The paper considers one approach to modeling the behavior of manufacturers of innovative products and their competitors in the market. The mathematical problem of choosing price strategies of manufacturers of products, taking into account information about changes in demand and prices for them, is posed. An algorithm for solving this problem has been implemented. Initially, when determining the price of a new product, information about the demand and prices of competitors is used. To determine the demand for a new product, the classical model of the diffusion of innovations by F. Bass is used. When a new product appears on the market and its further diffusion, the problem arises of managing prices for a new product and for competing ones. To solve it, it is proposed to consider a two-level combination of problems: one for finding prices and demand for a new product, and the second for determining the pricing strategies of other manufacturers. The parameters of the Bass model are identified, the assessment of the adequacy of the model is obtained, the combination of problems is solved and the pricing strategy is proposed in the paper.