2005・42

Profit-enhancing know-how disclosure: A strategic view
Noriaki Matsushima
Susumu Ogawa

Profit-enhancing know-how disclosure: A strategic view∗

Noriaki Matsushima† and

Susumu Ogawa

Graduate School of Business Administration, Kobe University
November 1, 2005

Abstract
In general, the disclosure of know-how and technological knowledge could harm the disclosing firm. Firms, however, often share their know-how freely and enhances their profits.
We provide a theoretical framework and a new insight for know-how disclosure. We consider
a multi-product oligopolistic market. An incumbent firm that can disclose its cost-reducing
know-how and several new entrants exist. Each firm supplies products in two separate markets. The incumbent firm has already allocated its production resources to one of the markets(market A) and discloses its know-how concerning production in market A. We show thatthe disclosure of know-how for cost reduction can enhance the profit of the incumbent (thedisclosing) firm. Using the disclosed know-how, the entrants can produce at a low cost at
market A and allocate their production resources to the other market. As a result, the competition at market A is milder than that in the case in which the incumbent does not disclose
its know-how. Moreover, the disclosure could harm the new entrants. The result implies thatthe incumbent firm may disclose its know-how in its industry as a payoff-enhancing entry
deterrent.

JEL classification codes: L13, M21, D21
Key words: know-how, disclosure, resource allocation, multi-product firms∗ We thank Toshihiro Matsumura for helpful comments and suggestions. We also thank the seminar participantsin Shinshu University. We gratefully acknowledge financial supports from Grant-in-Aid for Encouragement of Young
Scientists from the Japanese Ministry of Education, Science and Culture. Needless to say, we are responsible forany remaining errors.
† 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.jp1

1

Introduction

Disclosure of know-how and technological knowledge is beneficial from the viewpoint of social
welfare. Such behavior, however, could rebound on the disclosing firm. To encourage the disclosureof know-how or knowledge, in many countries, governments ensure exclusive rights of innovators
by patent laws, and innovators can license their know-how or technological knowledge for firms
and institutes. In the literature of know-how disclosure, therefore, the following two topics are
eagerly discussed: (1) how to licence (see Kamien and Tauman (1984, 1986), Katz and Shapiro(1985, 1986), and Muto (1993), among others) and (2) how to protect innovators (see Gilbert andShapiro (1990), Klemperer (1990), and other special issues of the RAND Journal of Economics(see Saloner (1990)) as well as Scotchmer (2004)).
On the other hand, some researchers point out that, oftentimes, innovating firms do not sellor license their innovation, but, instead, they freely reveal the details of their innovation. For
instance, von Hippel (1988) pointed out that rival firms routinely exchanged technical informationin the steel mini-mill industry and proposes a theory of know-how sharing based on the idea that it
reduces cost (see also von Hippel and Schrader (1996)). Eaton and Eswaran (2001) build a model
based on the idea of von Hippel (1988).
In the literature of economics, some researchers discuss the profitability of freely revealing
knowledge. In his examination of the history of technical advances in England’s Cleveland district
during the nineteenth century, Allen (1983, pp.18-20) provides three possibilities in which the revelation of technical information might have been profitable: (a) If the production process involves
a natural resource which commands a rent and if the invention lowers the costs of firms’ processing
only that portion of the resource with certain characteristics, then the owners of those firms might
benefit from releasing technical information; (b) If the world is characterized by competition amongfirms in different regions with different relative factor prices, each region can lower its costs andraise its resource rents relative to other regions by practicing collective invention and broadcasting
technical information; and (c) Output and profits would be greater if the existing regime of trade
secrets was replaced by a new regime of free information exchange. Based on the third possibility
listed by Allen (1983), Cowan and Jonard (2003) developed a formal model that account for the
dynamics of knowledge and collective invention and demonstrated that a communication network2

structure has a strong influence on system performance. De Fraja (1993) considers an R&D tournament in which two firms invest until an innovation occurs. In his model, when the payoff of theloser is close to that of the winner, the firms disclose their knowledge concerning R&D investments
because the disclosure shortens the expected time of the R&D competition and economizes on theinvestment costs.
Free revelation of knowledge and know-how is especially observed in the information technology
industry. Freeware is a typical example. Independent programmers develop applications, such as
text editing, graphics, and music, and they freely disclose the applications. A typical explanations
for this is that, in this manner, such programmers publicize their skills and abilities to theircommunities and computer firms (see Raymond (1999) and Lerner and Tirole (2002)). Opensource programs are also related to the free revelation of innovation. In the information technology
industry, commercial firms support open-source programming. Some explanations are as follows:
the program is a complement to the commercial firm’s product, and helping the programm damages
the rival of the helping firm (see Kende (1998)). As pointed out by Mustonen (2005), some firms
create competition by supporting open-source communities, in which programs are substituted
for another firm’s programs. Based on the idea of Lerner and Tirole (2002), Mustonen (2005)
developed an analytical model in which a copyright firm and a copyleft (open-source) community
compete in a program market and showed that the copyright firm makes its program compatible
with that of the copyleft community and supports the copyleft community if the network effect ofthe program is weak.
We can summarize the positive effects of knowledge disclosure in the literature: 1. Give and take(von Hippel (1988) and Eaton and Eswaran (2001)); 2. Input sector (Allen (1983)); 3. Interregional
trade (Allen (1983)); 4. Information exchange (Allen (1983) and Cowan and Jonard (2003)); 5.
Saving R&D expenditure (De Fraja (1993)); 6. Signaling (Reymond (1999)); 7. Complementarity(Kende (1998)); and 8. Network externality (Mustonen (2005)). In this paper, we provide a new
insight concerning knowledge disclosure. We focus on resource allocation strategies that have notbeen considered in the literature.
In this paper, we provide a theoretical framework to show a new insight for know-how disclosure.

3

We consider a multi-product oligopolistic market. An incumbent firm that can disclose its costreducing know-how and several new entrants exist. Each firm supplies its products in two separate
markets, A and B. Each multi-product firm has to allocate its production resource for the markets.
If a firm allocates its resource for market A, it can produce a lower marginal cost in market A, but
it has to incur a higher marginal cost in market B.1 The incumbent firm has already allocatedits resources to market A and discloses its know-how concerning production at market A. By thedisclosure, the entrants can economize on their production in market A. In our paper, we assume
that the disclosed know-how is more effective for an entrant that allocates its resources to market
B (called type B) than for one that allocates its resources to market A (called type A). In theliterature of R&D, as the efficiency of a product improves, the marginal effect of cost-reducing
activities decreases. We now apply these steps to our settings. At market A, type A is more
efficient than type B. Therefore, the benefit of the know-how disclosure for type A is smaller thanthat for type B.2
Those resource allocations are commonly observed in many industries. In the automobile
industry, the “market”, for example, represents car size for instance, and a resource allocation by afirm, for example, indicates that the firm produces small cars efficiently and large cars inefficiently.
In the consumer electronics industry, possible interpretations of the “market” include televisions,refrigerators, and electronic ovens, and a resource allocation by a firm could be interpreted as its
ability to produce televisions efficiently while it is unable to produce electronic ovens efficiently.
From the model, we show that the disclosure of know-how for cost reduction can enhance theprofit of the incumbent (the disclosing) firm. That is, it is possibility that revealing technicalinformation could be profitable. We now show the intuition behind the result. First, suppose thatthe incumbent does not disclose its know-how. In this case, some entrants allocate their resources
for market A, and some other entrants allocate their resources for market B. The number offirms that allocate their resources to market A is nearly equal to that of firms that allocate theirresources to market B. Now, suppose that the incumbent discloses its know-how. Using the
1 This setting is somewhat similar to the spatial discrimination model, in which firms choose their locations.

