Jump to ContentJump to Main Navigation
Show Summary Details
More options …

The B.E. Journal of Economic Analysis & Policy

Editor-in-Chief: Jürges, Hendrik / Ludwig, Sandra

Ed. by Auriol, Emmanuelle / Brunner, Johann / Fleck, Robert / Mastrobuoni, Giovanni / Mendola, Mariapia / Requate, Till / Schirle, Tammy / de Vries, Frans / Zulehner, Christine

4 Issues per year

IMPACT FACTOR 2017: 0.306
5-year IMPACT FACTOR: 0.492

CiteScore 2017: 0.50

SCImago Journal Rank (SJR) 2017: 0.414
Source Normalized Impact per Paper (SNIP) 2017: 0.531

See all formats and pricing
More options …
Volume 13, Issue 2


Volume 6 (2006)

Volume 4 (2004)

Volume 2 (2002)

Volume 1 (2001)

Loyalty Discounts

Uğur Akgün / Ioana Chioveanu
Published Online: 2013-09-26 | DOI: https://doi.org/10.1515/bejeap-2012-0047


This article analyses the use of loyalty inducing discounts in vertical supply chains. An upstream supplier and a competitive fringe sell differentiated products to a retailer who has private information about the stochastic demand. We compare the market outcomes, when the supplier uses two-part tariffs (2PT), all-unit quantity discounts (AU), and market-share discounts (MS). We show that the retailer’s risk attitude affects supplier’s preferences over these pricing schemes. When the retailer is risk neutral, it bears all the risk and the three schemes lead to the same outcome. When the retailer is risk averse, a 2PT performs the worst from the supplier’s perspective, but it leads to the highest welfare. For a wide range of parameter values (but not for all), the supplier prefers MS to AU. By limiting the retailer’s product substitution possibilities, MS makes the demand for the manufacturer’s product more inelastic. This reduces the amount (share of total profits) the supplier needs to leave to the retailer for the latter to participate in the scheme.

Keywords: vertical contracts; market-share discounts; asymmetric information

JEL: L42; L12; L13


  • Banerjee, A., and L. Summers. 1987/ “On Frequent Flyer Programs and Other Loyalty-Inducing Arrangements,” Harvard Institute of Economic Research, Discussion Paper Number 1337.Google Scholar

  • Caminal, R., and C. Matutes. 1990. “Endogenous Switching Costs in a Duopoly Model.” International Journal of Industrial Organization 8(3):353–73.Web of ScienceCrossrefGoogle Scholar

  • European Commission. 2005. “DG Competition Discussion Paper on the Application of Article 82 of the Treaty to Exclusionary Abuses.”Google Scholar

  • European Commission. 2009. “Guidance on the Commission’s Enforcement Priorities in Applying Article 82 of the EC Treaty to Abusive Exclusionary Conduct by Dominant Undertakings.”Google Scholar

  • Feess, E., and A. Wohlschlegel. 2010. “All-Unit Discounts and the Problem of Surplus Division.” Review of Industrial Organization 37(3):161–78.Web of ScienceCrossrefGoogle Scholar

  • Greenlee, P., D. Reitman, and D. Sibley. 2008. “An Antitrust Analysis of Bundled Loyalty Discounts.” International Journal of Industrial Organization 26(5):1132–52.CrossrefWeb of ScienceGoogle Scholar

  • Gual, J., M. Hellwig, A. Perrot, M. Polo, P. Rey, K. Schmidt, and R. Stenbacka. 2005. “An Economic Approach to Article 82,” Report by the European Advisory Group on Competition Policy.Google Scholar

  • Inderst, R., and G. Shaffer. 2010. “Market-Share Contracts as Facilitating Practices.” The RAND Journal of Economics 41(4):709–29.Web of ScienceCrossrefGoogle Scholar

  • Inderst, R., and T. Valletti. 2009. “Price Discrimination in Input Markets.” The RAND Journal of Economics 40(1):1–19.CrossrefGoogle Scholar

  • Kobayashi, B. 2005. “The Economics of Loyalty Discounts and Antitrust Law in the United States.” Competition Policy International 1:115–148.Google Scholar

  • Kolay, S., G. Shaffer, and J. Ordover. 2004. “All-Units Discounts in Retail Contracts.” Journal of Economics and Management Strategy 13(3):429–59.CrossrefGoogle Scholar

  • Majumdar, A., and G. Shaffer. 2009. “Market-Share Contracts with Asymmetric Information.” Journal of Economics and Management Strategy 18(2):393–421.Web of ScienceCrossrefGoogle Scholar

  • Marx, L., and G. Shaffer. 2004. “Rent-Shifting, Exclusion, and Market-Share Discounts,” Working Paper, Fuqua School of Business, Duke University.Google Scholar

  • Mills, D. 2010. “Inducing Downstream Selling Effort with Market Share Discounts.” International Journal of the Economics of Business 17(2):129–46.CrossrefGoogle Scholar

  • Nocke, V., and J. Thanassoulis. forthcoming. “Vertical Relations under Credit Constraints.” Journal of the European Economic Association.Google Scholar

  • Office of Fair Trading. 2005. “Discussion Paper on the Application of Article 82 of the Treaty to Exclusionary Abuses.”Google Scholar

  • Rey, P., and J. Tirole. 1986. “The Logic of Vertical Restraints.” American Economic Review 76(5):921–39.Google Scholar

  • Sloev, I. 2008. “Market Share Discounts and Investment Incentives,” Working Paper, Universidad Carlos III de Madrid.Google Scholar

  • Vives, X. 2001. Oligopoly Pricing: Old Ideas and New Tools. Cambridge, Massachusetts: The MIT Press.Google Scholar

About the article

Published Online: 2013-09-26

Economies of scale can occur at the overall production level or in fulfilling a specific order, but are less likely to relate to the total purchases of a customer over a certain period.

