Michael R. Baye and John Morgan, “Winner-Take-All Price Competition,” Economic Theory, Vol 19 (2002), pp. 271-282.
We analyze an oligopoly model of homogeneous product price competition that allows for discontinuities in demand and/or costs. Conditions under which only zero profit equilibrium outcomes obtain in such settings are provided. We then illustrate through a series of examples that the conditions provided are “tight” in the sense that their relaxation leads to positive profit outcomes.
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