<p>We consider bimatrix games where the strategies of the players are described by capacities, and the payoffs are determined by the Sugeno integral. In this model we establish when a row or column is never a best reply. We also study a version of Nash equilibrium, called Sugeno-Nash equilibrium, and show its existence. Finally, we characterize the cooperative payoff space of a bimatrix game attainable by capacities defined on the set of all payoff pairs in the bimatrix game.</p>