The EC guidelines require a dominant firm to provide an objective motivation for a discount scheme that can potentially make it harder for its rivals to compete: “It is incumbent upon the dominant undertaking to provide all the evidence necessary to demonstrate that the conduct concerned is objectively justified.” See paragraph 31 in European Commission (2009).

Lately, European and North American case law have focused on whether loyalty discounts can serve as exclusionary devices that would violate Article 102 of the EC Treaty or Section 2 of the Sherman Act. In addition, firms’ use of loyalty discounts in the distribution of their products has also been attacked as unlawful primary line price discrimination under the Robinson Patman Act and EC law (Art. 102c).

Mills (2010) and the Office of Fair Trading (2005) present comprehensive overviews of antitrust cases related to loyalty discounts in US and Europe. See also Kobayashi (2005), European Commission (2005, 2009), and Gual et al. (2005).

The term “all-unit” quantity discount is used to emphasize that we study rollback rebates. However, our setting also informs on the relative private desirability of “incremental-unit” quantity discounts (that do not rollback to inframarginal units once the target is reached), since they cannot improve upon 2PT under our information/risk setting.

Nocke and Thanassoulis (forthcoming) show that, in the presence of uncertainty, risk aversion may arise endogenously in supply chains when downstream firms face credit constraints in their future investments.

For example, Kolay et al. (2004) and Kolay, Shaffer, and Ordover (2004) focus on the relative profitability of these pricing schemes (for the upstream supplier) when they are used for optimal screening. In Section 5, we discuss how our work complements the previous work in understanding the supplier’s preferences over the different pricing schemes, when exclusion cannot be a motive.

In the EEA, when a dominant supplier restricts a downstream customer’s ability to resell its product to other businesses at the same level of the supply chain, but in other geographic markets, this action may be found incompatible with Article 101 and/or Article 102 of the EC Treaty.

For instance, consider a setting where only authorized dealers can sell the product.

Even if the implementation of market-share discounts requires costly monitoring of rival sales, there is a non-trivial range of costs for which the supplier might still strictly prefer using a market-share discount to using all-unit quantity discounts.

In a full information setting where the incumbent faces second period competition by entrants, Feess and Wohlschlegel (2010) show that all-unit discounts shift rents from the entrants. Greenlee, Reitman, and Sibley (2008) consider a monopolist that faces competition in a second market and shows that bundled loyalty discounts (that condition the rebate on the range of products purchased from the monopolist) have ambiguous welfare effects.

Another stream of literature analyses loyalty discounts as a source of endogenous switching costs in a dynamic, repeat-purchase context. See, for instance, Banerjee and Summers (1987) and Caminal and Matutes (1990).

In our setting, the retailers could be, for instance, relatively small convenience stores. It is plausible then that the manufacturer of a branded product offers the same contract to all retailers on a take it or leave it basis, rather than hold bilateral negotiations with each local retailer. So, if the supplier needs to deal with many local retailers, the transaction costs of negotiating individual contracts would justify his ability to make a take it or leave it offer. Finally, the assumption that the manufacturer makes a take it or leave it offer is not as restrictive as it may seem. For a relevant discussion, see footnote 9 in Inderst and Valletti (2009).

Given that the markets are identical apart from the resolution of the uncertainty, the expected outcome under different contracts can be captured by looking at the ex-ante situation for a given local market. Therefore, we suppress the multiplicity of markets for the rest of this article and refer to a single retailer while analysing the contracts.

We are very grateful to an anonymous referee for suggesting us to use this functional form to capture retailer risk aversion on a continuous scale.

See, for instance, Vives (2001).

The opposite is true when the demand is high, as the threshold in the optimal AU contract does not constrain the retailer’s choice in that case.

When the demand is low, under the AU contract, the retailer optimizes by choosing the quantity of the competitively supplied good corresponding to the threshold quantity of the manufacturer’s good and, although the sales are still distorted in favour of the competitively supplied good, the distortion is lower as

When the demand is high, for both contracts the retailer’s choices are governed by the first-order conditions and the distortion in the relative sales of the two goods is higher with the optimal AU contract

Total welfare is calculated as the difference between the gross utility of the consumers and the costs of production. Recall that the costs of production are normalized to zero in our model.

When acting on the share threshold, the retailer actually chooses the quantity of only one product (i.e. there is only one first-order condition in this case). The quantity of the substitute product is determined by the share requirement. Without loss of generality, we assume that the retailer chooses the quantity of the competitively supplied product ().

Nocke and Thanassoulis (forthcoming) show that, with an endogenously risk averse downstream firm, the optimal screening contract induces double marginalization and involves a fixed payment from the upstream firm to the downstream one. They argue that such slotting allowances are a risk sharing device. This interpretation is consistent with our results for the MS contract.

The contract they consider effectively requires the retailer to satisfy both a market-share target and a quantity target for achieving a certain price. This is different from the market-share contract we consider which only stipulates a market-share threshold.

Citation Information: The B.E. Journal of Economic Analysis & Policy, Volume 13, Issue 2, Pages 655–685, ISSN (Online) 1935-1682, ISSN (Print) 2194-6108, DOI: https://doi.org/10.1515/bejeap-2012-0047.

Export Citation

©2013 by Walter de Gruyter Berlin / Boston.Get Permission

Comments (0)

Please log in or register to comment.
Log in