Price and quality competition: The effect of differentiation and vertical integration

European Journal of Operational Research 180 (2007) 907–921 www.elsevier.com/locate/ejor

Interfaces with Other Disciplines

Price and quality competition: The effect of differentiation and vertical integration Nobuo Matsubayashi Department of Administration Engineering, Faculty of Science and Technology, Keio University, Hiyoshi 3-14-1 Kohoku-ku, Yokohama 223-8522, Japan Received 23 August 2004; accepted 3 April 2006 Available online 16 June 2006

Abstract This paper studies an instance of price and quality competition between firms as seen in the recent Internet market. Consumers purchase a product based on not only its price but also its quality level; therefore, two firms compete in determining their prices and quality levels to maximize their profits. Characterizing this competition from a microeconomic viewpoint, we consider two possible business strategies that firms can utilize to overcome the competition—the differentiation and the vertical integration with another complementary firm. We show an interesting result not seen in the wellknown Bertrand price competition: not only does the differentiation always increase the firms’ profits, but also it can increase the consumer’s welfare in a quality-sensitive market. We further derive that under some mild conditions the monopolistic vertical integration that excludes the combination-purchase with a competitor’s product is beneficial for both the integrated firm and its consumers.  2006 Elsevier B.V. All rights reserved. Keywords: Economics; Product differentiation; Vertical integration; Broadband internet market; Non-cooperative game

1. Introduction In this paper, we consider a price and quality competition between two firms. Consumers buy a product in consideration of not only its price but also its quality level, which is a measurable value exhibiting a ‘‘more is better’’ property. Under this demand structure, firms compete with each other in determining their prices and quality levels to maximize their profits. Using a game theoretic approach, we describe this competition theoretically and consider the two possible business strategies under the competition: the differentiation by some factors other than price and quality, and the vertical integration with another firm. The purpose of this paper is to analyze the effect of the above strategies in terms of the welfare of both firms and consumers from a microeconomic viewpoint by using a comparative static.

E-mail address: [email protected] 0377-2217/$ - see front matter  2006 Elsevier B.V. All rights reserved. doi:10.1016/j.ejor.2006.04.028

908

N. Matsubayashi / European Journal of Operational Research 180 (2007) 907–921

Yen 8000

NTT East or West EAccess + @Nifty

7000

6000

NTT (East or West) + @Nifty

Tokyo Metallic ACCA + @Nifty

5000

4000 Yahoo BB

3000

2000 12

1999

3

6

9

2000

12

3

6

2001

9

12

3

6

2002

9

12

3

6

2003

Year

Fig. 1.1. User’s fees for some Japanese ADSL services.

We note that this study is strongly motivated by a real-world case, that is, the competition among Internet service providers (ISPs) in the recently emerging broadband Internet market in Japan. Since the regional telecom carriers, NTT East and NTT West, and a new venture, Tokyo Metallic, launched their ADSL services in 1999 respectively, a number of new entrants have appeared in this market. The competition between these firms resulted in a sharp decline of the user’s fees (see Fig. 1.11). This surprising decline made the Japanese broadband Internet market progress rapidly and on average the user’s fees for Japanese ISP firms became lower than those in US, Korea and other countries, see MPHPT (2003). However, on the other hand, this competition yielded some losers, who were driven out of business. This prompted the Japanese Ministry of Public Management, Home Affairs, Posts and Telecommunications (MPHPT) to start an investigation and evaluation of the state of the competition, see MPHPT (2004a). This remarkable growth of the broadband Internet market in Japan even attracted the attention of other countries. We recognize that in offering a broadband Internet service the competition would have a different mechanism from the price competition usually discussed. That is, the consumers would require not only an acceptable price (user’s fee), but also the quality level necessary for a comfortable downloading of broadband contents (e.g. a movie, a voice and so on). This is confirmed by the results of a consumer questionnaire conducted by MPHPT (2004b) in which they state that consumers consider some factors of quality level (e.g. the maximum circuit speed rate) in making their choice of ISP. Therefore, the firms also should consider at least two factors—the price and the quality level, and optimize them in order to earn their profits. This action by a firm would cause the price and quality competition. How can the firms overcome the competition? We present two possible business strategies in this paper. One is the differentiation—whereby firms create their own value for a product by, for example, utilizing a brand name so that some consumers will want to buy their product regardless of its price and quality level. Therefore, we first attempt to analyze the effect of the differentiation under the price and quality competition. Subsequently, under varying levels of differentiation we consider the vertical integration with another firm offering the complementary product. Specifically, we focus on the monopolistic vertical integration, which does not allow the combination-purchase with the competitor’s product (see MPHPT, 2002). Indeed, in the above Japanese market, Yahoo BB has employed this business model where consumers can only buy its attractive online contents when also purchasing its ADSL service, see Taniwaki (2003). As shown in Fig. 1.1, the leader of the emerging progress, Yahoo BB, who suddenly entered the ADSL market in 2001, launched its service at a surprisingly low price and acquired numerous customers. However, does the mono-

1

This figure is drawn by extracting information on the monthly fee from some ISP’s web sites.

