  Nonlocality, one of the most remarkable aspects of quantum mechanics, is
closely related to Bayesian game theory. Quantum mechanics can offer advantages
to some Bayesian games, if the payoff functions are related to Bell
inequalities in some way. Most of these Bayesian games that have been discussed
are common interest games. Recently the first conflicting interest Bayesian
game is proposed in Phys. Rev. Lett. 114, 020401 (2015). In the present paper
we present three new conflicting interest Bayesian games where quantum
mechanics offers advantages. The first game is linked with Cereceda
inequalities, the second game is linked with a generalized Bell inequality with
3 possible measurement outcomes, and the third game is linked with a
generalized Bell inequality with 3 possible measurement settings.
