Symmetries of Imperfect Competition on a Circle

Taking location as given, we study imperfect competition on a circular city. In Bertrandoligopoly, we identify price harmonics as a function of firm unit costs and locations. The sumof oligopoly profits is larger when costs and/or locations are more dispersed in the ‘dihedralmajorization’ sense. This also tends to be the case in which prices are more variable. We studyhow phase shifts between cost parameters and inter-firm distance parameters change productionand oligopoly profits. An exact characterization of production patterns is developed in terms ofthe eigenvalues for what we call the price harmonics matrix. The same techniques are applied toCournot oligopoly with spatial externalities on Circular City. Solutions are compared withmonopoly and with first-best. Production patterns can differ markedly when cost spillovers arenegative.[...]