N. Matsubayashi / European Journal of Operational Research 180 (2007) 907–921

909

polistic integration employed by the leader really contribute to increase the welfare of the firm and its consumers? Intuitively, to release its online contents which are attractive to other ISPs’ consumers seems rather more profitable, does not it? In this paper, we try to answer this question by theoretically analyzing the monopolistic vertical integration under the price and quality competition. As is indicated above, the Internet market motivates our study; however, it would also be applicable to other business scenes. For example, consider a competition among PC manufacturers. The consumers would determine the purchase of a PC based on not only its price but also its quality level—CPU speed, memory capacity, and so on. If a PC were differentiated by some factors (e.g. design, brand, etc.), it would attract the consumers to buy it. Thus, the manufacturers also face the price and quality competition, and the differentiation strategy. On the other hand, when software is offered only with a specific PC/OS, it would be possible to describe this situation as our model of the monopolistic vertical integration. We develop our analysis in a microeconomic framework. There are a number of the microeconomic literatures in existence, which focus on price and quality competition. Specifically, the spatial competition model originated by Hotelling (1929) is one that is widely used as a model of a product differentiation, where a customer’s ‘‘location’’ can be interpreted by an ‘‘ideal-point’’ of the consumer’s taste preference. While much of the marketing literature is based on the Hotelling’s model, some different approaches have recently been employed to formulate a price and quality competition. For example, Li and Lee (1994) analyze a competition between two firms, which involves a price and a delivery-speed, where a queuing model describes the delivery performance. However, our study is more closely related to Banker et al. (1998). They investigate a price and quality competition under a duopolistic setting, where the consumers’ demand is modeled as a linear function of a price and a quality level and the cost as a quadratic function of the quality level. While the Hotelling’s model assumes that consumers have heterogeneous taste preference and each of them buys only the most preferred single product, this linear demand model considers a consumer’s utility from buying a multiple of differentiated products, see Oz (1995) for the detail. Banker et al. (1998) derive the equilibrium price and quality and analyze the impact of the relative cost advantage in quality improvement on the equilibrium quality level, the effect of the horizontal integration between two firms, and so on. However, they do not investigate our topics of interest—the differentiation and the vertical integration. Economides (1999), on the other hand, does show the important result of the vertical integration with the choice of a quality level. He examines whether the sole vertically-integrated monopolist can achieve higher profit and consumer surplus by providing a composite good, compared to the case where the dual disintegrated monopolists provide the complementary goods, respectively. Generally speaking, the vertical integration under a price competition solves the so-called ‘‘double marginalization problem’’ (see e.g. Tirole, 1990) and can increase the surplus of the firm and the consumer. Economides (1999) shows that this result also holds in the case where the quality choice is considered. However, it should be noted that the setting analyzed by Economides (1999) assumes the dual monopolists in pre-integration, not an existence of firms faced by a horizontal competition at all. In contrast, we assume the existence of three firms—two competitive firms providing a commodity and a monopolist providing the complementary commodity. In this case, the issue would be more complicated since the vertical integrated firm has alternatives about bundling strategy with the rest of their goods. Economides (1998) deals with the incentive for a monopolist in an upstream market to raise the costs of the rivals to his downstream subsidiary by discriminatory quality degradation. Oystein (2004) analyzes the vertical integration in the broadband Internet market; the main topics of discussion are the relation between a price regulation to the vertically-integrated firm and his strategy of investments for the quality improvement. Matsubayashi et al. (2002) examines the merger effect of two firms under a network equilibrium model. All of these studies have different viewpoints from ours. As previously specified, our model employed in this paper refers to Banker et al. (1998). We first assume that consumers determine their purchase based on a ‘‘perceived price,’’ which is a weighted combination of the price and the quality level. With this measure, we use a linear demand model. The latter seems more suitable for our purpose rather than the Hotelling’s model when taking into account the following observations in the Japanese broadband Internet market: (i) an agent often enters multiple ISPs’ services at once, e.g. one chooses ISP A for his business use and ISP B for his private use, and so on, and (ii) consumers frequently switch an ISP due to the low switching cost and this would be able to be regarded as the purchase of multiple brands in a short term. It is of importance that the parameters of the differentiation are separately expressed

910

N. Matsubayashi / European Journal of Operational Research 180 (2007) 907–921

from those of the consumer characteristic in our demand function. Thus, it is possible to observe the effect of the differentiation explicitly, which is not the case in the original Bankers’ model. With this demand structure, we formulate a non-cooperative game, where two firms compete with each other in determining their prices and quality levels simultaneously. The outcome of the game is characterized and the impacts of the differentiation on the outcome are analyzed in terms of the welfare of each firm and the consumers, i.e. the profits and the perceived price. Furthermore, we model the vertical integration under the price and quality competition and investigate the effect by using a comparative static. We first find some interesting insights in our price and quality competition, which are not seen in the wellknown Bertrand price competition. It is shown that the Nash equilibrium in our game does not exist unless both firms are relatively differentiated, while the Bertrand competition usually ensures the existence of the equilibrium even for a completely homogeneous case. Moreover, the differentiation surprisingly increases not only the welfare of firms but also that of consumers in a quality-sensitive market, while the Bertrand competition leads to a decrease of consumers’ welfare. We next show that the monopolistic vertical integration as seen in the above Yahoo BB’s business model has a positive effect. Specifically, the integration is beneficial for both the integrated firm and its consumers if all the competitor’s consumers switch to it after the integration. In contrast, we obtain an interesting result for the most highly differentiated case; if only less than half of the consumers switch, the integration is beneficial even in comparison with the situation where the integrated firm allows the combination-purchase with the competitor’s product. In addition, we show that the threshold of the switching rate for the integration to be beneficial decreases as the consumers’ valuation of quality becomes more sensitive. The rest of the paper is organized as follows. Section 2 introduces our model and formulates a price and quality competition between two firms as a non-cooperative game. Section 3 gives the Nash equilibrium of the game and analyzes the effect of the differentiation. In Section 4, we investigate the effect of the monopolistic vertical integration in comparison with the competitive environment. In Section 5, we further consider other possible situations and reevaluate the monopolistic integration. Section 6 summarizes our findings. All proofs of results are given in Appendix. 2. The model Let p(0 6 p) be the price and x(0 6 x) be the quality level of a commodity A, respectively. Here x implies a summary level of all more-is-better quality attributes of A. Consumers buy the commodity A based on the perceived price w  ap  bx, where a and b are positive parameters given by a market. We assume a duopoly market consisting of two firms, 1 and 2, offering A. To concentrate our attention on the effect of the differentiation between firms, we make simple assumptions that the two firms are symmetric and the consumers’ demand is given by a linear model. The linear demand model considers the ‘‘cross-price effect’’ (in terms of a perceived price), which is the consumer’s utility from buying a multiple of differentiated products, see Oz (1995) for further details. In order to express explicitly the parameters of the differentiation in our linear demand model, we start by introducing our inverse demand functions. That is, if the demand of A offered by firms 1 and firm 2 are q1 and q2 respectively, the perceived prices w1 and w2 are denoted by the following linear inverse demand functions2:        a b q1 c w1 ¼ þ ; ð1Þ b a c w2 q2 where a > b P 0 and c > 0. The value of b relative to a implies the degree of the differentiation by some factors other than price and quality (e.g. brands). That is, each firm’s perceived price wi is less affected by its competitor’s demand qj (i 5 j) as b decreases. So the firms become most highly differentiated as b approaches 0, while they become almost homogeneous as b approaches a.

2

The function is derived by considering a quadratic utility function uðq1 ; q2 Þ ¼  12 ðaq21 þ 2bq1 q2 þ aq22 Þ þ cq1 þ cq2 and maximizing the consumer’s surplus u(q1, q2)  w1q1  w2q2. For more details, see Dixit (1979) and Xavier (1988).

