Complete study of a Coopetitive R D Alliance

The paper proposes a mathematical model of coopetitive game that ana lyzes general asymmetric R D alliances The coopetitive point of view which con siders both collaboration and competition together allows to analyze the functioning of alliances that arise between small and large firms Starting from the economic models developed in managerial doctrine and from the model of coopetitive game in troduced by David Carf we adopt a mathematical analysis paying attention to some of the most debated quantitative questions and some analytical topics scarcely covered in the literature a mathematical model of coopetitive game particularly suitable for exploring a complex type of asymmetric R D alliances We propose a formal coopet itive approach with corresponding numerical example where the coopetitive variable of the model is a real variable A cooperative effort is suggested even if partners are potentially competitors in the marketplace and they could shape the payoff space by the coopetitive approach To maximize profits we suggested first of all a complete Pareto analysis introduced by David Carf secondly to share conveniently and fairly the utilities we propose a Kalai Smorodinsky solution of the bargaining deci sion problem in which the decisional constraint is the Pareto boundary of maximum collective utility