Information Sharing and Upstream Exclusion
Tianle Song*
April, 2017
Abstract
This paper investigates how information sharing between rivals affects exclusion in a
dynamic model. The paper presents a novel mechanism for information sharing, showing
that the vertical contracting practices between the incumbent firm and the retailers can
induce strategic sharing by different types of entrants: when an entrant’s cost-efficiency is
its private information, the high efficient entrants choose to share the information with the
incumbent, while the relatively less efficient entrants refrain from doing so. Under
voluntary sharing, the sharing entrants enter the market earlier, while the non-sharing ones
may enter later. Since entry intensifies competition, information sharing analyzed here may
well have significant pro-competitive effects. Meanwhile, the model also indicates that too
much transparency may reduce social welfare. Policy implications for antitrust regulation
are then discussed.
Keywords: information sharing, upstream exclusion, dynamic entry, vertical practices,
antitrust
JEL Codes: D43, K21, L14, L22, L40, L81
* Song: Department of Economics, School of Business and Management, Hong Kong University of Science and Technology, Room
4063, Lee Shau Kee Business Building, Hong Kong (e-mail: [email protected]).
1
1. Introduction
The competitive impact of information sharing has been an important and controversial
issue in the antitrust arena. It is observed that while courts often conclude that the sharing
of price information is a per se violation of antitrust laws due to the potential anticompetitive effects (e.g., facilitating collusion between rival firms), they may adopt the “rule
of reason” approach to the sharing of non-price information (e.g., the unit cost of
production, the sales quantity and etc.). For instance, the U.S. Supreme court in the Maple
Flooring Manufacturers case takes a sympathetic view of sharing the non-price information,
recognizing that sharing such information may improve market efficiencies. 1 The E.U.
courts, in contrast, adopt a much harsher approach to discourage the sharing of
competitively sensitive information (both the price and the non-price) among the firms. 2 In
the famous UK Agricultural Tractor Exchange case, for example, the European
Commission rejected an agreement to the sharing of information between tractor
manufacturers on the ground that the agreement would lead to significant barriers to entry
in a concentrated market, regardless of whether the new entrants join the exchange system
or not. 3
In the decision, it is noted that the commission also believes that the information
sharing agreements will put the new entrants at a disadvantage even if the entrants can
voluntarily choose to share their private information. The reason is as follows (see OECD
2010):
“…If a new supplier chooses not to become a member of the exchange, he would be
disadvantaged by the fact that he did not have access to the detailed and accurate
market information about other suppliers which is available to members of the
exchange. If, on the contrary, it chooses to become a member of the exchange, it would
be forced to reveal to its competitors its own confidential data on a very detailed level,
thus permitting the incumbent suppliers to use such information to prevent aggressive
market strategies by the new member.”
An observation is that the argument here has only emphasized the damage from the
incumbent firms and ignores the possible benefits for the entrants. In fact, the entrants may
also have incentives to share information. For instance, Armantier and Richard (2003a)
1
See Maple Flooring Manufacturers’ Assn. v. United States 268 U.S. 563 (1925).
2
See UK Agricultural Tractor Exchange OJ L 68/19 (1992) and the more recent cases, Dole Food Company et al. v. Commission, Case
T-588/08 and Case C-286/13 P. In the UK Agricultural Tractor Exchange case, the information shared is about the retail sales and the
market shares and is thus the “non-price” information.
3
See Organisation for Economic Co-operation and Development (OECD). 2010. “Information Exchanges between Competitors under
Competition Law.” http://www.oecd.org/competition/cartels/48379006.pdf.
2
find that information sharing among the entrants may encourage entry when the
correlation of the unit costs is low and the products are close substitutes. That is,
theoretically, entrants can gain from sharing information. Note that reaching an agreement
is not the only way for entrants to share information with incumbents. For example, a
mobile phone manufacturer that advertises detailed product information (new technology,
key components, prices and etc.) prior to entry is communicating information to incumbent
manufacturers. Yet, this sort of information sharing has not been formally analyzed in the
literature, and thus its competitive effects are still unclear.
The purpose of this paper is to provide a theoretical framework for filling in this gap.
The model considers a vertical market structure in which there are a potential entrant and
an active incumbent in the upstream and many retailers in the downstream, while entry
requires downstream accommodation. The entry game proceeds for infinitely many periods,
and the entrant may voluntarily share its private information about production efficiency
with the incumbent at any time. The pattern of entry is determined by the entrant’s
information sharing strategy as well as the interaction between all agents in the dynamic
game.
There are several specifications about the model to notice. First, the cost-efficiency of
the entrant is the only private information in the model. Thus, “information sharing”
considered here is essentially the unilateral sharing by the entrant. This setting can isolate
the effects of information sharing by other agents and let the analysis focus on the pure
effects of information sharing by the entrant. Second, the information shared is about the
unit cost of production. Hence, the discussion falls into the category of the non-price
information sharing. Third, the model shuts down the possibility of collusive activities
between the entrant and the incumbent both pre-entry and post-entry, which means that
entry will simply lead to competition in the upstream market. Thus, by ruling out the
collusive incentive for the rival firms to share information, the information sharing
mechanism investigated here can be highlighted.
The main finding of this paper is that the vertical contracting practices between the
incumbent firm and the retailers can be a driving force behind the voluntary sharing of
information by the entrant. In each period, the upstream incumbent offers each
downstream retailer a two-part-tariff contract which involves a wholesale price and a lump
sum transfer. The transfers are likely to have an exclusionary effect, as the retailers may
choose not to accommodate entry in order to protect the rent stream from the incumbent. 4
4
See Asker and Bar-Isaac (2014) for a detailed discussion on the exclusionary effects of the vertical practices.
3
The incumbent would want to offer such transfers only if entry will likely be denied, at least
for some period of time. However, if the entrant can offer a sufficiently high transfer to a
retailer, the retailer will find it profitable to accept the offer and accommodate entry. In this
case, transfers from both manufacturers will not occur, because the incumbent is not able to
prevent entry and then the entrant does not need to transfer. Hence, an entrant that can
earn a sufficiently high post-entry profit to transfer will voluntarily reveal its efficiency
information to the incumbent so as to avoid the costly entry.
Information sharing reveals the entrant’s type to the incumbent, which in turn has a
significant impact on the dynamic interaction between the agents. On one hand, the high
efficient entrants will voluntarily share their private information at the very beginning of
the game and enter immediately, because the shared information lowers the barrier to entry.
The less efficient entrants, on the other hand, will not reveal their types to the incumbent.
Rather, they will strategically keep silent to increase the likelihood of entry, because the
incumbent would take the entrant as an average type and react moderately. Moreover, the
non-sharing entrants may intentionally postpone entry in some equilibrium. The no-entry
events lower the incumbent’s expectation about the entrant’s type, which may further
reduce the barrier to entry. Hence, late entry can be more profitable. This finding differs
from the exclusion literature, in that exclusion here can be temporary.
Importantly, this paper may be applicable to the antitrust cases concerning the
appropriate treatment of information sharing agreements. In this model, the competitive
concern is whether and when entry can take place. The analysis shows that, if information
sharing is not allowed, early entry can be difficult for some high efficient entrants as the
incumbent would react more aggressively to prevent entry in earlier periods when the belief
is about the entire set of types. Thus, the model suggests that the harsh approach to the
sharing of information in the cases (e.g., the UK Agricultural Tractor Exchange case) may
in effect reduce market efficiency. Meanwhile, the model also shows that full revelation of
types will lead to a less efficient outcome in which more entrant types are perpetually
excluded than under voluntary sharing. In other words, policies that induce too much
transparency may be harmful to the market.
The remainder of the paper is organized as follows. Section 2 reviews the related
literature. Section 3 describes a benchmark model in which information is complete.
Section 4 presents a model in which information asymmetry exists and information sharing
is considered. Section 5 discusses the policy implications for antitrust regulation. Finally,
Section 6 concludes with a summary of results.
