• Bertrand
• Cournot
• Nash-equilibria
• oligopoly

This thesis delves into the analysis of equilibria in oligopolistic markets, with a focus on the Bertrand and Cournot models. Initially, we perform a preliminary analysis of the Nash equilibria of these individual models, and of the mixed-market scenario comprising two firms, one operating under the Bertrand model and the other under the Cournot model.
Building upon these foundational analyses, the thesis progresses to explore oligopolies with more than two firms, incorporating a combination of Bertrand and Cournot behaviors. To analyze equilibria within these complex settings, Nash equilibrium conditions are reformulated by using Ky Fan inequalities and descent algorithms are exploited for their computation.
Furthermore, the thesis includes empirical investigations via market simulations. To analyze the behavior at equilibria, we apply the proposed algorithm to appropriately generated datasets, leading to additional insight into the dynamics of oligopolistic markets.
By integrating theoretical analyses, mathematical modeling, and empirical experimentation, this research contributes to a deeper understanding of oligopoly dynamics and offers practical insights for decision-making in competitive markets.