buying groups and product variety - c r e s s e
TRANSCRIPT
Buying Groups and Product Variety
Marie-Laure Allain∗, Rémi Avignon†, Claire Chambolle‡
Preliminary and incomplete. Please do not circulate
Abstract
We study the impact of retailers’ buying groups on both product variety and the
profit sharing within the vertical chain. We consider a setting in which capacity con-
strained retailers operate in separated markets and must select their assortment among
a set of differentiated products. Retailers may either adopt an independent listing strat-
egy or a joint listing strategy (i.e they commit to listing the same product assortment)
which may cover the whole product line (full coverage) or only part of it (partial cover-
age). We show that retailers may enhance their buyer power by jointly committing to a
common listing strategy. As a result, buying groups reduce the overall product variety.
This results in lower overall consumer surplus. Interestingly buying groups with partial
coverage may be more profitable for the retailers than those with full coverage.
Keywords: Vertical relations, buying group, buyer power, vertical foreclosure.
JEL Classification: L13, L42, L81.
∗CREST, CNRS, Ecole polytechnique, Université Paris-Saclay; email: marie-
[email protected].†CREST, Université Paris-Saclay; email: [email protected].‡ALISS UR1303, INRA, Université Paris-Saclay, F-94200 Ivry-sur-Seine, France, and CREST; email:
1 Introduction
Buying groups, that is purchasing alliances between retailers, are widespread and often gather
retailers that operate in different countries. These agreements have long been well perceived
by competition authorities because they are likely to increase buyer-power and enable retailers
to obtain discounts that translate into lower consumer prices. This “countervailing power"
effect, first coined by Galbraith (1952), has been largely debated in the literature but recent
theoretical developments however point out that they rely on strong assumptions regarding
the shape of tariffs, namely linear contracts (see von Ungern-Sternberg (1996) and Iozzi and
Valletti (2014)). Yet it has been widely documented that tariffs in the retail sector are scarcely
linear (see Berto Villas-Boas (2007) Bonnet and Dubois (2010)). A more recent strand of
theory has developed to analyze the welfare effects of buyer power (see Roman Inderst and
Mazzarotto Nicola (2008)), pointing out its potential adverse effects on product variety,
innovation, and the scope for collusion. Despite these potential adverse effects, purchasing
alliances are not subject to approval by competition authorities, contrary to mergers.
Two waves of buying alliances in the grocery industry1 have recently attracted the at-
tention of the French competition authority. First, in 2014, three important purchasing
agreements have been signed in France. In September, System U and Auchan formed an
alliance, as well as Intermarché and Casino in November and Carrefour and Cora in Decem-
ber. This led the competition authority to take on a report on the welfare effects of buying
groups in 2015.2 The bright side of the analysis put forward that those buying groups were
likely to have limited anticompetitive effects, because their scope was restricted to national
brand products, hence they could not affect products manufactured by small suppliers, in
particular fresh agricultural products.3
In 2018, a second wave of international purchasing agreements involving French retailers
started.4 Three groups of retailers are involved. A first group called "Horizon" is composed1French grocery market shares in 2019 are the following: Carrefour (20.1%), E. Leclerc (21.3%), Inter-
marché (14.7%), Casino (11%), Système U (10.6%). Source: Kantar World Panel2See : Autorité de la concurrence (2015).3Following the report the Loi Macron 2015-990 made mandatory for retailers to notify to the Competition
Authority their decision to create a buying group at least two months in advance. Yet, no tools for controllingsuch alliances were granted to the Competition Authorities.
4The French competition authority launched a new evaluation in July 2018 in order to investigate "thecompetitive impact of these purchasing partnerships on the concerned markets, both upstream for the suppliers,
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of Auchan, Casino, Metro and Schiever, a second one is composed of Carrefour and Système
U and third one involves Carrefour and Tesco. An important difference between this wave
and the previous one is that the new buying groups gather retailers operating on separate
markets. Furthermore, they cover a wider scope of brands. In its press release of July 2018,
the French competition authority stipulates that new agreements "differ from the alliances
made in 2015 due to their larger scope involving an international dimension, and because they
include not only national brand goods but also store-brand products".5 The retailers argue that
this may give opportunities of international development to the suppliers of private labels.6
In this paper, we study the effect of buying groups on product variety, and we compare
the above-mentioned kinds of agreements, depending on whether or not their boundaries
include SMEs. To do so, we consider a setting in which two retailers act as monopolists
on two independent markets. They sell differentiated products manufactured by competing
suppliers: a large supplier who can offer two products denoted A and C in the two markets
(typically a multinational company selling well-know brands across markets), and, in each
market, a small local supplier who offers only one product l (typically, a private label SME).
To represent differences in the preferences of consumers living in different regions or even
different countries, we assume that, on one of these two markets preferences are such that
A > B > C, whereas this ranking is reversed on the other market (C > B > A).7 On each
market, the retailer is capacity constrained: each retailer can list two of the three available
products.
We consider that retailers may either adopt an independent listing strategy or a joint list-
ing strategy (i.e they commit to listing the same product assortment). Joint listing strategies
may cover the whole product line (full coverage, A, l and C), such as in the 2018 buying groups
quoted above, or only part of it (partial coverage, A and C), such as in the 2014 cases above.
In each of these situation, retailers and suppliers negotiate over three part tariffs as follows.
First, on each market, suppliers compete for being listed by the retailer by simultaneously
and downstream for the consumers."5For instance, Carrefour claimed that "the alliance will cover the strategic relationship with global sup-
pliers, the joint purchasing of own brand products and goods not for resale."(source: carrefour.com)6Horizon communication thus claimed that "Auchan Retail, Casino Group and METRO will assist SMEs
in their international development, [..] and will be able to launch invitations to tender for their generalexpenses and their non-differentiating basic private-label brands" (source: groupe-casino.fr).
7These assumptions are close to those made by Inderst and Shaffer (2007).
