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Exclusive contracts when the incumbent can establish a direct retailer

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Abstract

This paper constructs a model of anticompetitive exclusive dealings with potential downstream competition. Unlike in previous studies, the incumbent can establish a direct retailer with some fixed payment and can offer an exclusive contract to a downstream buyer twice. We show that the existence of these two options helps the incumbent deter socially efficient entry and earn almost monopoly profits even in the absence of scale economies and downstream competition.

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Notes

  1. See Posner (1976) and Bork (1978).

  2. See “Business sense” The Economist, Mar 4, 2004. (http://www.economist.com/node/2458055).

  3. Our results may be applicable when antitrust agencies construct guidelines for exclusive dealings. See, for example, Federal Trade Commission’s website: http://www.ftc.gov/bc/antitrust/exclusive_dealing.shtm, where exclusion with scale economies pointed out by Rasmusen et al. (1991) and Segal and Whinston (2000a) is discussed.

  4. There also exist works on procompetitive exclusive dealings. Several studies argue that exclusive dealings have a role in encouraging noncontractible investments. See, for example, Marvel (1982), Segal and Whinston (2000b), De Meza and Selvaggi (2007), and De Fontenay et al. (2010).

  5. Economists analyze anticompetitive exclusive dealings from not only a theoretical perspective but also an experimental perspective. See, for example, Boone and Suetens (2009), Landeo and Spier (2009), and Smith (2011).

  6. Fumagalli and Motta (2008) also show that exclusion arises because of coordination failure among buyers even when the incumbent does not have a first-mover advantage in making exclusive offers.

  7. Wright (2009) also points out that the equilibrium analysis of Fumagalli and Motta (2006) in the case of two-part tariffs contains some errors and shows that exclusion arises when scale economies are sufficiently large or when the entrant’s cost advantage is not too big.

  8. Rasmusen et al. (1991) and Segal and Whinston (2000b) point out that price commitments are unlikely if the nature of the product is not precisely described in advance. In the naked exclusion literature, it is known that if the incumbent can commit to wholesale prices, then anticompetitive exclusive dealings are enhanced. See Yong (1999) and Appendix B in Fumagalli and Motta (2006).

  9. This assumption implies that entry by the entrant takes a longer time than the establishment of a direct retailer. Therefore, we can interpret the entrant here as a foreign company or a capital-intensive company because these firms take more time to find a business partner, raise funds, and make investments in plant and machinery.

  10. The establishment cost of a direct retailer tends to be small in an industry where downstream firms are labor intensive rather than capital intensive or small companies rather than large companies.

  11. Katz (1991) points out that unobservable offers are more realistic than observable offers. This assumption avoids multiple equilibria. See Section III of Fumagalli and Motta (2006) and Section III of Simpson and Wickelgren (2007), wherein it is pointed out that if each retailer can observe the wholesale offer made to its rival, then there exist both an exclusion equilibrium and an entry equilibrium. Note that introducing differentiation between retailers also avoids multiple equilibria even under observable contracts, though the analysis does become a bit complicated. See Simpson and Wickelgren (2007) who point out that if retailers are not perfectly homogeneous but differentiated, then only the exclusion equilibrium is robust.

  12. Although the unobservable wholesale price offer solves the multiple equilibrium problem, it generates the commitment problem in Hart and Tirole (1990) that arises when a single upstream manufacturer sells to two competing retailers with two-part tariffs under unobservable wholesale contracts and passive beliefs. Following Rey and Verg (2004), Abito and Wright (2008) avoid the commitment problem when only the incumbent makes a wholesale price offer by assuming symmetric beliefs. We also follow this assumption.

  13. See, for example, Baake and von Schlippenbach (2011) for recent studies on vertical relations in the presence of long-term buyer-seller relationships.

  14. Under observable offers, the existing retailer can choose the market price by matching the wholesale price offer from the incumbent to the direct retailer. Given this pricing strategy, the incumbent is indifferent toward wholesale prices higher than its marginal cost because it then expects zero profits with any wholesale price offer \(w_{D|t=2}\ge c_I\). Therefore, there exists an entry equilibrium where the existing retailer does not sign the second exclusive contract in Period 2.2 by expecting that the incumbent offers sufficiently higher wholesale prices in Period 2.4 that lead to higher profits for the existing retailer.

