# Ultrabroadband competition in two-sided markets.

The paper is based on the multi-sided platform analysis (ARMSTRONG, 2004; CALABRESE et al., 2006; DOGANOGLU & WRIGHT, 2005; ROCHET & TIROLE, 2004a-b; and SCHIFF, 2003), that is on platforms that allow the interconnection of two different categories of players as, in the case of telecommunication and media industries, content providers and/or advertisers on one side of the platform and users (readers/viewers) on the other side (ARMSTRONG, 1999, 2005; GABSZEWICZ et al., 2005).The iteration between different clusters of users may be influenced by indirect network-effects, by strategic choices of the platforms (WRIGHT, 2002, 2003; EVANS, 2003; GABSZEWICZ et al., 2005), and by technological benefits available to the market players.

Ultrabroadband innovation involves the convergence between communication and telecommunication industries (Triple Play). Thus, the aim of the paper is to analyse, through a simulation approach, the impact of convergence on the pricing strategies of triple play operators. More specifically we have extended the CHAKRAVORTI & ROSON model (2006) in order to study the competition among triple play operators, each one characterised by different peculiarities. In fact, the ultrabroadband development allows the entry of new players into the market and changes the competition for traditional incumbents. Thus we consider the competition among four players--the incumbent (the traditional telecommunication or communication operator) and new entrants (both telecommunications and communication companies who, thanks to ultrabroadband, may now offer voice, data and video/TV through telecommunication networks)--in order to represent and analyse the development of the telecommunication industry.

The paper is organised as follows: first of all we define a two-sided market, highlighting the main contributions of the literature; then, we describe the ultrabroadband convergence (Triple Play), we introduce a mathematical model and we analyse the results of some numerical simulations. Finally, we conclude the paper with some observations and comments.

* Literature review

The paper is based on the two-sided industry research. The ultrabroadband innovation allows the telecommunications firms to enter the

two-sided markets (ARMSTRONG, 2004; CALABRESE et al., 2006; DOGANOGLU & WRIGHT, 2005; ROCHET & TIROLE, 2004a-b; ROSON, 2005; SCHIFF, 2003).The multi-sided platform markets can be defined as industries characterised by the interconnection between different groups of customers through a platform and by pricing strategies for each side (EVANS, 2003; ROCHET & TIROLE, 2004a-b).These industries range from computer games, to information technologies, to media, to telecommunication industries, to payment systems. According to the above definition a platform allows to increase the social surplus only if three necessary and sufficient conditions are observed: distinct groups of users, having their demand coordinated with each other, by means of a platform that coordinate their trade more efficiently than bilateral relationships (EVANS, 2003; ROCHET & TIROLE, 2004a-b). In an industrial economics framework the multi-sided platform industries are related to the concepts of network externalities and of multi-product pricing (ROCHET & TIROLE, 2004a-b).

The ultrabroadband telecommunications can be characterized even by the interaction of two different customers' categories: the contents providers and/or advertisers and the users (readers and/or viewers) (ARMSTRONG, 2005; GABSZEWICZ et al., 2005).The interaction between these categories of users is influenced by the presence of indirect network-effects: "advertisers value the service more if there are more members of an audience who will react positively to their messages; audiences value the service more if there are more useful messages" (EVANS, 2003).Thus the opposite network size represents a quality parameter in the platform selection (ROSON, 2005). Furthermore, according to WRIGHT (2002, 2003), such an interaction between the two market sides of a platform depends on their strategic choices. Viewers and readers can be both adverse to ads and interested in them, and some papers show the subsidiarization of readers by advertiser (GABSZEWICZ et al., 2005).

Many authors have studied the platform competition (CAILLAUD & JULLIEN, 2003; ROCHET & TIROLE, 2002, 2003) but the relationship between innovation and platform competition has received less attention from the literature (ARMSTRONG, 1999; DISTASO et al., 2006; MILNE, 2005; WICKELGREN, 2004; ZOU, 2006). Moreover, two-sided platforms can develop product/service innovations or price differentiations in order to deal with market competition effectively (CALABRESE et al., 2008).