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offering lump-sum slotting fees conditional on the number of their products listed by the re-
tailer. If the slotting fee is not accepted, the corresponding assortment will not be sold. If it
is accepted, the retailer is committed to enter into the second stage negotiation process with
the supplier but is not tied to sell the product. After the listing decision which is publicly
observed, retailers thus engage in a "Nash-in-Nash" bargaining with the supplier(s) of the
selected products. Finally, retailers sell their products on the downstream market.
We first show that creating a buying group reduces the overall variety of products, thereby
harming consumer surplus and welfare. Indeed, by assumption the preferred assortment
differs on the two markets, therefore committing to a similar assortment in the two markets
generates inefficiencies on at least one of the markets. Despite this inefficiency retailers
may find this strategy profitable because when committing to a common listing strategy
they enhance their buyer power, by reinforcing the threat of being delisted on all suppliers
who thus compete more fiercely at the listing stage. This result is in line with Inderst and
Shaffer (2007) however in contrast to their paper we show that the buying group creation
may generates inefficiency on both markets. Indeed, when the multi-product supplier is able
to impose its two products to the retailer, the resulting assortment AC is inefficient on the
two markets. Second, we show that retailers jointly find profitable to create a buying group
only when their bargaining power is low: in that case, the buying group enables the retailers
to receive "a larger share of a smaller pie". When their bargaining power is large enough,
retailers jointly prefer to implement the efficient assortment.
We then compare the impact of partial and full coverage buying groups. In case of full
coverage, we assume that a small producer of type B on one market would have to pay a
fixed cost to sell on the second market. This assumption aims at representing the cost for a
small supplier to expand at an international level. As the intermediate product l is sold less
often in the case of a full coverage buying group, consumer surplus can be worse off under
full than under partial coverage. Besides, full coverage is more harmful for small suppliers,
and, whenever it is jointly profitable for the retailers, it also harms the large supplier more
than partial coverage. Finally, retailers joint profit is larger with partial coverage than with
full coverage when, in equilibrium, the small producer is excluded. This happens when the
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consumers valuation for the intermediate product is not too high. Indeed, in that case, the
slotting fee received by the retailer is paid by the large supplier, and this fee is higher when
the competitive pressure exerted by the small supplier is high, that is, when he does not incur
the export cost he faces under full coverage. By contrast, when the small producer is not
excluded in equilibrium, the retailers profit is larger under full coverage. Indeed, in that case,
the retailer captures the whole profit of the small supplier through the slotting fee, and this
one is larger when the relative quality of product l is higher (namely, when the consumers’
valuation for the intermediate product is close to their valuation for their preferred variety).
This article contributes to the growing theoretical literature on buying groups. Some
papers explain the rationality of retailers’ purchasing cooperation through competition on
the downstream market. Caprice and Rey (2015) consider competing retailers facing a unique
efficient supplier, and a fringe of inefficient suppliers. They show that a buying group increases
buyer power by enhancing each retailer’s outside option in the negotiation with the supplier.
Indeed, in case of a breakdown in the negotiation, the profit of the retailer decreases less when
his competitors also delist the products of the supplier, which happens when the retailers
adopt a joint listing strategy. Piccolo and Miklós-Thal (2012) and Doyle and Han (2014) show
that buying groups agreements can improve retailers’ ability to sustain collusive equilibrium
downstream coordinating on high wholesale price and using back margins payments.
Another bunch of papers analyse buying groups among firms that do not compete on the
downstream market8. Inderst and Shaffer (2007), which is the closest to our analysis, propose
a setting rationalising purchasing cooperation of retailers present on different downstream
markets and sourcing through common suppliers. They show that by merging (or forming
a buying group) retailers can increase their profit by reducing the total number of products8It is the case for the above-mentioned alliance between Carrefour and Tesco. Tesco holds stores in five
countries in Europe (Ireland, Poland, Hungary, Slovakia, Czech republic) and four in Asia (China, Japan,Malaysia and Thailand). Tesco’s main market is the United-Kingdom in which it represents 27.7% of totalgrocery market shares in 2019 (source: Kantar WorldPanel). Carrefour holds stores in seven countriesin Europe (Belgium, France, Italy, Poland, Slovakia, Spain, Turkey), two in South-America (ArgentinaBrazil) and two in Asia (China, Taiwan). Carrefour and Tesco are simultaneously present in two countriesin Europe and one in Asia. Similarly, the Horizon alliance gathers retailers active on separate markets.Auchan holds supermarkets in ten countries in Europe (France, Spain, Hungary, Italy, Poland, Portugal,Romania, Russia, Ukraine), three countries in Asia (China, Taiwan, Vietnam), four countries in Africa(Tunisia, Senegal, Mauritania, Algeria). Casino is active only in France in Europe, in four countries in SouthAmerica (Argentina, Brazil, Colombia, Uruguay) and in Indian Ocean (Madagascar, Mayotte, Reunion...).Metro’s retail brand is Real which is active in three countries in Europe (Germany, Turkey, Romania).
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sold in the economy. In this framework, buying group implementation leads to the exclusion
of a supplier, reduction of product diversity available to consumers and reduction of the total
industry profit. Retailers are able to capture a larger share of a smaller profit.
This paper is also related to the literature that analyses network formation in vertically
related markets. Marx and Shaffer (2010), Chambolle and Molina (2018) show that retailers
can strategically use capacity constraints in order to increase their buyer power. In these
papers, constraints on stocking capacity and slotting fees are used by retailers to extract a
larger share of a smaller industry profit. In the same vein, Ho and Lee (2019) develop a
bargaining procedure called "Nash-in-Nash with threat of replacement". Using this concept,
they rationalise American health insurers hospital network reduction, for profit extraction
motives. This paper adopts the timing developped in Chambolle and Molina (2018). In
their paper, they highlight close connections between their setting with a slotting fee stage
followed by a Nash-in-Nash bargaining stage within the selected network and the one stage
"Nash-in-Nash with threat of replacement" bargaining developed by Ho and Lee (2019).
The article is organised as follows. Section 2 presents the model and notations. Section 3
gives bargaining results common to the three listing strategies we consider : No buying group,
partial coverage buying group, full coverage buying group. Section 4 derives the equilibrium
outcome for each of the considered listing strategies. In Section 5, we compare suppliers
profits, product variety and retailers profits for each listing strategy. In section 7 we discuss
policy implications and robustness of our results.
