2006・46

Inviting entrants may help incumbent firms

Ikuo Ishibashi
Noriaki Matsushima

Inviting entrants may help incumbent firms∗
Ikuo Ishibashi†
Department of Economics, Aoyama Gakuin University
Noriaki Matsushima‡
Graduate School of Business Administration, Kobe University
September 25, 2006

Abstract
This paper provides an example that incumbent firms might allow potential entrants to enter a market. The market consists of two sub-markets: a high-end market
and a low-end market. (i) If low-quality products are of no value to consumers in
the high-end market, (ii) consumers in the low-end market will not be concerned
about product quality; and (iii) if the low-end market is relatively small, then theentries of firms into the low-end market would be beneficial to the incumbent firms.
To be more specific, entry into a certain market represents a commitment to prevent
incumbent firms from fierce competition within the high-end market and guarantees
higher profits to the incumbent firms.

JEL classification numbers: M21, L13
Key words: entry, handover, heterogeneous consumers, commitment, oligopoly∗

The authors are grateful to Motonari Kurasawa, Masayoshi Maruyama, Keizo Mizuno, Tatsuhiko
Nariu, Takao Ohkawa, Yoshiyasu Ono, Daisuke Shimizu, Kentaro Tachi, Naoki Watanabe, and seminar
participants at Kyoto University for their helpful comments. Of course, any errors are the responsibilityof the authors.
†
Faculty of Economics, Aoyama Gakuin University 4-4-25 Shibuya, Shibuya-ku, Tokyo 150-8366
Japan. E-mail: ishibash@econ.aoyama.ac.jp‡
Correspondence author: Noriaki Matsushima, Graduate School of Business Administration, Kobe
University, 2-1 Rokkodai, Nada, Kobe, Hyogo 657-8501, Japan. Phone: +81-78-803-6981. E-mail:nmatsush@kobe-u.ac.jp01

Introduction

Standard microeconomics textbooks explain that, in an oligopoly market (e.g., Cournot
oligopoly), the equilibrium price decreases as the number of firms increases, and the profits
of the firms then decrease. In many real-world markets, the characteristics concerning reductions in profits and prices actually hold.1 In markets which have those characteristics,
it is natural for incumbent firms to be apprehensive about the possibility of other firms
entering the market. Protests by incumbent firms against the entry deregulation are typical examples of such apprehension. In fact, market prices have frequently been observed
to drop dramatically, and the profits of incumbent firms to decline, after a government
allows potential entrants to enter a market (e.g., the deregulation of the Japanese taxi industry). Therefore, many economists do speculate whether potential rivals are beneficial
for incumbent firms; however, they have often studied the conditions under which incumbent firms try to prevent and deter potential entrants into the market and the welfare
implication of entry deterrence by incumbent firms.2
On the contrary, we sometimes observed counter examples about the relation between
market prices and the number of firms. Established Japanese firms share their knowledge of the electricity industry with Chinese firms that are potential competitors of theJapanese.3 Intuitively, it appears that such technological transfers would lead to reductions in the profits of the incumbent firms; nevertheless, such transfers take place. In the1

In several papers, it has been reported that the total profits of an industry may result in an increasein the number of firms. Using a bilateral oligopoly model, Naylor (2002a) shows that for a small numberof firms, the increment in the number of firms enhances the overall profits of an industry.
2

See, for instance, Bernheim (1984), Dixit (1980), Eaton and Ware (1987), Gelman and Salop (1983),

McLean and Riordan (1989), Sørgard (1997), and Waldman (1987, 1991). Geroski (1995) provides an
excellent survey on the literature of entry problems. In the literature of spatial competition with entry
deterrence, see Bonanno (1987), Ishibashi (2003), Judd (1985), and Schmalensee (1978).
3

Evidence of this has been provided by engineers of the Sanyo Electric Co., Ltd.