Concerning the spatial discrimination model, see Hamilton et al. (1989), Anderson and Neven (1991), Pal (1998),
and Matsushima (2001), among others.
2 To clarify the analysis, we assume that the benefit of know-how disclosure for type A is sufficiently small.

the latter part of the Introduction, we provide the intuition behind the result based on the assumption.

4

Indisclosed know-how, each entrant can produce its product at a low marginal cost at market A.
Allocating their resources for market A is ineffective for the entrants. Know-how disclosure inducessome entrants to change the allocation patterns of their resources. The change in the allocation
patterns mitigates the competition at market A because the number of tough competitors at market
A (firms allocating their resources to market A) decreases by know-how disclosure. The decreasein the number is beneficial for the incumbent firm. Of course, know-how disclosure reduces the
production costs of entrants in market A who allocate their resources to market B. This is harmful
for the incumbent firm. These are trade-offs. In our model, if the incumbent firm sets the degreeof know-how disclosure appropriately, the former positive effect dominates the latter negative one.
Therefore, revealing technical information could have been profitable.
In the model, know-how disclosure can harm entrants who allocate their resources to market
B. As mentioned earlier, know-how disclosure reduces the production costs of entrants in market
A who allocate their resources to market B. This is beneficial for the entrants. On the other hand,know-how disclosure induces some entrants to change the allocation patterns of their resources.
It enhances the competition at market B because the number of tough competitors at market B(firms allocating their resources to market B) increases by know-how disclosure. These are tradeoffs. In this sense, the profits of the entrants who allocate their resources to market B are seenas the flip side of the profit of the incumbent. The result implies that the incumbent firm may
disclose its know-how in its industry as a payoff-enhancing entry deterrent.
The paper proceeds as follows. The next section provides the case of a Japanese supermarket
chain. Section 3 outlines the basic model. Section 4 provides the results. Finally, section 5 offerssome concluding remarks.

2

The case of a Japanese supermarket chain

2.1

BackgroundIn general, a firm would never take actions to disclose its know-how. However, there are firms who
act in a manner which is different from this common belief. For example, it is known that Kansai
Supermarket (hereinafter referred to as KSP), a regional supermarket chain in Japan, actively
disclosed its own know-how to potential rivals between 1970 and 1985, which was a growth period5for the supermarket industry in Japan.
KSP, a regional chain, was established in 1959. As the ”Kansai” in its name indicates, KSP
is a retailer with stores only in the Kansai region such as in Osaka and Hyogo. In March of fiscal
2004, the firm had gross sales of approximately 102 billion yen, with a total of 51 stores.
It has been widely acknowledged by the industry and academic societies that KSP was a pioneerin Japan in the establishment of the supermarket business (Ishihara (1998)). Until KSP began
to innovate, it was believed that the job of controlling the freshness of such perishable foods asvegetables and fish could only be performed by specialized craftsmen. In the 1970s KSP analyzed
the tacit knowledge possessed by craftsmen, broke down that knowledge, standardized it and put
it into a manual. As a result, it became possible for KSP to realize a sales space where even parttime workers, at low labor costs, could maintain freshness at the same level as that achieved bycraftsmen. It has been recognized in the industry that these activities of KSP were revolutionary,clarified by the fact that 91 articles about the activities of KSP appeared in the same monthly
trade journal Hanbai Kakushin, which means Revolution in Retailing in Japanese, between 1971
and 1984.

2.2

Know-how disclosure

The period from 1970 to 1985, when KSP was actively innovative, was the time that the supermarket industry was established in Japan, and it was also a period of growth for the industry.
Figure 1 shows the fluctuations in the number of stores and gross sales amounts from 1975 to 1985
for Maruetsu and Life (both major supermarket chains), Okuwa (which is about the same scale as
KSP) and KSP.
[Figure 1 about here]
The gross sales per store are the only data available by which to compare the business results
for the stores at the time - and in comparing these data we have found from Figure 2 that KSP’s
business results surpassed those of other firms.
[Figure 2 about here]
What we would like to draw attention to here is the fact that KSP, a supermarket chain
which had developed cutting-edge know-how, actively disclosed its know-how to other firms in the6same industry, including its rivals. Rather than limiting itself to disclosing know-how through theabove-mentioned magazine articles, the firm actively disclosed know-how through the activities
of a business exchange group. It has been reported that a maximum of 77 supermarket firms
participated in this group to absorb the know-how of KSP (Mizuno (2005)).
This case example is very interesting for a number of reasons. First is the fact that the knowhow which KSP disclosed was at the cutting edge in the industry at the time. Second is the timing
by which KSP disclosed its know-how at the same time that this know-how was developed. Thirdis the fact that among the firms to whom KSP disclosed its know-how were rival supermarkets who
had stores in the same geographical area as KSP. And finally is the fact that those firms sparedno effort to obtain the know-how in question. Innovation-related information such as know-how issometimes difficult to transfer (von Hippel (1994) and Ogawa (1998)). Thus, KSP not only allowed
those firms to observe its stores and lend them manuals, but also sometimes even dispatched its
own employees to instruct employees of the other firms, and brought employees from the otherfirms into its own stores for a number of years in order to transmit know-how to them.
It would be difficult to understand the above-mentioned actions of KSP from the viewpointthat know-how which is unique to one’s own firm should be protected. However, that is only if one
assumes that the firm in question is a single-product firm which only handles one product. The
moment one assumes that the firm in question handles two or more products, it becomes possible
for that firm to create a favorable situation for itself by disclosing its know-how to its rivals.
The KSP case presented here is not categorized into the patterns concerning the positive effects
of know-how disclosure (see Section 1). In the case of KSP, reciprocities of know-how among firms
do not exist (cases 1 and 4); KSP does not have input sectors or upstream firms (case 2); thecompetition among KSP and the other retailers holds in a region (case 3); and the production
complementarity or network externality among KSP and other retailers does not exist (cases 7 and
8). From the discussion above, we cannot say that the effects of cost saving or signaling do notexist (cases 5 and 6). The matter is discussed in Section 5.