2 Model
2.1 Firms and markets
There are two separated markets i ∈ {1, 2}. Each of these markets contains three firms
ki ∈ {si, li, ri}. Firms si and i are two suppliers offering horizontally differentiated goods of
characteristics θ through a monopolist retailer ri. Supplier l is a "large supplier", active on
the two markets (so l1 = l2 = l) and carrying two differentiated products of characteristics
θ ∈ {A,C}. By contrast, si is a "small supplier" active uniquely on one market and carry-
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ing only one product of characteristics θ = Bi, for the sake of simplicity we consider that
B1 = B2 = B.
Finally, in the economy there are three suppliers and two retailers ki ∈ {s1, s2, r1, r2} and
three characteristics of products θ ∈ {A,B,C}.
Suppliers have symmetric and constant marginal cost of production c, retailers do not
support any additional cost. Retailers have constrained stocking capacity N = 2, which
means that each retailer can source at most two varieties of products. On each market at
least one product is excluded.
2.2 Assumptions on industry profit
We introduce the primitive industry profit ΠXi and ΠXY
i (p) representing the maximum in-
dustry profit for a given assortment.
• ΠXi = arg maxs(p− c)DX
i (p) is the maximum industry profit on market i when ri offers
one product X.
DXi (p) denotes the demand function of product X sold at price p on market i when X
is the only product available on the market.
• ΠXYi = arg max{p,p′}(p − c)DXY
i (p, p′) + (p′ − c)DY Xi (p′, p) is the maximum industry
profit on market i when ri offers two products X and Y .
DXYi (p, p′) denotes the demand function for product X on market i when X and Y are
respectively sold at price p and p′ on the market.
We make the following assumptions on primitive industry profits:
Among all potential single product assortments, A (resp. C) generates the highest indus-
try profit on market 1 (resp. market 2):
ΠA1 ≥ ΠB
1 > ΠC1 > 0 (1)
ΠC2 ≥ ΠB
2 > ΠA2 > 0
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The above assumption implies that the preferences for the two products are inverted among
markets.
For the sake of simplicity, for each market, we will denote by "H" the preferred product,
"L" the least preferred product and M the middle one. Henceforth (1) becomes:
∀i ∈ {1, 2}ΠHi ≥ ΠM
i > ΠLi > 0 (2)
Among all two products assortments, AB (resp. BC) generates the highest industry profit
on market 1 (resp. market 2):
∀i ∈ {1, 2}ΠHMi ≥ ΠHL
i > ΠMLi > 0 (3)
Products can either be imperfect substitutes or independent, which implies that any
assortment of two products does not yield more surplus than the sum of industry profits
generated by each product:
∀i ∈ {1, 2}ΠHi + ΠL
i ≥ ΠHLi > ΠH
i (4)
The marginal contribution of M to the industry profit ΠHMi is lower than its marginal
contribution to the industry profit ΠMLi .
(ΠMLi − ΠL
i ) ≥ (ΠHMi − ΠH
i ) (5)
The only difference between market 1 and 2 is that preferences are inverted between
products A and C.
∀X ∈ {H,M,L},ΠX1 = ΠX
2 (6)
∀XY ∈ {HM,ML,HL},ΠXY1 = ΠXY
2
Assumption (1) is close to the one made Inderst and Shaffer (2007). Considering only one
market, assumptions (2) to (5) are common to Chambolle and Molina (2018). Assumption
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(6) is made for the sake of simplicity.
2.3 Timing and listing strategies
We are interested in comparing the economic outcome under three types of buying strategies:
no buying group, partial coverage buying group, full coverage buying group. For each case,
choices of suppliers and retailers can be represented by the following sequential game of two
stages:
- Stage 1: Suppliers observe retailers’ listing strategy and the set of listing assortments available.
They compete in slotting-fees for being listed. The number of products listed by each
retailer cannot exceed the capacity constraint N = 2. Slotting-fees are purely vertical,
they are conditional to bidder’s product(s) listed but cannot be conditional to other
supplier product(s) listed. Slotting fees are paid uniquely if the corresponding offer is
selected by the retailer.
- Stage 2: For listed products, retailer ri engages in a bilateral negotiation with suppliers to de-
termine the tariffs of products. Negotiation are simultaneous, contracts are secrets and
consist of a fixed-fee.
The three listing strategies may affect stage 1 of the game, other stages are unchanged.
Listing strategies are defined as follows.
• No buying group: Each retailer negotiates independently which product to list. Retailer
ri lists at most two products among: A and C offered by l and B offered by si. For
each market, suppliers si and l pay to ri the slotting fee corresponding to the chosen
listing assortment.
• Partial coverage buying group: Retailers take a joint listing decision on large supplier’s
product but continue to list independently small suppliers’ products. In this case,
asymmetric listing assortments of two product are not available: for example listing
AB in country 1 and BC in country 2 is not feasible.
Slotting fees are attributed as follows. For each market, assume si’s product listed,
then each retailer collect separately the corresponding slotting-fee. Now, assume l’s
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product(s) listed, then retailers collect and share a unique slotting-fee from l for both
markets. The chosen joint-listing decision is the one maximising the joint profit of
retailer. Common slotting fee sharing will discussed in section ...
• Full coverage buying group: Retailers take a joint listing decision over the whole product
line. Just like with limited coverage buying groups, retailers take a joint listing decision
on large supplier’s products. Under Full coverage buying group strategy, retailers take
a joint listing decision on small suppliers as well: at most one supplier of product B
is listed for serving both markets. In this case, small suppliers are able to serve both
markets at any fixed exporting cost E. The chosen joint-listing decision is the one
maximising the joint profit of retailer.
2.4 Equilibrium concept
The equilibrium concept we use here is the same as Chambolle and Molina (2018). In stage 2
of the game, each retailer engages in bilateral negotiation with suppliers of its listed products.
