Strong Nash equilibrium for oligopoly with quantity and price settings

This paper investigates the existence of strong Nash equilibrium in Cournot and Bertrand oligopoly models with smooth general functions of demand and costs. Strong Nash equilibrium can be considered as the sufficient conditions for firms not to have incentives to collude or to merge. Unlike the concept of Nash equilibrium, the concept of strong Nash equilibrium takes into account the possibility of joint deviations of the players. It gives an intuition of its applicability to the analysis of profitability of coalitions formations. Given the existence of Nash equilibrium in the model, I derive the necessary and sufficient condition for this equilibrium to be SNE in quantity setting model. Thus, Nash equilibrium in the quantity setting oligopoly is strong iff it is a saddle point of demand function or, equivalently, it is a competitive equilibrium. I obtain non-existence result for SNE in price settings oligopoly. The peculiarity of derived conditions leads to the proposition that firms do have incentives to collude or to merge in the most cases. It explains the growth of a number of international M&A deals with the well–known statistics of wide–spread failures among them.