2.3

Fact

As mentioned above, the following is clarified by the analysis in this paper. That is to say that,assuming that a firm handles more than one product, it may be possible for that firm to create7

a competitive advantage for itself by disclosing know-how to its rivals. If a firm discloses to arival know-how regarding a certain product, that means that the rival to whom the disclosure ismade will be in possession of know-how about the product in question - and so it will think it
reasonable to allocate management resources into another product. As a result, the firm to whom
the disclosure has been made will no longer sink management resources into the same productfield as the firm that has disclosed know-how, enabling the discloser to maintain its competitive
advantage.
The analysis findings given above have also been observed in the case example of KSP, towhich attention has been drawn by this paper. It has been reported that some of the rival firms
to whom know-how on the management of perishable foods was disclosed by KSP, took action todifferentiate themselves by selecting goods, including deluxe imported goods and prepared food,among others (Ogawa, August 1, 2005; interviews with president of KSP).

3

The model

There are four multi-product firms.3 Firm 0 is the incumbent firm and firms 1, 2, and 3 areentrants. Each firm supplies its products in two separated markets, A and B. Market i is theone for product i (i = A, B). Let pi denote the price of the production in market i (i = A, B)
and qi , its quantity in market i. The demand functions at markets A and B for the products are
represented by qA = 1 − pA and qB = 1 − pB , respectively. In each market, the firms compete inquantity.
Each multi-product firm supplies its products for the markets. Each of them has to locate at
one of the markets. The incumbent can produce its product without costs at the market in which it
locates, while it has to incur a constant marginal cost t to produce its product at the other market.
Each entrant incurs a constant marginal cost c(> 0) at the market in which it locates, while it has
to incur a constant marginal cost c + t to produce its product at the other market. That is, theentrants are less efficient than the incumbent. To assure positive quantities supplied by each firm,
we assume that t < (1 − 2c)/4. We can interpret “market” as varieties of goods and the point of a
3 The qualitative property of our results does not depend on the number of multi-product firms.

the case of n firms are available upon request.

8

All proofs forfirm’s location as the firm’s most efficient sector.4 For example, in the automobile industry, “space”
represents car size, and a firm’s location indicates that the firm produces small cars efficiently butlarge cars inefficiently. In the consumer electronics industry, possible interpretations of “space”
include televisions, refrigerators, and electric ovens, and a firm’s location could be interpreted as
its ability to produce televisions efficiently and its inability to produce electronic ovens efficiently.5
Firm 0 has already located at A, that is, it has already allocated its resources to product A.
The other firms decide where to locate. Before they choose their locations, firm 0 decides whether
to disclose its know-how concerning product A. If it discloses its know-how, a firm locating at B
can produce product A with a constant marginal cost c + t − e (e is a positive constant), and a firm
locating at A can produce product A with a constant marginal cost c − f (f (< e) is a positive
constant). That is, know-how disclosure by firm 0 reduces the marginal costs of the rivals. The
disclosure helps entrants making units of product A.
We think that the assumption, f < e, is plausible. In the literature of R&D, as the efficiency of
product improves, the marginal effect of cost-reducing activities decreases. We now imply it to our
setting. At market A, a firm that allocates its resource to market A (type A) is more efficient thanthat which allocates its resources to market B (type B). Therefore, the benefit of the disclosurefor type A (the value of f ) is smaller than that for type B (the value of e), that is, f < e.
[Table 1 about here]
To simplify the analysis, we assume that c = f = 0.6 The assumption means that the disclosure is
not useful for a firm allocating its resources to product A. We think that the assumption is plausible
because firms cannot produce units of product A more efficiently than the incumbent firm (firm0) that discloses its know-how and leads the production technology at market A.7 Controlling the
4 In a spatial price discrimination model, Matsushima and Matsumura (2003) use the interpretation.

We canalso interpret the marginal cost t as a transport cost to supply the market in which it does not locate.
5 This interpretation is similar to those of Eaton and Schmitt (1994) and Norman and Thisse (1999). To explain

flexible manufacturing systems (FMS), they use spatial price discrimination models.
6 The assumption that f = 0 is essential to derive the main result.

Even though an entrant which allocate its
resources to market A is more efficient than the incumbent (f > 0), our result holds when the difference between
the efficiencies of the incumbent and the entrant is small enough (f is small enough). We can show the result of thenon-simplified version.
7 As discussed in von Hippel (1994) and Ogawa (1998), innovation-related information, such as know-how, issometimes difficult to transfer. Therefore, we think that it is difficult for entrants to be more efficient than the9amount of information concerning the product which is efficiently produced by firm 0, firm 0 isable to control the level of e. The cost structures of the model are summarized as follows.
[Table 2 about here]
The game runs as follows. In the first stage, firm 0 decides whether it discloses its know-how
concerning product A. If it decides to disclose, it sets the level of e. In the second stage, given thedecision of firm 0, firms 1, 2, and 3 decide where to locate. In the third stage, given the locationsof the firms, each firm decides its quantities supplied at the markets.

4

ResultWe now show the main results of the paper. Before we discuss the main concern, we show theresult of n-firm quantity (Cournot) competition.8 Let ci (i = 1, . . . , n) be the constant marginal
cost of firm i. When the (inverse) demand function is p = 1 − Q (p: price; Q: the aggregate
industry output), the profit of firm i (πi ), Q, and consumer surplus (CS) are
πi =

(1 +

Pn

2
j=1 cj − (n + 1)ci ),(n + 1)2

Q=

n−

Pn

j=1 cjn+1, CS =Pn2
j=1 cj ).
2(n + 1)2

(n −

(1)

In the following two subsections, we consider two cases: (1) firm 0 does not disclose its knowhow; and (2) firm 0 discloses its know-how. We now discuss the locations of firms.

4.1

Non disclosure of know-how

Suppose that 4 − k firms locate at A and k firms locate at B (k = 0, 1, 2, 3). The profit of the firm
locating at A (denoted as πA (k)) and that of the firm locating at B (denote it as πB (k)) are
πA (k) ==πB (k) ==(1 + ((4 − k) × 0 + kt) − (4 + 1) × 0)2(1 + ((4 − k)t + k × 0) − (4 + 1)t)2+(4 + 1)2(4 + 1)22 2
2 − 2t + (1 + 2k + 2k )t,(2)
25(1 + ((4 − k)t + k × 0) − (4 + 1) × 0)2(1 + ((4 − k) × 0 + kt) − (4 + 1)t)2+
2(4 + 1)(4 + 1)2
2 − 2t + (41 − 18k + 2k 2 )t2
.
(3)
25

incumbent.
8 The way to derive the result is mentioned in Shy (1995, pp.126-7).