4
2. Related Literature
This paper is closely related to the literature on information sharing in oligopoly (e.g.,
Clarke 1983, Vives 1984, 1990, Li 1985, Gal-Or 1985, 1986, Shapiro 1986, Kirby 1988, Kuhn
and Vives 1995, Raith 1996, Armantier and Richard 2003a, 2003b, Levin et al. 2009, Asker
et al. 2016). Among these papers, Kuhn and Vives (1995) provide a comprehensive survey of
the literature and also discuss the UK Agricultural Tractor Exchange case. The authors
argue that the information sharing agreements may facilitate entry if the agreements can
generate positive informational externalities for the entrants. On the non-price information
sharing, Vives (1984) shows that, if firms have private information about the demand,
sharing the information is a dominant strategy for a firm when they compete in Bertrand
(Cournot) fashion and the goods are substitutes (complements). Armantier and Richard
(2003a) find that the sharing of cost information between the entrants may make entry
easier when the correlation of the unit costs is low and the products are close substitutes.
Armantier and Richard (2003b) analyze the effect of sharing cost information in the airline
industry. The paper indicates that the cost-sharing agreements may increase both firms’
profits and consumer surplus when multimarket entry is considered. Recent work by Asker
et al. (2016) examines the competitive impact of information sharing between rivals in a
dynamic auction model. The numerical results suggest that sharing the inventory
information is likely to be pro-competitive, as information sharing increases the output
level without affecting the total amount of welfare. Yet, to my knowledge, the literature has
been silent about information sharing between the entrants and the incumbent firms,
although it has received considerable attention in reality. This paper may take a first step
toward analyzing the competitive effects of this information sharing behavior.
The other related literature is that on exclusive dealing, which has been the subject of
policy debate for a long time. One strand of the literature has been trying to emphasize the
possible efficiencies arising from the exclusive dealing agreements (e.g., Klein 1988, Marvel
1982, Segal and Whinston 2000a), while the other strand argues that the agreements may
enable a firm to monopolize the market (e.g., Aghion and Bolton 1987, Asker and Bar-Isaac
2014, Rasmusen et al. 1991, Bernheim and Whinston 1998, Segal and Whinston 2000b,
Stefanadis 2016). The exclusive dealing agreements in this work are related to the vertical
practices such as slotting fees, loyalty rebates and etc., which have often been viewed as
anti-competitive (see Shaffer 1991, Marx and Shaffer 2007, Asker and Bar-Isaac 2014).
Within the literature, Rasmusen et al. (1991) show that an incumbent supplier may use
5
exclusive contracts to profitably exclude a rival when there is a lack of coordination among
the buyers. Later, Segal and Whinston (2000b) show that successful exclusion need not rely
on the assumption of buyer disorganization if the discriminatory exclusive contracts are
possible. Recent paper by Stefanadis (2016) considers a probabilistic naked exclusion model
and finds that high probability of innovation by the entrant may induce the incumbent firm
to adopt an accommodation strategy rather than a pure exclusion strategy. While much of
the literature is in static settings, Asker and Bar-Isaac (2014) study naked exclusion in a
dynamic model. The authors argue that the per-period transfers from the incumbent
supplier to the retailers may lead to upstream exclusion, if entry requires downstream
accommodation. However, the literature has not formally discussed how information
sharing affects the exclusion of rivals. This paper is an attempt to address this issue.
3. A Benchmark Model
In this section, I present a benchmark model in which information is complete. There are a
potential entrant (the entrant) and an active incumbent manufacturer (the incumbent) in
the upstream and 𝑛 ≥ 2 retailers in the downstream. Each manufacturer produces a single
product and the two products are differentiated. An active manufacturer sells its product to
the retailers for resale to final consumers. The retailers are perfect substitutes for each other
and compete in prices.
Within each period, if entry does not occur, the entrant earns zero profit and the
incumbent earns the monopoly profit 𝜋𝑀 > 0 . If entry occurs, the entrant and the
incumbent compete in the upstream and earn respectively 𝜋𝑒 (𝑐𝑒 ) > 0 and 𝜋(𝑐𝑒 ) > 0, where
𝑐𝑒 ∈ [0, ∞) is the entrant’s unit cost. 5 Several conditions are imposed on the profit functions.
First, 𝜋𝑒 (𝑐𝑒 ) is decreasing in 𝑐𝑒 and 𝜋(𝑐𝑒 ) is increasing in 𝑐𝑒 . Second, 𝜋(0) ≥ 0, 𝜋𝑒 (∞) = 0
and 𝜋(∞) = 𝜋𝑀 . Third, 𝜋𝑒 (0) > 𝑛1 [𝜋𝑀 − 𝜋(0)] + 𝐹𝑒 , where 𝐹𝑒 ≥ 0 is the fixed entry cost.
Fourth, −
𝜕𝜋𝑐𝑒 (𝑐𝑒 )
𝜕𝑐𝑒
𝑒)
> 𝑛1 𝜕𝜕(𝑐
for all 𝑐𝑒 ∈ [0, ∞) . The first two conditions describe how the
𝜕𝑐
𝑒
manufacturers’ profits depend on the entrant’s unit cost of production when the products
are imperfect substitutes. The third one assumes that the most efficient entrant (type 𝑐𝑒 = 0)
earns a sufficiently high industry profit every period after entry, which guarantees entry (of
some types of entrants) in every equilibrium. The last condition is less intuitive and mostly
5
To make the model as simple and transparent as possible, the incumbent’s unit cost 𝑐 is fixed. Thus, the two manufactures’ profits are
functions of the entrant’s unit cost 𝑐𝑒 only.
6
for a technical reason. It ensures the single crossing property of the aggregate profits of the
manufacturers, which greatly simplifies the results. 6
3.1 Timing
The game proceeds for infinitely many periods and all agents (the entrant, the incumbent
and the retailers) share a common discount factor 𝛿 ∈ (0,1). It is assumed that there is no
exit from the market in any period. The timing in a period with no entry is as follows:
1. The incumbent offers each retailer 𝑟 a two-part-tariff contract which involves a
wholesale price and a lump sum transfer 𝑇 𝑟 ∈ [0, ∞).
2. The retailers compete in prices in the downstream market.
3. The entrant offers each retailer 𝑟 a lump sum transfer 𝑇𝑒𝑟 ∈ [0, ∞).
4. The retailers simultaneously decide to accept or reject the entrant’s offer.
5. If at least one retailer accepts the entrant’s offer, entry is accommodated and the
transfer 𝑇𝑒𝑟 is paid immediately. Then, the entrant may choose to enter the market by
paying a fixed entry cost 𝐹𝑒 ≥ 0 at the beginning of the next period. After entry, the
manufacturers simultaneously offer the retailers two-part-tariff contracts and then
the retailers compete in prices. If no retailer accepts the entrant’s offer, entry is
deterred. The game starts from point 1 in the next period.
Period 𝑡
Period 𝑡 + 1
𝐹𝑒
Incumbent:
offer 𝑃 and 𝑇 𝑟 to
each retailer
Entrant:
offer 𝑇 𝑒𝑟 to
each retailer
Retailers:
accept or
reject 𝑇 𝑒𝑟
Accept 𝑇 𝑒𝑟
Entry
Reject 𝑇 𝑒𝑟
No entry
Period 𝑡 + 1
Figure 1: Timing of the Game
It is noted that “downstream accommodation” (see the point 5 above) is an important
assumption in this framework. It guarantees upstream competition in all periods after entry
if some retailer agrees to carry the entrant’s products. As such, the assumption ensures the
ongoing presence of the entrant in the upstream market, and the entry threat is necessary
6
Without this condition, the results are qualitatively the same but are more complicated.
7
for the retailers to obtain rents from the suppliers (e.g., Shaffer 1991, Marx and Shaffer
2007, Asker and Bar-Isaac 2014).
