The article considers the particularities of the relations between companies in the markets of joint products in Russia. These particularities correspond, first, to the production technology, when one input through unit production process gives several products; second, to the consequences of the privatization of production facilities created during the Soviet Union period. The article offers a game theory model that shows how companies may use antitrust authority in their interaction strategies. This in addition to other reasons might explain the amount of cases on the abuse of dominant position where companies, which produce joint products, are involved.