1

food industry, the invasion of private-label food products sometimes causes increases inprices and profits of name-brand products. For example, Ward et al. (2002) empiricallyshow that increases in the share of private-label goods are correlated with a rise in theprice of name-brand goods. Pauwels and Srinivasan (2004) empirically show that theinvasion of private-label food products produces increases in the profits of name-brandgoods. In the pharmaceutical industry, the entry of generic versions of brand-name drugs
results in increases in brand-name prices. For example, Frank and Salkever (1997) provide
evidence that brand-name prices increase after the entry of generic drugs into the market and are accompanied by large decreases in the prices of the generic drugs in general.
When the prices of brand-name products increase, profits may also rise.4
Speculation on this subject raises several questions. Some of these questions focus on
issues such as the reason that there are technology transfers that invite potential entrants
into the market; whether such an invitation is profitable for incumbent firms; in such acase, why it is profitable; and the reason that the invasion of private-label food products
induces an increment in the profits of name-brand goods.
In the examples reported above, a common market characteristic exists. Establishedproducts and non-established products exist in the same markets, and they are recognized
as differentiated products. For instance, in the food industry, name-brand products areproduced by established firms, and private-label food products are produced by nonestablished and established firms. These private-label food products are priced lower than
name-brand products and, they frequently offer equivalent quality.5 As summarized in
Soberman and Parker (2004), some empirical studies show that some consumers are willing
4This is not mentioned in Frank and Salkever (1997). Moreover, it is not possible to determine

whether increases in the prices of brand-name products also produce increases in profits. Nevertheless,
it is possible that there is a positive correlation between the prices and the profits of the brand-nameproducts.
5

See Hinloopen and Martin (1997) and Connor and Peterson (1992, 1997).

2

to pay more for advertised (name-brand) products. In other words, some consumers
believe that private-label products are the same as store-brands in regards to overall
quality, taste, availability, freshness, guarantee of satisfaction, clarity of labelling, andquality of packaging, among other attributes.
The questions listed above are answered below. In addition, we show, with the use ofa simple framework, how entries into the market can be profitable for incumbent firms
and the circumstances under which prices can be increased. In other words, the profits of
the incumbent firms could increase as new firms enter the market.
We consider the following market structure. The market consists of two sub-markets:a high-end market and a low-end one. Consumers in the high-end market require productsof higher quality. Low-quality products are of no value to those consumers. On the other
hand, consumers in the low-end market are less concerned with quality.6 The low-end
market is relatively small compared to the high-end market. In this study, there are two
incumbent firms and a potential entrant. Some entry barriers may prevent a potential
entrant from joining the market without the cooperation of an incumbent firm.7
In this setting, we show a subgame perfect equilibrium that enables an incumbent
6

In the personal computer (PC) industry, specific businesses may require more sophisticated hardware

to satisfy the demands of their business than household users, who may need a computer for personalreasons such as writing letters and listening to music. Those business users do not need PCs with lowlevel equipments. However, typical computer users are generally satisfied with word-processing softwareand programs that will enable them to use the Internet.
7

The setting discussed here is related to that in Rosenthal (1980). He also discusses a market structurein which two classes of consumers exist: those who view labels of companies as artifacts and purchase
only from the low-price company; and those who perceive significant differences among the brands andpurchase only from their respective favorite brands (see, Rosenthal (1980, p. 1575)). He shows thatthe equilibrium price increases as the number of firms increases. In his model, however, pure-strategy
equilibria do not exist and the increment of the equilibrium price is evaluated on the concept of stochastic
dominance. Rosenthal (1980) and most of the subsequent researches (e.g. Narasimhan (1988) and Baye etal. (2004)) discuss the topic of price dispersion but do not consider the relation between the profitabilityof incumbent firms and the existence of entrants.

3

firm to support a new entrant as a local monopolist in the low-end market. Without
the entry of a new firm, the incumbents will need to produce more because the low-end
market remains empty and sufficiently profitable. However, once incumbent firms sell
their products to consumers in the low-end market, the price in the high-end market
collapses, and then the profits of the incumbent firms drastically decrease. The entry isa credible commitment not to sell their high-quality products to consumers in the lowend market. As a result, the incumbent firms can secure high profits from the high-end
market.
We now report the theoretical contribution of our results. As stated above, we showthat entries might raise both the incumbent’s profits and the equilibrium price.8 To
our knowledge, no previous study has shown that the profits of incumbent firms andthe equilibrium price increase as a result of the entries of new firms into the market.
However, several studies have indicated that market entries produce increases in the priceof the incumbent firm’s product. Inderst (2002) considers how prices react to an increasein competition. In his model, an incumbent enjoys the advantage of having a locked-in
fraction of buyers. He shows that the price of a product produced by the incumbent firm
may increase. He does not show that the profit of the incumbent firm increases as a resultof the entry of new firms into the market. Davis el al. (2004) consider a duopoly model inwhich an incumbent firm and an entrant exist. When the entrant enters the market, theincumbent firm sets its price higher than that in the monopoly situation because serving
consumers with lower willingness to pay is not beneficial. They also consider the productpositioning of the firms, but they do not show the profit of the incumbent relative to that
8

Naylor (2002b) derives a similar result in the context of wage bargaining in unionized bilateraloligopoly. He considers a simple Cournot oligopoly model in which wages are determined by bargaining
in unionized bilateral oligopoly. In his model, the equilibrium price of the final product, however, always
decreases as the number of firms increases. This is quite different from the price change by the entries inour model.

