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Existence of Bertrand equilibrium revisited
Author(s) -
Dastidar Krishnendu Ghosh
Publication year - 2011
Publication title -
international journal of economic theory
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.351
H-Index - 11
eISSN - 1742-7363
pISSN - 1742-7355
DOI - 10.1111/j.1742-7363.2011.00166.x
Subject(s) - subadditivity , bertrand competition , superadditivity , mathematical economics , economics , symmetric equilibrium , markov perfect equilibrium , oligopoly , mathematics , equilibrium selection , nash equilibrium , game theory , repeated game , cournot competition , combinatorics
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.