Stability of vertically differentiated Cournot and Bertrand-type models when firms are boundedly rational

This paper compares the dynamic of Cournot and Bertrand duopolies with vertical product differentiation and under bounded rationality. We find that an increase in the product differentiation degree destabilizes the Nash equilibrium under quantity competition, while the Bertrand–Nash equilibrium becomes more stable. From a global dynamic analysis, we show that an increase in the firms’ adjustment speed constitutes a source of complexity in both models. There is a cascade of flip bifurcations leading to increasingly complex attractors, and there are global bifurcations generating complex basins of attraction.