4

of the new entrant.
The organization of the remainder of the paper is as follows. In the next section, we
describe a two-stage game model. In Section 3, we derive the subgame perfect equilibriumof the game constructed in the previous section. The last section is the conclusion.

2

Model

We consider an industry with two vertically differentiated products (h and l). h and l are
high- and low-quality products, respectively. There are two major firms (1 and 2) and one
minor firm (3). The major firms can produce h at a constant marginal cost normalized
to zero. We assume that neither major firm produces l. A minor firm cannot produce
any good at first. However, with a major firm’s support, a minor firm can produce l at aconstant marginal cost normalized to zero.9 No fixed cost is assumed for the productionof h or l.
We assume two groups of consumers, H (the high-end market) and L (the low-end
market). Consumers in H demand only h. That is, the quality of l is not at all sufficientfor consumers in H. The demand function of this high-end market, DH (ph ), is given by(

DH (ph ) =0
if ph ∈ (1, ∞),h
1 − p if ph ∈ [0, 1],

where ph is the price of h. Consumers in L are indifferent between h and l. That is, thehigh quality of h (compared to l) is of no use to consumers in L. The demand functionof this low-end market, DL (pl ), is given by(Ll

D (p ) =0
if pl ∈ (a, ∞),lb(1 − p /a) if pl ∈ [0, a],where pl is the price of l, and we assume 1/3 < a < 1/2.10 Note that DL (pl ) is a linear
9

The support might be some lectures on the basic technology, cheap license fees for the major firm’s

important patents, or the major firm’s cooperation for the outsourcing of the minor firm’s product.
10

While 1/3 < a is made to simplify the analysis, a < 1/2 is essential for our analysis.

5demand function such that the highest willingness to pay is measured by a and the largest
demand (at pl = 0) is measured by b.
In this paper, quantity competition is assumed. Let qi be firm i’s output level. In
addition, define q = (q1 , q2 , q3 ). Note that q1 + q2 is the (total) quantity of h, and q3 is
the quantity of l in the market.
We describe how ph and pl are determined given the above consumers. As long as
1 − (q1 + q2 ) ≥ a(1 − q3 /b), the high-end and low-end markets are separated. That is, noconsumer in L buys h. Therefore, ph is given by 1 − q1 − q2 , and pl is given by a(1 − q3 /b).
If 1 − (q1 + q2 ) < a(1 − q3 /b), the markets are connected. That is, some consumers
in L buy h. Because h and l are completely indifferent to consumers in L, this means
1 +q2 +q3 ))ph = pl = a(1+b−(qa+b.

In summary, the prices are determined as follows.

 1 − q1 − q2

if q1 + q2 ≤ 1 − a +aq3bph (q) =  a(1 + b − (q + q + q ))
1
2
3


otherwise.
a
+
b
 µ
¶
aq3
q3



if q1 + q2 ≤ 1 − a +
a
1
−

b
b
pl (q) = 
a(1
+
b
−
(q
+
q
+
q
))
1
2
3


otherwise.
a+b
Let πi (q) be firm i’s profit function. For i = 1, 2, it can be expressed as follows.

πi (q) = (1 − q1 − q2 )qi

if q1 + q2 ≤ 1 − a +a(1 + b − (q1 + q2 + q3 ))



qi

otherwise.

a+b

aq3
b

(1)

For i = 3, it can be expressed as follows.

π3 (q) =

 µ
¶
q3



q3
a 1 −

if q1 + q2 ≤ 1 − a + aqb3a(1 + b − (q1 + q2 + q3 ))


q3


otherwise.

b

a+b

(2)

The game consists of two stages and proceeds as follows. At the first stage, firm 1
6chooses whether or not it supports firm 3.11 For simplicity, we assume that the cost of
the support is zero. At the second stage, all firms in the market choose their quantities.
If firm 1 does not support firm 3 at the previous stage game, we set q3 = 0. At the endof the second stage, the market opens, and each firm collects its profit.

