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We show that loyalty discounts create an externality among buyers because each buyer who signs a loyalty discount contract softens competition and raises prices for all buyers. This externality can enable an incumbent to use loyalty discounts to effectively divide the market with its rival and raise prices. If loyalty discounts also include a buyer commitment to buy from the incumbent, then loyalty discounts can also deter entry under conditions in which ordinary exclusive dealing cannot. With or without buyer commitment, loyalty discounts will increase profits while reducing consumer welfare and total welfare as long as enough buyers exist and the entrant does not have too large a cost advantage. These propositions are true even if the entrant is more efficient and the loyalty discounts are above cost and cover less than half the market. We also prove that these propositions hold without assuming economies of scale, downstream competition, buyer switching costs, financial constraints, limits on rival expandability, or any intra-product bundle of contestable and incontestable demand
