Relative profit maximization and Bertrand equilibrium with convex cost functions
The authors study pure strategy Bertrand equilibria in a duopoly in which two firms produce a homogeneous good with convex cost functions, and they seek to maximize the weighted sum of their absolute and relative profits. They show that there exists a range of the equilibrium price in duopolistic equilibria. This range of the equilibrium price is narrower and lower than the range of the equilibrium price in duopolistic equilibria under pure absolute profit maximization, and the larger the weight on the relative profit, the narrower and lower the range of the equilibrium price. In this sense relative profit maximization is more aggressive than absolute profit maximization.
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- Dastidar, Krishnendu Ghosh, 1995. "On the Existence of Pure Strategy Bertrand Equilibrium," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 5(1), pages 19-32, January.
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- Satoh, Atsuhiro & Tanaka, Yasuhito, 2014. "Relative profit maximization and Bertrand equilibrium with quadratic cost functions," MPRA Paper 55893, University Library of Munich, Germany.
- Matsumura, Toshihiro & Matsushima, Noriaki & Cato, Susumu, 2013. "Competitiveness and R&D competition revisited," Economic Modelling, Elsevier, vol. 31(C), pages 541-547. Full references (including those not matched with items on IDEAS)
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