3

Equilibrium Analysis

We use the subgame perfect equilibrium (SPE, hereafter) as the solution concept. To
derive the SPE, we solve the game backward. Hereafter we use the superscript “*” todenote the equilibrium.

3.1

The second stage without firm 3

If firm 1 does not support firm 3 at the first stage, the second stage becomes a simple
duopolistic competition.
Moreover, because a > 1/3, the equilibrium price is less than or equal to a.12 In otherwords, h and l are connected at the Nash equilibrium.
Given this, the F.O.C. becomes as follows.
∂
∂qi

Ã

a(1 + b − (qi + qj ))qia+b!

a(1 + b − (2qi + qj ))= 0 (i 6= j)a+b
1 + b − qj
⇔ qi =
2=

Therefore, the Nash equilibrium is q1 = q2 = (1 + b)/3 and, each firm’s equilibrium profit
is a(1 + b)2 /(9(a + b)). We summarize this result as follows.
11

The assumption that only firm 1 can support firm 3 is made for simplicity.

12

If the whole market consists of only the high-end market, q1 = q2 = 1/3 is the unique Nashequilibrium, and the equilibrium price becomes 1/3(< a). This implies that p > a cannot be theequilibrium price in the subgame here.

7Lemma 1 Suppose that firm 1 does not support firm 3 at the first stage. The unique
Nash equilibrium exists in the corresponding subgame such that firms 1 and 2 obtaina(1 + b)2 /(9(a + b)).

3.2

The second stage with firm 3

If firm 1 supports firm 3 at the first stage, the second stage becomes quantity competitionby three firms. Potentially, there are two Nash equilibria in this subgame. One is suchthat h and l are separated, and the other is such that h and l are connected.
Hereafter, we restrict our attention to the former case because we are interested in
the strategic handover of the low-end market. To discuss equilibrium outcomes in whichfirm 3 exists, we divide the discussion into two steps and show the outcome. First, we
guess an equilibrium outcome in which h and l are separated. Second, we show that theoutcome discussed in the first step is really an equilibrium outcome.
If h and l are separated at the Nash equilibrium, the relevant demand function for firms
1 and 2 must be DH (ph ). Therefore, q1 = q2 = 1/3 becomes the Nash equilibrium after asimple calculation. The equilibrium profit becomes 1/9 for each firm. Because firm 3 plays
as the monopolist in the low-end market, q3 = b/2 and the equilibrium profit becomesab/4. We now denote the vector of the equilibrium outcome as q E ≡ (1/3, 1/3, b/2).
We now check whether or not q E is a Nash equilibrium. If q E appears as an equilibriumoutcome, firms 1 and 2 must not have the incentive to produce more so that h and l become
connected. We derive the condition under which such deviations do not occur. To connect
h and l, firm 1 must produce at least13
q1D ≡

2 a
− .
3 2

Differentiating π1 (q) with respect to q1 and substituting q2 = 1/3 and q3 = b/2 into it, we
13

Given q2 = 1/3, ph = 1 − q1 − q2 = 2/3 − q1 . Because 2/3 − q1 ≤ pl = a/2 is required to make h andl connected, firm 1 must produce at least 2/3 − a/2.

8

have
∂
∂q1

Ã

a(1 + b − (q1 + q2 + q3 ))q1
a+b

!¯
¯
¯
¯
¯

a
=
a+b
q2 ,q3Ã!

2 b+ − 2q1 .
3 2

If a + b/2 ≤ 2/3, this is negative for any q1 ≥ q1D , and then firm 1 does not have an
incentive to deviate. Otherwise, we have the interior solution from it:
q1 =

1 b
+ .
3 4

In this case, the profit of firm 1 is
a
a+b

Ã

4 + 3b12!2.

If this is smaller than the profit in which h and l are separated, that is,
a
a+b

Ã

4 + 3b12!2< 1/9,

the firm does not have an incentive to deviate. After some calculations, this can be
rewritten as 3a(8 + 3b) < 16.
Therefore, if a + b/2 ≤ 2/3 or 3a(8 + 3b) < 16 holds, no major firm wants to deviate.
Fortunately, 3a(8 + 3b) < 16 is automatically satisfied if a + b/2 ≤ 2/3 is satisfied.14 As aresult, the only relevant condition is 3a(8 + 3b) < 16, and we obtain the following lemma.
Lemma 2 Suppose that firm 1 supports firm 3 at the first stage. If 3a(8 + 3b) < 16, there
is a Nash equilibrium in the corresponding subgame such that firms 1 and 2 obtain 1/9.