The paper is based on CHAKRAVORTI & ROSON (2006). They construct a model to study competing payment networks offering differentiated products in terms of benefits to consumers and merchants. They analyse market equilibrium in several market structures: duopolistic competition and cartels, symmetric and asymmetric networks, taking into consideration alternative assumptions about consumer preferences in both cases. Their results show how competition increases consumer and merchant welfare.

* Ultrabroadband and convergence in telecommunication industries

Over the last few years there has been a growing interest in the ICT market for multimedia and interactive services, such as fast Internet access, Video on Demand, Pay per View, e-commerce, video-conferences, home banking, on-line work from home, interactive games, etc.

At present networks are generally categorised as being either broadband or narrowband, according to the capacity to transfer data which is available for the user.

The term broadband is utilised to describe a connection which can transport a great quantity of digital information. In this sense any transmission technology which allows a faster connection than the potential speed of an analogical modem in conjunction with a copper telephone line may be considered broadband.

The future of telecommunication systems will require considerable investments in order to develop the ultrabroadband infrastructure that will allow integrated communication using voice, data, television and more. The technologies, whose continuous innovations will allow the development of an ultrabroadband infrastructure, are for example xDSL, fibre optics, wireless, power line communications and so on.

Ultrabroadband allows telecommunications companies to enter into the communications markets (Triple Play). Traditional broadcasting is characterised by a price structure in which the audiences do not pay any fee while the advertisers pay a fee depending on the number of audiences.

The convergence involves that telecommunication/communication platforms will be characterised by interactivity, security, speed, interoperability, audience targetization and so on. These attributes represents the benefits that new telecommunications/communications platforms involve for both markets sides (readers/viewers and advertisers).

The aim of this paper is to analyse how the convergence, expressed in terms of some attributes (i.e. interactivity, security, speed, interoperability, audience targetization and so on), between communication and telecommunication platforms impacts on their pricing structure. In order to employ such an analysis we will develop some numerical simulation starting from the CHAKRAVORTI & ROSON (2006) model.

* The model

The model describes the competition among four market players: the incumbent, i.e., the traditional communication or telecommunication operator and three competitors, i.e., both telecommunication and communication companies which, thanks to ultrabroadband, may offer voice, date and IPTV. We assume no utility is obtained by either readers/viewers and advertisers in using traditional communication or telecommunication operators. We consider the advertisers have no utility in using the incumbent as a media for their ads hence its lack of targetization (the case of traditional broadcasting advertisement); on the audience side we consider that the contents impoverishment causes a null utility. Thus, according to the above assumptions we assume that all readers/viewers and advertisers do not pay any fees and do not obtain any benefits. In the following the triple play operators will be simply named as platforms; the competitors of our model will be the incumbent platform that will be simply named as incumbent and three new entrants that will be represented as platform 1, platform 2 and platform 3.

We adopt the main assumptions made by the CHAKRAVORTI & ROSON (2006) model and will adapt them to the case of convergence in the telecommunication industry:

* All readers/viewers adopt only a platform i=1,2,3 (singlehoming).

* Considering that advertisers allow producing contents, we can assume that advertisements have a positive effect on audiences. Thus, the total benefit that each reader/viewer obtains by utilising the platform i=1,2,3 is given by multiplying the benefit for each connection to the platform, [h.sup.c.sub.i], by the number of advertisers which use the platform i, [D.sup.m.sub.i]. The benefits, [h.sup.c.sub.i], are distributed according to a uniform distribution in [0,[[tau].sub.i]], where [[tau].sub.i] represents the maximum benefit that a reader/viewer may obtain from platform i and is calculated by adding the different attributes together, i.e interactivity, security, speed, interoperability and so on.