3.2 Analysis
Before proceeding, there are two important points to notice. 7 First, ignoring the transfers
from the manufacturers, the retailers obtain zero profit. This follows immediately from the
homogeneity of retailers who compete in prices. Since the sale prices will eventually be
driven to the wholesale prices, the retailers cannot gain from selling the product(s) to final
consumers. Second, the manufacturers will not make transfers to the retailers following
entry. To see this, note that the lump sum transfer in a contract does not affect the quantity
purchased by a retailer, and also it does not change the market structure if entry has
occurred. Thus, transfers will not occur because they play no strategic role in the game.
Since the incumbent moves first within each period, its actions, especially the transfers
in the contracts, are strategically important. The incumbent’s transfer strategies are defined
as follows.
Definition 1: At period 𝑡 , the transfer flow from the incumbent, {𝑇 𝑡 } , is an
accommodation strategy if 𝑇 𝜏 = 0 for all 𝜏 ≥ 𝑡, and it is an exclusion strategy if 𝑇 𝜏 > 0 at
least for some 𝜏 ≥ 𝑡.
I now characterize the exclusionary equilibria of the game, where “exclusionary” means
that the entry is never accommodated. 8 It is assumed that, when both manufacturers
transfer and a retailer is indifferent between accommodating entry and not, he will choose
not to accommodate entry; when neither manufacturer transfers, a retailer will always
accommodate entry. 9 The analysis focuses on the stationary equilibria in which all agents’
strategies and the market structure do not change over time.
Lemma 1: An exclusionary equilibrium exists if and only if there exists 𝑐𝑒 ∈ [0, 𝑐) such that
(1)
7
𝛿 𝜋𝑀 − 𝜋(𝑐𝑒 ) 𝜋𝑒 (𝑐𝑒 )
≥
− 𝐹𝑒 ,
1−𝛿
𝑛
1−𝛿
For a similar discussion, see Asker and Bar-Isaac (2014).
8
Although not the focus of this paper, the equilibria with no exclusion do exist. See Asker and Bar-Isaac (2014) for details.
9
The “zero transfer” setting is for simplicity.
8
𝑒 (𝑐𝑒 )
where 𝑐 solves 𝜋1−𝛿
− 𝐹𝑒 = 0. 10
Proof:
First, an entrant is called a “type 𝑐𝑒 entrant” if its unit cost of production is 𝑐𝑒 .
Facing a type 𝑐𝑒 entrant, the retailer 𝑟 will not accommodate entry if the transfer flow from
the incumbent is weakly higher than the lump sum transfer from the entrant
𝛿𝑇 𝑟 (𝑐𝑒 )
≥ 𝑇𝑒𝑟 (𝑐𝑒 ).
1−𝛿
(2)
Since the retailers are homogeneous, the incumbent will transfer 𝑇 (𝑐𝑒 ) = 𝑇 𝑟 (𝑐𝑒 ) to each
retailer 𝑟 to most effectively discourage entry. The entrant, on the other hand, will only need
to make a lump sum transfer 𝑇𝑒 (𝑐𝑒 ) = 𝑇𝑒𝑟 (𝑐𝑒 ) to one of the retailers for accommodation.
Within a period, the transfer from the incumbent cannot be larger than the monopoly profit
less the profit from allowing entry. That is, 𝜋𝑀 − 𝑛𝑛 (𝑐𝑒 ) ≥ 𝜋(𝑐𝑒 ). Then, the maximal perperiod transfer must bind the inequality, which gives 𝑇 (𝑐𝑒 ) = 𝜋
𝑀 −𝜋(𝑐
𝑛
𝑒)
. The entrant cannot
make the lump sum transfer larger than the profit from entering the market, 𝑇𝑒 (𝑐𝑒 ) ≤
𝑒 (𝑐𝑒 )
𝑒 (𝑐𝑒 )
𝛿�𝜋1−𝛿
− 𝐹𝑒 �. Hence, the maximal lump sum transfer is 𝑇𝑒 (𝑐𝑒 ) = 𝛿�𝜋1−𝛿
− 𝐹𝑒 �. Applying
(𝑐𝑒 )
inequality (2), 𝛿𝑇1−𝛿
≥ 𝑇𝑒 (𝑐𝑒 ), then gives the incentive compatibility (IC) condition for a
retailer not to accommodate entry
𝛿 𝜋𝑀 − 𝜋(𝑐𝑒 )
𝜋 (𝑐 )
≥ 𝛿 � 𝑒 𝑒 − 𝐹𝑒 �.
1−𝛿
𝑛
1−𝛿
(3)
On the other hand, the incumbent has an incentive to transfer if the return from
transferring is weakly higher than the return from not doing so
𝛿
𝜋𝑀 − 𝑛𝑇 ∗ (𝑐𝑒 )
≥ 𝜋𝑀 +
𝜋(𝑐𝑒 ),
1−𝛿
1−𝛿
(4)
∗
(𝑐𝑒 )
where 𝑇 ∗ (𝑐𝑒 ) = 1−𝛿
𝑇𝑒 (𝑐𝑒 ). Because 𝛿𝑇1−𝛿
= 𝑇𝑒 (𝑐𝑒 ), by assumption, {𝑇 ∗ (𝑐𝑒 )} is the transfer
𝛿
flow that blocks the type 𝑐𝑒 entrant. Rearranging inequality (4) immediately gives inequality
(1), which implies that inequality (4) and inequality (1) are equivalent.
In order for the exclusionary equilibrium to exist, inequality (1) and inequality (3) must
hold simultaneously. Note that if inequality (1) holds, inequality (3) must also hold. Hence,
the necessary and sufficient condition is then solely given by inequality (1).
Q.E.D.
10
For simplicity, the model eliminates the marginal entrant that earns zero industry profits.
9
The per-period transfers from the incumbent create an incentive for the retailers to
coordinate on the exclusionary outcomes, because a retailer will lose the rent stream if he
chooses to accommodate entry. That said, when the agents are sufficiently impatient (low
discount rate 𝛿), it is almost impossible for such an equilibrium to exist. Since entry does
not occur in the first period, the incumbent may value the first-period monopoly profit
more if the future profits are less attractive (low discounted value). In this case, entry can be
accommodated.
The proof has shown that the incumbent plays a more important role than the retailers
in excluding an entrant, although entry requires only the retailers’ accommodation. The
reason is that, as the first mover within a period, the incumbent has taken into
consideration the retailers’ decision rule when setting the optimal transfers. Therefore, the
incumbent can perfectly coordinate the retailers and “manipulate” their decisions not to
accommodate entry. Proposition 1 below characterizes the transfer strategies of the
manufacturers.
Proposition 1: In equilibrium, there exists a unique cut-off 𝑐𝑒∗ ∈ (0, 𝑐) such that
(a) if the entrant is type 𝑐𝑒 ∈ [0, 𝑐𝑒∗ ), the entry is accommodated. In this case, neither of the
manufacturers makes transfers in any period;
(b) if the entrant is type 𝑐𝑒 ∈ [𝑐𝑒∗ , 𝑐), the entry is deterred. In this case, the incumbent makes
a per-period transfer 𝑇 ∗ (𝑐𝑒 ) = 1−𝛿
𝑇𝑒 (𝑐𝑒 ) to each retailer and the entrant does not
𝛿
transfer in any period.
Proof: See the Appendix A.
𝑇 𝑒 𝑐𝑒
𝛿
𝑇 ∗ 𝑐∗𝑒
𝛿𝑇 𝑐𝑒
𝑇 ∗ 𝑐𝑒
1−𝛿
𝑐𝑒∗
0
Entry
𝑐
𝑐𝑒
𝑐𝑒∗
0
No Entry
Entry
(a)
𝑐
𝑐𝑒
No Entry
(b)
Figure 2: The Pattern of Entry (a) and the Per-period Transfer from the Incumbent (b)
10
The proposition shows that the incumbent’s transfer strategies are contingent on the
entrant’s type in a complete-information environment. The incumbent adopts an
accommodation strategy facing a (relatively) high efficient entrant (𝑐𝑒 ∈ [0, 𝑐𝑒∗ )), whereas it
adopts an exclusion strategy when the entrant’s efficiency is (relatively) low (𝑐𝑒 ∈ [𝑐𝑒∗ , 𝑐)).
