Heterogeneous trembles and model selection in the strategy frequency estimation method
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Heterogeneous trembles and model selection in the strategy frequency estimation method James R. Bland1 Received: 14 February 2019 / Revised: 20 July 2020 / Accepted: 27 October 2020 / Published online: 19 November 2020 © Economic Science Association 2020
Abstract The strategy frequency estimation method (Dal Bó and Fréchette in Am Econ Rev 101(1):411-429, 2011; Fudenberg in Am Econ Rev 102(2):720-749, 2012) allows us to estimate the fraction of subjects playing each of a list of strategies in an infinitely repeated game. Currently, this method assumes that subjects tremble with the same probability. This paper extends this method, so that subjects’ trembles can be heterogeneous. Out of 60 ex ante plausible specifications, the selected model uses the six strategies described in Dal Bó and Fréchette (2018), and allows the distribution of trembles to vary by strategy. Keywords Prisoner’s dilemma · Strategy frequency estimation method · Mixture model · Model selection · Trembles JEL Classification C15 · C52 · C57 · C73
I would like to thank Huanren Zhang and Guillaume Fréchette for valuable advice at the beginning of this project, and Aleksandr Alekseev, Xiaoxue Sherry Gao, John Ham, an anonymous reviewer, and attendees of the 2018 North American Economic Science Association meeting for helpful comments. I acknowledge funding support from the University of Toledo Kohler International Grants. Electronic supplementary material The online version of this article (https://doi.org/10.1007/s4088 1-020-00097-y) contains supplementary material, which is available to authorized users. * James R. Bland [email protected] 1
Department of Economics, The University of Toledo, Toledo, USA
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1 Introduction A common issue with experiments studying infinitely repeated games is that while we observe subjects’ actions, we do not observe the strategies that generated these actions.1 We can, however, infer strategies from actions using the Strategy Frequency Estimation Method (SFEM) (Dal Bó and Fréchette 2011; Fudenberg et al. 2012). The most commonly used SFEM in the literature assumes a finite, pre-determined list of strategies, and estimates the fraction of subjects who behave according to each strategy. Others’ extensions of this have expanded the list of strategies (Sherstyuk et al. 2013; Rand et al. 2015; Aoyagi et al. 2018; Fréchette and Yuksel 2017), added mixed or behavioral strategies (Fudenberg et al. 2012; Dvorak and Fehrler 2020), and permitted subjects to change their strategies between rounds (Dvorak and Fehrler 2017).2 Out of both econometric necessity (the likelihood function is flat if just one subject’s choices are inconsistent with all strategies under consideration) and behavioral plausibility (following a strategy might be cognitively difficult), the SFEM does not assume that subjects implement their strategy perfectly. Instead, subjects are assumed to tremble with positive probability. For a 2-action stage game like the Prisoner’s dilemma, this means that subje
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