* Each reader/viewer pays the platform i a flat fee, [f.sup.c.sub.i].

* The reader/viewer utility [U.sup.c] (in using one of the three platforms) is calculated from the difference between total benefits and fees. Moreover, let us assume that once a reader/viewer becomes a member of a platform, he/she will use this platform exclusively (such an assumption is always true in each time unit); thus the utility for a generic reader/viewer [U.sup.c] can be expressed as:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. [1]

* Each advertiser can broadcast advertisements on several platforms simultaneously (multihoming). Moreover it pays a fee for each advertisement, [f.sup.m.sub.i].

* The benefit, [h.sup.m.sub.i], which each advertiser obtains from platform i, when it provides an advertisement, is distributed according a uniform distribution in [0,[[mu].sub.i], where [[mu].sub.i] represents the maximum advertiser's benefit. [[mu].sub.i] is calculated by adding different attributes together i.e. interactivity, speed, interoperability, audience targetization and so on.

* The advertiser's utility [U.sup.m] in using platform i is calculated from the difference between benefits and fees. An advertiser will use a platform if he/she obtains a positive benefit from it; thus the utility for each advertiser Um can be expressed as:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. [2]

where Dic represents the number of readers/viewers using theplatform i.

Readers/viewers utilise an alternative platform to the incumbent if such a platform meets two requirements: it produces a positive utility and the readers/viewers' utility ([U.sup.c]) is greater than the utility provided by other platforms.

We use the same assumptions as the CHAKRAVORTI & ROSON (2006) model, but expand on them in order to encompass competition between the three platforms. The market share can be seen in figure 1, where each reader/viewer is represented by a point whose coordinates ([h.sub.1.sup.c] [D.sup.1.sub.m], [h.sub.2.sup.c] [D.sup.1.sub.m], [h.sub.3.sup.c] [D.sup.3.sub.m]) express the total benefits of using platforms 1, 2 or 3 (each point is obtained by multiplying the three benefits hic by the number of advertisers who choose the platform i, [D.sup.m.sub.i]).

In figure 1, the parallelepiped is divided into 8 sections. Each one is derived from the intersection of the parallelepiped with the three planes that are obtained according to the values assumed by [f.sup.c.sub.i]. Readers/viewers within section 1 use the incumbent platform, since the net benefits offered by the other three platforms are negative. In sections 5, 2 and 4 readers/viewers choose the operator which offers them positive utility. In sections 6, 8, and 3 the competition is only between the two platforms that offer a positive net benefit. In figure 2, we show section 6 of parallelepiped (of figure 1) where, in this particular case, the competition is between platform 1 and platform 2. In fact in section 6 since [h.sup.c.sub.1] [D.sup.m.sub.1] > [f.sup.c.sub.1] and [h.sup.c.sub.2] [D.sup.m.sub.2] > [f.sup.c.sub.2], the platform 1 and platform 2 offer positive net benefits; while given that [h.sup.c.sub.3] [D.sup.m.sub.3] > [f.sup.c.sub.3], platform 3 offers a negative net benefit to readers/viewers. Figure 2 shows a volume divided into two parts. The grey section represents the percentage of demand equally divided between two platforms (platform 1, platform 2, platform 3). In fact, if platforms offer readers/viewers the same value of net benefits (grey volume of figure 2), readers/viewers choose on the basis of relative utility and the border between the two market shares is given by a 45 degree plane that splits the grey volume into two sections (CHAKRAVORTI & ROSON, 2006). The white volume represents the additional percentage of demand to be added to the platform which offers the greatest net benefit to the readers/viewers. Only the platform offering the highest readers/viewers surplus ([tau][D.sup.m]-[f.sup.c]) attracts readers/viewers in the white volume (Chakravorti and Roson, 2006); for example if ([[tau].sub.2] [D.sup.m.sub.2]-[f.sup.c.sub.2])>( [[tau].sub.1] [D.sup.m.sub.1]-[f.sup.c.sub.1]) the readers/viewers utility is the greatest using platform 2.

