A note on Bertrand competition with asymmetric fixed costs

We consider a model of Bertrand competition with fixed costs of entry or production. We show that, contrary to most of the existing literature that focuses on symmetric firms and hence symmetric equilibria, if we allow these fixed costs to be different for each firm, competition may prevent higher cost firms from entering this market, even if the differences in cost are small. Specifically, all firms except for the two with the lowest fixed cost find entry blockaded, and the two firms with the lowest fixed costs compete ignoring the threat of potential entry.