  Interesting connection has been established between two apparently unrelated
concepts, namely, quantum nonlocality and Bayesian game theory. It has been
shown that nonlocal correlations in the form of advice can outperform classical
equilibrium strategies in common interest Bayesian games and also in
conflicting interest games. However, classical equilibrium strategies can be of
two types, fair and unfair. Whereas in fair equilibrium payoffs of different
players are same, in unfair case they differ. Advantage of nonlocal correlation
has been demonstrated over fair strategies. In this work we show that quantum
strategies can outperform even the unfair classical equilibrium strategies. For
this purpose we consider a class of two players games which as a special case
includes the conflicting game proposed in [Phys. Rev. Lett. 114, 020401
(2015)]. These games can have both fair and unfair classical equilibria and
also can have only unfair ones. We provide a simple analytic characterization
of the nonlocal correlations that are advantageous over the classical
equilibrium strategies in these games.