[FIGURE 1 OMITTED]

[FIGURE 2 OMITTED]

Section 7 represents the only volume in which readers/viewers obtain a positive utility in using all three platforms (1,2,3). The market share of each platform is represented in figure 3. The white cube at the bottom left of figure 3 is obtained by the third power of the minimum among [[tau].sub.1] [D.sup.m.sub.1]-[f.sup.c.sub.1], [[tau].sub.2] [D.sup.m.sub.2]- [f.sup.c.sub.2]and [[tau].sub.3] [D.sup.m.sub.3]-[f.sup.c.sub.3], that is, the utility of the platform which provides the minimum net benefit among all platforms. Since each platform provides a positive utility, each platform gains 1/3 of the white cube. In order to obtain the grey volume in figure 3, we found the intermediate value among [[tau].sub.1] [D.sup.m.sub.1]- [f.sup.c.sub.1]., [[tau].sub.2] [D.sup.m.sub.2]-[f.sup.c.sub.2] and [[tau].sub.3] [D.sup.m.sub.3]-[f.sup.c.sub.3]. The two platforms that offer the greatest net benefits gain half of the grey volume to sum to their respective market shares. In order to obtain the white parallelepiped at the right of figure 3, we calculated the maximum among [[tau].sub.1] [D.sup.m.sub.1]-[f.sup.c.sub.1]., [[tau].sub.2] [D.sup.m.sub.2]- [f.sup.c.sub.2] and [[tau].sub.3] [D.sup.m.sub.3]-[f.sup.c.sub.3]; then we calculated the volume of this parallelepiped. Only the platform that provides the maximum value of net benefit gains the additional market share represented by this parallelepiped.

[FIGURE 3 OMITTED]

The market shares of readers/viewers' demand, for each platform, are obtained by adding the volumes (2, 3, 4, 5, 6, 7, 8) in figure 1, divided by the total market demand ([m.sub.1.sup.*] [m.sub.2.sup.*] [m.sub.3]). The total readers/viewers' demand for

each platform is represented respectively by the following Equations [3]:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

where:

[m.sub.i] = [[tau].sub.i] x [D.sup.m.sub.i] [for all]i = 1,2,3;

[b.sub.i] = [m.sub.i]-[f.sup.c.sub.i] [for all]i = 1,2,3;

C = total number of readers/viewers;

B = min{[b.sub.1], [b.sub.2] [b.sub.3]}; > A= max{[b.sub.1], [b.sub.2], [b.sub.3]}; M=max{min{[b.sub.1], [b.sub.2]};min{[b.sub.1], [b.sub.3]};min{[b.sub.2], [b.sub.3]}};

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

[B.sup.3] represents the white cube in the left of parallelepiped of figure 3: according to Equation [3] for each platform (platform 1, platform 2, platform 3), 1/3*[B.sup.3] has to be added to market shares. M2*B-[B.sup.3] represents the grey area in figure 3: according to Equation [3] for two platforms (platform 1, platform 2, platform 3) that offer the greatest net benefits, 1/2*(M2*B-[B.sup.3]) has to be added to 1/3*[B.sup.3]. (A-M)*M*B represents the white volume on the right part of the parallelepiped of figure 3: according to

Equation [3] for the platform (platform 1, platform 2, platform 3) that provide maximum net benefits (A-M)*M*B has to be added to 1/3*[B.sup.3] + 1/2*(M2*B-[B.sup.3]).

Under the assumption that the advertisers use the platform j if and only if the benefits are greater than the costs ([h.sup.i.sub.m][greater than or equal to] [f.sup.i.sub.m] the demand of the advertisers is equal to:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] [4]

where M represents the number of advertisers on the market.

For simplicity, let us assume that the advertisers benefits are distributed with a uniform distribution, [K.sup.m.sub.i], in [0,[[micro].sub.i],].