N. Matsubayashi / European Journal of Operational Research 180 (2007) 907–921

911

By solving (1) for q1 and q2, we have the demand functions of p1, p2, x1 and x2 as follows: aa ab ba bb c ; p þ 2 p þ 2 x  2 x þ 2 1 2 2 2 1 2 2 a þ b b a b a b a b ab aa bb ba c q2 ðp1 ; p2 ; x1 ; x2 Þ ¼ 2 : p  2 p  2 x þ 2 x þ 2 1 2 2 2 1 2 2 aþb a b a b a b a b

q1 ðp1 ; p2 ; x1 ; x2 Þ ¼ 

a2

It is important to note that unlike usual expressions of linear demand functions, the parameters of the differentiation (a and b) are expressed separately from those of the consumer characteristic (a and b) in our demand functions. This separation enables us to analyze the effect of the differentiation. According to Banker et al. (1998), we next give wi (i = 1, 2) as the cost function for firm i. The symmetry is also assumed here and denoted by wi  ðxi þ vÞqi þ /x2i ;

i ¼ 1; 2;

where v > 0,  > 0 and / > 0. Thus the quality level xi affects not only the variable production cost linearly, but also the fixed cost quadratically. One may interpret it as one of the most basic models representing a nonlinear impact of a quality level on the total costs. In fact, this type of cost function is often used in the marketing literature on a product design, see Desai (2001) and Kim and Chhajed (2002) as examples. To ensure the feasibility of our duopolistic setup, we assume c  av > 0. In other words, this assumption ensures that each firm’s demand qi(p1, p2, x1, x2) is positive at the worst quality levels (x1 = x2 = 0) and the unit-cost prices (p1 = p2 = v). The profit functions p1 and p2 are given as follows: p1 ðp1 ; p2 ; x1 ; x2 Þ ¼ ðp1  x1  vÞq1 ðp1 ; p2 ; x1 ; x2 Þ  /x21 ; p2 ðp1 ; p2 ; x1 ; x2 Þ ¼ ðp2  x2  vÞq2 ðp1 ; p2 ; x1 ; x2 Þ  /x22 : We define a strategic-form game with the strategies (pi, xi) and the payoffs pi (i = 1, 2) as G. The first step of our study is to analyze the Nash equilibrium of G. 3. The Nash equilibrium and effects of the differentiation From the symmetry of firms, the equilibrium prices and quality levels if they exist are identical for both firms. So we now denote them as p* and x*. As we state the following theorem, the equilibrium is clearly characterized by the sign of T  b  a which means the consumers’ valuation of quality level relative to price (normalized by the variable cost of the quality level). Theorem 3.1. The unique Nash equilibrium (p*, x*) exists if, and only if 4a/(a2  b2)  aT2 > 0. (p*, x*) is described as follows: 1. when T 6 0: p ¼ ðabÞcþaav , x* = 0, að2abÞ 2. when T P 0: p ¼

aT ðc  vbÞ þ 2/ða þ bÞfða  bÞc þ aavg ; 2/að2a  bÞða þ bÞ  aT 2

x ¼

aðc  avÞT : 2/að2a  bÞða þ bÞ  aT 2

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi T2 The above necessary and sufficient condition for the existence of equilibrium can be rewritten as ba < 1  4aa/ : therefore it follows that equilibrium does not exist unless both firms are relatively differentiated. We should note that our case requires the differentiation for ensuring the existence of the equilibrium, while a usual Bertrand price competition ensures an existence of an equilibrium even if a market is completely homogeneous (see Oz, 1995). The key to understanding the result is that under price and quality competition firms always have an alternative to increase their profits by opting for either higher quality or lower price, while under the Bertrand price competition price is the only decision variable for firms. For example, let us suppose that both firms earn zero profits at the lowest price level in a homogeneous market. In this situation, in the Bertrand

912

N. Matsubayashi / European Journal of Operational Research 180 (2007) 907–921

case, this state is an equilibrium since the increase of one firm’s price cannot grab its competitor’s consumers while the decrease of its price makes its profit negative. However, in our competition firms can choose another option in which they appropriately increase both their quality levels and prices. This action results in the capture of the competitor’s consumers and earns positive profit. Therefore, this state is not an equilibrium and the differentiation is required for deviating from such a competition. Under the existence of the equilibrium, in the price-sensitive market (T 6 0), the equilibrium quality level is necessarily 0 independently of the value of T. In the context of the broadband Internet market, the ADSL market for personal users would correspond to this case, for example. It seems that a simple price competition arises in this case. On the other hand, in the quality-sensitive market (T P 0), a quality competition arises and both of the equilibrium quality and price increase as T increases. We now assume that the condition for our problem to be feasible, 4a/(a2  b2)  aT2 > 0 holds. Then the equilibrium profits and perceived prices are also identical for both firms and we denote them as p* and w*. They are precisely described as follows: • when T 6 0: p ¼

aða  bÞðc  avÞ 2

2

að2a  bÞ ða þ bÞ

;

w ¼

ða  bÞc þ aav ; 2a  b

• when T P 0: p ¼

/aðc  avÞ2 ð4a/ða2  b2 Þ  aT 2 Þ ð2a/ð2a  bÞða þ bÞ  aT 2 Þ

2

;

w ¼

2a/ða þ bÞfða  bÞc þ aavg  acT 2 : 2a/ð2a  bÞða þ bÞ  aT 2

We first observe the relation between these equilibrium values and the parameter T capturing the consumer characteristic. In the price-sensitive market, as T decreases (that is, the parameter of price valuation a increases), both of the equilibrium firms’ profit and consumers’ surplus decrease (that is, p* decreases while w* increases). This observation is different from an insight appearing in a usual Bertrand price competition (see, e.g. Oz, 1995) that the equilibrium price decreases as the parameter of price valuation increases. An inference that can be drawn from our result can be described as follows: under our competition the form keeps the equilibrium quality level at 0 as a increases. This in turn has a negative impact on consumers’ valuation, which becomes more intense than the positive impact of the lower equilibrium price as a increases. In the quality sensitive market, on the other hand, we can easily obtain ow < 0 from direct calculations. Therefore it follows oT that as the parameter of quality valuation b increases, the equilibrium consumers’ surplus increases. This implies that the positive impact of high quality level exceeds the negative impact of high price on the consumers’ valuation. We next refer to one of our main results. The following theorem states how the differentiation affects the equilibrium. Theorem 3.2. For any b such that 4a/(a2  b2)  aT2 > 0, 



