Anticompetitive Market Division through Loyalty Discounts without Buyer Commitment

We show that loyalty discounts without buyer commitment 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. 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, segmenting the market and reducing consumer welfare and total welfare. These propositions are true even if the buyers coordinate, the entrant is more efficient, the loyalty discounts cover less than half the market, and all the loyalty discounts are above cost. We also prove that these propositions hold even if we assume no economies of scale, no downstream competition, no buyer switching costs, no financial constraints, no limits on rival expandability, and no intraproduct bundle of contestable and incontestable demand.