Each platform faces two types of costs: the cost, [g.sub.i], on the readers/ viewers' side and a cost, [c.sub.i], on the advertisers' side.

The profit of each platform is given by:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] [5]

* The numerical simulations: the impact of convergence between communication and telecommunication platforms on price structures

In this section we will analyse the impact of convergence between communication and telecommunication platforms on their pricing strategies. In order to do this we will employ some numerical simulations whose data has been tested by interviews with experts on such industries. The simulations will be developed through the use of Matlab (MATrix LABoratory) software; they are based on the following assumptions:

1. The cost [g.sub.i], on the readers/viewers' side and the cost c, on the advertisers' side are equal to zero.

2. We consider eight scenarios, each one based on the following assumptions:

* For three scenarios (see tables 1, 2 and 3) we consider that the benefits offered by platform 1 are lower than the others competitors, the benefits offered by the platform 3 are the greatest and finally the benefits offered by platform 2 are between the benefits of the others two competitors (see tables 1, 2 and 3). The three scenarios are based on the following assumptions:

--In the first scenario (A) the values of [[tau].sub.i] are equal to [[mu].sub.i] (see table 1), in the second scenario (B) the values [[tau].sub.i] are greater than (see table 2), finally in the third scenario (C) the values of [[tau].sub.i] are lower than [[mu].sub.i] (see table 3).

--For each scenario we fixed the starting values of v, and [[mu].sub.i] (for 1=1,2,3)--In particular, in the scenario A the values of % and [[mu].sub.i] are equal to

1 for the platform 1 ; 1.5 for the platform 2 and 2 for the platform 3. In the scenario B, the values of [[tau].sub.i] are equal to 1 for the platform 1; 1.5 for the platform 2 and 2 for the platform 3, while the values of [[mu].sub.i] are equal to 0.5; 1; 1.5 respectively. In the scenario C the values of [[??].sub.i], are equal to 0.5; 1 and 1.5 respectively, while the values of [[??].sub.i] are equal to 1; 1.5 and 2.

--For each scenario (A, B, C) we compare the starting situation, (described above), with the four other cases. In particular, in the first case both the readers/viewers benefit level, [[??].sub.i], and the advertisers benefit level, [[??].sub.i] increase, with respect to the starting situation, of 0.5; in the second case of 1; in the third case of 1.5 and finally in the fourth case of 2 (see tables 1,2 and 3).

* In the scenarios D, E and F we suppose that the three platforms (1,2,3) offer the same benefits and that each platform fix [[??].sub.i]=[[mu].sub.i] (see tables 4, 5 and 6). In particular, in the scenario [[??].sub.i] and [[??].sub.i] are equal to 0.1 (see table 4); in the scenario E [[??].sub.i] and [[mu].sub.i] are equal to 2 (see table 5); and finally, in the scenario F [[??].sub.i] and [[mu].sub.i] are equal to 4 (see table 6).

* In the scenarios G and H we suppose that the three platforms (1,2,3) offer the same benefits both to the readers/viewers and the advertisers (see tables 7 and 8). In particular, in the scenario G [[??].sub.i] =..4 and [[??].sub.i] = 0.1 (see table 7); while in the scenario H [[??].sub.i] =0.1 and [[mu].sub.i] = 4 (see table 8).

3. Our inputs are both the benefit values([[tau].sub.i] and [[mu].sub.i]) and the costs ([g.sub.i] and [c.sub.i]).

4. Our outputs: the platform profits and market shares (calculated using the model described in the previous section); the advertisers fees and the readers/viewers fees (determinated through the use of Matlab code).

We provide some numerical examples in order to analyse the relationships between convergence and platforms pricing structures.

The table 1 shows that when the platforms offer to both market sides the same benefit levels ([[tau].sub.t]= [[mu].sub.i]), the platforms fix the readers/viewers fees equal to the advertisers fees ([f.sup.c]/[D.sup.m] = [f.sup.m]).

