  While it is known that shared quantum entanglement can offer improved
solutions to a number of purely cooperative tasks for groups of remote agents,
controversy remains regarding the legitimacy of quantum games in a competitive
setting--in particular, whether they offer any advantage beyond what is
achievable using classical resources. We construct a competitive game between
four players based on the minority game where the maximal Nash-equilibrium
payoff when played with the appropriate quantum resource is greater than that
obtainable by classical means, assuming a local hidden variable model. The game
is constructed in a manner analogous to a Bell inequality. This result is
important in confirming the legitimacy of quantum games.