We use a bargaining protocol à la Horn and Wolinsky (1988) commonly referred as the "Nash-
in-Nash" according to Collard-Wexler et al. (2019), which is an extension of the contract
equilibrium concept developed in Crémer and Riordan (1987) and Allain and Chambolle
(2011). Several assumptions are made in this bargaining framework. First, negotiations
are simultaneous and contracts are secrets. Second, firms are assumed to be schizophrenic,
which means that a firm negotiating with a given firm do not know anything about its own
negotiations with other firms. Because of secret negotiation and schizophrenia, for a given
negotiation firms must perform beliefs on outcome of other negotiations outcomes. In this
setting, firms have passive beliefs which means that players don’t change their beliefs on
the other players’ action if they receive an offer out of the equilibrium path (McAfee and
Schwartz (1994)). Third, firm can have asymmetric exogenous bargaining, α (resp. (1 − α)
denotes exogenous bargaining power of the retailer (resp. supplier).
In this setting, some products are not listed because of the limited listing capacity of retailers,
thus suppliers compete for being listed. Scarce listing capacity play a role in the division of
surplus between retailers and suppliers through combination of stage 1 and stage 2. This
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framework closely relates to the bargaining literature on bargaining with outside options (eg :
Shaked and Sutton (1984), Binmore et al. (1989) ). In this literature status-quo payoff differs
from bargainer’s outside option. The status-quo payoff correspond to bargainer’s position if
negotiation lasts forever without finding an agreement whereas the outside option refers to
bargainer’s best alternative outside the negotiated agreement.
3 Resolution of the bargaining stage
Regardless of the listing strategy, the outcome of stage 2 negotiation depends on the outcome
of stage 1 assortment decision. The bargaining resolution is common to the three listing
strategies. The results founded here will be used in the following sections considering others
strategies. We consider the bargaining solution in one country, for a given outcome of stage
1 listing decision; results are symmetric in the other.
Assortment HL is chosen In this case, there is only one negotiation for each retailer,
who negotiates with the same supplier for both products simultaneously. Straightforward
resolution of the Nash bargaining in stage 2 yields the following equilibrium fee FHLli =
(1− α)ΠHL for the large supplier, and zero for the small one whose production is not sold.
In equilibrium, the retailer thus receives a share α and the large supplier a share 1−α of
the joint profit .
πHLri = αΠHL
πHLli = (1− α)ΠHL
πHLsi = 0
Product M is listed Consider first the subgames where retailer ri sells product M, that
is, assortment is XM , with X ∈ {H,L}. Straightforward resolution of the Nash bargaining
in stage 2 yields the following equilibrium fees:
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FXMli = (1− α)(ΠXM − ΠM) (7)
FXMsi = (1− α)(ΠXM − ΠX) (8)
Each supplier thus receives (1−α) times his contribution to the joint profit, and equilibrium
profits are as follows:
πXMli = FXM
li = (1− α)(ΠXM − ΠM)
πXMsi = FXM
si = (1− α)(ΠXM − ΠX)
πXMri = ΠXM − FXM
li − FXMsi = (1− α)(ΠX + ΠM) + (−1 + 2α)ΠXM
4 Resolution and equilibrium profits
In this section, we solve the game and present equilibrium profits for each listing strategy of
the retailers.
4.1 No buying group
Assume first that retailers have opted for no buying group strategy. In stage 1, for each
market suppliers si and l compete in slotting fees to be listed by retailer ri. Listing decision
are independent, we present here the resolution for a given market.
First note that large supplier l is never ready to pay a positive slotting fee to have only
one of its products listed by retailer ri: indeed, as there is only one possible other supplier
selling only one product, and as ri prefers to attributes its two slots, l does not have to pay
to have one product listed. He must however compete with the small supplier whenever he
wishes to ensure that his two products are sold, hence he will be ready to pay a positive fee
SHLli .
Assume now that retailer ri lists productM from si. Then ri is better off listing H instead
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of L, as the slotting fee paid by the small supplier is unchanged (by assumption the slotting
fee paid by the small supplier is not conditional upon the other product sold), and the sales
profit is higher:
πHMri > πML
ri (9)
⇔α(ΠHM − ΠML) + (1− α)((ΠML − ΠL)− (ΠHM − ΠH)) > 0 By assumption 5
Hence retailer ri will choose either to sell the assortment HM , or to sell the assortment
HL. Let us know consider the competition between the large and the small suppliers.
The maximum fee the large supplier will be ready to pay to have product L listed is:
SHLli ≡ πHL
li − πHMli (10)
= (1− α)(ΠHL − ΠHM + ΠM) (11)
The maximum fee the small supplier will be ready to pay to have product M listed is:
SHM
si ≡ πHMsi (12)
= (1− α)(ΠHM − ΠH) (13)
Proposition 1 In the baseline model with independent sourcing, markets are fully separated.
The equilibrium is such that in each country, the two favourite products are sold at the
equilibrium, i.e AB on market 1 and BC on market 2. Small suppliers s1 and s2 have to pay
a slotting fee for not being replaced by l ’s excluded good.
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Equilibrium profits are the followings:
ΠHMri = ΠHL − (1− α)(ΠHM − ΠM) if ΠHL − α(1− α)ΠH > 0 (14)
= (1− α)(ΠH + ΠM)− (1− 2α)ΠHM otherwise
ΠHMli = (1− α)(ΠHM − ΠM) (15)
ΠHMsi = ΠHM − ΠHL if ΠHL − α(1− α)ΠH > 0 (16)
= (1− α)(ΠHM − ΠH) otherwise
Sketch of proof for Proposition 1 For each market assortment HM is always chosen at
the equilibrium because small supplier is willing to offer an higher profit to have his product
listed than large supplier to have his two products listed. Formally it can be written as
follows :
πHMri + S
M
si ≥ πHLri + S
HL
li (17)
At the equilibrium, si secures a slot and maximises his profit, thus makes an offer such
that the retailer ri is indifferent between choosing HM and HL, so we have:
SHMsi = πHL
ri − πHMri + S
HLli (18)
⇔SHMsi = ΠHL − αΠHM − (1− α)ΠH .
