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Asymmetric guessing games

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Zafer Akin
Zafer Akin
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This paper theoretically and experimentally investigates the behavior of asymmetric players in guessing games. The asymmetry is created by introducing r>1r>1r>1 replicas of one of the players. Two-player and restricted N-player cases are examined in detail. Based on the model parameters, the equilibrium is either unique in which all players choose zero or mixed in which the weak player (r=1r=1) imitates the strong player (r>1r>1r>1). A series of experiments involving two and three-player repeated guessing games with unique equilibrium is conducted. We find that equilibrium behavior is observed less frequently and overall choices are farther from the equilibrium in two-player asymmetric games in contrast to symmetric games, but this is not the case in three-player games. Convergence towards equilibrium exists in all cases but asymmetry slows down the speed of convergence to the equilibrium in two, but not in three-player games. Furthermore, the strong players have a slight earning advantage over the weak players, and asymmetry increases the discrepancy in choices (defined as the squared distance of choices from the winning number) in both games.
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Asymmetric guessing games
Zafer Akin
1
Accepted: 26 August 2022 / Published online: 27 September 2022
©The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature
2022
Abstract
This paper theoretically and experimentally investigates the behavior of asymmetric
players in guessing games. The asymmetry is created by introducing r[1 replicas
of one of the players. Two-player and restricted N-player cases are examined in
detail. Based on the model parameters, the equilibrium is either unique in which all
players choose zero or mixed in which the weak player (r¼1) imitates the strong
player (r[1). A series of experiments involving two and three-player repeated
guessing games with unique equilibrium is conducted. We find that equilibrium
behavior is observed less frequently and overall choices are farther from the equi-
librium in two-player asymmetric games in contrast to symmetric games, but this is
not the case in three-player games. Convergence towards equilibrium exists in all
cases but asymmetry slows down the speed of convergence to the equilibrium in two,
but not in three-player games. Furthermore, the strong players have a slight earning
advantage over the weak players, and asymmetry increases the discrepancy in
choices (defined as the squared distance of choices from the winning number) in both
games.
Keywords Guessing game · Asymmetry · Convergence · Game theory ·
Experimental economics
1 Introduction
Any investment situation that can be considered a complex game with its potentially
high number of players and strategies, requires both deep reasoning and strategic
thinking due to the mutual determination of the resulting outcomes. The “guessing”
or “p-beauty contest”games (inspired by Keynes, 1936) capture this insight and
resemble decision-making in financial markets. In the standard N-player guessing
&Zafer Akin
zakin@aud.edu
1
Department of Decision Sciences and Economics, American University in Dubai, Dubai, UAE
123
Theory and Decision (2023) 94:637–676
https://doi.org/10.1007/s11238-022-09908-6(0123456789().,-volV)(0123456789().,-volV)
Content courtesy of Springer Nature, terms of use apply. Rights reserved.
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