Abstract: According to the phenomena of games among corporations in economic activities, the paper puts forwards a concept of multidimensional game, then describes its characteristics and strategy forms and extends the Nash equilibrium to the multidimensional Nash equilibrium. Meanwhile, a two-dimensional static game model in duopoly and its two-dimensional Nash equilibrium on price strategy are discussed for two kinds of products with a certain substitutive relationship. It is shown that the Bertrand game model, as well as its Nash equilibrium, is the special case of the two-dimensional Bertrand model proposed in this paper.