Equilibrium profits are determined as follows :
ΠHMri = πHM
ri + SHMsi if + SHM
si > 0
= πHMri otherwise
ΠHMli = πHM
li
ΠHMsi = πHM
si − SHMsi if + SHM
si > 0
= πHMsi otherwise
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4.2 Limited coverage buying group
Assume now that retailers r1 and r2 have opted for a limited coverage buying-group. In stage
1, suppliers si, sj and l compete in slotting fees to be listed by retailers. Listing decision are
no longer independent because the listing decision on large supplier product(s) is common
for the two retailers. With such a limited coverage buying group, any asymmetric assortment
of two products by market is not feasible: both retailers commit to selling the same product
assortment, that is, either AB, BC, or AC – whenever product l is in the assortment however,
each retailer sources from his own local supplier.
As in the no buying group case, the large supplier l is never ready to pay a positive slotting
fee to have only one of its products listed by retailers. Consider now the supplier’s willingness
to pay for having its two products listed. Note that, because of assumption (5), retailers and
suppliers are indifferent between listing AB or BC, the two listing decisions give perfectly
symmetric economic outcome and arise at same conditions. For the sake of simplicity, we
focus here on competition between the large and small suppliers on assortments AB and AC.
The case of the assortment BC will be symmetric.
Lemma 1 large supplier l has a higher willingness to pay for having its two products listed
in both markets when retailers have opted for limited coverage buying group compared to the
case when they have opted for no buying group.
Sketch of proof for Lemma 1 The maximum fee the large supplier is ready to pay to
have product C listed is the difference between the profit he receives when he sells the two
products on both markets, and the profit he receives when he sells only one product on both
markets, that is,
SHLl ≡(πHL
l1 − πHMl1 ) + (πHL
l2 − πMLl2 )
This fee is larger than (πHLl1 − πHM
l1 ) + (πHLl2 − πHM
l2 ), the total willingness to pay of supplier
l for having its two products sold in each market with no buying group strategy.
Lemma 2 Sum of suppliers willingness to pay to have their products listed on market 1 and
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2 when retailers have opted for limited coverage buying group compared to the case when they
have opted for no buying group.
Ss = SHM
s1 + SML
s2 (19)
With SHMs1 = πHM
s1 and SMLs2 = πML
s2
The maximum fee small supplier 1 will be ready to pay to have product B listed on
market 1 is the same as in the no buying group case SHM
s1 = πHMs1 . The maximum fee small
supplier 2 will be ready to pay to have product B listed on market 2 is higher than in the no
buying group case SMLs2 = πML
s2 because of assumption (5).
Lemma 3 Product B is listed on market 1 if and only if it is listed on market 2. Retailers
decision to list product B on each market depends of the sum of slotting fees proposed by the
two small suppliers. Thus there exists a continuum of slotting fee SHMs1 and SML
s2 leading to
assortment AB.
Retailers take the listing decision which leads to the highest joint profit, so the listing
agreements depends of the sum of slotting fees proposed by the two suppliers. Finally, small
suppliers stay on the market if and only if:
ΠHMr1 + ΠML
r2 ≥ ΠHLr1 + ΠHL
r2 (20)
⇔πHMr1 + πML
r2 + SHMs1 + S
MLs2 ≥ πHL
r1 + πHLr2 + S
HLl
⇔(ΠHM1 − ΠHL
1 )− (ΠHL2 − ΠML
2 ) ≥ 0
⇔ΠHM + ΠML ≥ 2ΠHL
Proposition 2 When retailers have opted for limited coverage buying group, two types of
listing assortments can arise at the equilibrium:
• Large supplier partial listing: If ΠHM + ΠML ≥ 2ΠHL, listing decision is AB or
BC. Each small supplier si has its product listed on market i, large supplier l has a
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unique product listed on both markets. Resulting profits are:
ΠAB,pr = ΠAB
r1 + ΠABr2
= 2ΠHL + (1− α)(2ΠM − ΠML − ΠHM) if SABl ≥ 0
= (1− α)(ΠH + ΠL + 2ΠM − ΠHM − ΠML) + α(ΠHM + ΠML) otherwise
ΠAB,ps = ΠHM + ΠML − 2ΠHL if SAB
l ≥ 0
= (1− α)(ΠHM − ΠH + ΠML − ΠL) otherwise
ΠAB,pl = ΠAC
l1 + ΠACl2
= (1− α)(ΠHM − ΠM) + (1− α)(ΠML − ΠM)
• Small suppliers exclusion: If 2ΠHL > ΠHM + ΠML, listing decision is AC, thus
large supplier has its two products listed and small suppliers s1 and s2 are excluded.
Resulting profits are:
ΠAC,pr = ΠAC
r1 + ΠACr2
= α(ΠHM + ΠML) + 2(1− α)ΠM if SACl ≥ 0
= 2αΠHL otherwise
ΠAC,ps = ΠAC
s1 + ΠACs2 = 0
ΠAC,pl = ΠAC
l1 + ΠACl2
= 2ΠHL − α(ΠHM + ΠML)− 2(1− α)ΠM if SACl ≥ 0
= 2(1− α)ΠHL otherwise
Sketch of proof for Proposition 2 Retailers choose assortment AB against AC if small
suppliers s1 and s2 offer a slotting fee such that:
πHMr1 + πML
r2 + SAB,ps ≥ πHL
r1 + πHLr2 + S
HLl
16
With SAB,ps = SHM
s1 + SMLs2 . So we have:
SAB,ps = (πHL
r1 + πHLr2 + S
HLl )− (πHM
r1 + πMLr2 )
= 2ΠHL − (1− α)(ΠH + ΠL)− α(ΠHM + ΠML)
Retailers choose assortment AC against AB if large supplierl offers a slotting fee such that:
πHLr1 + πHL
r2 + SAC,pl ≥ πHM
r1 + πMLr2 + Ss
So we have:
SAC,pl = πHM
r1 + πMLr2 + Ss − (πHL
r1 + πHLr2 )
= Max{0, 2(1− α)ΠM + α(ΠHM + ΠML − 2ΠHL)}
When assortment AB is chosen equilibrium profits are determined as follow :
ΠAB,pr = πHM
ri + πMLri + SAB,f
s if SAB,ps > 0
= πHMri + πML
ri otherwise
ΠAB,ps = πHM
si + πMLsi − SAB,f
s if SAB,ps > 0
= πHMsi + πML
si otherwise
ΠAB,pl = πHM
li + πMLli
When assortment AC is chosen equilibrium profits are determined as follow :
ΠAC,pr = 2πHL
ri + SAC,pl if SAC,p
l > 0
= 2πHLri otherwise
ΠAC,ps = 0
ΠAC,pl = 2πHL
li − SAC,pl if SAC,p
l > 0
= 2πHL,pl1 otherwise
17
4.3 Full coverage buying group
Assume that retailers have opted for full coverage buying group strategy. This agreement
implies that retailers take a joint listing decision over the whole product line. The difference
with limited coverage buying group is that in this case, at most one supplier of product B is
listed for serving both markets. Serving both markets generate a fixed exporting cost E for
small suppliers. Products listed by each retailers are exactly the same (same product offered
by the same supplier). Candidate listing assortments are : AB, BC, AC.
