We extend and complete recent work concerning the analytic solution of the minority game. Nash equilibria (NE) of the game have been found to be related to the ground states of a disordered Hamiltonian with replica symmetry breaking (RSB), signalling the presence of a large number of NE. Here we study the number of NE both analytically and numerically. We then analyse the stability of the recently obtained replica-symmetric solution and, in the region where it becomes unstable, derive the solution within one-step RSB approximation. We are finally able to draw a detailed phase diagram of the model.