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Games with the total bandwagon property meet the Quint–Shubik conjecture

Jun Honda ()
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Jun Honda: University of Innsbruck, Universitätsstraße 15

International Journal of Game Theory, 2018, vol. 47, issue 3, 893-912

Abstract: Abstract This paper revisits the total bandwagon property (TBP) introduced by Kandori and Rob (Games Econ Behav 22:30–60, 1998). With this property, we characterize the class of two-player symmetric $$n\times n$$ n × n games, showing that a game has TBP if and only if the game has $$2^{n}-1$$ 2 n - 1 symmetric Nash equilibria. We extend this result to bimatrix games by generalizing TBP. This sheds light on the (wrong) conjecture of Quint and Shubik (Int J Game Theory 26:353–359, 1997) that any nondegenerate $$n\times n$$ n × n bimatrix game has at most $$2^{n}-1$$ 2 n - 1 Nash equilibria. We also provide an equilibrium selection criterion to two subclasses of games with TBP.

Keywords: Bandwagon; Nash equilibrium; Number of equilibria; Coordination game; Equilibrium selection (search for similar items in EconPapers)
JEL-codes: C62 C72 C73 (search for similar items in EconPapers)
Date: 2018
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Handle: RePEc:spr:jogath:v:47:y:2018:i:3:d:10.1007_s00182-017-0609-3