Piecewise Linear Bertrand Oligopoly

Abstract

We describe a modell of price competition between firms with piecewise linear cost functions. Thus, we consider “Bertrand oligopoly”, an n-person noncooperative game in which players choose prices and the market, reflected by a decreasing demand function, reacts discontinuously as total demand concentrates on those firms that offer minimal prices. Firms do not have to be identical. But a notion of similarity between firms is necessary in order to prove the existence of a Nash (-Bertrand) equilibrium. Here we are only interested in an equilibrium involving all firms — the case of subgroups with “similar” members deserves an additional study.