The design of complex mechanical systems usually involves multiple mutually coupled disciplines and competing objectives which requires complicated and time-consuming interactive analysis during the design process. Multidisciplinary design optimization (MDO) is a systematic design methodology to improve the design efficiency of complex mechanical systems specifically in non-cooperative design environments. In the other hand game theory is set of mathematical constructs that study the interaction between multiple intelligent rational decision makers. In this paper, a new game theoretic approach is proposed and applied for multi-objective MDO problems in non-cooperative design environments, considering the intrinsic similarity between the MDO and game theory. In this way, genetic programming is used as a surrogate to construct the approximate rational reaction sets (RRS) of players. Furthermore, in order to find the intersection of RRS of players in Nash game models, an objective function is proposed which should be minimized. The effectiveness of the proposed framework is demonstrated by the design of three cases study in the field of engineering design optimization in non-cooperative environment. The results show that the presented approach is able to approximate complicated RRS, in addition has the ability to find multiple Nash solutions when the Nash solution is not a singleton and generally found solutions better than those reported in the literature.