# Bertrand-Edgeworth equilibrium: Manipulable residual demand

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## Abstract

In this paper we seek to provide a resolution of the Edgeworth paradox for the case where firms are free to supply less than the quantity demanded, the residual demand function is {\it manipulable} (a generalization of the proportional one) and prices vary over a grid. We demonstrate that a unique equilibrium in pure strategies exist whenever the number of firms is sufficiently large. Interestingly, the equilibrium involves excess production. Moreover, depending on the parameter values, the `folk theorem' of perfect competition may or may not hold. The results go through even if the firms are asymmetric, or produce to order.

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