1. when T 6 0: op < 0 and ow < 0 always hold, ob  ob op 2. when T P 0: ob 0. ob 

The negativity of op at any b ensures that p* is decreasing in b, i.e., the equilibrium profit decreases as the ob two products are less differentiated. Thus the above theorem first states that the differentiation by some factors other than price and quality is useful for both firms to increase their profits. On the other hand, more differentiation makes consumer’s welfare decrease if the market has relatively sensitive valuation of price. These results are similar to that in the well-known Bertrand price competition (see, e.g. Oz, 1995). However, what is surprising is that in the quality-sensitive market the differentiation does not necessarily increase the perceived price. On the contrary, when the market has more sensitive valuation of quality, the more the firms

N. Matsubayashi / European Journal of Operational Research 180 (2007) 907–921

913

are differentiated, the less the equilibrium perceived price is. That is, both firms’ and consumers’ welfare are increased by the differentiation in this case. This is an interesting insight, which does not appear in the Bertrand price competition. We can infer that the results in the price sensitive market will be as follows: under the differentiation both firms can charge higher prices so that some consumers will want to buy the product regardless of its price and therefore higher equilibrium price and profit levels can be achieved. However, in the case of the quality-sensitive market we need additional discussion: if the two firms are less differentiated, an intense quality competition arises. Then the differentiation motivates firms to save their costs by decreasing quality levels. Thus in the case of less differentiated firms, the more they are differentiated, the less the equi librium quality level is (oxob > 0 for a2 < b). This results in the increase of the equilibrium perceived price because of consumers’ sensitive valuation of quality. In the case of highly differentiated firms, on the other hand, the effect of increasing revenues by charging higher prices exceeds that of cost reduction by decreasing quality levels. Therefore, this differentiation results in an increase of the equilibrium price and quality level, which decreases pffiffiffiffiffiffiffiffiffi the equilibrium perceived price. In particular, if the market has more sensitive valuation of quality 32aa/ ( 3 < T ), the equilibrium does not exist unless both firms are highly differentiated and therefore the equilibrium perceived price necessarily decreases. 4. The effects of the vertical integration As seen in the previous section, the differentiation between two firms is beneficial to the welfare of both consumers and firms under price and quality competition. Then in this section, we try to investigate the effect of the vertical integration with another complementary firm under a differentiated situation. Specifically, under varying levels of differentiation between two firms offering commodity A, we consider the vertical integration between one of the two firms (say firm 1) and another firm offering the complementary commodity B (say firm 3). We assume that the firm 3 is a monopolist who offers B. For example, if the specific online digital contents are considered as B, this assumption is adequate as discussed in Dewan et al. (2000). The model scenario is illustrated in Fig. 4.1. According to the general instruction, we would expect that the vertical integration solves the so-called ‘‘double marginalization problem’’ (see e.g. Tirole, 1990). However, in our pre-integration setting, two firms offering commodity A face a competition with each other and the lower price and higher demand levels of commodity A attained by the competition may be beneficial for firm 3. Loosely speaking, our aim in this section is to make clear the relation between these two effects. 4.1. The model of the pre-integration We suppose that a consumer who buys either A or B does not exist. Let qi3 be the demand of A offered by firm i (i = 1, 2), which equals that of B offered by firm 3 to the consumers of firms i. Given a price pi, a quality

Fig. 4.1. Model scenario of monopolistic vertical integration.

914

N. Matsubayashi / European Journal of Operational Research 180 (2007) 907–921

level xi (i = 1, 2) and a price of B set by firm 3, p3, the perceived prices wi3  a(pi + p3)  bxi are denoted by the following linear inverse demand functions:        a b q13 c w13 ¼ þ : ð2Þ b a c w23 q23 Assumptions regarding a, b and c are same as in (1). By solving (2) for q13 and q23, we have the demand functions of p1, p2, p3, x1 and x2 as follows: aa ab a ba bb c p þ ; p1 þ 2 p2  x1  2 x2 þ a þ b 3 a2  b2 aþb a2  b2 a  b2 a  b2 ab aa a bb ba c q23 ðp1 ; p2 ; p3 ; x1 ; x2 Þ ¼ 2 p3  2 : p  2 p  x þ 2 x þ 2 1 2 2 2 1 2 2 a þ b a þ b a b a b a b a b

q13 ðp1 ; p2 ; p3 ; x1 ; x2 Þ ¼ 

The profit functions of firms 1, 2 and 3 are given as follows: p11 ðp1 ; p2 ; p3 ; x1 ; x2 Þ  ðp1  x1  vÞq13 ðp1 ; p2 ; p3 ; x1 ; x2 Þ  /x21 ; p12 ðp1 ; p2 ; p3 ; x1 ; x2 Þ  ðp2  x2  vÞq23 ðp1 ; p2 ; p3 ; x1 ; x2 Þ  /x22 ; p13 ðp1 ; p2 ; p3 ; x1 ; x2 Þ  p3 ðq13 ðp1 ; p2 ; p3 ; x1 ; x2 Þ þ q23 ðp1 ; p2 ; p3 ; x1 ; x2 ÞÞ: The production cost for firm 3 to produce B is assumed here to be zero. In fact, it may also be adequate for a production of an online digital content, as seen in Dewan et al. (2000). We now define a game G1, where the strategies of firm i (i = 1, 2) are (pi, xi), of firm 3 is p3 and the payoffs are pi (i = 1, 2, 3). The Nash equilibrium of G1 is described in the following theorem. Theorem 4.1. The unique Nash equilibrium of G1 exists if, and only if 4a/(a2  b2)  aT2 > 0. The precise descriptions are given as follows: 1. when T 6 0: p1 ¼ p2 ¼ p1 ¼ p2 ¼

ða  bÞc þ 2aav ; að3a  bÞ

p3 ¼

aða  bÞðc  avÞ2 aða þ bÞð3a  bÞ

; 2

aðc  avÞ ; að3a  bÞ

p3 ¼

x1 ¼ x2 ¼ 0;

2a2 ðc  avÞ2 2

aða þ bÞð3a  bÞ

w13 ¼ w23 ¼

ð2a  bÞc þ aav ; ð3a  bÞ

;

2. when T P 0: p1 ¼ p2 ¼

aT ðc  vbÞ þ 2ða þ bÞ/fða  bÞc þ 2aavg ; 2/að3a  bÞða þ bÞ  aT 2

x1 ¼ x2 ¼

aðc  avÞT ; 2/að3a  bÞða þ bÞ  aT 2

w13 ¼ w23 ¼

2

p1 ¼ p2 ¼

a/ðc  avÞ f4a/ða2  b2 Þ  aT 2 g 2 2

f2a/ð3a  bÞða þ bÞ  aT g

;

p3 ¼

p3 ¼

2aða þ bÞðc  avÞ/ ; 2/að3a  bÞða þ bÞ  aT 2

acT 2 þ 2ða þ bÞa/fð2a  bÞc þ aavg ; 2/að3a  bÞða þ bÞ  aT 2 8a2 a/2 ða þ bÞðc  avÞ

