Three-players conflicting interest games and nonlocality

We outline the general construction of three-players games with incomplete information which fulfil the following conditions: (i) symmetry with respect to the exchange of the players; (ii) the existence of the upper bound for total payoff resulting from Bell inequalities; (iii) the existence of both fair and unfair Nash equilibria saturating this bound. Conditions (i)$\div$(iii) imply that we are dealing with conflicting interest games. An explicit example of such a game is given. A quantum counterpart of this game is considered which is obtained by keeping the same utilities but replacing classical advisor by a quantum one. It is shown that the quantum game possesses only fair equilibria with strictly higher payoffs than in the classical case. This implies that quantum nonlocality can be used to resolve a conflict between players.
Comment: New version with some references added; all conclusions remain unchanged; 16 pages, no figures