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 paper provides a metaanalysis 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.

Revealed reputations in the finitely repeated prisoners’ dilemma

“…Inconsistent with Kreps et al (1982), they find no evidence that players anticipate opponents' beliefs and attempt to mimic an irrational player, while they find that increased chat about the round in which the opponent will defect is accompanied by an increase in cooperation over the course of the experiment. This finding is also consistent with Embrey et al (2014), who find that players learn to play "threshold strategies" in which they conditionally cooperate for a fixed length of time and then defect. Though players converge to these strategies, unraveling of cooperation occurs very slowly across supergames.…”

“…Strategy s 11 is defined as defecting in every round. In addition to the Kagel and McGee (2014) chat evidence, Embrey, Fréchette, and Yuksel (2014) find that subjects learn with 30 This approach is similar to Radner (1986), in which players have arbitrary beliefs about the opponent's trigger strategy choice in a simultaneous-move FRPD and choose a best-response trigger strategy given these beliefs. 31 Selten and Stoecker (1986) propose an alternative non-Bayesian model of learning from histories of play in FRPDs which predicts a general pattern of behavior that is consistent with our data.…”

Trust and Communication in a Property Rights Dilemma

“…The No-CHAT treatment reported in this paper is reported in both the present paper and Ahn et al where it is referred to as VCP treatment. maximizers of own payoff), or that they are mimicking such preferences for as long as this proves beneficial (Reuben and Suetens, 2012;Embrey, Frechette and Yuksel, 2015). Cooperation gradually decays because some are seen to be less cooperative than others, lowering conditional cooperators' expectations of cooperation (Fischbacher, Gächter and Fehr, 2001;Fischbacher and Gächter, 2010).…”

Risk and Temptation: A Meta-Study on Social Dilemma Games

“…To the extent that we interpret communication as reducing strategic uncertainty this is consistent with our results. In an ongoing meta study Embrey et al (2014) ask whether behaviour in the finitely repeated prisoner's dilemma is consistent with backward induction. They find that the mean time to first defection is predicted well by a "basin of attraction" index which combines elements of risk and temptation.…”

“…Different theories of human cooperation have been proposed (Dresher (1961); Kreps et al (1982); Axelrod (1984); Hamerstein (2003) ;Fischbacher et al (2001)) and different factors favourable or unfavourable to cooperation have been studied in laboratory experiments (Andreoni and Miller (1993); Andreoni and Varian (1999); Bereby-Meyer and Roth (2006); Grimm and Mengel (2009) ;Friedman and Oprea (2012)). While there is agreement in the literature on some matters, the evidence is mixed on a number of other issues such as the role of the matching protocol (Andreoni and Croson (2008)), the importance of backward induction (Embrey et al (2014)) or gender differences (Croson and Gneezy (2009)).…”