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Piecewise Linear Bertrand Oligopoly

In: Perspectives on Operations Research

Author

Listed:
  • Joachim Rosenmüller

    (University of Bielefeld)

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.

Suggested Citation

  • Joachim Rosenmüller, 2006. "Piecewise Linear Bertrand Oligopoly," Springer Books, in: Martin Morlock & Christoph Schwindt & Norbert Trautmann & Jürgen Zimmermann (ed.), Perspectives on Operations Research, pages 425-443, Springer.
    • Handle: RePEc:spr:sprchp:978-3-8350-9064-4_23
    DOI: 10.1007/978-3-8350-9064-4_23
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