In this paper, a new approach based on game theory has been proposed to multi responses problem optimization. Game theory is a useful tool for decision making in the conflict of interests between intelligent players in order to select the best joint strategy for them through selecting the best joint desirability. Present research uses the game theory approach via definition of each response as each player and factors as strategies of each player. This approach cans determine the best predictor factor sets in order to obtain the best joint desirability of responses. For this aim, the signal to noise ratio(SN) index for each response have been calculated with considering the joint values of strategies then obtained SN ratios for each strategy is modeled in the game theory table. Finally, using Nash Equilibrium method, the best strategy which is the best values of predictor factors is determined. A real case and a numerical example are given to show the efficiency of the proposed method. In addition, the performance of the proposed method is compared with the VIKOR method.

Keywords: Game theory, multi responses, signal to noise ratio, Nash equilibrium, VIKOR

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