10If πA (k) > πB (k + 1), the firms locating at A do not have an incentive to move to B. If πB (k) >πA (k − 1), the firms locating at B do not have an incentive to move to A. Therefore, if theinequalities hold, the location pattern in which k firms locate at B is an equilibrium outcome. We
have the following lemma:
Lemma 1 The following location pattern is a unique equilibrium outcome: 2 firms (including firm0) locate at A, and 2 firms locate at B. Under the location pattern, each firm’s profit isπA (2) = πB (2) =2 − 2t + 13t2
.
25

(4)

The location pattern is quite natural. As the number of firms at a location (market) increases,
the intensity of competition at that market is enhanced. The intensity of competition at the othermarket diminishes. If the number of firms at the first market is larger than that at the other market,
to avoid tough competition at the first market, some of the firms move to the other market, which
has a smaller number of firms. In equilibrium, each market has the same number of firms.
From (1), consumer surplus (denote as CSn ) is
CSn = 2 ×

(4 − 2t)24(2 − t)2=.
2
2(4 + 1)
25

(5)

From (4) and (5), social welfare (denote as SWn ) is
SWn = CSn + 2πA (2) + 2πB (2) =4.2

8(3 − 3t + 7t2 )
.
25

(6)

Disclosure of know-how

Suppose that 4 − k firms locate at A and k firms locate at B (k = 0, 1, 2, 3). The profit of the firmddlocating at A (denote it as πA(k)) and the profit of the firm locating at B (denote it as πB(k)) are(1 + ((4 − k)t + k × 0) − (4 + 1)t)2(1 + ((4 − k) × 0 + k(t − e)) − (4 + 1) × 0)2+(4 + 1)2(4 + 1)22 2
2 − 2t + (1 + 2k + 2k )tek(2 + (2t − e)k)
=
−
,
(7)
25
25
(1 + ((4 − k) × 0 + k(t − e)) − (4 + 1)(t − e))2
(1 + ((4 − k)t + k × 0) − (4 + 1) × 0)2
d
πB
(k) =
+
2
(4 + 1)(4 + 1)2e(5 − k)(2 − (2t − e)(5 − k))2 − 2t + (41 − 18k + 2k 2 )t2
+
.
(8)
=
25
25
d
πA
(k) =

d
d
d
If πA
(k) > πB
(k + 1), the firms locating at A do not have an incentive to move to B. If πB
(k) >
d
πA
(k − 1), the firms locating at B do not have an incentive to move to A. Therefore, if the11inequalities hold, the location pattern in which k firms locate at B is an equilibrium outcome. We
have the following lemma:
Lemma 2 Suppose that e satisfies the following inequalities:
t2 < e.

(9)

The following location pattern is the unique equilibrium outcome: firm 0 locates at A and the other3 firms locate at B. Under the location pattern, each firm’s profit is
d
(3) =
πA
d
πB
(3) =

2 − 6e + 9e2 − 2(1 + 9e)t + 25t2,
252(1 + 2e + 2e2 ) − 2(1 + 4e)t + 5t2
.
25

(10)
(11)

d
(3) isOn the range described in (9), the supreme of πA(2 − 2t + t2 )(1 + 9t2 )
,
25

(12)

which is achieved when e converges to t2 .
As shown in Table 2, locating at B is cost-advantageous for firms. Firms locating at B areable to supply products to market A at a low marginal cost (t − e), but firms locating at A haveto incur the higher marginal cost t to supply product to market B. As the value of e increases,
the cost advantage is more significant. Given a location pattern in which the number of firms isthe same at both markets, as the value of e increases, to get the cost advantage, some of the firmsthat would locate at A move from A to B. Therefore, under the level of e in (9), a firm changes
its location from A to B.
From (1), consumer surplus (denote as CSd ) isCSd =(4 − 3(t − e))2(4 − t)2
32 + 24e + 9e2 − 2(9e + 16)t + 10t2+=.
2(4 + 1)2
2(4 + 1)2
50

(13)

From (10), (11), and (13), social welfare (denote as SWd ) isdd
SWd = CSd + πA(3) + 3πB
(3) =

4.3

3(16 + 12e + 17e2 − 2(8 + 17e)t + 30t2 )
.
50

(14)

The incumbent firm

In this subsection, we assume that e satisfies the inequalities in (9). The discussion turns now tothe difference in firm 0’s profit when it discloses its know-how and when it does not. From (4) and12

(10), the difference is as follows:dπA(3) − πA (2) =3(4t2 − 2(1 + 3t)e + 3e2 )
.
25

(15)

d
If this is positive, that is, πA(3) − πA (2) > 0, the disclosure of its know-how is beneficial for firm

0. From (9) and (15), we have the following proposition:
Proposition 1 Disclosing its know-how enhances the profit of firm 0, if and only if it sets thelevel of e as follows:
2

t <e<

1 + 3t −√1 + 6t − 3t2
.
3

(16)

[Figure 3 about here]
As the value of e increases, the cost advantage of firms locating at B is enhanced. In other words,
the disadvantage of the firm disclosing its know-how is enhanced by the increment in the level of
e. Based on the property, someone may think that such know-how disclosure is obviously harmful
for the disclosing firm. In our model, however, another viewpoint has been provided.
The viewpoint is that know-how disclosure induces some firms to change their plans of location(”specialized” product). As mentioned in Lemma 2, these firms change their specialized productfrom product A to product B. The change mitigates the competition at market A and is beneficial
for the firm disclosing its know-how. The viewpoint is not discussed in the literature of know-how
disclosure, thus constituting a new insight into the issue.
Know-how disclosure has the positive and negative effects reported above. When the firm
disclosing its know-how sets an appropriate level of e (the level induces a firm to change its
location but is not too large), the positive effect dominates the negative one. As a result, knowhow disclosure which reduces the costs of its rivals, really increases its own profit.

4.4

Entrants

In this subsection, we consider the entry deterrent effects of know-how disclosure. As mentioned
in Section 4.2, know-how disclosure enhances the efficiencies of the rival firms. As first glance, itwould increase the profits of the rivals. In the model, however, the converse holds.

13

In each case, the firms earn the same profit levels (see the discussion in Sections 4.1 and 4.2
and equations in (4) and (11)). We now calculate the difference between the profit in which firm
0 discloses its know-how and that in which it does not. From (4) and (11), we have the difference:dπB(3) − πB (2) =4(e2 + (1 − 2t)e − 2t2 )< 0, for any e in (16).
25

(17)

From the inequality, we have the following proposition:
Proposition 2 Suppose that firm 0 sets the level of e within the range in (16). Disclosing theknow-how of firm 0 decreases the profits of the other three firms.
By the disclosure, a firm that would locate at A moves to B. This enhances the competition atmarket B. If the level of e were large enough, the transport cost reduction (positive) effect ofthe disclosure would dominate the negative effect of the competition. In this case, however, thedisclosing firm sets the level of e at an intermediate level (see (16)). Therefore, the enhanced
competition harms the other three firms. In this sense, the profits of the entrants that allocate
their resources to market B can be seen as the flip side of the profit of the incumbent. The result
implies that the incumbent firm may disclose its know-how in its industry as a payoff-enhancing
entry deterrent.

