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Playing a symmetric bi-matrix game is usually physically implemented bysharing pairs of 'objects' between two players. A new setting is proposed thatexplicitly shows effects of quantum correlations between the pairs on thestructure of payoff relations and the 'solutions' of the game. The settingallows a re-expression of the game such that the players play the classicalgame when their moves are performed on pairs of objects having correlationsthat satisfy the Bell's inequalities. If players receive pairs having quantumcorrelations the resulting game cannot be considered another classicalsymmetric bi-matrix game. Also the Nash equilibria of the game are found to bedecided by the nature of the correlations.Comment: minor correction

Quantum correlations and Nash equilibria of a bi-matrix game