2

f2a/ð3a  bÞða þ bÞ  aT 2 g

2

:

We first note that with regard to firms 1 and 2 the equilibrium is completely symmetric and has some properties similar to those in Theorem 3.1: equilibrium exists under the same condition on the differentiation as Theorem 3.1. Under the existence of the equilibrium, the equilibrium quality level is necessarily 0 independently of the value of T in the price-sensitive market, whereas both of the equilibrium quality and price increase as T increases in the quality-sensitive market, and so on. Subsequently, we should observe how the differentiation affects the equilibrium profits. It is easy to see that p1 and p2 are decreasing function of b regardless of T. That is, the differentiation has a positive impact on firms 1 and 2. In contrast, p3 is increasing in b for all T, which implies a negative impact of the differentiation on firm 3. In other words, an intense competition between firms 1 and 2 offering commodity A is beneficial for firm 3 since the lower perceived price of A attained by the competition gives firm 3 an incentive to increase its price.

N. Matsubayashi / European Journal of Operational Research 180 (2007) 907–921

915

4.2. The model of the post-integration We next consider a monopolistic situation where firms 1 and 3 are integrated vertically and commodity B is offered only by an integration firm {1, 3}. That is, consumers cannot buy B with A offered by firm 2. We then assume that if the total perceived price of A and B is invariant after the integration, all consumers of firm 2 switch to firm {1, 3} and continue to buy A and B, while all consumers of firm 1 from the first continue to buy from firm {1, 3}. (This assumption is relaxed in Section 5.) Then this implies that the total perceived price of A and B attained by the integrated firm {1, 3} offering q13 is identical to that by firms 1 and 2 offering q213 in the equilibrium of the game G1, respectively. (Recall that the equilibrium demand quantities always become identical for both firms.) Therefore the inverse demand function faced by firm {1, 3} is as follows: aþb q13 þ c; 2  13  ap13  bx1 and p13 is the total price of A and B set by firm {1, 3}. where w By solving (3) for q13, the profit function of firm {1, 3} is given as follows:  13 ¼  w

ð3Þ

p213 ðp13 ; x1 Þ  ðp13  x1  vÞq13 ðp13 ; x1 Þ  /x21 : We define G2 as a problem for {1, 3} to optimize p13 and x1 (see Remark). The optimal price p 13 , the quality   level x , the perceived price w and the profit p are described in the following theorem. 1 13 13 Theorem 4.2. The unique optimal solution to G2 exists if and only if 2a /(a + b)  T2 > 0. The precise descriptions of the solution are as follows: 1. when T 6 0: p 13 ¼

c þ av ; 2a

x 1 ¼ 0;

w 13 ¼

c þ av ; 2

2

p 13 ¼

ðc  avÞ ; 2aða þ bÞ

2. when T P 0F p 13 ¼

ða þ bÞðc þ avÞ/ þ ðc  bvÞT ; 2a/ða þ bÞ  T 2

x 1 ¼

ðc  avÞT ; 2a/ða þ bÞ  T 2

w 13 ¼

a/ða þ bÞðc þ avÞ  cT 2 ; 2a/ða þ bÞ  T 2

/ðc  avÞ : 2a/ða þ bÞ  T 2

2

p 13 ¼

The condition for the existence of the unique optimal solution excludes the possibility of the integrated firm to increase its profit indefinitely by taking quality level sufficiently high. It is easy to see that with regard to the differentiation parameter b, the optimal perceived price is constant in the price sensitive market and increasing in the quality-sensitive market. Furthermore, it can be easily verified that the optimal profit is decreasing in b for both cases. That is, the more the firms 1 and 2 are differentiated in the pre-integration, the more the both integrated firm’s and its consumers’ welfare increase. We can draw an inference from this result as follows: in the pre-integration the differentiation between firms 1 and 2 has a positive impact on their demand quantities (it is easy to see that q13 + q23 is decreasing function in b). Therefore our assumption that all consumers of firm 2 switch to the integrated firm after the integration ensures that the differentiation in the pre-integration also has a positive impact on the demand level of the integrated firm, which results in the increase of its profit. Remark. Regarding the description of the monopolistic integration, one may consider the situation where the integrated firm {1, 3} takes p3 extremely high in game G1 so that no consumers buy B with A offered by firm 2. However, note that the demand model described by (2) cannot reflect an important situation where some consumers of firm 2 switch to the integrated firm. As explained in Section 2, this model considers the ‘‘crossprice effect’’ (in terms of a perceived price) under the existence of both firms 1 and 2 and thus does not consider the situation where the commodity is offered by a single firm. For example, consider the case with b = 0. Since q13 is determined independently of the value of w23 in this case, the high value of p3 does not affect the value of q13 at all, whereas yielding q23 = 0. However, in practice it would be essential to consider

916

N. Matsubayashi / European Journal of Operational Research 180 (2007) 907–921

consumers who switch to firm {1, 3} after the integration. So, we formulate the problem G2 based on the new demand structure. 4.3. The effects of the integration In order to observe effects of the integration, we attempt to compare the equilibrium profits and perceived prices in G1 with the optimal profit and perceived price in G2, respectively. To ensure the existence of both of the Nash equilibrium of G1 and the optimal solution to G2, we assume here min{4a/(a2  b2)  aT2, 2a/ (a + b)  T2} > 0. We now refer to the relation between p1 þ p3 (the total equilibrium profit of firms 1 and 3 in G1) and p 13 (the optimal profit of firm {1, 3} in G2), and the relation between w13 (the total equilibrium perceived price via firms 1 and 3 in G1) and w 13 (the optimal perceived price via firm {1, 3} in G2). The following theorem shows that the vertical integration is effective in terms of both firms’ and consumers’ welfare.     Theorem 4.3. For any feasible T and b, p 13 P ðp1 þ p3 Þ and w13 P w13 .

