Multi Responses Optimization Through Game TheoryApproach

In this paper, a new game theoretic-based approach is proposed formulti-response optimization problem. Game theory is a useful tool fordecision making in the conflict of interests between intelligent playersin order to select the best joint strategy for them through selecting thebest joint desirability. Present research uses the game theoryapproach via definition of each response as each player and factorsas strategies of each player. This approach can determine the bestpredictor factor sets in order to obtain the best joint desirability ofresponses. For this aim, the signal to noise ratio(SN) index for eachresponse have been calculated with considering the joint values ofstrategies; then obtained SN ratios for each strategy is modeled in thegame theory table. Finally, using Nash Equilibrium, the best strategywhich is the best values of predictor factors is determined. A real caseand a numerical example are given to show the efficiency of theproposed method. In addition, the performance of the proposedmethod is compared with the VIKOR method

Keywords:

Game theory , Multi responses , Signal to noise ratio , Nash equilibrium , VIKOR