A Coopetitive Game Theory Approach to Asymmetric R&D Alliances

The paper proposes a mathematical model of coopetitive game that analyzes general asymmetric R&D alliances. The coopetitive point of view, which considers 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 introduced by David Carfì, we adopt an analysis paying attention to some of the most debated questions and some of the topics not yet covered in the literature. A mathematical model of coopetitive game is particularly suitable for exploring a complex type of asymmetric R&D alliances. We propose a formal coopetitive approach, where the coopetitive variable of the model is a real variable; a cooperative effort is required even though partners are potentially competitors in the marketplace and shape the common payoff space that they create. To maximize profit we have suggested; first of all, a complete Pareto analysis (David Carfì), secondly - to share conveniently and fairly the utilities - we propose a Kalai Smorodinsky solution of the bargaining decision problem, in which the decisional constraint is the Pareto boundary of maximum collective utility.