Aug 5, 2011 - competition as a two-stage game of complete information; the model ...... http://www.crownfibre.govt.nz/media/4824/invitation-to-participate.pdf.
New Zealand's Ultra-Fast Broadband Network
Fernando Beltrán ISOM Department University of Auckland Business School Auckland, New Zealand
August 2011
Introduction The government of New Zealand is currently building a nation-wide fibre-optics network, a project known as the Ultra-Fast Broadband (UFB) initiative that will lay out an entirely new infrastructure with the capacity to fast track innovation in network-based business models and new applications. Ultra-fast broadband access is defined as a minimum 100 Mbps downlink and 50 Mbps uplink; the UFB network will cover 75 percent of New Zealanders over ten years. Crown Holdings Fibre (CFH), the government agency in charge of UFB deployment, has invested NZD $1.5 billion (or about USD $1.1 billion) and a similar investment is expected from invited private partners with whom CFH has established regional network operators also known as Local Fibre Companies (LFCs). In the broadband ecosystem facilitated by the UFB initiative, market creation does not follow evolution patterns which are typical of other markets; conditions will be created faster than in any other market that has spawned out of commercial utilization of technological innovations. Thus, not only is the fibre project aimed to reach all New Zealanders with broadband access but it also seeks to stimulate the provision of services by entrepreneurs other than the LFCs. UFB will be an open-access infrastructure with LFCs providing wholesale Layer-2 services – a denomination that basically follows the Metro Ethernet Forum standards – to Retail
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Electronic copy available at: http://ssrn.com/abstract=1985752
Service Providers (RSPs) who will, in turn, either sell them to resellers or provide communication services and applications to end-users. In this paper we analyze the institutional arrangements in place for the development of the New Zealand’s broadband ecosystem, with a focus on elements of the regulatory scheme that starts being delineated by CFH’s decisions and negotiated agreements. We also investigate the possible effects on service competition of proposed wholesale (Layer 2) service pricing schemes as access is open and purchased by service providers on a wholesale basis. Underlying the open-access condition is the government’s vision to create conditions for new, innovative services provided by new entrepreneurs - diminishing the incentives for vertical integration by current telecommunication operators, especially the dominant firm Telecom. This paper is structured as follows. Section 1 presents the New Zealand UFB project from its origins up to its current state. It discusses the seeming benefits of its ownership structure and the mechanisms proposed for operation and maintenance responsibility and eventual ownership transfer. In Section 2 we discuss the open access principle which supports the network neutrality mandate recently reasserted in different countries. Section 3 highlights and analyzes the proposed fragmentation and separation of regulatory functions that Crown Fibre Holdings would hold as they will not be performed by the Commerce Commission. Section 4 presents a model of competition as a two-stage game of complete information; the model is used to illustrate several scenarios that correspond to different pricing schemes, allowing us to perform a comparative analysis between relative effects of pricing mechanisms on the discussed end-user service markets. Section 5 summarises some preliminary conclusions and discusses further realistic scenarios to study a sort of “inter-modal” competition in which users can opt for either Internet-based, best effort services provided on one of the retail service offers of RSPs, or communications services directly built on the NGN platform by RSP (such as VoIP).
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Electronic copy available at: http://ssrn.com/abstract=1985752
Section 1: New Zealand’s Ultra-Fast Broadband Initiative As a small, remote country New Zealand’s ability to remain competitive in a global marketplace is clearly linked to the quality of its telecommunications infrastructure in both urban and rural areas (CFH, 2010). Telecom New Zealand (Telecom NZ) is the dominating telecommunication infrastructure operator in New Zealand; it provides both telephony (fixed and wireless) and Internet service around urban and rural New Zealand. Competitors in the Internet access market provide broadband service via Telecom’s own infrastructure and by reselling its wholesale products (Milner, 2009). About two thirds of New Zealand’s total exports are from the agriculture, horticulture and forestry sectors, all mostly produced in rural areas, in which approximately 14% of New Zealanders live and work. The latter makes the rural sector an important contributor to the New Zealand economy. Nevertheless, as the dominant broadband operator, Telecom NZ has built little fibre backhaul infrastructure in rural New Zealand, which in turn means that broadband capability in rural areas is limited in both coverage and performance capability. In 2005, the New Zealand government acknowledged the country was lagging behind most of the developed world in terms of broadband capability and penetration, a fact highlighted by its 22nd place in the OECD rankings (Milner, 2009). Although the Commerce Commission has warned that if New Zealand was to “overcome the tyranny of distance from markets and transform its economy into a high skill, high earning, knowledge economy” the starting point would be a reform of the telecommunications regulatory framework to reduce costs and monopoly profits, increase competition, drive new innovative services, and spur infrastructure investment, regulatory reform alone would be not enough to create the right conditions to ensure that the New Zealand telecommunications markets propels the economy in the desired direction. Being the 22nd fastest of 45 countries in terms of Internet speed and 35th of 66 countries in terms of broadband Quality of Service (QoS), New Zealand government consequently proposed the deployment of a countrywide fibre infrastructure into New Zealand cities (Milner, 2009). In 2008, the 3
