A case of evolutionarily stable attainable equilibrium in the laboratory
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A case of evolutionarily stable attainable equilibrium in the laboratory Christoph Kuzmics1
· Daniel Rodenburger2
Received: 17 May 2018 / Accepted: 12 August 2019 © The Author(s) 2019
Abstract We reinvestigate data from the voting experiment of Forsythe et al. (Soc Choice Welf 10:223–247, 1993). In every one of 24 rounds, 28 players were randomly (re)allocated into two groups of 14 to play a voting stage game with or without a preceding opinion poll phase. We find that the null hypothesis that play in every round is given by a particular evolutionarily stable attainable equilibrium of the 14-player stage game cannot be rejected if we account for risk aversion (or a heightened concern for coordination), calibrated in another treatment. Keywords Opinion polls · Elections · Testing · Nash equilibrium · Attainable equilibrium · Evolutionary stability JEL Classification C57 · C72 · D72
1 Introduction The purpose of this paper is to demonstrate, by means of a case study, how careful theory can be helpful in analyzing the data of laboratory experiments of (strategic)
We are very grateful to Thomas Rietz for sharing his data set with us. We thank Marina Agranov, John Duffy, Daniel Houser, Philipp Külpmann, Tom Palfrey and two anonymous referees and one anonymous associate editor for helpful comments and suggestions. Electronic supplementary material The online version of this article (https://doi.org/10.1007/s00199019-01224-5) contains supplementary material, which is available to authorized users.
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Christoph Kuzmics [email protected] Daniel Rodenburger [email protected]
1
University of Graz, Universitätsstrasse 15, 8010 Graz, Austria
2
University of Jena, Carl-Zeiß-Straße 3, 07743 Jena, Germany
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C. Kuzmics, D. Rodenburger
human interaction. For this case study, we chose an experiment performed by Forsythe et al. (1993). The authors’ aim was to perform an exploratory analysis of how opinion polls impact voting behavior in an election and to experimentally assess Duverger’s “law,” see Duverger (1954), that in any majority-rule election only two parties receive votes. They did not perform a full theoretical analysis of the game that the subjects played in the experiment. This experiment is close to perfect for our undertaking for the following reasons. First, it has a very clean and elegant design, which we explain in detail in Sect. 2. Second, it is a somewhat complicated game with a stage game that involves 14 players of three different types. Thus, the game has a large set of possible strategy profiles. This means that the game could possibly have (and indeed does have) a large number of Nash equilibria. Yet, the game has certain symmetries that pose subtle, but important restrictions on the set of feasible strategy profiles and thus on the set of feasible (or attainable) Nash equilibria in the sense of Alos-Ferrer and Kuzmics (2013).1 Third, the game is played recurrently. This means players are repeatedly randomly chosen and matched up from a bigger pool of players to engage i
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