Coalitions in the quantum Minority game: classical cheats and quantum bullies

In a one-off Minority game, when a group of players agree to collaborate they gain an advantage over the remaining players. We consider the advantage obtained in a quantum Minority game by a coalition sharing an initially entangled state versus that obtained by a coalition that uses classical communication to arrive at an optimal group strategy. In a model of the quantum Minority game where the final measurement basis is randomized, quantum coalitions outperform classical ones when carried out by up to four players, but an unrestricted amount of classical communication is better for larger coalition sizes.