Einer Elhauge & Abraham L. Wickelgren, Anti-Competitive Exclusion and Market Division Through Loyalty Discounts (U. Texas L. & Econ. Res. Paper No. 216, Sept. 3, 2011).
Abstract: We show that loyalty discounts create an externality among buyers even without economies of scale or downstream competition, and whether or not buyers make any commitment. Each buyer who signs a loyalty discount contract softens competition and raises prices for all buyers. We prove that, provided the entrant’s cost advantage is not too large, with enough buyers, this externality implies that in any equilibrium some buyers sign loyalty discount contracts, reducing total welfare. Moreover, if loyalty discounts require buyers to commit to buy only from the incumbent, there exists an equilibrium in which all buyers sign, foreclosing the rival entirely. As a result, the incumbent can use loyalty discounts to increase its profit and decrease both buyer and total welfare.