Robust Exclusion Through Loyalty Discounts

Abstract

We consider loyalty discounts whereby the seller promises to give buyers who commit to buy from it a lower price than the seller gives to uncommitted buyers. We show that an incumbent seller can use loyalty discounts to soften price competition between itself and a rival, which raises market prices to all buyers. Each individual buyer’s agreement to a loyalty discount externalizes most of the harm of that individual agreement onto all the other buyers. The resulting externality among buyers makes it possible for an incumbent to induce buyers to sign these contracts even if they reduce buyer and total welfare. Thus, if the entrant cost advantage is not too large, we prove that with a sufficient number of buyers, there does not exist any equilibrium in which at least some buyers do not sign loyalty discount contracts, and there exists an equilibrium in which all buyers sign and the rival is foreclosed from entry. As a result, with a sufficient number of buyers, an incumbent can use loyalty discounts to increase its profit and decrease both buyer and total welfare. Further, the necessary number of buyers can be as few as three. These effects occur even in the absence of economies of scale in production and even if the buyers are not intermediaries who compete with each other in a downstream market.