Exploring Dynamic Behavior in a Competition Duopoly Game Based on Corporate Social Responsibility

This study investigates dynamic behaviors within a competition Cournot duopoly framework incorporating consumer surplus, and social welfare through the bounded rationality method. The distinctive aspect of the competition game is the incorporation of discrete difference equations into the players’ optimization problems. Both rivals seek to achieve optimal quantity outcomes by maximizing their respective objective functions. The first firm seeks to enhance the average between consumer surplus and its profit, while the second firm focuses on its profit optimization with a social welfare component. The game map features four fixed points, with one being the Nash equilibrium point at the intersection of marginal objective functions. Our analysis explores equilibrium stability, dynamic complexities, basins of attraction, and the emergence of chaos through double routes via flip bifurcation and Neimark-Sacker bifurcations. We observe that increased adjustment speeds can destabilize the system, leading to a richness of dynamic complexity.