WE STUDY QUANTUM STRATEGIES IN GAMES OF INCOMPLETE INFORMATION USING A FORMALISM OF GAME THEORY BASED ON MULTI-SECTOR PROBABILITY MATRIX. WE ANALYZE AN EXTENSION OF THE WELL-KNOWN GAME OF BATTLE OF SEXES USING AN EXTENDED WERNER-LIKE STATE FOCUSING IN HOW ITS MIXEDNESS AND ENTANGLEMENT AFFECT THE BAYESIAN NASH PAYOFFS OF THE PLAYER. IT IS SHOWN THAT ENTANGLEMENT IS NEEDED TO OUTPERFORM CLASSICAL PAYOFFS BUT NOT ALL ENTANGLED STATES ARE USEFUL DUE TO THE PRESENCE OF MIXEDNESS. A THRESHOLD FOR THE MIXEDNESS PARAMETER AND THE MINIMUM ENTANGLEMENT VALUE WERE FOUND.