4.5

WelfareWe now discuss the welfare implications of know-how disclosure.
The first implication if know-how disclosure is the difference between the consumer surplus whenfirm 0 discloses its know-how and when it does not. From (5) and (13), we have the difference:
CSd − CSn =2t2 + 6(4 − 3t)e + 9e2> 0, for any t < 1/4.
50

(18)

From the inequality, we have the following proposition:
Proposition 3 Disclosing the know-how of firm 0 enhances consumer surplus.
Suppose that a fixed amount of the product exists in the markets. Equal allocation of the productto markets A and B is the worst way from the viewpoint of consumer surplus because consumer
surplus is convex with respect to the quantity supplied. An asymmetric allocation of the productoccurs by the relocation induced by the disclosure. The asymmetric allocation increases consumer
surplus.
14

[Figure 4 about here]
The second implication is the difference between social welfare when firm 0 discloses its knowhow and when it does not. From (6) and (14), we have the difference:
SWd − SWn =51e2 + 6(6 − 17t)e − 22t2
.
50

(19)

From the equation, we have the following proposition:
Proposition 4 Suppose that firm 0 sets the level of e within the range in (16). Disclosing theknow-how of firm 0 enhances social welfare if and only if
!
Ã

√

51 − 1887
,
for any e,t ∈ 0,


51


"
!

√
√


51
−
1887
21
−
231



,
,
 t∈
51
27

p
e≥

(20)
3(108 − 612t + 1241t2 ) − 3(6 − 17)t
51

≡ ē,

otherwise, it diminishes social welfare.
From the viewpoint of social welfare, know-how disclosure has two effects. One is an efficiencyenhancing effect, and the other is a location-distorting effect. The former is positive and the latteris negative. The positive effect is enhanced by the increment in the level of e because the efficiency
of firms locating at B improves. The negative effect stems from the reduced competitiveness,
which is induced by the asymmetric location pattern, at market A. As the level of t increases, thecompetition at A is weakened because the entrants locating at B becomes less aggressive at A.
Therefore, Proposition 4 holds.

5

Concluding remarks

We examined the positive effects of a firm’s disclosing its know-how to rival firms. In general, firms
do not disclose to rival firms know-how that would give these rival firms a competitive advantage.
This is because, once a firm has disclosed its know-how, the rival firm will probably use that
information to try to diminish the competitive advantage of the discloser. As a result, the firm
which has disclosed the information might lose its competitive advantage. This is why it is generally
assumed that a firm should never disclose its know-how.

15

However, there was a regional retail-chain which acted in a manner which is different from thiscommon belief. KSP was an innovator in supermarket operations and actively disclosed its own
know-how to existing and potential rivals between 1970 and 1985, which was a growth period forthe supermarket industry in Japan.
On the basis of this observation, we provided a theoretical framework to explain such knowhow disclosure to rivals. We showed that a firm could create a competitive advantage for itself bydisclosing its know-how to its rivals if we assume that a firm handles more than one product. If a
firm discloses to a rival its know-how regarding a certain product, the rival to whom the disclosure
is made will be in possession of the know-how about the product in question; thus it would bereasonable for the rival to allocate management resources into another product. As a result, therival will no longer allocate management resources into the same product field as the discloser, andthe discloser will be able to maintain its competitive advantage.
The case of KSP provides a good example. Some of the rival firms to whom know-how on the
management of perishable foods was disclosed by KSP, took action to differentiate themselves from
KSP by selecting goods, including deluxe imported goods and prepared food, among others. As aconsequence, KSP maintained its competitive advantage.
An implication of this study is that a multi-product firm could gain a competitive advantage
from know-how disclosure when the product markets of the firm are growing. Particularly, thisstrategy could be attractive to mass merchandisers such as Wal-Mart because such retailers generally handle two or more product categories and always search for new promising product categories.
For example, in the growing Electric Commerce market, amazon.com might be able to maintained
its competitive advantage if it discloses its know-how in book inventory management to rival firms.
We believe that our model could be applicable not only to retailing but also to multi-productmanufacturers. For instance, in the digital home appliance market, such as DVDs or cameras, it
might be a good strategy for Panasonic to disclose its know-how in DVD production to Samsung andHaier Electronics Group to maintain its global market leadership. In this respect, the applicability
and generalizability of our model will need to be explored.
As discussed by many researchers, know-how disclosure has several effects on the disclosing
firms or persons. In this paper, we discussed the effect on the resource allocation strategies of16

firms. In the case of KSP, as discussed by Reymond (1999), signaling effects might be important.
By disclosing its know-how, KSP might intend to appeal to upstream firms and rivals for its cost
efficiency. First, we mentioned the effect of know-how disclosure on upstream firms. KSP buys
many goods from upstream firms and sells the goods to consumers. As discussed in the literatureof industrial organization, wholesale prices set by upstream firms decrease as the efficiency ofthe downstream firm is improved. Therefore, appealing its efficiency by the know-how disclosure
would be effective for KSP. As reported by Mizuno and Ogawa (2004), know-how disclosure by
KSP reduces wholesale prices. Providing a model to explain this effect is a considerable future
research. Second, we mentioned the effect of know-how disclosure on rivals. If rivals recognize
KSP’s cost efficiency on a particular product, they will tend to avoid allocating their resources
to that particular product because they will realize that it is difficult to make a profit from thatparticular product. The effect on the rivals will strengthen our main results.
[2005.11.1 732]

17

Appendix
Proof of Lemma 1

To show the lemma, we solve the following inequalities:
πA (k) > πB (k + 1), πB (k) > πA (k − 1).

Solving the inequalities, we haveπA (k) − πB (k + 1)=

πB (k) − πA (k − 1) =3
8(2k − 3)t2
> 0, ⇒ k > ,25
28(5 − 2k)t2
5> 0, ⇒ k < .
25
2

(21)
(22)

The integer of k which satisfies both inequalities in (21) and (22) is 2. Therefore, Lemma 1 holds.
Q.E.D.
Proof of Lemma 2

To show the lemma, we solve the following inequality:ddπB(k) > πA(k − 1).