Table 2 shows that when [[??].sub.i] > [[mu].sub.i] the platforms fix [f.sub.i.sup.c]/[D.sup.m]> [f.sub.i.sup.m] while table 3 shows that when v, < m the platforms fix [f.sub.i.sup.c]/[D.sup.m]> [f.sub.m.sup.i].

Tables 1, 2 and 3 show that the platform which offers the greatest benefit levels, compared to competitors, fixes the highest fees (platform 3); moreover the fees are always related to the broadband benefits.

Tables 4, 5 and 6 show that when [[tau].sub.i] = [[mu].sub.i] the readers/viewers fees are almost equal to the advertisers fees.

Tables 1, 2, 3, 4, 5 and 6 show that an increase in the benefit levels ([tau] and [??]), due to ultrabroadband innovation, increases both the readers/viewers and the advertisers fees.

Table 8 shows that when t,<h, then f c/Dm< f m.

Tables 2,3,7 and 8 show that for some values of ri and $ the platforms fix the readers/viewers fees or the advertisers fees equal to zero. In particular, when the values of [[tau].sub.i], <=1 the readers/viewers fees are equal to zero (see tables 3 and 8), instead, when [[mu].sub.i]<= 0.5 the advertisers fees are equal to zero (see tables 2 and 7). The table 4 shows an anomaly if compared to tables 2,3,7 and 8. In fact, the values of [[tau].sub.i] and of [[mu].sub.i] are equal to 0.1 but the fees are different from zero. Thus, we developed other numerical simulations (see appendix), which showed--both when the platforms provide equal and different benefits--that the fees tend to zero only if the values of [[tau].sub.i] and/or[[tau].sub.i] are low and if there is a substantial asymmetry between the readers/viewers benefit levels and the advertisers benefit levels. In particular, the market side characterized by minor benefit has fees equal to zero (see tables 9 and 10).

* Conclusion

The simulations show a relation between the benefits provided by ultrabroaband convergence (triple play) and the pricing structures. In the case of benefits homogeneity ([[tau].sub.i] [[mu].sub.i]) on both sides, the pricing structure is composed by identical prices on both sides (see tables 1, 4, 5 and 6). Instead, in the case of benefits heterogeneity ([[tau].sub.i] [not equal to] [[mu].sub.i]) between the two sides of the market, the pricing structure is composed of higher prices on the market side characterized by higher benefit levels (see tables 2, 3, 7 and 8).

Furthermore, the results show that the higher the benefit levels are the greater is the price level and thus each price on each platform side (see tables 1, 2 and 3).

Finally, in the case of low values of both [[tau].sub.i] and/or [[mu].sub.i] and of a substantial asymmetry between the readers/viewers benefit levels and the advertisers benefit levels, platforms fix the fees equal to zero on the market side characterized by the lowest benefit levels.

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Armando CALABRESE, Irene IACOVELLI & Nathan LEVIALDI GHIRON