The result illustrates a simple pattern of entry: the high efficient entrants can enter the
market without additional transfers, while the relatively less efficient entrants can never
enter. The intuition is clear. To exclude a strong entrant, the incumbent has to make
sufficiently high transfers to the retailers, which is costly. In this case, the incumbent will
simply accommodate entry. When the entrant is weak, however, convincing the retailers not
to accommodate entry becomes less costly. Thus, it is profitable for the incumbent to share
the industry rents with the retailers and monopolize the market.
The complete information model provides an important benchmark for the analysis of
information sharing. As is shown in Proposition 1, the incumbent treats different types of
entrants differently when information is complete. Given that, the entrants must take into
account the incumbent’s complete-information strategies when they make the information
sharing decisions. We will see later that information sharing can be strategic among
different types of entrants.
The benchmark model is also crucial for evaluating the welfare impact of information
sharing. To find the optimal treatment of information sharing, this paper compares the
social welfare respectively in three cases: mandatory sharing, voluntary sharing, and
sharing prohibition. The benchmark model is the case of “mandatory sharing”, which
contributes to the discussion on whether more transparency will lead to higher social
welfare. As such, the model may provide a foundation for policy makers to induce the
optimal amount of information in the market.
4. A Model of Information Sharing
In this section, I study information sharing itself and its impact on the market. I extend the
benchmark model to allow for information asymmetry and the decision to share
information. To be specific, the unit cost of production is now the entrant’s private
information, and the entrant can choose whether or not to share this information with the
incumbent. 11
11
Since a retailer’s accommodation decision is simply based on the comparison of transfers from the manufacturers, this information is
irrelevant to the decisions by retailers. Therefore, the model focuses only on the information sharing between the entrant and the
incumbent.
11
If the entrant chooses not to share the information, the incumbent must have an initial
belief about the entrant’s type, which is drawn from a cumulative distribution 𝐺(·) with
positive density 𝑔(·) on [0, 𝑐). Note that in this dynamic game, the incumbent’s belief may
change over time. Denote 𝛺𝑡 and 𝐺𝑡 (·) respectively the set of possible types and the updated
cumulative distribution at period 𝑡, where 𝐺𝑡 (·) has positive density 𝑔𝑡 (·) on 𝛺𝑡 ⊆ [0, 𝑐) for
all 𝑡. It is assumed that the proportion of the relatively less efficient entrants 1 − 𝐺(𝑐𝑒∗ ) is
large enough so that equilibria with exclusion can be guaranteed in some cases. 12
The timing of the game is similar to that in the benchmark model except that:
1. The entrant can choose to share its private information with the incumbent at any
period and any stage within a period.
2. The entrant’s unit cost becomes observable by all agents after entry.
For simplicity, it is assumed that the entrant can truthfully and credibly share its cost
information, and information sharing is costless. 13 I adopt the tie-breaking rule that, when
the entrant is indifferent between sharing the information and not, it will choose not to
share the information.
4.1 Analysis
The analysis proceeds in two stages. First, I study the timing and the incentive for the
entrant to share information, which is important for understanding the dynamic interaction
between the agents in the game. Then, I characterize the equilibria in which exclusion exists.
Here, “exclusion” means that entry does not occur for at least two periods (note that there is
no entry in the first period). In this sense, exclusion is not necessarily perpetual. 14
The benchmark model has shown that the transfers from the incumbent are key to the
upstream exclusion: the future transfer flow can constitute a barrier to entry in the current
period. However, the incumbent may also adopt an accommodation strategy rather than an
exclusion strategy when information is accurate, which provides an incentive to share
information. Lemma 2 below characterizes the pattern of information sharing by entrant
type.
12
Specifically, 1 − 𝐺(𝑐𝑒∗ ) ≥
𝑐
𝛿
𝜋𝑀 +1−𝛿
∫0 𝜋(𝑐𝑒 )𝑑𝑑(𝑐𝑒 )
𝑐
∫ ∗ 𝜋(𝑐𝑒 )𝑑𝑑(𝑐𝑒 )
𝛿 𝑐𝑒
𝜋𝑀 +1−𝛿
∗)
1−𝐺(𝑐𝑒
. Note that the main results do not depend on this assumption. It is only made for
analytical tractability in Section 4.3.
13
These assumptions are for simplicity and tractability. Note that other channels, such as signaling through prices, can be substitutes
for the settings in this model.
14
That is, “exclusion” here is somewhat different from “exclusionary” in Section 3.
12
Lemma 2: The high efficient entrants (𝑐𝑒 ∈ [0, 𝑐𝑒∗ )) will share their private information,
whereas the relatively less efficient entrants (𝑐𝑒 ∈ [𝑐𝑒∗ , 𝑐)) will never share. In particular,
information sharing occurs only prior to the contracting stage in the first period.
Proof: See the Appendix A.
The information sharing strategies constitute the initial information structure of the
game, which gives the incumbent an initial belief about the entrant’s type when information
sharing does not occur. We will see later that this initial belief is rather important for the
entry game, as it will significantly affect the incumbent’s transfers in a dynamic way.
Moreover, I would like to clarify that the set of possible types 𝛺𝑡 must take a simply form
∗
such that 𝛺𝑡 = [𝑐�,
�
𝑒,𝑡 𝑐) ⊆ [0, 𝑐) for some 𝑐
𝑒,𝑡 ≥ 𝑐𝑒 . The reason is that, if entry does not occur
at period 𝑡, the incumbent must rationally believe that the entrant’s efficiency is below some
level, 𝑐𝑒 ≥ 𝑐�,
𝑒,𝑡 because an entrant’s opportunity cost of not-to-enter (the loss of industry
profits) is increasing with its efficiency. Therefore, the set 𝛺𝑡 must consist of a continuum of
types.
Since the incumbent’s beliefs may change over time, the equilibrium transfers {𝑇 𝑡 } are
not necessarily stationary. For analytical convenience, the analysis will focus on the
equilibria with stationary transfers in the periods when the market structure and the beliefs
do not adjust over time. 15 Similar to the mechanism in the benchmark model, the transfer
flow from the incumbent {𝑇 𝑡+1 , 𝑇 𝑡+2 , … } can induce exclusion at period 𝑡. Denote 𝑐𝑒,𝑡 the
marginal type that cannot enter the market at period 𝑡, where 𝑐𝑒,𝑡 solves 𝛿 �
𝜋𝑒 �𝑐𝑒,𝑡 �
1−𝛿
− 𝐹𝑒 � =
∑∞
𝛿 𝜏−𝑡 𝑇 𝜏 . Lemma 3 gives an important result about 𝑐𝑒,𝑡 and 𝛺𝑡 .
𝜏=𝑡+1
Lemma 3: In an equilibrium with perpetual exclusion, there exist 𝑐𝑒∗∗ and a period 𝜏 , such
that 𝛺𝑡 = [𝑐𝑒∗∗ , 𝑐) in all periods 𝑡 ≥ 𝜏 + 1, where 𝑐𝑒∗∗ ∈ [0, 𝑐).
Proof: See the Appendix A.
Lemma 3 indicates that the marginal type and the incumbent’s belief converge to a
“steady state” over time. Intuitively, if entry does not occur in a period, the incumbent may
15
For instance, there may be many possible transfer flows {𝑇 𝑡+1 , 𝑇 𝑡+2 , … } that lead to the exclusion of the [𝑐�,
𝑒 𝑐) types with stationary
beliefs 𝛺𝜏 = [𝑐�,
𝑒 𝑐) for all 𝜏 ≥ 𝑡 + 1. To obtain qualitatively the same results, it suffices to focus on the equilibria with stationary transfers
𝑇 𝜏 = 𝑇 for all 𝜏 ≥ 𝑡 + 1.