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Acknowledgments

An earlier version of this paper was circulated under the title “Exclusive Contracts with Options.” We thank Noriyuki Doi, Makoto Hanazono, Takeshi Ikeda, Akira Ishii, Taisuke Matsubae, Noriaki Matsushima, June Nakabayashi, Sobei H. Oda, Tadashi Sekiguchi, Shiro Takeda, Takashi Yanagawa, the conference participants at the Japanese Economic Association and the Japanese Association for Applied Economics, and the seminar participants at the Kyoto Sangyo University for helpful discussions and comments. We also thank the editor—Giacomo G. Corneo—and an anonymous referee for their very helpful comments and suggestions that significantly improved this paper. The second author gratefully acknowledges the financial support from JSPS Grant-in-Aid for Research Activity Start-up No. 22830075, for Young Scientists (B) No. 24730220, and for Scientific Research (A) No. 22243022 organized by Masaki Nakabayashi. The views expressed in this paper are those of the authors and do not necessarily represent the views of JFTC or any other organization.

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Authors and Affiliations

  1. Faculty of Economics, Kyoto Sangyo University, Motoyama, Kamigamo, Kita-ku, Kyoto, 603-8555, Japan

    Hiroshi Kitamura

  2. Graduate School of Economics, George Washington University, 2115 G street, NW Monroe Hall 340, Washington, DC, 20052, USA

    Misato Sato

  3. Competition Policy Research Center, Japan Fair Trade Commission, 1-1-1, Kasumigaseki, Chiyoda-ku, Tokyo, 100-8987, Japan

    Koki Arai

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  1. Hiroshi Kitamura
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  2. Misato Sato
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  3. Koki Arai
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Correspondence to Hiroshi Kitamura.

Appendix A: Proofs of all results

Appendix A: Proofs of all results

1.1 A.1 Proof of Lemma 1

Note that the analysis of a single exclusive offer corresponds with the subgame analysis in Period 2 after the existing retailer rejects the first exclusive offer in Period 1.1. Therefore, we explore the existence of exclusion in Period 2 when the existing retailer rejects the first exclusive offer in Period 1.1. Because our goal here is to explore the decision in Period 2.2, we first consider what happens in each of the possible subgames after Period 2.2. To start with, suppose that the existing retailer signs the second exclusive contract in Period 2.2. Then, the entrant does not enter the upstream market in Period 2.3 and only the incumbent makes the wholesale price offer \((w_I=c_I, \psi _I=1/16)\) to the existing retailer in Period 2.4. Before compensation, the incumbent earns \(1/16\) and the existing retailer earns nothing in Period 2.5.

Next, suppose that the existing retailer does not sign the second exclusive contract in Period 2.2. In this subgame, the entrant enters the upstream market in Period 2.3 and both the incumbent and the entrant make wholesale price offers to the existing retailer in Period 2.4. The incumbent lowers the price to \((w_{I|t=2}=c_I, \psi _{I|t=2}=0)\) to attract the existing retailer. The entrant only has to match this wholesale price to attract the existing retailer and offers \((w_{E|t=2}=c_E, \psi _{E|t=2}=\{(1-c_E)^2/4-1/16-\varepsilon \})\), where \(\varepsilon \) is some infinitesimally small number. In the equilibrium, the existing retailer deals with the entrant, and the incumbent earns nothing and the existing retailer earns \(1/16+\varepsilon \).

Now we consider the decision in Period 2.2. For the existence of the exclusion equilibrium, the second exclusive offer \(x_2\) needs to satisfy the following two conditions. First, the incumbent needs to earn positive profits: that is, \(1/16 \ge x_2\). Second, the existing retailer is better off accepting the second exclusive offer: that is, \(x_2\ge 1/16+\varepsilon \). It is easy to see that these two conditions never hold simultaneously. Therefore, exclusion is impossible. \(\square \)

1.2 A.2 Proof of Lemma 2

Note that the analysis of a single exclusive offer corresponds with the subgame analysis in Period 2 after the existing retailer rejects the first exclusive offer in Period 1.1. Therefore, we explore the existence of exclusion in Period 2 when the existing retailer rejects the first exclusive offer in Period 1.1. Because our goal here is to explore the decision in Period 2.1, we first consider what happens in each of the possible subgames after Period 2.1. First, suppose that the incumbent does not establish a direct retailer in Period 2.1. Then, as we have proved in Lemma 1, the entrant enters the upstream market. In the equilibrium, the incumbent earns nothing and the existing retailer earns \(1/16+\varepsilon \).

