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

Author

Listed:
• Jun Honda

(University of Innsbruck, Universitätsstraße 15)

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.

Suggested Citation

• Jun Honda, 2018. "Games with the total bandwagon property meet the Quint–Shubik conjecture," International Journal of Game Theory, Springer;Game Theory Society, vol. 47(3), pages 893-912, September.
• Handle: RePEc:spr:jogath:v:47:y:2018:i:3:d:10.1007_s00182-017-0609-3
DOI: 10.1007/s00182-017-0609-3
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Keywords

Bandwagon; Nash equilibrium; Number of equilibria; Coordination game; Equilibrium selection;
All these keywords.

JEL classification:

• C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
• C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
• C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games

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