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We consider a Bertrand-Edgeworth model of price competition. Firms have identical and constant marginal costs and finite exogeneous capacities. Firms choose prices. Our interest is in the set of those prices which are left over after the iterated elimination of dominated strategies. We show that in two circumstances this set will be close to the set containing only the marketclearing (Walrasian) price: (i) if any n − 1 out of n firms assumed to be in the market have sufficient capacity to cover demand at marginal costs; (ii) if any given total capacity is owned by a very large number of very small firms.