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.