Abstract: According to the theory of dynamic multidimensional game,the paper discusses dynamic two-dimensional output-price game model with complete information for two kinds of products with certain substitution between two firms It is proved that dynamic independent output-price game model for two kinds of products without certain substitution between two firms is a special case of this two-dimensional game model,and that equilibrium strategies in which two enterprises independently participate in game for every kind of product are inferior to equilibrium strategies in which each enterprise considers two kinds of product jointly to participate in the two-dimensional game. The results show that firms want to think over its substitution when two firms take two-dimensional game for a kind of product output strategies with unsaturated market and another kind of product price strategies with saturated market, thus selected output and price strategies are optimal strategies.

Key words: multidimensional game, equilibrium, substitutive relationship, output, price, dynamic