Theorem 4.3 shows that the firms 1 and 3 benefit from the monopolistic vertical integration under every level of differentiation. Furthermore, it is shown that their consumers’ surplus is also increased by the integration under every level of differentiation. The decline of the perceived price suggests that the integration solves the so-called ‘‘double marginalization problem’’ existing under pre-integration. As seen in the previous subsections, on the other hand, in a less differentiated case the competition between firms 1 and 2 makes firm 3 gain more benefits while the vertical integration has little effect. This would make the effect of the integration unexpected in some cases. However, Theorem 4.3 proves that the effect of solution of the ‘‘double marginalization problem’’ always exceeds that of the competition between firms 1 and 2. 5. The integration effect under other possible situations In the previous section, the effect of the monopolistic vertical integration is discussed by making a comparison in a situation where the three firms simply compete with each other. However, in order to suggest that the effect always occurs, it would not suffice to analyze this case only. Specifically, it may be more profitable for the integration firm to allow consumers the combination of B and firm 2’s A. In addition, the assumption under which all consumers of firm 2 switch to firm {1, 3} after the integration may be inadequate under highly differentiated situation, since some consumers of firm 2 may decide not to purchase B due to the impossibility of combining their purchase with an additional desired product. Thus, in this section, we consider the following two cases and try to evaluate again the effect of the monopolistic integration in consideration of these settings. • Case 1: The integration firm {1, 3} allows consumers to buy B with A offered by firm 2. • Case 2: h(0 6 h 6 1) is the ratio of consumers of firm 2 who switch to {1, 3} after the integration. The model scenarios in consideration of Cases 1 and 2 are illustrated in Fig. 5.1. We analyze here only a case with b = 0 because of the intractability for other cases. However, we note that the large b tends to have no Nash equilibrium for the game defined in Case 1. Furthermore, it should be noted that b = 0 expresses the most highly differentiated situation; the integrated firm is expected to be most affected by excluding the combination of B and firm 2’s A. Therefore, we believe that the analysis for b = 0 gives us some useful suggestions for other cases. 5.1. The model for Case 1 We suppose that the integrated firm {1, 3} offers B not only to its customers but also to firm 2’s consumers with a price p3. Therefore, the total perceived price of A and B via firm 2 is w23 = a(p2 + p3)  bx2. The corresponding inverse demand functions are given as follows:

N. Matsubayashi / European Journal of Operational Research 180 (2007) 907–921

917

Fig. 5.1. Model scenario of vertical integration in Section 5.



 13 w w23



 ¼

ap13  bx1 aðp2 þ p3 Þ  bx2



 ¼

a 0 0 a



q13 q23

 þ

  c : c

ð4Þ

By solving (4) for q13 and q23, we obtain the demand functions of p13, p2, p3, x1 and x2. The profit functions of firms {1, 3} and 2 are p313 ðp13 ; p2 ; p3 ; x1 ; x2 Þ  ðp13  x1  vÞq13 ðp13 ; p2 ; p3 ; x1 ; x2 Þ þ p3 q23 ðp13 ; p2 ; p3 ; x1 ; x2 Þ  /x21 ; p32 ðp13 ; p2 ; p3 ; x1 ; x2 Þ  ðp2  x2  vÞq23 ðp13 ; p2 ; p3 ; x1 ; x2 Þ  /x22 : We now define a game G3, where the strategy of firm {1, 3} is (p13, p3, x1), of firm 2 is (p2, x2) and the payoffs are p3i ði ¼ f1; 3g; 2Þ. The Nash equilibrium of G3 is described in the following theorem. Theorem 5.1. The unique Nash equilibrium of G3 exists if and only if 4a/a  T2 > 0. The precise descriptions are given as follows: 1. when T 6 0: c þ av c þ 2av c  av ; p ; p ; x ¼ ¼ ¼ x ¼ 0; 2 3 1 2 2a 3a 3a 2 c þ av 2c þ av 13ðc  avÞ ðc  avÞ2   ; w ; p ; p ; ¼ ¼ ¼ ¼ 23 13 2 2 3 36aa 9aa

p 13 ¼ w 13

2. when T P 0 ðc  vbÞT þ 2a/ðc þ avÞ ðc  vbÞT þ 2a/ðc þ 2avÞ 2a/ðc  avÞ ; p ¼ ; p ¼ ; 2 3 2 2 4/aa  T 6a/a  T 6a/a  T 2 ðc  avÞT ðc  avÞT 2aa/ðc þ avÞ  cT 2 2aa/ð2c þ avÞ  cT 2    ¼ ; x ¼ ; w ¼ ; w ¼ ; 2 13 23 4a/a  T 2 6a/a  T 2 4a/a  T 2 6a/a  T 2

p 13 ¼ x 1

2

p 13 ¼

2

/ðc  avÞ fð6a/a  T 2 Þ þ 4a/að4a/a  T 2 Þg 2

ð4a/a  T 2 Þð6a/a  T 2 Þ

2

;

p ¼ 2

/ðc  avÞ ð4a/a  T 2 Þ ð6a/a  T 2 Þ

2

:

Unlike the game G1, the equilibrium is asymmetric regarding the total perceived price of A and B. Specifically, in both price and quality-sensitive markets, the equilibrium perceived price via firm {1, 3} is attained at lower level than in the pre-integration whereas that via firm 2 is attained at the same level. Furthermore it can

918

N. Matsubayashi / European Journal of Operational Research 180 (2007) 907–921

be verified that only firm {1, 3}’s demand quantity increases by the integration, which results in an increase of its welfare. Therefore it is clear that even the non-monopolistic vertical integration contributes to solving the ‘‘double marginalization problem.’’ However, this does not have any impact on firm 2’s and its consumers’ welfare under the most highly differentiated situation. 5.2. The model for Case 2 We now suppose that only the ratio h(0 6 h 6 1) of firm 2’s consumers switches to {1, 3} after the integration, provided that the total perceived price of A and B is invariant after the integration. All consumers of firm 1 from the first continue to purchase A and B from firm {1, 3}. It is obvious that the assumption in Section 4.2 is a special case with h = 1. Then, for the reason similar to that in Section 4.2, the total perceived price of A and B attained by the integrated firm {1, 3} offering ð1 þ hÞq013 equals that by firms 1 and 2 offering q013 in the equilib 013 be the perceived price attained by {1, 3} and ^h  1 þ h. Then the rium of the game G1, respectively. Let w 0  13 and the output level ^ relation of w q13 by firm {1, 3} can be expressed by the following inverse demand function: a  13 ¼  ^ q13 þ c: ð5Þ w ^ h ^ ¼ 2. Note that the Eq. (5) is identical to (3) with h ^213 as follows: By solving the demand function ^ q13 from (5), we now obtain the firm {1, 3}’s profit function p ^213 ðp13 ; x1 Þ  ðp13  x1  vÞ^ q13 ðp13 ; x1 Þ  /x21 : p We define G2 0 as a problem for firm {1, 3} to optimize p13 and x1. The optimal price ^p x 13 , the quality level ^ 1 ,   ^ 13 and the profit p ^13 are described in the following theorem. the perceived price w Theorem 5.2. The unique optimal solution to G2 0 exists if and only if ^ha/a  T 2 > 0. The precise descriptions of the solution are as follows: 1. when T 6 0: ^ p 13 ¼

c þ av ; 2a

^x 1 ¼ 0;