3.3

SPE

In this subsection, using the results obtained so far, we derive the condition for the
existence of the SPE such that firm 1 supports firm 3 at the first stage on the equilibrium
path.
14

Multiplying both sides of a + b/2 ≤ 2/3 by 24 yields 24a + 12b ≤ 16. Because a < 1/2 by assumption,

12b > 9ab. Therefore, it is enough to focus on 3a(8 + 3b) < 16.

9

We require two conditions. One is 3a(8 + 3b) < 16 as the analysis in the previous
subsection shows. The other is that firm 1 actually benefits from the strategic handoverof the low-end market. That is,1a(1 + b)2≥
⇔ 1 ≥ a(2 + b).
99(a + b)
However, a simple calculation shows that 3a(8 + 3b) < 16 is automatically satisfied ifa(2 + b) ≤ 1 holds.15 Therefore, we obtain the following result.
Proposition 1 If a(2 + b) ≤ 1 holds, then there is a subgame perfect equilibrium in which
the strategic handover occurs on the equilibrium path.
Figure 1 shows the region in which Proposition 1 holds. Note that a(2 + b) ≤ 1 does
not hold for any b > 0 as long as a > 1/2. The rough intuition of Proposition 1 is asfollows. If firm 3 does not enter the low-end market, the price elasticity at a lower pricethan a becomes higher than that of DH (ph ). This property induces the firms to produce
more. However, those increases in production are not profitable to firms 1 and 2 if thelow-end market is small in terms of both willingness to pay (measured by a) and market
size (measured by b). Therefore, the handover of the low-end market to firm 3 (as credible
commitment not to overproduce) becomes beneficial to firms 1 and 2.
We have to note that two incumbent firms are needed to derive our main result. In
other words, if there is only one incumbent firm, such an invitation of entrants is notprofitable for the incumbent firm. When there is one incumbent firm, it can set its
quantity with no fear of the rival firm’s response. If a firm assumes that supplying its
product for consumers at H and L is optimal, then it will do so; otherwise, it will not. By
entering, the monopolist loses this kind of freedom. The entry act as a constraint on the15a(2 + b) ≤ 1 can be rewritten as 32a + 16ab ≤ 16. The LHS of this inequality is larger than

3a(8 + 3b) = 24a + 9ab.

10

monopolist and does not provide any benefit to it. In the setting selected for this study,
the entrant firm must show commitment against fierce competition.

3.4

Welfare Analysis

In this subsection, we investigate whether or not the social welfare improves as a result offirm 3’s entry. Define q A ≡ ((1 + b)/3, (1 + b)/3, 0). q A is the output profile at the Nashequilibrium in Lemma 1 or the output profile when firm 3 is out of the market. Aftersome calculations, we obtain the quantities demanded by consumers in H and those in L
as follows:DH =2a + 3b − abb(3a + 2b − 1)
, DL =.
3(a + b)3(a + b)When firm 3 enters the low-end market, q E (= (1/3, 1/3, b/2)) is realized as shown in
Section 3.2. Because the markets are separated, the quantities demanded by consumers
in H and those in L are2b
DH = , DL = .
3
2
We now define ∆qH and ∆qL as follows:
2 2a + 3b − abb(1 − a)−=−(< 0),
3
3(a + b)3(a + b)b b(3a + 2b − 1)b(2 − 3a − b)
≡
−
=
.
2
3(a + b)6(a + b)

∆qH ≡
∆qL

In words, ∆qH (∆qL ) is the amount of change in the consumption level at H (L) by theentry of firm 3. The consumption level at H decreases by the entry.
We now evaluate those amounts and social welfare. The sign of ∆qL depends on theparameter values of a and b. If ∆qL is negative, the consumption levels in both groups
decrease. In this case, it is clear that firm 3’s entry is not socially beneficial. We now
consider the case in which ∆qL is positive. Consider the Nash equilibrium in Lemma
1. It is noteworthy that the marginal consumers in H and L have the same willingness
to pay at this equilibrium (before the entry). Given this situation, if we decrease the11consumption level at H by ∆(> 0) and increase the consumption level at L by thesame amount ∆, then social welfare decreases by the manipulation because the (gross)consumer surplus generated by consumers (who loss the consumption opportunity) at H islarger than that by consumers (who receive the consumption opportunity) at L. Because|∆qH | − |∆qL | = b/6 > 0, the decrease in the consumption level at H is larger than theincrease in the consumption level at L. Therefore, the entry of firm 3 is undesirable fromthe viewpoint of social welfare.
Proposition 2 The entry of firm 3 decreases social welfare.
The paradoxical result is quite different from the traditional discussion about the excess
entry theorem (e.g., Mankiw and Whinston (1986), Suzumura and Kiyono (1987), Matsumura (2000)). In the discussion, the reason that an additional entry harms social welfare
stems from the entry cost (fixed cost) incurred by the entrant and the business-stealing
effect (the pure replacement of the incumbent firms’ supply by the entrant’s). In ourpaper, we do not take a fixed cost incurred by an entrant into account. The driving forceof the result is the decrease in the quantities supplied by the incumbent firms. Note that,
if we allow more potential entrants to enter the low-end market, Proposition 2 would not
hold because ∆qL (the increment in the quantity demanded by consumers at L) increases
as the number of entrants increases.