As in the two previous cases, large supplier l is never ready to pay a positive slotting fee
to have only one product listed. As in the limited coverage buying group case, retailers and
suppliers are indifferent between assortments AB or BC. Let us consider retailers choice
between listing assortment AB and AC.
large supplier l has the same willingness to pay to have its two products listed in both
countries than in the limited coverage buying group case.
SAC
l = (πHLl1 − πHM
l1 ) + (πHLl2 − πHM
l2 )
Each small supplier si has to choose between being listed for the two market or not being
listed.
SACsi = (πHM
si + πMLsi )− E (21)
Retailers take the joint listing decision which leads to the highest joint profit. Assortment
AB is chosen if and only if :
ΠHMr1 + ΠML
r2 ≥ ΠHLr1 + ΠHL
r2
⇔πHMr1 + πML
r2 + SACs ≥ πHL
r1 + πHLr2 + S
HLl (22)
⇔(ΠHM1 − ΠHL
1 )− (ΠHL2 − ΠML
2 )− E ≥ 0
18
Proposition 3 When retailers have opted for full coverage buying group, two types of listing
assortments can arise at the equilibrium:
• large supplier partial listing: If ΠHM +ΠML−E ≥ 2ΠHL, listing decision is AB or
BC. One of the two small supplier si has its product listed on both market, the second is
excluded, large supplier l has a unique product listed on both markets. Resulting profits
are :
ΠAB,fr = (1− α)(2ΠM) + α(ΠHM + ΠML)− E (23)
ΠAB,fs = 0 (24)
ΠAB,fl = (1− α)((ΠHM − ΠM) + (ΠML − ΠM)) (25)
• Small suppliers exclusion: If 2ΠHL > ΠHM + ΠML − E, listing decision is AC.
Small suppliers are excluded and large supplier has its two products listed on both mar-
kets. Resulting profits are :
ΠAC,fr = 2(1− α)(ΠM) + α(ΠML + ΠHM)− E if SAC
l > 0 (26)
= 2αΠHL otherwise
ΠAC,fs = 0 (27)
ΠAC,fl = 2ΠHL − 2(1− α)ΠM − α(ΠHM + ΠML) + E if SAC
l > 0 (28)
= 2(1− α)ΠHL otherwise
Sketch of proof for Proposition 3 Assume retailers choose listing assortment AB. Equi-
librium slotting fee paid by the chosen small supplier do not depend of large supplier willing-
ness to pay to have two products listed. Small suppliers compete in price and sell perfectly
substitutes products. Each retailer offers it maximal willingness to pay, no matter large
suppliers willingness to pay for selling two products:
SAB,fsi = (πHM
si + πMLsi )− E
= Max{0, (1− α)((ΠHM − ΠH) + (ΠML − ΠL))− E}
19
Assume now that retailers choose listing assortment AC. Slotting fee paid by large
supplier to have its two products listed depends of small suppliers willingness to pay. Retailers
choose assortment AC if large supplier l offers a slotting fee such that:
πHLr1 + πHL
r2 + Sl ≥ πHMr1 + πML
r2 + SABsi
So we have:
SACl = πHM
r1 + πMLr2 + SAB
si − (πHLr1 + πHL
r2 )
= Max{0, (1− α)(2ΠM) + α(ΠHM + ΠML − 2ΠHL)− E}
When assortment AB is chosen equilibrium profits are determined as follows :
ΠAB,fr = πHM
ri + πMLri + SAB,f
s
ΠAB,fs = 0
ΠAB,fl = πAC
li + πACli
When assortment AC is chosen equilibrium profits are determined as follows :
ΠAC,fr = 2πHL
ri + SAC,fl if SAC,f
l > 0
= 2πHLri otherwise
ΠAC,fs = 0
ΠAC,fl = 2πHL
l1 − SAC,fl if SAC,f
l > 0
= 2πHLl1 otherwise
5 Comparison of the different listing strategies
In this section we compare suppliers profits, consumer surplus and retailers profits for the
different listing strategies.
20
5.1 Listing strategies consequences for small suppliers profits
Proposition 4 (i) Small suppliers’ profit is negatively affected by the two types of buying-
groups (ie: their profits are reduced and they can be excluded from the market). (ii) full
coverage buying group is more harmful than partial coverage buying group (ie: exclusion is
more likely and profit reduction is larger).
Πs ≥ Πps ≥ Πf
s
Where Πs = Πs1 + Πs2
Sketch of proof for Proposition 4 (i) We show that Πs ≥ Πps ≥ Πf
s is always satisfied.
It is straightforward that Πps ≥ Πf
s and Πs ≥ Πfs are satisfied since Πf
s = 0 whereas Πps ≥ 0
and Πs. Πs ≥ Πps can be show comparing slotting fees paid by small suppliers. Assume there
is a situation in which Πs < Πps. It must in a situation in which with partial coverage buying
group assortment AB is chosen. Indeed, Πps = 0 when AC is chosen. As tariffs negotiated in
stage 2 are the same, SAB,ps > Ss must be satisfied, but this inequality is never satisfied.
