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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 Business School.
  • 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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    More about this item

    Keywords

    repeated games; prisoners dilemma; threshold strategies; basin of attraction;
    All these keywords.

    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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