To consider the location choices of firms, suppose that k − 1 firms locate at B and 5 − k firmsdlocate at A (k = 1, 2, 3). In the case, the profit of the firm which locates at A is πA(k − 1). If oneof the firms locating at A changes its location, the number of firms which locate at B is k, and thedprofit of the relocating firm is then πB(k). Therefore, if the inequality holds for any k (k = 1, 2, 3),

in any case, the entrants do not locate at A, that is, 3 firms locate at B in equilibrium. Solving
the inequality, we haveddπB(k) − πA(k − 1) =4[e(2 + e − 2t) + 5(e2 − 2et + 2t2 ) − 2k(e2 − 2et + 2t2 )]
> 0,
25
µ
¶
5
e(2 + e − 2t)⇒ k < + H,
H≡
.
(23)
2
2(e2 − 2et + 2t2 )When e satisfies the inequalities in (9), H satisfies 1/2 < H. The integers of k which satisfy theinequality in (23) are 1, 2, and 3. Therefore, Lemma 2 holds.
Proof of Proposition 1

Q.E.D.

dπA(3) − πA (2) in (15) is positive if and only if√
1 + 3t − 1 + 6t − 3t2e<.
3

The right-hand side of the inequality is larger than t2 in (9). Therefore, Proposition 1 holds.
Q.E.D.
18

d
Proof of Proposition 2 πB
(3) − πB (2) in (17) is increasing in e. Substituting e = (1 + 3t −√d
1 + 6t − 3t2 )/3 into πB(3) − πB (2) in (17), we have:

−

4

¡√

¢
1 + 6t − 3t2 − (1 + 3t − 6t2 ).
45√This is negative because ( 1 + 6t − 3t2 )2 − (1 + 3t − 6t2 )2 = 36(1 − t)t2 > 0.

Q.E.D.

Proof of Proposition 4 SWd − SWn in (19) is increasing in e. Substituting e = t2 and√e = (1 + 3t − 1 + 6t − 3t2 )/3 into SWd − SWn in (19), we havet2 (14 − 102t + 51t2 ), (e = t2 )50√
p
(7 + 21 − 27t2 ) − 7 1 + 6t − 3t2, (e = (1 + 3t − 1 + 6t − 3t2 )/3).
15√
The former value is positive if and only if t < (51 − 1887)/51 and the latter one is positive if and√√only if t < (21 − 231)/27. Therefore, if t < (51 − 1887)/51, SWd − SWn in (19) is positive for√any e, and, if t > (21 − 231)/27, SWd − SWn in (19) is negative for any e. SWd − SWn in (19)is equal to zero if and only if e is equal to ē in (20). Therefore, proposition 4 holds.

19

Q.E.D.

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Economics 50, 197–234.
20

Matsushima, N. 2001. “Cournot competition and spatial agglomeration revisited,” Economics
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21

Location / Cost
Locating at A
Locating at B

MC at Acc+t

MC at Bc+tc

Location / Cost
Locating at A
Locating at B

(Non disclosure)

MC at Ac−fc+t−e

MC at Bc+tc(Disclosure)

MC: the constant marginal cost
Table 1: The cost structures.

Location / Cost
Locating at A
Locating at B

MC at A0t

MC at Bt
0

Location / Cost
Locating at A
Locating at B

(Non disclosure)

MC at A0t−e(Disclosure)

MC: the constant marginal cost
Table 2: The cost structures (simplified)22

MC at Bt0

Figure 1: Number of Stores and Fluctuation in Overall Gross Sales between 1975
and 1985
Note 1: The authors referred to Guide to Distribution Economics, 1975-1987 Issue (Nihon Keizai
Shimbun, Inc.) in producing this graph.
Note 2: The bar graph shows the number of stores. The sequential line graph shows overall grosssales.

23

Figure 2: Fluctuation in Gross Sales per Store between 1975 and 1985
The authors referred to Guide to Distribution Economics, 1975-1987 Issue (Nihon Keizai Shimbun,
Inc.) in producing this graph.

24

e
0.1

0.05

0

1/8

1/4

t

((t, e) in the shaded area satisfies the inequalities in (16))
Figure 3: Profit enhancing freely disclosure25<(an asymmetric allocation)(the equal allocation)

The consumer surplus in the right-hand side is larger than that in the left-hand side.
Figure 4: Consumer surplus

26

Supplementary Material
We now consider n-firm case. The procedure of the proof is similar to that of the main part.
We assume that t < 2/(n + 4). This assumption ensures positive quantities supplied by the firms.

5.1

Non disclosure of know-how

Suppose that n − k firms locate at A and k firms locate at B (k = 0, 1, 2, n − 1). The profit of
the firm locating at A (denote it as πA (k)) and the profit of the firm locating at B (denote it asπB (k)) are:πA (k)==

πB (k)==(1 + ((n − k)t + k × 0) − (n + 1)t)2(1 + ((n − k) × 0 + kt) − (n + 1) × 0)2+2(n + 1)(n + 1)2
2 − 2t + (1 + 2k + 2k 2 )t2,(24)(n + 1)2(1 + ((n − k) × 0 + kt) − (n + 1)t)2(1 + ((n − k)t + k × 0) − (n + 1) × 0)2+2(n + 1)(n + 1)2
2 − 2t + (1 + 2n + 2n2 − 2(1 + 2n)k + 2k 2 )t2.
(25)(n + 1)2

If πA (k) > πB (k + 1) and πB (k) > πA (k − 1), the location pattern in which k firms locate at B isan equilibrium outcome. We have the following lemma:
Lemma 3 The following location pattern is a unique equilibrium outcome: n/2 firms (including
firm 0) locate at A and n/2 firms locate at B. Under the location pattern, each firm’s profit is:
πA (n/2) = πB (n/2) =4 − 4t + (2 + 2n + n2 )t2.
2(n + 1)2

(26)

From (1), consumer surplus (denote it as CSn ) is:CSn =n2 (2 − t)2.
4(n + 1)2

(27)

From (26) and (27), social welfare (denote it as SWn ) is:
SWn = CSn + (n/2)πA (n/2) + (n/2)πB (n/2) =5.2

n2 (12 − 12t + (5 + 4n + 2n2 )t2 ).
4(n + 1)2(28)

Disclosure of know-how

Suppose that n − k firms locate at A and k firms locate at B (k = 0, 1, 2, n − 1). The profit ofdthe firm locating at A (denote it as πA(k)) and the profit of the firm locating at B (denote it asdπB (k)) are:(1 + ((n − k)t + k × 0) − (n + 1)t)2(1 + ((n − k) × 0 + k(t − e)) − (n + 1) × 0)2+2(n + 1)(n + 1)2
ek(2 + (2t − e)k)2 − 2t + (1 + 2k + 2k 2 )t2
−
,
(29)
=
(n + 1)2(n + 1)2(1 + ((n − k) × 0 + k(t − e)) − (n + 1)(t − e))2
(1 + ((n − k)t + k × 0) − (n + 1) × 0)2
d
πB
(k) =
+
(n + 1)2(n + 1)22
2 2
e(n + 1 − k)(2 − (2t − e)(n + 1 − k))2 − 2t + (1 + 2n + 2n − 2(1 + 2n)k + 2k )t
+
(30)
.
=
(n + 1)2(n + 1)2
d
πA
(k) =

i

d
d
d
d
If πA
(k) > πB
(k + 1) and πB(k) > πA(k − 1), the location pattern in which k firms locate at B isan equilibrium outcome. We have the following lemma:

