Nash versus coarse correlation
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Nash versus coarse correlation Konstantinos Georgalos1 · Indrajit Ray2,3 · Sonali SenGupta1 Received: 17 January 2018 / Revised: 25 January 2020 / Accepted: 3 February 2020 © The Author(s) 2020
Abstract We run a laboratory experiment to test the concept of coarse correlated equilibrium (Moulin and Vial in Int J Game Theory 7:201–221, 1978), with a two-person game with unique pure Nash equilibrium which is also the solution of iterative elimination of strictly dominated strategies. The subjects are asked to commit to a device that randomly picks one of three symmetric outcomes (including the Nash point) with higher ex-ante expected payoff than the Nash equilibrium payoff. We find that the subjects do not accept this lottery (which is a coarse correlated equilibrium); instead, they choose to play the game and coordinate on the Nash equilibrium. However, given an individual choice between a lottery with equal probabilities of the same outcomes and the sure payoff as in the Nash point, the lottery is chosen by the subjects. This result is robust against a few variations. We explain our result as selecting risk-dominance over payoff dominance in equilibrium. Keywords Correlation · Coordination · Lottery · Risk dominance JEL Classification C72 · C91 · C92 · D63 · D83
This paper supersedes the previous version titled Coarse Correlation and Coordination in a Game: An Experiment. We wish to thank all seminar and conference participants at Cardiff, Jadavpur, Queen Mary, Royal Holloway and Visva-Bharati, for stimulating conversations and helpful comments, and particularly, Antonio Cabrales, Timothy Cason, David Cooper, Nicholas Feltovich, Kim Kaivanto, Friederike Mengel, Hervé Moulin, Anders Poulsen and Tridib Sharma for their constructive suggestions on a previously-circulated version. We are enormously grateful to two anonymous referees and the editors of this journal, Lata Gangadharan and Roberto Weber, for their constructive suggestions in successive rounds that helped us to prepare this final version. We also would like to thank the Department of Economics at the Lancaster University Management School for the funding and the Lancaster Experimental Economics Lab (LExEL), Lancaster University, for the use of their experimental laboratory, to run this experiment. Electronic supplementary material The online version of this article (https://doi.org/10.1007/s1068 3-020-09647-x) contains supplementary material, which is available to authorized users. * Indrajit Ray [email protected]; [email protected] Extended author information available on the last page of the article
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1 Introduction The problem of multiple equilibria and coordination in games, even in a 2 × 2 game, has been one of the major themes of research in experimental economics (Cooper et al. 1989, 1990, 1992; Van Huyck et al. 1990, 1991, 1992; Straub 1995). Experimental research suggests that players are able to coordinate if they are helped to do so (see Devetag and Ortmann 2007 for a survey) or by
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