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Entry deterrence in the Schmalensee–Salop model

The question of entry deterrence in a Schmalensee type product differentiation market, that is in a market that can be depicted by a circle with circumference of 1, is investigated. It is normally assumed that incumbent firms or brands locate equidistantly whereas an entrant settles exactly in the middle between two firms. For questions of entry deterrence it has become customary to treat the n + 1 model with n incumbents and one entrant as if there were 2n firms located equidistantly. For this to hold, strong assumptions are needed. Using the Salop specification of the Schmalensee model, but without these strong assumptions, the number of entry deterring firms is calculated.