13
attribute the “no entry” to the entrant’s low efficiency, so that its expectation about the
efficiency can be further lowered. Thus, the set of possible entrants keeps “shrinking”
towards the least efficient type over time. If the expected efficiency is sufficiently low at
some period 𝑡, the incumbent would be willing to exclude the whole set of possible entrants
𝛺𝑡 in that period. In this case, entry will not occur in future periods and the belief will
become stationary.
In essence, the role of 𝑐𝑒∗∗ resembles that of 𝑐𝑒∗ in the benchmark model, as they both
indicate the level of perpetual exclusion. That is, in equilibrium the low efficient entrants
(𝑐𝑒 ∈ [𝑐𝑒∗∗ , 𝑐)) will never enter the market even if they strategically choose not to reveal their
types. In this sense, the marginal values 𝑐𝑒∗∗ and 𝑐𝑒∗ can be called the “exclusionary effect of
transfers” or simply the “exclusionary effect” in this model. A larger marginal value means a
smaller exclusionary effect. Proposition 2 below gives a general result of 𝑐𝑒∗∗ .
Proposition 2: In any equilibrium, the exclusionary effect is strictly smaller under
voluntary sharing than under complete information. That is, 𝑐𝑒∗∗ > 𝑐𝑒∗ .
Proof: See the Appendix A.
The intuition behind this Proposition is the following. When information sharing is
voluntary, “no sharing” will make the incumbent form an expectation about the entrant’s
type. Since the entrants that do not share can only be the relatively low types, the
incumbent has no incentive to make high transfers and thus it pays less, which will then be
less effective in exclusion. On the other hand, the relatively low efficient entrants have an
incentive to keep the incumbent uninformed because they have nothing to lose and will
probably gain from information asymmetry.
I now turn to the entry behavior of entrants. Prior to entry, an entrant faces a fixed entry
cost 𝐹𝑒 ≥ 0 and has to give a lump sum transfer 𝑇𝑒 ≥ 0 to a retailer for accommodation.
Given that the outside payoff is zero, all types of entrants must want to enter the market if
𝐹𝑒 and 𝑇𝑒 are not too high. Then, the important decision here is the timing of entry. It is
true that early entry allows an entrant to earn a high total industry profit. However, the
entrant will also take into account the transfers set by the incumbent, because the transfer
flow may generate different levels of entry barriers across periods. Hence, entry can be
strategic. This discussion is summarized in the following proposition.
14
Proposition 3: In equilibrium, the pattern of entry is that the type [0, 𝑐𝑒∗∗ ) entrants enter
the market, whereas the type [𝑐𝑒∗∗ , 𝑐) entrants never enter. In particular, the type [0, 𝑐𝑒∗ )
entrants enter at period 2 and the type [𝑐𝑒∗ , 𝑐𝑒∗∗ ) entrants enter at some later period 𝑡 ≥ 2.
Proof: See the Appendix A.
Sharing
No Sharing
𝑐𝑒∗
0
Early Entry
𝑐𝑒∗∗
Late Entry
𝑐
𝑐𝑒
No Entry
Figure 3: The Pattern of Sharing and the Pattern of Entry
Proposition 3 shows that, under voluntary sharing, the timing of entry differs among the
entrants. The high efficient entrants (𝑐𝑒 ∈ [0, 𝑐𝑒∗∗ )) incur no additional costs after revealing
their types, and thus it is optimal for them to enter immediately. In contrast, the
intermediate types ( 𝑐𝑒 ∈ [𝑐𝑒∗ , 𝑐𝑒∗∗ ) ) will face an additional fee paid to a retailer for
accommodation. Then, these entrants will trade off between early entry and late entry
because they are likely to gain from a lower “entry fee” in some future period, even if
sacrificing early periods’ industry profits is costly. For this reason, late entry can be
profitable.
The interesting part in this result is the postponed entry. The main reason for such
equilibria to exist is the uncertainty about the entrant’s type. Because of uncertainty, there
are cases in which “no entry” can be a signaling device. That is, when entry does not occur,
the incumbent may believe that the entrant can be less efficient and it pays less to the
retailers. If this process can generate lower barrier to entry in some later period, then some
entrants may profitably postpone their entry. An example of the equilibrium with
postponed entry is illustrated below.
Example 1: Assume that
𝜋𝑒 (𝑐𝑒 ) = �
10 − 𝑐𝑒 𝑖𝑖 𝑐𝑒 ∈ [0,10);
𝑐
and 𝜋(𝑐𝑒 ) = � 𝑒
0 𝑖𝑖 𝑐𝑒 ∈ [10, ∞),
16
𝑖𝑖 𝑐𝑒 ∈ [0,16);
𝑖𝑖 𝑐𝑒 ∈ [16, ∞),
and the values of the other parameters are 𝜋𝑀 = 16, 𝐹𝑒 = 0, 𝛿 = 12 and 𝑛 = 2. By Lemma 1,
we obtain 𝑐𝑒∗ = 8 and 𝑐 = 10.
Assume also that 𝐺(·) is uniformly distributed on [0,10). Consider the transfer flow
{𝑇 1 , 𝑇 2 , 𝑇 3 , 𝑇 4 … } = {0,2,1,1 … } from the incumbent to each retailer, where 𝑇 𝑡 = 1 for all
15
𝑡 ≥ 3. 16 Using the equation 𝛿 �
𝜋𝑒 �𝑐𝑒,𝑡 �
1−𝛿
− 𝐹𝑒 � = ∑∞
𝛿 𝜏−𝑡 𝑇 𝜏 , we obtain 𝑐𝑒,1 = 8.5, 𝑐𝑒,𝑡 = 9 for
𝜏=𝑡+1
all 𝑡 ≥ 2 and 𝑐𝑒∗∗ = 9.
Given the cut-off values above, it is easy to see that there are only two possible timing for
making the entry decision: period 1 and period 2. There is no sense in which entry is
postponed to a period after period 2 because the entry barriers are the same for 𝑡 ≥ 2. At
period 1, an entrant will postpone entry if the return from postponing entry is weakly higher
than the return from transferring to a retailer for accommodation at period 1
𝛿2 �
(5)
𝜋𝑒 (𝑐𝑒 ) − 𝜋𝑒 (9)
𝜋 (𝑐 ) − 𝜋𝑒 (8.5)
� ≥ 𝛿� 𝑒 𝑒
�,
1−𝛿
1−𝛿
from which we obtain the marginal type 𝑐�𝑒 = 8 that is indifferent between postponing and
not. By inequality (5), it is immediate that the type [8,8.5) entrants will voluntarily postpone
entry, even if they can pay to a retailer for accommodation at period 1.
In this case, the incumbent’s belief does not change at period 2, because all the possible
entrants choose not to enter. That is, 𝛺2 = 𝛺1 = [8,10). However, the belief will be updated
to 𝛺3 = [9,10) at period 3 if entry does not occur, given that the type [0,9) entrants must
have entered on or before period 3. Consistent beliefs will then imply 𝛺𝑡 = [9,10) for all
𝑡 ≥ 3.
Note that postponed entry does not always happen in equilibrium. Consider instead the
transfer flow {𝑇 1 , 𝑇 2 , 𝑇 3 , 𝑇 4 … } = {1,1,1,1 … } from the incumbent to each retailer, where
𝑇 𝑡 = 1 for all 𝑡 ≥ 1. This transfer flow implies 𝑐𝑒,𝑡 = 𝑐𝑒∗∗ = 9 for all 𝑡 ≥ 1. Hence in this case,
all the possible entry must occur at period 2.
