Piecewise Linear Bertrand Oligopoly
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.
KeywordsCost Function Demand Function Price Competition Profit Function Bertrand Equilibrium
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