Electronic copy available at: http://ssrn.com/abstract=1985752
newly elected National Government stepped up its campaign initiative to provide fibre-to-the-home to about 75% of New Zealanders living in urban New Zealand (Milner, 2009). This was the origin of UFB. In 2009, the New Zealand government set on track the Ultra-Fast Broadband (UFB) project. The purpose of the project is to accelerate the roll-out of an access network, deploying optical fibre infrastructure (next-generation infrastructure) to 75 percent of New Zealanders by the end of 2019. The priority of this project are broadband users such as businesses, schools and health services, in addition to greenfield developments in particular residential areas (CrownFibreHoldings, 2009). UFB guarantees the residential broadband services at a speed of 100 megabits per second (Mbps) downstream (from the internet to the user) and 50 Mbps upstream (from the user to the internet), with higher speeds for priority users. Investment on UFB is NZD $1.35 billion and at least the same amount of money is expected from private investors. In late 2009, the Ministry of Economic Development (MED) prepared and issued an ‘Invitation to Participate’ (ITP) by which potential investors would submit their proposals on how they would co-invest with the government to achieve the UFB objective in one or more candidate areas. In 2010, 14 parties, among them, Alpine Energy Limited, Central North Island Fibre Consortium, and Northpower Limited were shortlisted as private investors (Alpine Energy Limited, 2010). The new public-private partnerships are known as Local Fibre Companies (LFCs). After the two final LFCs - Christchurch City Holdings Limited (through its fibre business Enable Networks) and Telecom Corporation of New Zealand Limited (through its Chorus business) – were announced in May 2011 the amount of private investment amounted to about $1.1 billion NZD (CFH, 2011b). Thus, New Zealanders will have to deal with a regional LFC according to the location of their homes and business as follows: in the Whangarei region (north) regional LFC is Northpower Limited. In Hamilton, Tauranga, New Plymouth, Wanganui, Hawera and Tokoroa regions, users will deal with Ultrafast Fibre Limited, whereas in Christchurch, Rolleston or Rangiora, the LFC is Enable Networks Limited. 4
All other towns and cities, comprising about 70% of the country, will be served by Chorus, a unit of Telecom Corporation of New Zealand Ltd.
Section 2: Open Access and Network Neutrality The International Telecommunication Union (ITU) defines a Next-Generation Network (NGN) as “a packet-based network able to provide services including telecommunication services and able to make use of multiple broadband, QoS-enabled transport technologies and in which service-related functions are independent from underlying transport-related technologies”(ITU, 2004). NGNs appear as a collection of networks that could support a flexible platform for service delivery (Chae-Sub & Knight, 2005). Unlike the public switched telecommunications networks, PSTN, NGN’s IP base enables the independency of protocol layers (upper and lower). The latter means that a NGN provides connections independent of any sub-layer network type such as ATM or frame relay. One distinctive feature of NGNs is its predicted ability to combine the best of both worlds, the PSTN and the Internet, with high speeds and QoS (Chae-Sub & Knight, 2005). A NGN can be regarded as a platform over which providers, whose ownership is not necessarily shared with that of the platform, meet users who seek to purchase communication services; thus, access to lower layer (infrastructure) services is essential to the success of any provider’s business plan. Internet, for instance, can be regarded as an open platform for innovation, investment, job creation, economic growth,
competition,
and
free
expression
by
the
public
(FederalCommunicationsCommission, 2010); while Internet Service Provider (ISPs), either owned by telephone companies or cable operators are not necessarily concerned with open access, innovators, end-user application developers, and the public in general understand the virtues of open access to Internet. The Internet was designed as an open network with “no gatekeepers over new content or services” [2]; its layered, end-to-end architecture places network intelligence at the edges rather
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than at the core. Such technical features are the sources of the wide range of services and innovative offers only possible by avoiding central control and by incentivizing innovation at the edges. The ‘open access’ debate can be briefly described as conflicts between the private interests of broadband providers and the public’s interest in a competitive innovation environment centered on the Internet (Wu, 2003). After several years of dispute between the claims of the ISP of a large U.S. cable TV operator and the Federal Communications Commission (FCC)1, the latter, in December 2010, released its “Open Internet Order” on the accepted practices that ISPs should follow (Moya, 2010). The order is based on four core principles: transparency of the network management practices; no blocking of non-harmful and lawful content and applications; no unreasonable discrimination while transferring non-harmful and lawful content and applications; and reasonable network management practices (FederalCommunicationsCommission, 2010). The open access principle supports the network neutrality mandate recently reasserted in different countries. The network neutrality principle proposes that no operator can discriminate against content or traffic that travels on its network or against particular websites and devices used to the access the Internet. Recently, some countries have enshrined the net neutrality in their laws. On the 22nd of June 2011 The Netherlands was the first country in European to do so (BBC, 2011). As of then, for instance Internet Service Providers in The Netherlands can charge “bit-hungry content” extra fees but have to inform customers about the reason for it; they cannot block VoIP provider Skype and free text application WhatsApp; they cannot inspect customers’ traffic and so on. Although customers and content
