Dynamical coopetitive games in pharmaceutical R & D alliances with fractal-like trajectories

In this paper we propose a mathematical model of a coopetitive game in order to show how the adoption of a dynamical co-opetitive framework, which considers cooperation and competition simultaneously and repeatedly, may advance the controllability and convenience of asymmetric research and development (R & D) alliances. Our analysis aims at exploring interactions between young-small firms and large multinational enterprises. We have created this dynamical co-optative model, particularly suitable for the biopharmaceutical industry, considering the literature on asymmetric R & D cooperation and coopetition. In particular, we propose a formal co-opetitive approach, where coopetition becomes a real one-dimensional strategy. We graphically show that cooperative efforts are required and beneficial even though partners potentially compete in the market by depicting the common payoff space they interactively create. Specifically, we study different dynamical interactions between a big pharmaceutical firm, called LF, and a small pharmaceutical firm, called SF. Then, we study the dynamical evolution of the model, by pointing out different fractal-like trajectories, determined by repeating our initial model every year, by means of the gains raised during the preceding year.