Lemma 4 Suppose that e satisfies the following inequalities:√
1 + 2t − 1 + 4t − 8t2
2
t <e<
.
2

(9)

The following location pattern is a unique equilibrium outcome: n/2 − 1 firms (including firm 0)
locate at A and n/2 + 1 firms locate at B. Under the location pattern, each firm’s profit is:dπA(1 + n/2) =dπB(1 + n/2)=

8 − 4(n + 2)e + (n + 2)2 e2 − 2(4 + (n + 2)2 e)t + 2(10 + 6n + n2 )t2, (32)(n + 1)2
8 + 4ne + n2 e2 − 2(4 + n2 e)t + 2(2 − 2n + n2 )t2.
(33)
4(n + 1)2

From (1), consumer surplus (denote it as CSd ) is:
CSd

=
=

(2n − (n + 2)(t − e))2(2n − (n − 2)t)2+8(n + 1)28(n + 1)2
8n2 + 4n(n + 2)e + (n + 2)2 e2 − 2(4n2 + (n + 2)2 e)t + 2(n2 + 4)t2.
8(n + 1)2

(34)

From (32), (33), and (34), social welfare (denote it as SWd ) is:
SWd

=
=

5.3

d
d
CSd + πA
(1 + n/2) + 3πB(1 + n/2)(n + 2)(8n + 4(n + 2)e + (2n2 + n − 2)e2 )8(n + 1)2
(n + 2)(−2(4n + (2n2 + n − 2)e)t + 2(n + 2)(2n − 3)t2 )+.
8(n + 1)2

(35)

Comparison

In this subsection, we assume that e satisfies the inequalities in (9). We now discuss the difference
between firm 0’s profit in which it discloses its know-how and that in which it does not do. From(26) and (32), we have the difference:dπA(n/2 + 1) − πA (n/2) =(n + 2)(8t2 − 2(2 + (n + 2)t)e + (n + 2)e2 ).
4(n + 1)2

(36)

d
If this is positive, that is, πA(n/2 + 1) − πA (n/2) > 0, the disclosure of know-how is beneficial forfirm 0. From (9) and (36), we have the following proposition:

Proposition 5 Disclosing its know-how enhances the profit of firm 0, if and only if it sets thelevel of e as follows:p
2 + (n + 2)t − 4 + 4(n + 2)t + (n − 6)(n + 2)t2.
(37)
t2 < e <n+2ii

We now discuss the other firms’ profits. In each case, each of them earns the same profit (seethe discussion in the former subsections and equations in (26) and (33)). The difference between
the profit in which firm 0 discloses its know-how and that in which it does not do. From (26) and(33), we have the difference:dπB(n/2 + 1) − πB (n/2) =n(ne2 − (2nt − 4)e − 8t2 )< 0, for any e in (37).
4(n + 1)2

(38)

From the inequality, we have the following proposition:
Proposition 6 Suppose that firm 0 sets the level of e on the range in (37). Disclosing the knowhow of firm 0 decreases the profits of the other three firms.
The difference between the consumer surplus in which firm 0 discloses its know-how and thatin which it does not do. From (27) and (34), we have the difference:
CSd − CSn =8t2 + 2(n + 2)(2n − (n + 2)t)e + (n + 2)2 e2> 0, for any t < 2/(n + 4).
8(n + 1)2

(39)

From the inequality, we have the following proposition:
Proposition 7 Disclosing the know-how of firm 0 enhances consumer surplus.
The difference between social welfare in which firm 0 discloses its know-how and that in which
it does not do. From (28) and (35), we have the difference:
SWd − SWn =(n + 2)(2n2 + n − 2)e2 + 2(n + 2)(2(n + 2) − (2n2 + n − 2)t)e − 8(2n + 3)t2
. (40)
8(n + 1)2

From the equation, we have the following proposition:
Proposition 8 Suppose that firm 0 sets the level of e on the range in (37). Disclosing the knowhow of firm 0 enhances social welfare, if and only ifs!
Ã
3 + n2 + 4
2n t ∈ 0, 1 −, for any e,(2n2 + n − 2)(n + 2)







s
s
"
Ã
!!



3n + 22n3 + n2 + 4
3n2 − 4



t∈ 1−
,
1−
,


(2n2 + n − 2)(n + 2) 2(2n + 1)
(3n + 2)(n + 2)






















e≥

1
2n2 + n − 2¡ 2(2n + n − 2)t − 2(n + 2)s+(4(n + 2)3 − 4(n + 2)2 (2n2 + n − 2)t + (2n2 + n − 2)(2n3 + 5n2 + 16n + 20)t2 )(n + 2)otherwise, it diminishes social welfare.

iii

!
,

(41)

5.4

Cost structure

In the material, we consider the other setting which is variant of the basic model discussed in themain part. We now describe the setting which is different from that in the main.
Each multi-product firm supplies its products for the markets. Each of them has to locate at
one of the markets. The incumbent can produce its product without costs at the market in which
it locates, while it has to incur a constant marginal cost t to produce its product at the othermarket. Each entrant incurs a constant marginal cost c > 0 at the market in which it locates,
while it has to incur a constant marginal cost c + t to produce its product at the other market.
That is, the entrants are less efficient than the incumbent.
Firm 0 has already located at A, that is, it has already allocated its resources to product A.
The other firms decide where to locate. Before they choose their locations, firm 0 decides whether
it discloses its know-how concerning product A. If it discloses its know-how, a firm locating at B
can produce product A with a constant marginal cost c + t − e (e is a positive constant) and a firm
locating at A can produce product A with a constant marginal cost c − f (f (< e) is a positive
constant). That is, know-how disclosure by firm 0 reduces the marginal costs of the rivals.
The game runs as follows. In the first stage, firm 0 decides whether it discloses its know-how
concerning product A. If it decides to disclose, it sets the level of e. In the second stage, given thedecision of firm 0, firms 1, 2, and 3 decide where to locate. In the third stage, given the locationsof the firms, each firm decides its quantities supplied at the markets.

