A Cournot-Bertrand Model Using Various Products

Imperfect competition represent a known issue on modern economic analysis. Monopoly case classical induce a worse solution for consumer side but in the oligopoly competition scenario it will be possible to obtain a solution close to perfect competition situation. In this case, two of the most well-known game theory models in imperfect competition are Cournot model, respectively Bertrand model. First one offers an output equilibrium solution, while the second one, advocating for price competition, highlights an equilibrium solution in terms of price. Alongside these two models, in the last period, we can also note an increasing interest for the Cournot-Bertrand mixed scenario. All these three behavioral types can be identified in the real market. This paper aims to analyze a duopoly market, with linear demand and cost functions, as well as product differentiation characteristics, where a Cournot behavior is adopted by one firm and a Bertrand behavior by the other one. Both firms manage to survive on the market and a stable equilibrium will be manifested if there is sufficient product differentiation. In a very low product differentiation / very high product homogeneity scenario instead, the adjustment process proves to be a divergent one, undermining the equilibrium stability. In a homogenous products context, the Cournot-type firm will produce the perfectly competitive output level and the Bertrand-type competitor will leave the market. The selling price will match the marginal cost and duopoly profit will be null. Even with just one firm on the market, the basic threat of a Bertrand – type potential competitor, warrants a very prudential behavior while also further ensuring the perfect competitive outcome level. The paper is looking to also analyse in detail the existence of Nash equilibrium point, its local stability and uniqueness, as well as the product differentiation impact on this equilibrium and players surviving potential on the market. The final part of the paper contains a simulated study case for price, quantity and profit evolution for various values of model parameters.