This paper discusses the role of technological spillovers and technological races in dynamic strategic interactions setup. Two multiproduct regional monopolies invest simultaneously into new products creation and into further development of the quality of these products. They can benefit from the costless technological spillover in the development of each such a product in the case the others quality is higher. At the same time they cooperate in the joint creation of new products. The dynamic interaction in this setting previously considered only the situation with one of the monopolies being the constant technological leader. In this paper the full spectrum of possible equilibria of the game is studied. It is demonstrated, that the closer in terms of technology two firms are to each other, the more intense is the competition and overall research output is threatened, resembling inverted-U relationship between technology and competition.