Bertrand-Edgeworth Duopoly with Proportional Residual Demand

Beth Allen and Martin Hellwig

International Economic Review, 1993, vol. 34, issue 1, 39-60

Abstract: A complete characterization is given for the prices charged by Bertrand-Edgeworth duopolists with capacity constraints. In general, for the game in which firms' strategy spaces consist of price offers, Nash equilibrium involves nondegenerate mixed strategi es. Equilibria never extend below the highest competitive price. With tw o firms, the Bertrand-Edgeworth model displays a bias for the highest of several market clearing prices. Moreover, these strategies never stop short of the lowest monopoly price. If firms are of unequal siz e, the larger firm assigns positive probability to a monopoly price, possibly even to several monopoly prices. Copyright 1993 by Economics Department of the University of Pennsylvania and the Osaka University Institute of Social and Economic Research Association.

Date: 1993
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