Cooperation in the Finitely Repeated Prisoner’s Dilemma*

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.

Risk and Temptation: A Meta‐study on Prisoner's Dilemma Games

“…Embrey et al (2016), for example, assume that players in the finitely repeated game decide only between GT and the strategy 'allD', where GT denotes grim-trigger, i.e. In these games people have a larger strategy set available.…”

“…Embrey et al (2016), for example, assume that players in the finitely repeated game decide only between GT and the strategy 'allD', where GT denotes grim-trigger, i.e. 14 Based on S 1 , Embrey et al (2016) derive an index that captures the probability that a player must assign to the other player playing GT so that they are indifferent between GT and 'allD' themselves (Blonski et al, 2011;Dal B o and Fr echette, 2011). I denote this strategy set by S 1 = {GT, all D}.…”

“…To the extent that I interpret communication as reducing strategic uncertainty this is consistent with the results. In a recent meta study Embrey et al (2016) ask whether behaviour in the finitely repeated prisoner's dilemma ('partner' setting) is consistent with backward induction. Consistent with the evidence, they find that there are no differences on average between co-operation rates of men and women.…”

“…I cannot say anything about this question, since in all the studies, I consider participants do not know the gender or sex of their opponent. In Section 3, I discuss how they compare the indices used by Murnighan and Roth (1983) and Embrey et al (2016). In a recent meta study Embrey et al (2016) ask whether behaviour in the finitely repeated prisoner's dilemma ('partner' setting) is consistent with backward induction.…”

A note on the equilibria of the unbounded traveler’s dilemma

“…For example, it may account for the reduction in exit times in the centipede due to an increase in the number of players (Rapoport et al, 2003) as well as for the increase in initial rounds of cooperation in the finitely repeated prisoners dilemma due to an increase in the number of repetitions and a reduction in the attractiveness of defecting (Embrey et al, 2014).…”