Dynamic study of the duopoly market stability based on open innovation rate integration and intellectual property

In this paper, we present a model detailing the benefits of two competing firms in a duopoly market, where profit maximization is linked to their production levels using the Cournot method. Our primary objective is to develop a collaborative strategy within the framework of open innovation to optimize their profits. Furthermore, we analyze how these firms can integrate an additional source of revenue in the form of intellectual property, without negatively impacting their open innovation strategies. To achieve this, we conducted a dynamic study of these strategies by introducing this intellectual property, to assess the impact of its components, such as patent licensing fees and royalties, on the equilibrium of strategies adopted by these firms. Our aim is to provide recommendations for optimal management of this intellectual property, thus enabling firms to fully leverage its benefits while preserving their competitive position in the market.