^  w 13 ¼

c þ av ; 2

^ p 13 ¼

^hðc  avÞ2 ; 4aa

2. when T P 0 ^ hðc  avÞT ; 4a/a  ^hT 2

^p 13 ¼

2aðc þ avÞ/ þ ^ hðc  bvÞT ; 4a/a  ^ hT 2

^x 1 ¼

^  w 13 ¼

2a/aðc þ avÞ  c^ hT 2 ; 4a/a  ^ hT 2

^ h/ðc  avÞ2 : 4a/a  ^hT 2

^ p 13 ¼

The result can be seen as the generalization of that in Theorem 4.2. However, we should note that the switching rate ^ h plays more important role in the quality-sensitive market (T P 0): in the price-sensitive market (T 6 0), both optimal price and quality level do not depend on ^h and thus the switching rate affects only the demand quantity of the integrated firm. On the other hand, in the quality-sensitive market, it has an impact even on the optimal price and quality level and the integrated firm can benefit significantly from an increase of the rate as consumers’ valuation of quality becomes more sensitive. This would make an expectation that the monopolistic integration is likely to be the most beneficial option at least in the highly qualitysensitive market. We indeed prove this in the next subsection. 5.3. The reevaluation of the effect of the monopolistic vertical integration In this subsection, we reevaluate the effect of the monopolistic vertical integration based on the results of the game G3 and the optimization problem G2 0 . In advance, we assume a/a  T2 > 0 in order to ensure the ^ feasibility of both G3 and G2 0 . We now refer to the relation between p 13 and p 13 (the equilibrium profit of

N. Matsubayashi / European Journal of Operational Research 180 (2007) 907–921

919

Fig. 5.2. The region of parameter h such that p ^ 13 6 p 13 .

^  firm {1, 3} in G3 and the optimal profit in G2 0 , respectively) and between w 13 and w 13 (the equilibrium per0 ceived price in G3 and the optimal one in G2 , respectively) in the following theorem. Theorem 5.3 ^ 1. There exists the threshold h* such that when h exceeds h*, p 13 6 p 13 holds. Specifically,  4 (a) when T 6 0: h ¼ 9, 2 Þ2 (b) T P 0: h ¼ 36að4aa/T 2 a2 /2 8aa/T 2 .  ^  ^  2. For all h, w 13 P w 13 . If T 6 0, w13 ¼ w 13 always holds.

  By Theorem 5.3 and the fact that p 13 > p1 þ p3 always holds, we can clarify the threshold of the switching rate for the monopolistic vertical integration to be profitable. The threshold depends on the demand structure. In the price-sensitive market (T 6 0), it is the constant four-ninths. On the other hand, in the quality-sensitive  market (T P 0), it decreases as consumers’ valuation of quality becomes more sensitive (oh is always negative oT in our feasible region). As shown in Fig. 5.2, the switch of p less than one-third of consumers makes the profffiffiffiffiffiffiffiffiffi itable monopolistic integration in the neighborhood of T ¼ a/a, which is the upper bound of T in our problem. Therefore, in the context of the broadband Internet market, these results at the very least imply that if a content service provider has more and more attractive contents, he is better off forming an association with only one Internet service provider and excluding other providers’ users.   ^ Note that when h* > h, p 13 > p 13 > p1 þ p3 holds, that is, the non-monopolistic integration is rather more profitable than other our settings. On the other hand, the perceived price under the monopolistic integration always attains the more preferred level in terms of consumers’ welfare. This implies that the monopolistic vertical integration contributes to the solution of the ‘‘double marginalization problem.’’

6. Concluding remarks In this study, we explored some topics arising from the price and quality competition between two symmetric firms by utilizing a game theoretic approach. For the analysis, a typical linear demand model was employed which incorporated explicitly the degree of the differentiation between the firms. First we showed that the differentiation was required for the existence of the Nash equilibrium and that the characteristic of the equilibrium depended on the demand structure—consumers’ relative valuation of the price and the quality level. Furthermore, the relation between the degree of the differentiation and the equilibrium firm’s and consumers’ welfare were clarified. Interestingly, in the quality-sensitive market, more differentiation made the welfare of both firms and consumers increase, which differed from the result in a usual Bertrand price competition. We next examined the vertical integration with another firm offering the complementary commodity. The results shown indicated that the monopolistic integration, which excluded the combination-purchase with the competitor’s good, had a positive effect in comparison with the competitive situation. That is, for every case in terms of the differentiation and consumers’ valuation, we showed that the integration was beneficial for both the integrated firm and its consumers if all the competitor’s consumers switched to it after the integration. In contrast, we proved that for the most highly differentiated case, the switch of only less than half of the consumers made the integration beneficial even in comparison with the situation where the integrated firm allowed the combination-purchase with the competitor’s product. Moreover, we showed that the threshold of the switching rate for the integration to be beneficial decreased as the consumers’ valuation of quality became more sensitive.

920

N. Matsubayashi / European Journal of Operational Research 180 (2007) 907–921

We employed some assumptions to make our models tractable. While we are sure that our results under these reasonable assumptions provide a conceptual benchmark and offer many managerial insights, the relaxation of these assumptions is left open to provide for the possibility of further investigation. For example, the relations between the differentiation and consumers’ welfare under various demand and cost structures other than our setting are not necessarily clear. In addition, we assumed that the rate of consumers who switch to the monopolistic integrated firm from its competitor is independent of the differentiation parameter. However, in some cases it may be more realistic to assume that the rate depends on the degree of the differentiation in the pre-integration since consumers may switch because of not only the impossibility of the bundle but also low differentiation. So it would be interesting to investigate the cross effect of differentiation and vertical integration. Finally, we employed the comparative static approach to study the effect of differentiation and vertical integration. An incentive problem for competitive firms for differentiation and/or vertical integration would be a challenge for the future. This study was strongly motivated by the real-world scene, that is, the emerging broadband Internet market in Japan. We hope that the insights obtained by this theoretical analysis will help practitioners to consider their business strategies or policies. Acknowledgement The author acknowledges constructive comments by two anonymous referees on an earlier draft. Appendix Proof of Theorem 3.1. As stated above, the equilibrium is symmetric if it exists. Thus we first rewrite profit functions pi by completing the square and substitute p1 = p2 = p and x1 = x2 = x. Then p1 = p2 = p can be described as follows: pðp;xÞ ¼ 

