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A growing experimental literature studies the determinants of cooperation in infinitely repeated games, tests different predictions of the theory, and suggests an empirical solution to the problem of multiple equilibria. To provide a robust description of the literature’s findings, we gather and analyze a metadata set of experiments on infinitely repeated prisoner’s dilemma games. The experimental data show that cooperation is affected by infinite repetition and is more likely to arise when it can be supported in equilibrium. However, the fact that cooperation can be supported in equilibrium does not imply that most subjects will cooperate. High cooperation rates will emerge only when the parameters of the repeated game are such that cooperation is very robust to strategic uncertainty. We also review the results regarding the effect of imperfect monitoring, changing partners, and personal characteristics on cooperation and the strategies used to support it.

A usual criticism of the theory of infinitely repeated games is that it does not provide sharp predictions since there may be a multiplicity of equilibria. To address this issue, we present experimental evidence on the evolution of cooperation in infinitely repeated prisoner's dilemma games as subjects gain experience. We show that cooperation may prevail in infinitely repeated games, but the conditions under which this occurs are more stringent than the subgame perfect conditions usually considered or even a condition based on risk dominance. (JEL C71, C73)

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.

We study the experimental play of the repeated prisoner's dilemma when intended actions are implemented with noise. In treatments where cooperation is an equilibrium, subjects cooperate substantially more than in treatments without cooperative equilibria. In all settings there was considerable strategic diversity, indicating that subjects had not fully learned the distribution of play. Furthermore, cooperative strategies yielded higher payoffs than uncooperative strategies in the treatments with cooperative equilibria. In these treatments successful strategies were \"lenient\" in not retaliating for the first defection, and many were \"forgiving\" in trying to return to cooperation after inflicting a punishment.

Blockchains are distributed ledgers, operated within peer-to-peer networks. We model the proof-of-work blockchain protocol as a stochastic game and analyze the equilibrium strategies of rational, strategic miners. Mining the longest chain is a Markov perfect equilibrium, without forking, in line with Nakamoto (2008). The blockchain protocol, however, is a coordination game, with multiple equilibria. There exist equilibria with forks, leading to orphaned blocks and persistent divergence between chains. We also show how forks can be generated by information delays and software upgrades. Last we identify negative externalities implying that equilibrium investment in computing capacity is excessive.

This article reports the results of a meta-study of 96 prisoner's dilemma studies comprising more than 3,500 participants. I disentangle the role of 'risk' (to co-operate unilaterally) and 'temptation' (to defect against a co-operator) and find that: (i) an index of risk best explains the variation in cooperation rates across one-shot games, while (ii) an index of temptation best explains the variation in finitely repeated games. Risk and temptation indices also affect gender comparisons. Women are more co-operative than the average man if risk is low and less co-operative if risk is high. There are no gender differences on average.

We use a novel experimental design to reliably elicit subjects’ strategies in an infinitely repeated prisoner’s dilemma experiment with perfect monitoring. We find that three simple strategies represent the majority of the chosen strategies: Always Defect, Tit-for-Tat, and Grim. In addition, we identify how the strategies systematically vary with the parameters of the game. Finally, we use the elicited strategies to test the ability to recover strategies using statistical methods based on observed round-by-round cooperation choices and find that this can be done fairly well, but only under certain conditions.

In the presence of litigation-facing suppliers, the supply chain relationship is at risk. Suppliers with principal customers (dependent suppliers) have a higher concentration of sales to customers, and they are more at risk relative to suppliers without principal customers (non-dependent suppliers). As a result, we predict and find that litigation disclosure patterns differ for the two supplier types: dependent suppliers are more likely to delay bad news and accelerate good news related to litigation outcomes, compared to non-dependent suppliers. Such strategic disclosure patterns in our end-game setting are opposite to those documented in the existing supply chain literature for the repeated-game setting (for example, Hui, Klasa, and Yeung 2012).

Equilibrium payoff bounds from reputation effects are derived for repeated games with imperfect public monitoring in which a long-run player interacts frequently with a population of short-run players and the monitoring technology scales with the length of the period of interaction. The bounds depend on the monitoring technology through the flow of information, a measure of signal informativeness per unit of time based on relative entropy. Examples are shown where, under complete information, the set of equilibrium payoffs of the long-run player converges, as the period length tends to zero, to the set of static equilibrium payoffs, whereas when the game is perturbed by a small ex ante probability on commitment types, reputation effects remain powerful in the high-frequency limit.

This paper compares behavior under four different implementations of infinitely repeated games in the laboratory: the standard random termination method [proposed by Roth and Murnighan (J Math Psychol 17:189–198, 1978 )] and three other methods that de-couple the expected number of rounds and the discount factor. Two of these methods involve a fixed number of repetitions with payoff discounting, followed by random termination [proposed by Sabater-Grande and Georgantzis (J Econ Behav Organ 48:37–50, 2002 )] or followed by a coordination game [proposed in (Andersson and Wengström in J Econ Behav Organ 81:207–219, 2012 ; Cooper and Kuhn in Am Econ J Microecon 6:247–278, 2014a )]. We also propose a new method—block random termination—in which subjects receive feedback about termination in blocks of rounds. We find that behavior is consistent with the presence of dynamic incentives only with methods using random termination, with the standard method generating the highest level of cooperation. Subject behavior in the other two methods display two features: a higher level of stability in cooperation rates and less dependence on past experience. Estimates of the strategies used by subjects reveal that across implementations, even when the discount rate is the same, if interactions are expected to be longer defection increases and the use of the Grim strategy decreases.