(ii) We show that joint listing strategies can lead small retailers to be excluded and
particularly when a full coverage buying group is implemented. Small suppliers are never
excluded when there is no buying group, they are excluded when 2ΠHL > ΠHM + ΠML with
partial coverage buying group and when 2ΠHL > ΠHM + ΠML−E with full coverage buying
group. As E is positive it is clear that exclusion is more likely with full coverage buying
group.
5.2 Listing strategies consequences for large suppliers profits
Proposition 5 (i) The worst listing strategy for large suppliers profit is partial coverage
listing strategy. (ii) Large suppliers may earn higher profits when retailers adopt full coverage
listing strategy than when the adopt independent listing strategies.
Πpl ≤ Πl and Πp
l ≤ Πfl
21
Sketch of proof for Proposition 5 (i) Large suppliers’ profit is lower when retailers
have formed partial coverage buying group than when they have not formed buying group.
Assume retailers have formed a partial coverage buying group and assortment is either AB
or BC, as in the case without buying group large supplier do not pay any slotting fee for
having one product listed. But in this case large supplier sell the least preferred good on one
of the market instead of the preferred good, so he earns a smaller tariff. Assume now that
with partial coverage buying group AC is chosen: large supplier pay a slotting fee to sell its
two products on both market instead of selling the preferred good in each market. Tariffs
increase on sales do not compensate the slotting fee (otherwise AC would arise in the no
buying group case) so its profit is lower than with no buying group.
Large suppliers’ profit is lower when retailers have formed a partial coverage buying group
than when they have formed a full coverage buying group. Assume retailers have formed a
full coverage buying group and assortment is either AB or BC: large supplier profit is the
same than with limited coverage buying group. Indeed, assortment would have been the
same under partial coverage buying group and for both listing strategy large suppliers do not
pay slotting fee. Assume now that retailers have formed a full coverage buying group and
assortment is AC. With partial coverage buying group assortment would have been AB or
AC. In both cases, large supplier pay a slotting fee less important with full coverage buying
group because of the exporting cost that reduce profitability to enter the market for small
suppliers.
(ii) Assume retailers have formed a full coverage buying group and the exporting cost E
for small supplier is so high that it is not profitable for small suppliers to enter the market,
then large suppliers are in a monopolistic situation, they do not have to pay a positive slotting
fee for having their two products listed.
5.3 Listing strategy consequences for consumers
Proposition 6 (i) Joint listing strategies exclude the efficient assortment where the two
preferred goods HM are sold in both markets. (ii) Full coverage buying group implementation
may generates more assortment inefficiency than partial coverage buying group.
22
Sketch of proof for Proposition 6 (i) When retailers do not form buying group, the two
preferred products are sold in each market, AB on market 1 and BC on market 2. When
retailers adopt a joint listing strategy, the best assortment is not available by assumption.
Equilibrium assortments of the two joint listing assortments are either AB, BC or AC sold
in both markets. When the product assortment is AB or BC, on one of the two markets
the preferred product in no longer available. When the product assortment is AC, the least
preferred product is sold in both markets instead of the medium one.
(ii) When ΠHM + ΠML > 2ΠHL > ΠHM + ΠML − E assortments AB or BC are more
efficient than AC (ΠHM + ΠML > 2ΠHL), they are chosen when retailers have formed a
partial coverage buying group but not when they have formed a full coverage buying group
because 2ΠHL > ΠHM + ΠML − E. In this case
5.4 Listing strategy consequences for retailers
In this subsection we provide first general results on retailers joint profitability without
demand specification then we use a linear demand to provide more insights.
5.4.1 General results
Proposition 7 Joint listing strategy is jointly profitable for the two retailers if and only if
their bargaining power α is not too large.
Sketch of proof for Proposition 7 Result (i) is in accordance to Inderst and Shaffer
(2007). Creating a buying group reduces the overall variety of products, thereby harming
industry profit. Indeed, by assumption the preferred assortment differs on the two markets,
therefore committing to a similar assortment in the two markets generates inefficiencies on
at least one of the markets. Despite this efficiency retailers may find this strategy profitable
because committing to a common listing strategy they enhances their buyer power, as the
threat of being delisted on all markets enhances competition between the suppliers at the
listing stage. Forming a buying group retailers "capture a larger share of a smaller pie", this
is profitable when α is not to big, ie when not forming a buying group retailers capture a
relatively small share of the industry profit.
23
Lemma 4 When 2ΠHL > ΠHM +ΠML−E full coverage buying group is dominated by partial
coverage buying group.
Sketch of proof for Lemma 4 When 2ΠHL > ΠHM +ΠML−E retailers listing assortment
is AC when they form a partial or full coverage buying group. Comparing retailers profits
for the two joint listing strategies consist in comparing slotting fees paid by large suppliers
which is increasing with small retailers willingness to pay to be listed. As with full coverage
buying group small suppliers support and exporting cost E their willingness to pay to be
listed is reduced.
5.4.2 Results obtained with linear demand application
In order to have more insights on best listing strategies we use a linear demand model and
provide graphic illustrations. For x, z ∈ {h,m, l} & x 6= z we assume that representative
consumer utility can be written as follows:
UxZ = xqx + zqz −12(q2
x + q2z)− aqx ∗ qz − pxqx − pzqz
Which leads to the following demand functions :
qx = x− az − px + apz
a2 − 1qz = z − ax− pz + apx
a2 − 1
Parameter a represents the degree of substitutability between goods. h,m, l represents
intrinsic preference for goods H,M,L. We assume h = 2, l = 1 m ∈ [1, 2] and a ∈ [0; 0.5]
which satisfies the hypothesis of the model.
