 The entanglement of players' choices can have the effect of a "contract" by preventing players from profiting from other player's betrayal.The concepts of a quantum player, a zero-sum quantum game and the associated expected payoff were defined by A. Boukas in 1999 (for finite games) and in 2020 by L. Accardi and A. Boukas (for infinite games) within the framework of the spectral theorem for self-adjoint operators on Hilbert spaces.Quantum versions of Von Neumann's minimax theorem were proved.,