Abstract. The models of quantitative competition under duopoly of differentiated products in which the controlled variable of the producer (production amount) is considered a random variable is proposed. The class of distributions of random production amounts that guarantees the existence of solutions of non-cooperative games is described. Explicit formulas are obtained to find a “corrected” Nash equilibrium first for a duopoly with random controlled variable of one producer and then for both producers. The method for estimating the measure of risk of producer is proposed.

Keywords: quantitative competition, duopoly, differentiated product, “corrected” Nash equilibrium, risk level.