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

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.