Bertrand-Edgeworth equilibrium with a large number of firms

Roy Chowdhury, Prabal (2007): Bertrand-Edgeworth equilibrium with a large number of firms.

Abstract

We examine a model of price competition with strictly convex costs where the firms simultaneously decide on both price and quantity, are free to supply less than the quantity demanded, and there is discrete pricing. If firms are symmetric then, for a large class of residual demand functions, there is a unique equilibrium in pure strategies whenever, for a fixed grid size, the number of firms is sufficiently large. Moreover, this equilibrium price is within a grid-unit of the competitive price. The results go through to a large extent when the firms are asymmetric, or they are symmetric but play a two stage game and the tie-breaking rule is `weakly manipulable'.

• Item Type: MPRA Paper
• Institution: Indian Statistical Institute, Delhi Center
• Language: English
• Keywords: Bertrand equilibrium; Edgeworth paradox; tie-breaking rule; rationing rule; folk theorem of perfect competition
• Subjects: D - Microeconomics > D4 - Market Structure, Pricing, and Design > D41 - Perfect Competition; D - Microeconomics > D4 - Market Structure, Pricing, and Design > D43 - Oligopoly and Other Forms of Market Imperfection; L - Industrial Organization > L1 - Market Structure, Firm Strategy, and Market Performance > L13 - Oligopoly and Other Imperfect Markets

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