Cooperation in the Finitely Repeated Prisoner’s Dilemma

Matthew Embrey, Guillaume R Fréchette and Sevgi Yuksel

The Quarterly Journal of Economics, 2018, vol. 133, issue 1, 509-551

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.

Date: 2018
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The Quarterly Journal of Economics is currently edited by Robert J. Barro, Lawrence F. Katz, Nathan Nunn, Andrei Shleifer and Stefanie Stantcheva

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