Bertrand competition and Cournot outcomes: a correction

We received independent comments from Dan Kovenock and Luis Ubeda regarding proofs of Lemma 1 and Theorem 1 in Boccard and Wauthy [Econ. Lett. 68 (2002) 279] (hereafter BW). Claim 4 is indeed poorly stated and proved while in the proof of Theorem 1 payoffs for the price subgame are incorrectly derived. We apologize for these shortcomings. Fortunately the spirit of the proof is not altered. By slightly weakening the scope of the analysis for capacity choice from mixed strategies into pure ones, we are able to shorten the proof that is presented hereafter.