Bertrand-Edgeworth Oligopoly in Large Markets

Beth Allen and Martin Hellwig

The Review of Economic Studies, 1986, vol. 53, issue 2, 175-204

Abstract: The relation between perfectly competitive and monopolistically competitive equilibria is analysed for a Bertrand-Edgeworth model of a single market in which capacity constrained firms choose prices as strategies. The market always has a Nash equilibrium in pure or mixed strategies. As the number of firms increases, the corresponding equilibria converge in distribution to a perfectly competitive price. This result provides a justification for perfect competition that is based on an explicit account of price formation. However, monopoly prices persist with a positive but vanishing probability. Regularity or well defined inverse demand functions are not required.

Date: 1986
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