4.2 Exclusionary Effect
We have seen that the exclusionary effect 𝑐𝑒∗∗ is an important variable in this model, as it
indicates the effectiveness of the vertical practices in exclusion. It is then natural to ask the
question: what factors may affect the exclusionary effect 𝑐𝑒∗∗ ? To discuss this, I first
introduce a new variable 𝑐𝑒∗∗ ≡ 𝑖𝑖𝑖 {𝑐𝑒∗∗ } , which can be interpreted as the “maximal
exclusionary effect” in the model. There are two reasons for introducing such a variable.
First, 𝑐𝑒∗∗ is a good representative of the exclusionary effects {𝑐𝑒∗∗ }. In this model where
multiple equilibria exist (multiple {𝑐𝑒∗∗ }), the maximal exclusionary effect 𝑐𝑒∗∗ can be more
16
It is easy to verify that the transfer flow satisfies the incumbent’s IC condition.
16
informative than other exclusionary effects, as it indicates the greatest extent to which the
vertical practices can affect the upstream exclusion. Second, when there are multiple {𝑐𝑒∗∗ },
it is difficult to discuss the exclusionary effects in general. In contrast, 𝑐𝑒∗∗ is well defined and
available for comparative static analysis.
Proposition 4: The maximal exclusionary effect 𝑐𝑒∗∗ is larger when the monopoly profit 𝜋𝑀
is higher or the number of retailers 𝑛 is smaller.
Proof: See the Appendix A.
The proposition indicates that, other things equal, higher monopoly profit or fewer
retailers will encourage a more aggressive exclusive reaction of the incumbent. Intuitively,
higher monopoly profit implies a larger gap between the monopoly profit and the
competition profit. The larger gap can increase the incumbent’s willingness to pay, because
higher transfers reduce the likelihood of losing the monopoly rents. In terms of the retailer
effect, it is apparent that the incumbent’s cost will be lower when there are fewer retailers to
pay off, which implies a net marginal benefit from raising the transfers. As a result, the
incumbent will make higher transfers to each retailer so that the likelihood of upstream
exclusion is increased.
This result is related to the discussion in Asker and Bar-Isaac (2014) who argue that
higher monopoly profit or fewer downstream retailers may make it easier to ensure
upstream exclusion when information is complete. That is, their result is robust to the
change in the information structure of the game. To see why the effects carry through, note
that information asymmetry only influences the incumbent’s transfers quantitatively. That
is, in equilibrium the transfers have qualitatively the same exclusionary effects in the two
models. Hence, it is easy to understand why the incumbent responds in much the same way
as it does under complete information.
4.3 Prohibition of Information Sharing
In this section, I consider the situation in which information sharing is prohibited. The
main purpose of the extension is to provide a formal analysis for the cases in which
information sharing agreements are strictly prohibited. 17 The focus is still on the pattern of
17
See, for instance, the UK Agricultural Tractor Exchange case.
17
entry across all types of entrants. In what follows, I first analyze the “type space of entry” in
which the entrants can enter the market, and then the timing of entry of all entrants.
Proposition 5: The type space of entry (in which the entrants can enter the market) is
smaller under sharing prohibition than under voluntary sharing.
Proof: See the Appendix A.
Proposition 6: An exclusion strategy in the voluntary sharing model does not affect the
entry pattern of the type [𝑐𝑒∗ , 𝑐) entrants but may delay the entry of the type [0, 𝑐𝑒∗ ) entrants
in the sharing prohibition model.
Proof: See the Appendix A.
Example 2: Consider the transfer flow {𝑇 1 , 𝑇 2 , 𝑇 3 , 𝑇 4 … } = {0,3,1,1 … } from the
incumbent to each retailer, where 𝑇 𝑡 = 1 for all 𝑡 ≥ 3. It is easy to check that this exclusion
strategy is implementable in both the voluntary sharing model and the sharing prohibition
model. Following the logic in Example 1, we obtain 𝑐𝑒,1 = 8, 𝑐𝑒,𝑡 = 9 for all 𝑡 ≥ 2 and 𝑐𝑒∗∗ = 9.
)−𝜋𝑒 (9)
)−𝜋𝑒 (8)
Then, by solving 𝛿 2 �𝜋𝑒 (𝑐𝑒1−𝛿
� = 𝛿�𝜋𝑒 (𝑐𝑒1−𝛿
�, we obtain the marginal type 𝑐�𝑒 = 7 that is
indifferent between postponing and not. In this case, the type [7,8) entrants, which enter the
market at period 2 under voluntary sharing, now enter at period 3.
The main implication here is that a prohibition of information sharing can negatively
impact the market. There are two important results. First, more types of entrants may be
prevented from entering the market. To understand this, note that the incumbent’s
willingness to pay is positively correlated with the entrant’s efficiency. Thus, intuitively, the
incumbent would react more aggressively to prevent entry if the entrant is likely to be a high
efficient type. Second, the entry of the high efficient entrants may be delayed. The intuition
is quite similar. In this case, these entrants are unable to distinguish themselves from the
relatively low type entrants, and are thus subjected to the exclusion strategies. If the
incumbent’s reaction is sufficiently aggressive, efficient entry can be delayed.
Another point to notice is that entry is now costly to everyone (ignoring the fixed entry
cost 𝐹𝑒 ), as all types of entrants resemble the non-sharing entrants in the previous case and
face the same exclusion strategy. However, social welfare is less negatively affected by the
exclusion strategy if entry takes place in early periods. This is because the costly entry event
18
in which the entrant transfers rents to a retailer is merely a redistribution of the optimal
total surplus. 18 Hence, as long as entry can occur, the exclusion strategies will not cause
serious competitive harm to the market. 19
5. Policy Implications
The paper has analyzed the pattern of entry respectively in three different cases: mandatory
sharing, voluntary sharing, and sharing prohibition. The main interest here is in which of
the three cases generates the highest social welfare. There are two measures of social
welfare in this model: one is the “type space of entry” and the other is the “timing of entry”
for a certain type of entrant. Here, the paper is concerned more with the former measure
than with the latter one because first, for a given type, entry generates strictly higher social
welfare than does no-entry in equilibrium, and second, the timing of entry makes little
difference to the total social surplus when all agents are patient enough (𝛿 is sufficiently
large). Of course, if two models generate the same type space of entry, then the one with
earlier entry of all types implies higher social welfare.
By Proposition 2, 5 and 6, it is immediate that voluntary sharing generates the highest
social welfare among the three cases. In particular, by comparing the voluntary sharing
model with the sharing prohibition model and the mandatory sharing model respectively,
we obtain two important results: (i) information sharing can be pro-competitive, and (ii) it
is optimal to have a moderate amount of information shared on the market. To the extent
that the model may capture some aspects of the antitrust concerns, there are some policy
implications. I now discuss each in turn.
First, by illustrating the potential efficiency gains from sharing the non-price
information, the model suggests that a prohibition of the agreements to the sharing of nonprice information may reduce social welfare. In particular, the theory may work for the
cases in which entry requires downstream accommodation. As is shown in this model,
information sharing serves to induce accommodation and is thus pro-competitive. The
result contrasts with the argument that the incumbent firm can easily raise the barrier to
entry if it has access to the detailed information of the entrant (the E.U. cases). In fact, if an
entrant shares information, it must have some incentive to do so. Then, simply prohibiting
the agreements may deprive an entrant of the right to use its private information
18
By “optimal”, I mean the surplus under competition. Note that the competitive outcome is implied following entry.
19
This contrasts with some exclusion literature in which an exclusion strategy can ensure exclusion (e.g., Shaffer 1991, Marx and
Shaffer 2007, Asker and Bar-Isaac 2014).
19
strategically. Also, efficiency gains have been recognized in several other cases such as
American Column (1921), Linseed Oil (1923) and First Cement (1925). Thus, if the
efficiency gains from information sharing are sufficiently large, a prohibition may have a
negative effect on social welfare.