These graphs provide three main insights :
(i) Forming a buying group is not profitable for retailers when m is close to l. In this
case, slotting fees paid by small suppliers on each market or close to their contribution to the
industry profit, hence it is not profitable to avoid the efficient assortment for rent extraction
motives. (ii) Forming a full coverage buying group is profitable when m is close to h. When
24
forming a full listing decision retailers capture the whole profit generated by small suppliers.
it is interesting to do so when M has an important contribution to the industry profit and E
is not to high. (iii) Forming a partial coverage buying group is profitable is profitable when
m take intermediate values. When m is relatively low AC is chosen, the large supplier accept
to pay a high slotting fee to have his to products listed in the two markets.
(a) α = 0.1, E = 0.2 (b) α = 0.3, E = 0.2
(c) α = 0.5, E = 0.2
Figure 1. Listing strategies and market structures
25
6 Robustness checks and policy implications
6.1 Discussion on retailers’ endogenous choice of listing strategy
Until now we have not endogenize the listing strategy decision. Here, we discuss quickly
challenges raised by such an endogenization. Assume an extension of the game we have
considered until now in which retailers choose their listing strategy before Stage 1. We
discuss the following decision rule : Retailers always adopt the listing strategy maximizing
their joint profit. Such a decision is always a best strategy for each retailer only if they
are able to commit on slotting fee sharing such that each of them is assured that he will
earn at least the same profit without forming a buying group. Sharing equally slotting
fees jointly earned may not satisfy this condition. Indeed, when joint listing strategy is
formed and asymmetric equilibrium assortment is chosen (either AB or BC) one of the two
retailers support an inefficient assortment on its market whereas the other continue to sell
the two preferred goods. Forming a buying group leading to small suppliers exclusion (listing
assortment is AC) always supports equal sharing of slotting fees jointly earned.
6.2 Tariffs
We have assumed that tariffs negotiated in stage 2 consist of a fixed fee. However, our
results extend to a more general secret contract framework with efficient two-part tariffs, as
Bernheim and Whinston (1985) O’Brien and Shaffer (1997) have shown that in a vertical
structure where manufacturers sell to a common retailer, bilateral efficiency requires that
unit wholesale prices are set to marginal cost. This result hold for public or secret contracts.
More generally, any setup leading to efficient, cost based tariff would yield the same result.
6.3 Policy implications
In line with Inderst and Shaffer (2007) this article shows that buying groups may harm welfare
by reducing product variety. This paper provides additional insights for competition policy
in particularly it is the first to question the economic impact of the buying group coverage.
This is precisely the question the french competition authority mentioned in July 2018 when
26
opening its new investigation. First, we show that full coverage buying groups may be more
harmful for consumers than partial coverage buying groups because they increase retailers
incentives to choose inefficient assortment for profit extraction purpose. Second, we show
that full coverage buying groups affect more suppliers than partial coverage buying groups.
Finally we show that small suppliers may be affected by buying groups implementation even
if they are outside of the agreement’s coverage.
7 Conclusion
This article analyzes the impact of retailers’ buying groups on both product variety and profit
sharing within the vertical chain.
First, we find that creating a buying group reduces the overall variety of products, thereby
harming consumer surplus and welfare. Retailers may find this strategy profitable because
when committing to a common listing strategy they enhance their buyer power, then they
are able to capture a larger share of a smaller industry profit. This result is in line with
Inderst and Shaffer (2007), however we show that the buying group creation may generate
inefficiency on both markets.
Second, we find that buying groups affect negatively suppliers profits. For small suppliers,
both types of buying groups are harmful but full coverage is the worst. For large suppliers,
full coverage buying groups are worst than partial coverage buying groups whenever they are
jointly profitable for the retailers. Finally, retailers joint profit is larger with partial coverage
than with full coverage when, in equilibrium, the small producer is excluded.
27
8 Appendix
8.1 Stage 2 negotiation
8.1.1 Product M is sold
Consider first the subgames where retailer ri sells product M, that is, assortment is XM ,
with X ∈ {H,L}.
Consider the negotiation between retailer ri and supplier b. The retailer’s profit when he
succeeds in both negotiations is ΠXM −FXMli −FXM
si , while his status quo profit in case of a
breakdown is ΠM−FXMsi . The supplier’s profit if the negotiation succeeds is FXM
li +Flj, while
his status quo profit in case of a breakdonw is Flj. Consider now the negotiation between
retailer ri and supplier si. The retailer’s profit when he succeeds in both negotiations is
ΠXM − FXMli − FXM
si , while his status quo profit in case of a breakdown is ΠM − FXMli . The
supplier’s profit if the negotiation succeeds is FXMsi , while his status quo profit in case of a
breakdonw is 0.
Standard resolution of the Nash bargaining thus yields the following profit sharing:
(1− α)(ΠXM − FXMli − FXM
si − (ΠM − FXMsi ) = α(FXM
li + Flj − Flj)
(1− α)(ΠXM − FXMli − FXM
si − (ΠM − FXMli ) = αFXM
si
It leads to the following equilibrium values:
FXMli = (1− α)(ΠXM − ΠM) (29)
πXMri = ΠXM − FXM
li − FXMsi = (1− α)(ΠX + ΠM) + (−1 + 2α)ΠXM (30)
πXMli = FXM
li = (1− α)(ΠXM − ΠM) (31)
πXMsi = FXM
si = (1− α)(ΠXM − ΠX) (32)
28
8.1.2 Assortment HL is chosen
Consider the negotiation between retailer ri and supplier b. The retailer’s profit when he
succeeds in both negotiations is ΠHL−FHLli , while his status quo profit in case of a breakdown
is 0. The supplier’s profit if the negotiation succeeds is FHLli +FHL
lj , while his status quo profit
in case of a breakdonw is FHLlj . In this case, there is only one negotiation, retailer negotiate
for both products simultaneously, and the nash condition can be written as follows:
(1− α)(ΠHL − FHLli ) = αFHL
li
It leads to the following equilibrium values:
FHLli = (1− α)(ΠHL) (33)
πHLri = ΠHL − FHL
l1 = αΠHL (34)
πHLli = FHL
li = (1− α)(ΠHL) (35)
πHLsi = 0 (36)
29
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