Partial collusion fosters minimum product differentiation

We investigate a spatial duopoly in which the firms simultaneously select locations at the beginning of time; once chosen, the locations are fixed forever, but the firms will choose prices in each of a countably infinite succession of time periods. We are interested in equilibrium behavior when the firms will collusively arrange a trigger strategy equilibrium in prices, and will select their locations knowing that a particular such trigger strategy price equilibrium will ensue. Specifically, we restrict our attention to prices that support an outcome on the profit possibility frontier at which the ratio of firm 1's profits to those of firm 2 is positively related to the similar ratio of profits at the single-shot noncooperative equilibrium. For these profit-sharing rules the resulting location equilibrium is unique and involves the pairing of firms at the market center.