Second, the model suggests that inducing too much transparency in an industry may
also reduce social welfare, although information revelation can be welfare-improving. A
related issue is the disclosure laws that mandate sellers to disclose the quality of their
products.
20
For instance, the U.S. Food and Drug Administration requires food
manufacturers to disclose the ingredients and the nutritional information; the Federal
Trade Commission requires gasoline sellers to post the octane rating of the products. Given
that quality is highly related to production efficiency, this model may be somewhat
informative. 21 It is noted that the welfare loss here is due to the exclusion of types, which is
a serious consequence because exclusion not only reduces entrants’ profits but also lowers
consumer welfare. Thus, contrary to the conventional view, more transparency may not
always promote competition and raise consumer surplus. 22 Also, there are efficiency gains
from withholding information, because information asymmetry is likely to moderate the
exclusive practices and protect some low efficient entrants. Therefore, policies that induce
too much transparency may have limited effectiveness in improving social welfare.
6. Conclusion
This paper has described and analyzed a novel mechanism for information sharing, showing
that the exclusive contracting practices can be a driving force behind the voluntary sharing
of information. In this framework, information sharing is strategic among different types of
entrants: the high efficient entrants choose to share their efficiency information, whereas
the less efficient entrants refrain from doing so. In equilibrium, revealing efficiency can
induce the incumbent to accommodate entry, and withholding the information can make
entry more likely by moderating the incumbent’s exclusion strategy. Since entry intensifies
competition, there are efficiency gains from both the “sharing” behavior and the “nonsharing” behavior.
20
Dranove and Jin (2010) provide a comprehensive survey on quality disclosure and certification.
21
For a given quality, efficiency in production can be easily predicted by pricing.
22
This implication is in line with the argument that mandatory disclosure may not always lead to higher social welfare (e.g., Jovanovic
1982, Matthews and Postlewaite 1985, Dranove et al. 2003, Gavazza and Lizzeri 2007, Bar-Isaac et al. 2012).
20
Importantly, the paper may shed light on the antitrust treatment of information sharing.
First, the model indicates a pro-competitive aspect of non-price information, showing that
revealing the efficiency-relevant information, such as the cost of production, may prevent
the exclusive practices between the incumbent firms, so that early entry can be guaranteed.
Thus, it is suggested that prohibiting the agreements to the sharing of non-price
information may result in an inefficient outcome if the efficiency gains are sufficiently large.
In addition, by illustrating the benefits from “non-sharing”, the model suggests that it is
optimal to have a moderate amount of information shared on the market. In this sense,
rules or laws that mandate firms to disclose the efficiency-relevant information may have a
negative effect on social welfare.
Appendix A
Proof of Proposition 1:
(𝑐𝑒 )
𝑒)
(a) By the assumptions on the profit functions, it is immediate that 𝑇𝑒 (𝑐
and 𝛿𝑇1−𝛿
are
𝛿
(𝑐𝑒 )
𝑒)
strictly decreasing, and cross only once with 𝑇𝑒 (𝑐
cutting 𝛿𝑇1−𝛿
from above (see Figure 2(a)).
𝛿
(𝑐𝑒 )
𝑒)
If the entrant is type 𝑐𝑒 ∈ [0, 𝑐𝑒∗ ), then 𝛿𝑇1−𝛿
< 𝑇𝑒 (𝑐
, which violates the condition in Lemma 1.
𝛿
Hence, the incumbent has no incentive to transfer, which implies that the entrant does not
need to transfer. In this case, entry is accommodated.
(𝑐𝑒 )
𝑒)
(b) If the entrant is type 𝑐𝑒 ∈ [𝑐𝑒∗ , 𝑐), then 𝛿𝑇1−𝛿
≥ 𝑇𝑒 (𝑐
. This means that it is profitable for
𝛿
𝑇𝑒 (𝑐𝑒 )
the incumbent to deter entry. Since information is complete, transferring 𝑇 ∗ (𝑐𝑒 ) = 1−𝛿
𝛿
is enough to ensure upstream exclusion. Thus, there is no sense in which the entrant makes
any positive transfers. In this case, entry is deterred.
Q.E.D.
Proof of Lemma 2:
By Proposition 1, sharing information leads to two outcomes: accommodation and complete
exclusion. Since an exclusion strategy raises the barrier to entry, it is immediate that the
high efficient entrants (𝑐𝑒 ∈ [0, 𝑐𝑒∗ )) will share, while the relatively less efficient entrants
(𝑐𝑒 ∈ [𝑐𝑒∗ , 𝑐)) will not do so. 23 Further, in order to enter at period 2 without additional costs,
23
See the Appendix B for the existence of an exclusionary equilibrium under asymmetric information.
21
the high efficient entrants must share in the first period prior to the contracting stage,
because doing so will induce the incumbent to internalize the information and include zero
transfers in the contracts.
Q.E.D.
Proof of Lemma 3:
For any series {𝑐𝑒,𝑡 }, there must be an earliest period 𝜏 in which 𝑐𝑒∗∗ = 𝑖𝑖𝑖{𝑐𝑒,𝑡 } is the
marginal type. It is immediate that 𝑐𝑒,𝑡 ≥ 𝑐𝑒∗∗ for 𝑡 ≥ 𝜏 . Then, the type [0, 𝑐𝑒∗∗ ) entrants must
have paid for entry on or before period 𝜏 . Consistent beliefs then imply that 𝛺𝑡 = [𝑐𝑒∗∗ , 𝑐) in
all periods 𝑡 ≥ 𝜏 + 1.
Q.E.D.
Proof of Proposition 2:
Suppose that the incumbent wants to deter the type [𝑐𝑒∗ , 𝑐) entrants in all periods. Then, the
minimal expenditure is to make a per-period transfer 𝑇 ∗ (𝑐𝑒∗ ) = 1−𝛿
𝑇𝑒 (𝑐𝑒∗ ) to each retailer.
𝛿
However, this minimal expenditure violates the incumbent’s IC condition. That is,
𝜋𝑀 −𝑛𝑇 ∗ (𝑐𝑒∗ )
1−𝛿
∗
𝑐
𝛿
𝑒 )−𝐺(𝑐𝑒 )
< 𝜋𝑀 + 1−𝛿
∫∗ 𝜋(𝑐𝑒 )𝑑𝐺∗ (𝑐𝑒 ) , where 𝐺∗ (𝑐𝑒 ) = 𝐺(𝑐1−𝐺(𝑐
. In other words, the
∗)
𝑐𝑒
𝑒
incumbent has no incentive to deter all types in [𝑐𝑒∗ , 𝑐), because it is too costly to do so.
Hence, the incumbent will pay less, which implies that the exclusionary effect 𝑐𝑒∗∗ is strictly
smaller than 𝑐𝑒∗ in any equilibrium.
Q.E.D.
Proof of Proposition 3:
For any transfer flow {𝑇 𝑡 } that generates the exclusionary effect 𝑐𝑒∗∗ , it is clear that the type
[0, 𝑐𝑒∗∗ ) entrants can profitably enter the market and the type [𝑐𝑒∗∗ , 𝑐) entrants can never enter.
By Lemma 2, the type [0, 𝑐𝑒∗ ) entrants choose to share information and thus it is optimal for
them to enter at period 2. In contrast, the type [𝑐𝑒∗ , 𝑐𝑒∗∗ ) entrants choose not to reveal their
types because inducing accommodation is not possible. In this case, there are multiple
equilibria in which the entrants will trade off the benefits between early entry and late entry.
Hence, the timing of entry will be some period 𝑡 ≥ 2. Example 1 illustrates examples of a
postponed entry and a period-2 entry.
Q.E.D.
22
Proof of Proposition 4:
∫
Denote 𝑇 (𝑐𝑒 ) ≡
𝑐
𝜋(𝑐)𝑑𝑑(𝑐)
𝜋𝑀 − 𝑐𝑒1−𝐺(𝑐
𝑛
𝑒)
. By definition, the maximal exclusionary effect 𝑐𝑒∗∗ must satisfy
the following equation
𝑐
𝜋𝑀 − 𝑛𝑛 (𝑐𝑒∗∗ )
𝛿 ∫𝑐𝑒∗∗ 𝜋(𝑐)𝑑𝑑(𝑐)
= 𝜋𝑀 +
.
