Price regulation in a spatial duopoly with possible non-buyers

If the price is regulated in a spatial duopoly where consumers have a finite upper bound as to the price they are willing to pay for the differentiated product, in most cases the Principle of Minimum Differentiation does not apply, Depending on the market structure firms either (i) form local monopolies, or (ii) differentiate intermediately, or (iii) agglomerate at the market centre. Minimum differentiation is never total-surplus-maximizing nor desired by firms. In most cases the regulator sets a price below that maximizing industry profits. For a substantial range of market configurations the regulated (first-best) price exceeds marginal cost. This induces firms to serve a larger part of the market.