4

Discussion

Those results are consistent with the following two empirical studies. We now show theempirical results that are related to ours.
Pauwels and Srinivasan (2004) demonstrate permanent performance effects of store
brand entry, typically benefiting the retailer, the consumers, and premium-brand manufacturers. For the manufacturers, store brand entry is typically beneficial for premiumprice national brands, but not for second-tier national brands. The increment in the12profits of national brands appears in our model. Their empirical results are consistent
with those of ours.16
Using supermarket scanner data, Ward et al. (2002) test several hypotheses: for
instance, private-label brands have lower prices than name brands; name-brand firms
defend their brands against the private-label invasion by lowering their prices. They showthat when the share of private-label goods rises, the prices of name-brand goods tend torise.17 They also show that an increase in private-label share is correlated with either noeffect or a decrease in the price of private-label goods, no effect or an increase in the price ofbranded goods and usually no effect or a negative effect on the overall price. As discussed
in the main part, those properties hold in our model. In our model, the number of entrants
does not affect the equilibrium price of incumbent firms (branded goods) but decreases
the equilibrium price of the entrants (private-label goods). Moreover, as the number ofentrants increases, the share of entrants (private-label goods) increases. Therefore, we
think that our model can be applied to the discussion about private brands.
We can also apply the model presented here to another situation related to international trade. We now suppose that there are two markets, domestic and foreign. The
demand structure is similar to that in Section 2. The domestic market is the high-end
market and the foreign one is the low-end market. Two incumbent domestic firms are able
to supply their products without any cost, and no transport cost exists. Under such a situation, let us suppose that one of the incumbent firms gives a new firm its own technology
and induces the entry of a new firm. By the technological transfer, the incumbent firms
resign from the foreign market and only supply their products to the domestic market. It
is noteworthy that, if the foreign market is expected to grow gradually, such an invitation
16

In our paper, however, we do not distinguish between the incumbent firms (national brand firms).

Therefore, we cannot explain the decrease in the second-tier price in our model.
17

As pointed out in Ward et al. (2002), a similar phenomenon has been observed in the pharmaceuticalmarket, see, for instance, Frank and Salkever (1997).

13

of new entrants would be unprofitable for incumbent firms.

5

Concluding Remarks

In this paper, we show that it might be beneficial for incumbent firms to focus on competition in the high-end market by the handover of the low-end market to other firms.
The handover keeps the price in the high-end market relatively high and the resulting
incumbents’ profit also becomes high if the low-end market is relatively small. We should
remember that, for incumbent firms, entry is preferable to no entry. This is different fromthe argument of Ashiya (2000) in which an incumbent firm might invite a weak firm’s
entry to prevent a strong firm’s entry.
We should mention that our result is (weakly) strengthened if we consider multiple
potential entrants. Suppose that incumbent firms can earn more profits when they abandon the low-end market. Even if one entrant in the low-end market is not enough forincumbent firms to abandon, they can surely prevent their own deviations by making the
low-end market sufficiently competitive.
As mentioned in footnote 16, we do not distinguish between the incumbent firms(national brand firms). Therefore, we cannot explain the result presented by Ward et al.
(2002): the decrease in the second-tier price. The construction of a framework that would
explain pricing behavior would be a worthy undertaking for future research.
[2006.09.25, 786]

14

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15

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1
0.8
0.6
0.4
0.2
3.5 3.75

4.25 4.5 4.75

5Figure 1: The parameter range in which the handover is beneficial.
(Horizontal: 10a, Vertical: b)

19