University of Rome "Tor Vergata", Italy

Massimo GASTALDI

University of L'Aquila, Italy

Appendix Input & pricing structures Platform 1 Platform 2 Platform 3 [tau] 0.1 0.12 0.14 [mu] 0.11 0.13 0.15 [f.sup.m] 0.0228 0.0273 0.0336 [f.sup.c]/[D.sup.m] 0.0127 0.0175 0.0233 [tau] 0.1 0.13 0.15 [mu] 0.12 0.14 0.16 [f.sup.m] 0.0289 0.0298 0.0358 [f.sup.c]/[D.sup.m] 0.0089 0.0196 0.0257 [tau] 0.1 0.14 0.16 [mu] 0.13 0.15 0.17 [f.sup.m] 0.0350 0.0319 0.0381 [f.sup.c]/[D.sup.m] 0.0051 0.0219 0.0279 [tau] 0.1 0.15 0.17 [mu] 0.14 0.16 0.18 [f.sup.m] 0.0411 0.0342 0.0403 [f.sup.c]/[D.sup.m] 0.0012 0.0241 0.0301 [tau] 0.1 0.16 0.18 [mu] 0.15 0.17 0.19 [f.sup.m] 0.0456 0.0366 0.0427 [f.sup.c]/[D.sup.m] 0 0.0266 0.0326 [tau] 0.1 0.15 0.2 [mu] 0.15 0.2 0.25 [f.sup.m] 0.0411 0.0569 0.0725 [f.sup.c]/[D.sup.m] 0 0.0070 0.0225 [tau] 0.1 0.15 0.2 [mu] 0.15 0.22 0.27 [f.sup.m] 0.0391 0.0668 0.0839 [f.sup.c]/[D.sup.m] 0 0 0.0138 [tau] 0.1 0.15 0.2 [mu] 0.15 0.22 0.3 [f.sup.m] 0.0378 0.0650 0.1021 [f.sup.c]/[D.sup.m] 0 0 0.0022 [tau] 0.1 0.15 0.2 [mu] 0.15 0.22 0.32 [f.sup.m] 0.0375 0.0647 0.1106 [f.sup.c]/[D.sup.m] 0 0 0 [tau] 0.1 0.2 0.3 [mu] 0.15 0.25 0.35 [f.sup.m] 0.0459 0.0709 0.1021 [f.sup.c]/[D.sup.m] 0 0.0210 0.0519 [tau] 0.1 0.1 0.1 [mu] 0.4 0.4 0.4 [f.sup.m] 0.1000 0.1000 0.1000 [f.sup.c]/[D.sup.m] 0 0 0 [tau] 2.5 3 3.5 [mu] 3 3.5 4 [f.sup.m] 0.6964 0.8129 0.9652 [f.sup.c]/[D.sup.m] 0.1965 0.3128 0.4650 Table 1--Scenario A Input & pricing structures Platform 1 Platform 2 Platform 3 [tau] 1 1.5 2 [mu] 1 1.5 2 [f.sup.m] 0.1897 0.3061 0.4585 [f.sup.c]/[D.sup.m] 0.1897 0.3061 0.4585 [tau] 1.5 2 2.5 [mu] 1.5 2 2.5 [f.sup.m] 0.2735 0.3897 0.5412 [f.sup.c]/[D.sup.m] 0.2737 0.3896 0.5410 [tau] 2 2.5 3 [mu] 2 2.5 3 [f.sup.m] 0.3570 0.4730 0.6238 [f.sup.c]/[D.sup.m] 0.3570 0.4729 0.6236 [tau] 2.5 3 3.5 [mu] 2.5 3 3.5 [f.sup.m] 0.4402 0.5561 0.7064 [f.sup.c]/[D.sup.m] 0.4404 0.5561 0.7063 [tau] 3 3.5 4 [mu] 3 3.5 4 [f.sup.m] 0.5234 0.6392 0.7892 [f.sup.c]/[D.sup.m] 0.5235 0.6392 0.7889 Table 2--Scenario B Input & pricing structures Platform 1 Platform 2 Platform 3 [tau] 1 1.5 2 [mu] 0.5 1 1.5 [f.sup.m] 0 0.0307 0.1794 [f.sup.c]/[D.sup.m] 0.3588 0.5306 0.6794 [tau] 1.5 2 2.5 [mu] 1 1.5 2 [f.sup.m] 0.0039 0.1210 0.2696 [f.sup.c]/[D.sup.m] 0.5041 0.6212 0.7693 [tau] 2 2.5 3 [mu] 1.5 2 2.5 [f.sup.m] 0.0917 0.2082 0.3562 [f.sup.c]/[D.sup.m] 0.5919 0.7081 0.8562 [tau] 2.5 3 3.5 [mu] 2 2.5 