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In the general setting of modeling for system design it is assumed that all decision-makers cooperate in order to choose the optimal set of the variable design. Sometimes there are conflicts between the different tasks, so that the design process is studied as a multi-player game. In this work we deal with a preliminary application of the design of a wing by studying its optimal configuration by considering some of the standard parameters of the plant design. The choice of the parameters value is done by optimizing two tasks: the weight and the drag. This two-objective optimization problem is approached by a cooperative model, just minimizing the sum of the weight and the drag, as well by a non-cooperative model by means of the Nash equilibrium concept. Both situations will be studied and some test cases will be presented.