1−𝛿
1 − 𝛿 1 − 𝐺(𝑐𝑒∗∗ )
(6)
Rearranging equation (6) gives
1
𝛿
𝑇 (𝑐𝑒∗∗ ) = 𝑇𝑒 (𝑐𝑒∗∗ ).
1−𝛿
𝛿
(7)
Note that both 1𝛿 𝑇𝑒 (𝑐𝑒∗∗ ) and
1
𝑇 (𝑐∗∗ )
𝛿 𝑒 𝑒
𝛿
𝑇 (𝑐𝑒∗∗ )
1−𝛿
𝛿
are decreasing in 𝑐𝑒∗∗ . Since 1𝛿 𝑇𝑒 (0) > 1−𝛿
𝑇 (0) ,
𝛿
must cut 1−𝛿
𝑇 (𝑐𝑒∗∗ ) from above and
𝜕[1
𝛿𝑇𝑒 (𝑐𝑒 )]
𝜕𝑐𝑒
<
𝛿
𝜕[1−𝛿
𝑇 (𝑐𝑒 )]
𝜕𝑐𝑒
on (𝑐𝑒∗∗ − 𝜀, 𝑐𝑒∗∗ + 𝜀) for some
𝜀 > 0. Then, taking derivative on both sides of equation (7) w.r.t respectively 𝜋𝑀 and 𝑛
yeilds
(8)
⎧𝜕 �1 𝑇 (𝑐∗∗ )� 𝜕 � 𝛿 𝑇 (𝑐𝑒∗∗ )�⎫ ∗∗
� 𝛿 𝑒 𝑒
� 𝜕𝑐𝑒
𝛿 1
1−𝛿
−
=
∗∗
∗∗
𝑀
⎨
⎬ 𝜕𝜋
𝜕𝑐𝑒
1−𝛿𝑛
𝜕𝑐𝑒
�
�
⎩
⎭
and
(9)
⎧𝜕 �1 𝑇 (𝑐∗∗ )� 𝜕 � 𝛿 𝑇 (𝑐𝑒∗∗ )�⎫ ∗∗
� 𝛿 𝑒 𝑒
� 𝜕𝑐𝑒
𝛿 𝜋𝑀
1−𝛿
−
=
−
,
⎨
⎬ 𝜕𝜕
𝜕𝑐𝑒∗∗
𝜕𝑐𝑒∗∗
1 − 𝛿 𝑛2
�
�
⎩
⎭
∗∗
∗∗
𝜕𝑐𝑒
𝜕𝑐𝑒
which immediately imply 𝜕𝜋
𝑀 < 0 and 𝜕𝜕 > 0.
Q.E.D.
Proof of Proposition 5:
Since the analysis focuses on the exclusion strategies that are implementable, it suffices to
check the incumbent’s initial incentive to transfer. Consider a transfer flow {𝑇 𝑡 } that
satisfies the incumbent’s IC condition under voluntary sharing
𝑐
(10)
𝐸[𝑐𝑒∗ ,𝑐) (𝜋) ≥ 𝜋𝑀
𝛿 ∫𝑐𝑒∗ 𝜋(𝑐)𝑑𝑑(𝑐)
+
.
1 − 𝛿 1 − 𝐺(𝑐𝑒∗ )
23
I then show that this transfer flow must also satisfy the incumbent’s IC condition under
sharing prohibition. The expected profit under sharing prohibition is given by 𝐸[0,𝑐) (𝜋) =
𝐺(𝑐𝑒∗ )𝐸[0,𝑐𝑒∗ ) (𝜋) + [1 − 𝐺(𝑐𝑒∗ )]𝐸[𝑐𝑒∗ ,𝑐) (𝜋). By the assumption on 1 − 𝐺(𝑐𝑒∗ ) (see footnote 12) and
inequality (10), it is immediate that
𝐸[0,𝑐) (𝜋) ≥ 𝜋𝑀 +
(11)
𝑐
𝛿
� 𝜋(𝑐)𝑑𝑑(𝑐).
1−𝛿 0
This implies that the incumbent has a (weakly) larger transfer strategy space under
sharing prohibition than under voluntary sharing. Therefore, the type space of entry must
be (weakly) smaller under sharing prohibition than under voluntary sharing.
Q.E.D.
Proof of Proposition 6:
Following the proof of Proposition 5, the incumbent’s transfer strategies under voluntary
sharing can also be adopted under sharing prohibition. Thus, these strategies will generate
the same entry pattern of the type [𝑐𝑒∗ , 𝑐) entrants in the two cases. In contrast, the type
[0, 𝑐𝑒∗ ) entrants can induce accommodation by sharing information and enter at period 2
under voluntary sharing. However, these entrants are unable to do so under sharing
prohibition and are thus subjected to the exclusion strategies. Hence, the timing of entry for
these entrants will be (weakly) later than period 2. The exclusion strategies that strictly
delay the entry of the type [0, 𝑐𝑒∗ ) entrants can be constructed by setting high transfers in
early periods. Example 2 gives an example of a delayed entry.
Q.E.D.
Appendix B
The Existence of an Exclusionary Equilibrium under Asymmetric Information
Proposition 7: An exclusionary equilibrium under asymmetric information exists if there
exists 𝑐𝑒 ∈ [0, 𝑐) such that
𝑐
(12)
𝛿
1−𝛿
𝜋𝑀 −
∫ 𝜋(𝑐)𝑑𝑑(𝑐)
𝑐𝑒
1 − 𝐺(𝑐𝑒 )
𝑛
≥ �1 + (1 − 𝛿)
24
𝐺(𝑐𝑒 )
𝜋 (𝑐 )
� [ 𝑒 𝑒 − 𝐹𝑒 ].
1 − 𝐺(𝑐𝑒 ) 1 − 𝛿
Proof:
I focus on the equilibria in which the transfers from the incumbent are stationary
over time. Consider the transfer flow {𝑇 (𝑐𝑒 )} such that 𝑇 (𝑐𝑒 ) = 1−𝛿
𝑇𝑒 (𝑐𝑒 ) in all periods.
𝛿
Since the incumbent must have an incentive to transfer at every period, the IC conditions
for transferring {𝑇 (𝑐𝑒 )} are given by
𝐸[0,𝑐) [𝜋(𝑐𝑒 )] ≥ 𝜋𝑀 +
(13)
𝑐
𝛿
� 𝜋(𝑐)𝑑𝑑(𝑐)
1−𝛿 0
and
𝑐
𝐸[𝑐𝑒 ,𝑐) [𝜋(𝑐𝑒 )] ≥ 𝜋𝑀
(14)
𝛿 ∫𝑐𝑒 𝜋(𝑐)𝑑𝑑(𝑐)
+
,
1 − 𝛿 1 − 𝐺(𝑐𝑒 )
where 𝐸[0,𝑐) [𝜋(𝑐𝑒 )] and 𝐸[𝑐𝑒 ,𝑐) [𝜋(𝑐𝑒 )] are the expected profits respectively in period 1 and in
period 𝑡 ≥ 1. 24 Rearranging inequality (13) and inequality (14) gives
𝑐
𝛿
1−𝛿
(15)
𝜋
𝑀
−
∫ 𝜋(𝑐)𝑑𝑑(𝑐)
𝑐𝑒
1 − 𝐺(𝑐𝑒 )
𝑛
≥ �1 + (1 − 𝛿)
𝐺(𝑐𝑒 )
𝜋 (𝑐 )
� [ 𝑒 𝑒 − 𝐹𝑒 ].
1 − 𝐺(𝑐𝑒 ) 1 − 𝛿
Q.E.D.
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