 2  2 aa ðða  bÞb þ aaÞx þ ða  bÞc þ aav S 2ða  bÞðS 0 x  aðc  avÞT Þ /aðc  avÞ2 S p   þ ; 2 2 2 2 2 að2a  bÞ ð2a  bÞS a b aða  b Þ S0

where S  4a/(a2  b2)  aT2 and S 0  2a/(2a  b)(a + b)  aT2. (Note that S corresponds to a Hessian of pi (i = 1, 2).) We observe the first term of the right hand side. Since ððabÞbþaaÞxþðabÞcþaav > 0 for any x P 0, it can be seen að2abÞ ððabÞbþaaÞxþðabÞcþaav is the unique p which maximizes p for given x. We next observe the second term. that ^ p¼ að2abÞ If S > 0, we have S 0 > 0 since S 0 > S holds. Hence when T P 0, x ¼ aðcavÞT is the unique quality level which S0 maximizes p and when T 6 0, so x* = 0 is. By substituting x* into ^p, we now obtain the unique Nash equilibrium (p*, x*). On the other hand, if S 6 0, we can increase p indefinitely by taking x sufficiently large and setting p ¼ ððabÞbþaaÞxþðabÞcþaav . This implies that no equilibrium exists. h að2abÞ 



Proof of Theorem 3.2. It can be easily obtained from direct calculations that op < 0 and ow < 0 when T 6 0. ob ob  op with T P 0. Also it can be verified that ob < 0 when T P 0. So we give a proof only for the result of ow ob 2

2

2aa/ðcavÞð2ðaþbÞ a/aT Þ Let S 0  2a/(2a  b)(a + b)  aT2. It follows from direct calculations that ow and ob ¼ S 02 2 2 * ^ ^ hence w is a concave function of b and has a unique maximizer b which satisfies 2ða þ bÞ a/  aT ¼ 0. This  2 2 implies that ow ob > 0 if 2(a + b) a/  aT < 0. On the other hand, it is necessary that b satisfies 4a/ 2 2 2  2 a/  aT 2 < 0 (a  b )  aT > 0 from the condition for the existence of the equilibrium. Hence, if 2ða þ bÞ  for  b such that 4a/ða2   b2 Þ  aT 2 ¼ 0, then ow feasible b. So, since 4a/ða2  b2 Þ  aT 2 ¼ ob > 0 holds for every qffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2 4aa/T a 0 > 2ða þ  bÞ a/  aT 2 , we can rewrite this condition as b ¼ a 4aa/ < 3. We now obtain the result by solving this inequality for T. h 

Proofs of Theorems 4.1, 4.2, 5.1 and 5.2. They follow steps similar to that of Theorem 3.1 and the details are omitted. h

N. Matsubayashi / European Journal of Operational Research 180 (2007) 907–921

921

    Proof of Theorem 4.3. By direct calculations, we can derive the non-negativity of p 13  ðp1 þ p3 Þ and w13  w13 for each case of T P 0 and T 6 0 respectively. It should be noted that the assumption of c  av > 0 is used to prove the result of w13  w h 13 . The detail of the proof is lengthy and is omitted here.  ^ Proof of Theorem 5.3. We calculate p 13  p13 directly by using the results of Theorems 5.1 and 5.2 and obtain  ^ ^ the condition on h to ensure the non-negativity of p 13  p13 . The result of Part 1 can be obtained by applying ^ h ¼ h  1 to this condition. The result of Part 2 can be easily derived by direct calculations. h

References Banker, R.D., Khosla, I., Sinha, K.K., 1998. Quality and competition. Management Science 44 (9), 1179–1192. Desai, P.S., 2001. Quality segmentation in spatial markets: When does cannibalization affect product line design? Marketing Science 20 (3), 265–283. Dewan, R., Freimer, M., Seidmann, A., 2000. Organizing distribution channels for information goods on the Internet. Management Science 46 (4), 483–495. Dixit, A., 1979. A model of duopoly suggesting a theory of entry barriers. Bell Journal of Economics 10, 20–32. Economides, N., 1998. The incentive for non-price discrimination by an input monopolist. International Journal of Industrial Organization 16, 271–284. Economides, N., 1999. Quality choice and vertical integration. International Journal of Industrial Organization 17, 903–914. Hotelling, H., 1929. Stability in competition. Economic Journal 39, 41–57. Kim, K., Chhajed, D., 2002. Product design with multiple quality-type attributes. Management Science 48 (11), 1502–1511. Li, L., Lee, Y.S., 1994. Pricing and delivery-time in a competitive environment. Management Science 40 (5), 633–646. Matsubayashi, N., Umezawa, M., Masuda, Y., Nishino, H., 2002. Merger effect of two firms under network equilibrium. European Journal of Operational Research 137, 434–447. MPHPT (Ministry of Public Management, Home Affairs, Posts and Telecommunications, Japan), 2002. Final report from Study Group on New Business Models and Grand Design of the Competitive Environments for the New Information and Communications Era, Press Release by MPHPT, June 6. MPHPT (Ministry of Public Management, Home Affairs, Posts and Telecommunications, Japan), 2003. WHITE PAPER Information and Communications in Japan, Tokyo. MPHPT (Ministry of Public Management, Home Affairs, Posts and Telecommunications, Japan), 2004a. MPHPT announces State of the Market in the Telecommunications Business Field in Fiscal 2003—Areas of Internet Connection and Internal Corporate Networks, Press Release by MPHPT, April 27. MPHPT (Ministry of Public Management, Home Affairs, Posts and Telecommunications, Japan), 2004b. ‘‘Symposium on Evaluation of the State of Competition in Telecommunications Field to Be Held’’, MPHPT Communications News, 22. Oystein, F., 2004. Strategic investments with spillovers, vertical integration and foreclosure in the broadband access market. International Journal of Industrial Organization 22, 1–24. Oz, Shy, 1995. Industrial organization: Theory and applications. The MIT Press, Cambridge. Taniwaki, Y., 2003. Emerging Broadband Market and the Relevant Policy Agenda in Japan. Journal of Interactive Advertising 4-1. Tirole, J., 1990. The Theory of Industrial Organization. The MIT Press, Cambridge. Xavier, V., 1988. Efficiency of Bertrand and Cournot equilibria with product differentiation. In: Daughety, A.F. (Ed.), Cournot Oligopoly. Cambridge University Press, Cambridge.