A note on the equilibria of an economic model with local competition "à la Cournot"

Guirao and Rubio [6] introduces an economic model, which generalizes the classical duopoly of Cournot type, where the competitors are located around a circle or a line and each rm competes à la Cournot with its right and left neighboring. For the case of having three and four players we describe completely the bifurcations of equilibria in terms of the production costs of each rm and we study the stability of them. Moreover, for the case of four players we provide some information on the two periodic orbits of the system.