Next, suppose that the incumbent establishes a direct retailer in Period 2.1. Suppose that the existing retailer signs the second exclusive contract in Period 2.2. In this case, the entrant does not enter the upstream market in Period 2.3 and the existing retailer deals with the incumbent. The incumbent offers \((w_{I|t=2}=3/4, \psi _{I|t=2}=0)\) to the existing retailer and \((w_{D|t=2}=3/4,\psi _{D|t=2}=0)\) to the direct retailer in Period 2.4. Before compensation, the incumbent earns \(1/16\) and both the existing retailer and the direct retailer earn nothing in Period 2.5. In contrast, suppose that the existing retailer does not sign the second exclusive contract in Period 2.2. The incumbent offers \((w_{I|t=2}=c_I, \psi _{I|t=2}=0)\) to attract the existing retailer and it also offers \((w_{D|t=2}=c_I,\psi _{D|t=2}=0)\) to the direct retailer. The existing retailer’s alternative to the entrant’s offer is to buy from the incumbent at \((w_{I|t=2}=c_I,\psi _{I|t=2}=0)\). If the existing retailer deals with the incumbent, then it obtains nothing because of competition with the direct retailer. To attract the existing retailer, the entrant offers \((w_{E|t=2}=c_E,\psi _{E|t=2}=\{(1-c_E)^2/4-\varepsilon \})\). In the equilibrium, both the incumbent and the direct retailer earn nothing but the existing retailer earns \(\varepsilon \).Footnote 14 Now, we consider the decision in Period 2.2. As we have discussed in the proof of Lemma 1, for the existence of the exclusion equilibrium, the following two conditions must be satisfied: \(1/16 \ge x_2\) and \(x_2\ge \varepsilon \). It is easy to see that there exists \(x_2\ge 0\) that satisfies these two conditions. The equilibrium transfer therefore becomes \(x^*_2=\varepsilon \).

Finally, we consider the decision in Period 2.1. When the incumbent establishes a direct retailer, the incumbent earns \(1/16-F-\varepsilon >0\). In contrast, when the incumbent does not establish a direct retailer, the incumbent earns nothing. Therefore, the incumbent establishes a direct retailer in Period 2.1 and deters socially efficient entry with an exclusive contract. \(\square \)

1.3 A.3 Proof of Proposition 1

Because our goal here is to explore the decisions in Period 1.1, we first consider what happens in each of the possible subgames after Period 1.1. First, suppose that the existing retailer does not sign the first exclusive contract in Period 1.1. In this case, the games go to Period 2. From the discussion in the proof of Lemma 2, by using the second exclusive offer, the existing retailer earns \(\varepsilon \) and the incumbent earns \(1/16-F-\varepsilon \) in the equilibrium outcomes in Period 2.

Suppose next that the existing retailer does sign the first exclusive contract in Period 1.1. In this case, the incumbent offers \((w_{I|t=1}=c_I,\psi _{I|t=1}=1/16)\) to the existing retailer in Period 1.2, and before compensation, the incumbent earns \(1/16\) but the existing retailer earns nothing in Period 1.3.

Finally, we consider the decisions in Period 1.1. It is easy to see that for \(x^*_1\ge x^*_2=\varepsilon \), the existing retailer signs the first exclusive contract in Period 1.1. In addition, with this exclusive offer, the incumbent earns \(1/16-\varepsilon \), which is strictly higher than the incumbent’s net profits with the second exclusive offer. Therefore, the incumbent prefers exclusion with the first exclusive offer. \(\square \)

1.4 A.4 Proof of Proposition 2

To prove Proposition 2, we first prove the following lemmas.

Lemma 3

Suppose that upstream firms offer linear wholesale prices. Suppose also that the incumbent does not establish a direct retailer in Period 2.1. Then, in the absence of scale economies and downstream competition, the incumbent cannot exclude socially efficient entry by using exclusive contracts in Period 2.2.

Proof

Because our goal here is to explore the decision in Period 2.2, we first consider what happens in each of the possible subgames after Period 2.2. First, suppose that the existing retailer signs the second exclusive contract in Period 2.2. Then, the entrant does not enter the upstream market in Period 2.3 and only the incumbent makes a wholesale price offer \(w_I=3/4\) to the existing retailer in Period 2.4. Before compensation, the incumbent earns \(1/32\) and the existing retailer earns \(1/64\) in Period 2.5. Next, suppose that the existing retailer does not sign the second exclusive contract in Period 2.2. In this subgame, the entrant enters the upstream market in Period 2.3 and both the incumbent and the entrant make wholesale price offers to the existing retailer in Period 2.4. The incumbent lowers prices to \(w_{I|t=2}=c_I\) to attract the existing retailer. The entrant only has to match this wholesale price to attract the existing retailer, and offers \(w_{E|t=2}=c_I\). In the equilibrium, the existing retailer deals with the entrant, and the incumbent earns nothing and the existing retailer earns \(1/16\).