5.5

Non disclosure of know-how

Suppose that 4 − k firms locate at A and k firms locate at B (k = 0, 1, 2, 3). The profit of theeincumbent (denote it as πI (k)), the profit of the entrant locating at A (denote it as πA(k)), andethe profit of the entrant locating at B (denote it as πB (k)) areπI (k) =
=
e
πA
(k) =

=
e
πB
(k) =

=

(1 + (0 + (3 − k)c + k(c + t)) − (4 + 1) × 0)2(1 + (t + (3 − k)(c + t) + kc) − (4 + 1)t)2+(4 + 1)2(4 + 1)22
2 2
2(1 + 3c) − 2(1 + 3c)t + (1 + 2k + 2k )t
,
(42)
25
2
(1 + (t + (3 − k)(c + t) + kc) − (4 + 1)(c + t))2
(1 + (0 + (3 − k)c + k(c + t)) − (4 + 1)c)+
(4 + 1)2(4 + 1)2
2(1 − 2c)2 − 2(1 − 2c)t + (1 + 2k + 2k 2 )t2
,
(43)
25
(1 + (0 + (3 − k)c + k(c + t)) − (4 + 1)(c + t))2
(1 + (t + (3 − k)(c + t) + kc) − (4 + 1)c)2+(4 + 1)2(4 + 1)22
2 2
2(1 − 2c) − 2(1 − 2c)t + (41 − 18k + 2k )t
.
(44)
25

We have the following lemma:
Lemma 5 The following location pattern is a unique equilibrium outcome: 2 firms (including firm0) locate at A and 2 firms locate at B. Under the location pattern, each firm’s profit isπI (k) =2(1 − 2c)2 − 2(1 − 2c)t + 13t2
2(1 + 3c)2 − 2(1 + 3c)t + 13t2ee
, πA(2) = πB(2) =. (45)
25
25
iv

e
e
e
e
e
e
Proof: If πB(2)−πA(1) > 0 and πA(2)−πB(3) > 0, Lemma 5 holds. πB(2)−πA(1) = 8t2 /25 > 0eeand πA(2) − πB(3) = 8t2 /25 > 0. Therefore, Lemma 5 holds.
Q.E.D.

5.6

Disclosure of know-how

Suppose that 4 − k firms locate at A and k firms locate at B. The profit of the incumbent (denotee
it as πId (k)), the profit of the entrant locating at A (denote it as πAd(k)), and the profit of theeentrant locating at B (denote it as πBd (k)) are(1 + (0 + (3 − k)(c − f ) + k(c + t − e)) − (4 + 1) × 0)2(4 + 1)2(1 + (t + (3 − k)(c + t) + kc) − (4 + 1)t)2+(4 + 1)2
2(1 + 3c) + (1 + 3c − 3f )2 − 2(1 + 3c − 3f )(e − f )k + (e − f )2 k 2=
25−2(1 + 3c + 3f k + (e − f )k 2 )t + (1 + 2k + 2k 2 )t2,+
25(1 + (0 + (3 − k)(c − f ) + k(c + t − e)) − (4 + 1) × 0)2
e
πAd
(k) =
(4 + 1)2(1 + (t + (3 − k)(c + t) + kc) − (4 + 1)t)2+(4 + 1)222((1 − 2c) + 2(1 − 2c)f + 2f 2 ) − 2(1 − 2c + 2f )(e − f )k + (e − f )2 k 2=
25−2(1 − 2c − 2f k + (e − f )k 2 )t + (1 + 2k + 2k 2 )t2+,
25(1 + (0 + (3 − k)(c − f ) + k(c + t − e)) − (4 + 1)(t − e))2
e
(k) =
πBd
(4 + 1)2(1 + (t + (3 − k)(c + t) + kc) − (4 + 1) × 0)2+(4 + 1)2
2
2(1 − 2c) + (5e − 3f )(2 − 4c + 5e − 3f ) − 2(1 − 2c + 5e − 3f )(e − f )k + (e − f )2 k 2=
25−2(1 − 2c + 5(5e − 3f ) − 2(5e − 4f )k + (e − f )k 2 )t + (41 − 18k + 2k 2 )t2
+
.
25
e
e
If πBd(3) > πAd(2), that is,
πId (k) =8((1 − 2(c − f ))e − (f (1 − 2(c − f )) + 2f + t2 ))> 0,
25
all entrants locating at B do not have an incentive to move to A and then the location pattern inwhich 3 firms locate at B is an equilibrium outcome. We have the following lemma:eeπBd(3) − πAd(2) =Lemma 6 Suppose that e satisfies the following inequality:f (1 − 2(c − f )) + 2f + t2
< e.
1 − 2(c − f )(46)

The following location pattern is the unique equilibrium outcome: firm 0 locates at A and the other3 firms locate at B. Under the location pattern, each firm’s profit isπId (3)=2(1 + 3c)2 − 6(1 + 3c)e + 9e2 − 2(1 + 3c + 9e)t + 25t2
,
25
v

(47)

e
πBd
(3)

5.7

=

2((1 − 2c)2 + 2(1 − 2c)e + 2e2 ) − 2(1 − 2c + 4e)t + 5t2
.
25

(48)

Comparison

In this subsection, we assume that e satisfies the inequalities in (46). We now discuss the difference
between firm 0’s profit in which it discloses its know-how and that in which it does not do. From(45) and (47), we have the difference:
πId (3) − πI (2) =3(4t2 − 2(1 + 3c + 3t)e + 3e2 )
.
25

(49)

If this is positive, that is, πId (3) − πI (2) > 0, the disclosure of know-how is beneficial for firm 0.
From (46) and (49), we have the following proposition:
Proposition 9 Disclosing its know-how enhances the profit of firm 0, if and only if it sets thelevel of e as follows:p
1 + 3c + 3t − (1 + 3c)2 + 6(1 + 3c)t − 3t2
f (1 − 2(c − f )) + 2f + t2
B≡
< e, e <≡ B̄. (50)
1 − 2(c − f )3
We provide the values of B and B̄ and the condition that e is not empty (see, Figures 1’, 2’, 3’,
and 4’)
In each case, the entrants earn the same profit levels. We now calculate the difference between
the profit in which firm 0 discloses its know-how and that in which it does not do. From (45) and(48), we have the difference:
e
e
(2) =
(3) − πB
πBd

4(e2 + (1 − 2c − 2t)e − 2t2 )< 0, for any e in (50).
25

(51)

From the inequality, we have the following proposition:
Proposition 10 Suppose that firm 0 sets the level of e on the range in (50). Disclosing theknow-how of firm 0 decreases the profits of the other three firms.

vi

0.01

0.1

0.005

0.075

0
0
0.025

0.05
0.025

0.05
0.075

0.10

Figure 1’: The lower bound (B) in (50) when f = 0

0.015
0.01
0.005
0
0
0.025

0.1
0.075
0.05
0.025

0.05
0.075

0.10

Figure 2’: The upper bound (B̄) in (50)

vii

0.1

0.08

0.06

0.04

0.02

0

0

0.02

0.04

0.06

0.08

0.1

Figure 3’: The condition that e is not empty when f = 0.001: Horizontal t, Vertical c(The right-hand region represents the vector (t, c) which ensures the condition)

0.01

0.1

0.005
0
0
0.025

0.075
0.05
0.025

0.05
0.075

0.10

Figure 4’: The lower bound (B) in (50) when f = 0.001

viii