The one player guessing game: a diagnosis on the relationship between equilibrium play, beliefs, and best responses
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The one player guessing game: a diagnosis on the relationship between equilibrium play, beliefs, and best responses Ciril Bosch‑Rosa1 · Thomas Meissner2 Received: 9 November 2018 / Revised: 10 December 2019 / Accepted: 2 January 2020 © The Author(s) 2020
Abstract Experiments involving games have two dimensions of difficulty for subjects in the laboratory. One is understanding the rules and structure of the game and the other is forming beliefs about the behavior of other players. Typically, these two dimensions cannot be disentangled as belief formation crucially depends on the understanding of the game. We present the one-player guessing game, a variation of the two-player guessing game (Grosskopf and Nagel 2008), which turns an otherwise strategic game into an individual decision-making task. The results show that a majority of subjects fail to understand the structure of the game. Moreover, subjects with a better understanding of the structure of the game form more accurate beliefs of other player’s choices, and also better-respond to these beliefs. Keywords Guessing game · Strategic thinking · Cognitive sophistication JEL Classification C91 · D12 · D84 · G11
1 Introduction Subjects in laboratory experiments consistently deviate from equilibrium behavior (Camerer 2003). Many models of bounded rationality try to explain these deviations through errors in belief formation (e.g., Nagel 1995; Ho et al. 1998; Weizsäcker
Electronic supplementary material The online version of this article (https://doi.org/10.1007/s1068 3-020-09642-2) contains supplementary material, which is available to authorized users. * Ciril Bosch‑Rosa [email protected] 1
Chair of Macroeconomics, Technische Universität Berlin, Berlin, Germany
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Department of Microeconomics and Public Economics, Maastricht University, Maastricht, The Netherlands
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2003). Another explanation is that subjects fail to fully understand the structure of the game (Chou et al. 2009 refer to this as an absence of “game form recognition”). Generally, when analyzing deviations from equilibrium behavior, one would expect both of these effects to play a role. However it is typically hard (if not impossible) to distinguish between the two, as correct belief formation crucially depends on a correct understanding of the structure of the game. With the help of a novel oneplayer guessing game experiment, we are able to disentangle these two effects, thus improving the understanding of why subjects deviate from equilibrium behavior. An extensive literature has attempted to analyze both belief formation and understanding the structure of the game. Costa-Gomes and Crawford (2006) present subjects with a series of two-player dominance-solvable games and conclude that most subjects understand the games, but play non-equilibrium strategies due to their “simplified models of others’ decisions.” In Costa-Gomes and Weizsäcker (2008) the authors look at subject’s actions and their stated beliefs, and find that subjects
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