Heidelberg, Department of Economics.
    12. Marvao, Catarina & Spagnolo, Giancarlo & Buccirossi, Paolo, 2015. "Leniency and Damages," SITE Working Paper Series 32, Stockholm School of Economics, Stockholm Institute of Transition Economics, revised 13 Jan 2016.
    13. repec:gam:jgames:v:9:y:2018:i:1:p:5-:d:129502 is not listed on IDEAS
    14. Marvao, Catarina & Spagnolo, Giancarlo, 2016. "Cartels and Leniency: Taking stock of what we learnt," SITE Working Paper Series 39, Stockholm School of Economics, Stockholm Institute of Transition Economics, revised 16 Nov 2016.
    15. repec:eee:eecrev:v:104:y:2018:i:c:p:185-219 is not listed on IDEAS

    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

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