Abstract
We show that loyalty discounts with buyer commitments create anticompetitive effects beyond those possible with pure exclusive dealing. The loyalty discount adds a seller commitment to maintain a distinction between the loyal and disloyal price. This seller commitment reduces the seller's incentives to compete for free buyers because the loyalty discount means that lowering prices to free buyers requires lowering prices to committed buyers. This softened seller competition reduces the rival's incentive to lower its own prices to free buyers. The result is inflated prices to free buyers, which in turn inflates prices to committed buyers because they are priced at a loyalty discount from those free buyer prices. Because each buyer who signs a loyalty discount contract thus softens competition and raises prices for all buyers, the result is to create an externality among buyers even without economies of scale or downstream competition. If enough buyers exist and the entrant's cost advantage is not too large, we prove that this externality means that: (1) in any equilibrium, enough buyers sign loyalty discount contracts to anticompetitively increase prices; and (2) there always exists a possible equilibrium in which all buyers sign, completely foreclosing a more efficient rival. As a result, the incumbent can use loyalty discounts to increase its profit and decrease both buyer and total welfare.
Highlights
The proper antitrust treatment of loyalty discounts has been a contentious issue
We show that the incumbent can profitably guarantee that there does not exist an equilibrium in which all buyers reject the loyalty discount contract
Unless the entrant cost advantage is sufficiently large, this equilibrium with anticompetitive effects will always occur for a sufficient number of buyers
Summary
The proper antitrust treatment of loyalty discounts has been a contentious issue. Some courts have held that loyalty discounts cannot be anticompetitive unless they are below cost, while other courts have rejected that proposition.[1]. Elhauge (2009) assumes sequential rather than simultaneous pricing case when determining whether buyers will accept loyalty discount contracts.[6] As a result, he finds there always exists an equilibrium in which loyalty discounts with buyer commitments have no effect because all buyers reject them.[7] In contrast, by considering simultaneous pricing, we find that given a sufficient number of buyers (in our linear demand analysis, “sufficient” can mean three buyers), there does not exist an equilibrium in which all buyers reject a loyalty discount with buyer commitments The reason for this is that with simultaneous pricing, if the entrant enters, there is a mixed strategy pricing equilibrium.[8] In this mixed strategy equilibrium, the incumbent’s price distribution varies smoothly with the number of signers. This assumption makes the analysis of the standard is (1 − )( − ) ( ) If all buyers purchase from ’s profit is ( − − ) ( − ) + (1 − )( − ) ( ) while ’s profit is zero
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