3 [f.sup.m] 0.1776 0.2936 0.4415 [f.sup.c]/[D.sup.m] 0.6777 0.7935 0.9414 [tau] 3 3.5 4 [mu] 2.5 3 3.5 [f.sup.m] 0.2624 0.3783 0.5260 [f.sup.c]/[D.sup.m] 0.7625 0.8781 1.0258 Table 3--Scenario C Input & pricing structures Platform 1 Platform 2 Platform 3 [tau] 0.5 1 1.5 [mu] 1 1.5 2 [f.sup.m] 0.2699 0.4915 0.6509 [f.sup.c]/[D.sup.m] 0 0 0.1509 [tau] 1 1.5 2 [mu] 1.5 2 2.5 [f.sup.m] 0.4114 0.5696 0.7248 [f.sup.c]/[D.sup.m] 0 0.0698 0.2247 [tau] 1.5 2 2.5 [mu] 2 2.5 3 [f.sup.m] 0.5307 0.6474 0.8015 [f.sup.c]/[D.sup.m] 0.0308 0.1474 0.3013 [tau] 2 2.5 3 [mu] 2.5 3 3.5 [f.sup.m] 0.6136 0.7301 0.8832 [f.sup.c]/[D.sup.m] 0.1136 0.2302 0.3831 [tau] 2.5 3 3.5 [mu] 3 3.5 4 [f.sup.m] 0.6964 0.8129 0.9652 [f.sup.c]/[D.sup.m] 0.1965 0.3128 0.4650 Table 4--Scenario D Input & pricing structures Platform 1 Platform 2 Platform 3 [tau] 0.1 0.1 0.1 mu 0.1 0.1 0.1 [f.sup.m] 0.0167 0.0167 0.0167 [f.sup.c]/[D.sup.m] 0.0165 0.0165 0.0165 Table 5--Scenario E Input & pricing structures Platform 1 Platform 2 Platform 3 [tau] 2 2 2 mu 2 2 2 [f.sup.m] 0.3319 0.3319 0.3319 [f.sup.c]/[D.sup.m] 0.3317 0.3317 0.3317 Table 6--Scenario F Input & pricing structures Platform 1 Platform 2 Platform 3 [tau] 4 4 4 [mu] 4 4 4 [f.sup.m] 0.6637 0.6637 0.6637 [f.sup.c]/[D.sup.m] 0.6635 0.6635 0.6635 Table 7--Scenario G Input & pricing structures Platform 1 Platform 2 Platform 3 [tau] 4 4 4 [mu] 0.1 0.1 0.1 [f.sup.m] 0 0 0 [f.sup.c]/[D.sup.m] 1.2888 1.2888 1.2888 Table 8--Scenario H Input & pricing structures Platform 1 Platform 2 Platform 3 [tau] 0.1 0.1 0.1 [mu] 4 4 4 [f.sup.m] 1 1 1 [f.sup.c]/[D.sup.m] 0 0 0 Table 9--Different benefits between the platforms Input & pricing structures Platform 1 Platform 2 Platform 3 [tau] 0.1 0.15 0.2 [mu] 0.15 0.22 0.32 [f.sup.m] 0.0375 0.0647 0.1106 [f.sup.c]/[D.sup.m] 0 0 0 Table 10--Equal benefits between the platforms Input & pricing structures Platform 1 Platform 2 Platform 3 [tau] 0.1 0.1 0.1 [mu] 0.4 0.4 0.4 [f.sup.m] 0.1 0.1 0.1 [f.sup.c]/[D.sup.m] 0 0 0

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Title Annotation: | Ultrabroadband: the next stage in communications |
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Author: | Calabrese, Armando; Iacovelli, Irene; Levialdi Ghiron, Nathan; Gastaldi, Massimo |

Publication: | Communications & Strategies |

Date: | Nov 1, 2008 |

Words: | 5813 |

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