A Bertrand model of pricing and entry

We analyze an oligopolistic pricing and entry model in which there is a sunk cost of entry and in which firms' outputs are homogeneous. Firms' pure strategies consist of a binary entry decision, and conditional on entry a uniform or non-linear price schedule. There does not exist a pure strategy Nash equilibrium in this model, so we analyze the symmetric mixed strategy equilibrium. The main result is that if there exists a positive sunk cost of entry, then an increase in the number of potential competitors puts more probability weight on higher prices. This result is counter to the usual intuition that underlies current antitrust policy.