Infinitely repeated games in the laboratory: four perspectives on discounting and random termination
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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.
KeywordsInfinitely repeated games Discounting Random termination Prisoner’s dilemma
JEL ClassificationC9 C72 C73 C91 C92
We would like to thank two anonymous referees, David Cooper, Drew Fudenberg, Ryan Oprea, Andrew Schotter, Ekatarina Sherstyuk, Alistair Wilson, participants at the 2011 ESA Conference and the NYU experimental group for helpful comments, Emanuel Vespa for his help developing the ztree code to conduct the experiment; also CESS and the C.V. Starr Center for financial support. Fréchette gratefully acknowledges the support of the NSF via Grants SES-0924780, SES-1225779, and SES-1558857.
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