Now we consider the decision in Period 2.2. The second exclusive offer \(x_2\) needs to satisfy the following two conditions. First, the incumbent needs to earn positive profits: that is, \(1/32 \ge x_2\). Second, the existing retailer is better off accepting the second exclusive offer: that is, \(x_2\ge 1/16\). It is easy to see that these two conditions never hold simultaneously. Therefore, entry is a unique equilibrium outcome. This completes the proof of Lemma 3.

Lemma 4

Suppose that the upstream firms offer linear wholesale prices. When the incumbent decides not to make the first exclusive offer in Period 0 or the existing retailer rejects the first exclusive offer in Period 1.1, the incumbent establishes a direct retailer in Period 2.1, and the existing retailer accepts the second exclusive offer in Period 2.2.

Proof

Because our goal here is to explore the decision in Period 2.1, we first consider what happens in each of the possible subgames after Period 2.1. First, suppose that the incumbent does not establish a direct retailer in Period 2.1. Then, as we have proved in Lemma 3, the entrant enters the upstream market. In the equilibrium, the incumbent earns nothing and the existing retailer earns \(1/16\).

Next, suppose that the incumbent establishes a direct retailer in Period 2.1. Suppose that the existing retailer signs the second exclusive contract in Period 2.2. In this case, the entrant does not enter the upstream market in Period 2.3 and the existing retailer deals with the incumbent. The incumbent offers \(w_{I|t=2}=3/4\) to the existing retailer in Period 2.4, and \(w_{D|t=2}=3/4\). Before compensation, the incumbent earns \(1/16\) and both the existing retailer and the direct retailer earn nothing in Period 2.5. On the contrary, suppose that the existing retailer does not sign the second exclusive contract in Period 2.2. The incumbent offers \(w_{I|t=2}=c_I\) to attract the existing retailer and also offers \(w_{D|t=2}=c_I\) to the direct retailer. To attract the existing retailer, the entrant offers \(w_{E|t=2}=c_I\). In the equilibrium, both the incumbent and the retailers earn nothing. Now, we consider the decision in Period 2.2. As we have discussed in the proof of Lemma 3, for the existence of the exclusion equilibrium, the following two conditions must be satisfied: \(1/16 \ge x_2\) and \(x_2\ge 0\). It is easy to see that these two inequalities hold simultaneously. The equilibrium transfer therefore becomes \(x^*_2=0\).

Finally, we consider the decision in Period 2.1. When the incumbent establishes a direct retailer, the incumbent earns \(1/16-F>0\). In contrast, when the incumbent does not establish a direct retailer, the incumbent earns nothing. Therefore, the incumbent establishes a direct retailer in Period 2.1 and it deters socially efficient entry with an exclusive contract. This ends the proof of Lemma 4.

Note that our goal here is to explore the decisions in Period 0. When the incumbent decides not to make the first exclusive offer, the game goes to Period 2.1. From Lemma 4, the incumbent establishes a direct retailer in Period 2.1 and earns \(1/16-F\). In contrast, when the incumbent decided to make the first exclusive offer, the game goes to Period 1.1.

To explore the decisions in Period 1.1, we first consider what happens in each of the possible subgames after Period 1.1. First, suppose that the existing retailer does not sign the first exclusive contract in Period 1.1. In this case, the games go to Period 2. From the discussion in the proof of Lemma 4, by using the second exclusive offer, the existing retailer earns nothing and the incumbent earns \(1/16-F\) in the equilibrium outcomes in Period 2. Suppose next that the existing retailer does sign the first exclusive contract in Period 1.1. In this case, the incumbent offers \(w_{I|t=1}=3/4\) to the existing retailer in Period 1.2, and before compensation, the incumbent earns \(1/32\) but the existing retailer earns \(1/64\) in Period 1.3. Finally, we consider the decisions in Period 1.1. The existing retailer signs the first exclusive contract in Period 1.1 if \(x_{1}+1/64\ge 0\). It is easy to see that the existing retailer signs the first exclusive offer even when \(x^{*}_{1}=0\). With this offer, the incumbent earns \(1/32\).

Now we consider the decisions in Period 0. Comparing the first exclusive offer with the second exclusive offer, the incumbent prefers exclusion with the second exclusive offer for \(0<F\le 1/32\) but it prefers exclusion with the first exclusive offer for \(1/32<F<1/16\). \(\square \)

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Kitamura, H., Sato, M. & Arai, K. Exclusive contracts when the incumbent can establish a direct retailer. J Econ 112, 47–60 (2014). https://doi.org/10.1007/s00712-013-0335-7

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