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Existence of Bertrand equilibrium revisited
Authors:Krishnendu Ghosh Dastidar
Affiliation:Centre for Economic Studies and Planning, School of Social Sciences, Jawaharlal Nehru University, New Delhi 110067, INDIA. Email: kgd12@yahoo.com, kgd0302@mail.jnu.ac.in
Abstract:In this paper we reconsider existence of Bertrand equilibrium in a symmetric‐cost, homogenous‐product oligopoly. We prove the following main results. (a) If the cost function is strictly superadditive on [0, ∞) then there exists a pure strategy Bertrand equilibrium. Such Bertrand equilibria are necessarily non‐unique. (b) If the cost function is strictly subadditive on [0, ∞) then there exists no Bertrand equilibrium, either in pure strategies or in mixed strategies.
Keywords:Bertrand equilibrium  pure strategy  mixed strategy  L13  D43
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