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In 2007, the U.S. largest home ISP Comcast throttled traffic generated and managed by BitTorrent, a
peer-to-peer Internet service. Comcast explained to the public that their decision would protect other subscribers from internet traffic congestion. Although critics and the U.S. Federal Communications Commission (FCC) deemed Comcast’s network management behavior as against the open access principles, in 2009 the U.S. Court of Appeals for the District of Columbia sided with Comcast in the long-running dispute over the ISP’s ability to manage its network traffic. 6
providers welcomed this law, Internet Service Providers such as T-Mobile and Vodafone Netherlands aired their disappointment (BBC, 2011). With an obviously broader view, the European Commission has adopted a “wait-and-see” policy to watch the markets closely and promised to deliver findings on the issues at the end of 2011. In New Zealand the Commerce Commission has not yet signaled any decision on network neutrality, but CFH’s contractual terms on UFB operation favours open access because of its support of a competitive outcome, which has been thought as both suitable and attractive to the industry and private-sector investors. Thus, CFH has made open access a key principle underlying the UFB initiative by asserting that “services provided by a LFC should be offered to all access seekers on the same terms and conditions except where variations can be objectively justified, even if the access seeker is a competitor or a downstream arm of a network competitor” (CrownFibreHoldings, 2010b).
Section 3 Regulatory Oversight of the UFB in the Making Crown Fibre Holdings Ltd (CFH) was created by the Ministry of ICT to manage the investment on the UFB infrastructure. CFH replaces the Ministry’s duties regarding the UFB network after its operation gets started, but both the Ministry and Treasury will have an on-going oversight and monitoring role of CFH (CrownFibreHoldings, 2011b). Neither the NZ government, through its Ministry of ICT, nor the newly created CFH are keen on addressing the regulatory functions necessary for the efficient development of the UFB market. Their public signalling away from establishing any clear regulatory guideline has marked the debate on what many future market players demand in the form of a regulatory framework. Following the path of the dubious New Zealand approach to telecommunications regulation in the 1990s, an unsuccessful attempt to address regulation (or the lack of) of UFB was the October 2010 announcement by the government that the UFB
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market would face a 10-year ‘regulatory holiday’,
in fact excluding the LFCs from
the Telecommunications Act until 2020 (Labour, 2010). The government stated that the 10-year regulatory holiday aimed to encourage certainty for the LFCs and its investors on this green-field market investment. The Telecommunications Minister Steven Joyce staunchly defended the 10-year regulatory holiday saying “without a regulatory holiday, UFB service providers would face significant uncertainty” and “there’s no established best-practice in the telecommunications industry for rolling-out and regulating ultra-fast broadband networks, so it’s a matter of doing what’s best at the time, with reviews of the regulatory environment every few years” in April, 2011 (Watson, 2011). Without a clear regulation of the UFB market, some network management practices might not be transparent, competition will not be encouraged and customers may face monopoly power. Those negative aspects are issues that the regulatory authorities are not keen on especially after the U.S. and European Union (EU) released regulations protecting network neutrality (FCC, 2010), (Crocioni, 2011). On the other hand, a strict price regulation, for instance, in the initial period of UFB market business operation could limit the ability of respondents to “put their best foot forward” (MinisterforCommunicationsandInformationTechnology, 2010). The government is obviously protecting private investors’ incentives since money is sought to complete the UFB network. In addition, in order to protect business competition the government has to strictly oversee the LFCs’ network management practices to make sure that access to the UFB infrastructure remains open. Under pressure from many sector players and the political opposition, on May 18th 2011, the Minister announced that the regulatory holiday would be removed from the Telecommunications Amendment Bill, claiming that contractual mechanisms will be used to replace the provisions “if significant changes are made to price or other key features of the UFB regime over the build period” (Techday, 2011). It is also expected that the Commerce Commission will fully overlook the new regime to make sure customers are getting the value for their money (Hall, 2011).
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After a careful consideration of the UFB network business model CFH has determined that Layer-1 and Layer-2 services are required to be provided in a non-discriminatory standard in the initial period - which ends on December 31st 2019 - and will be provided in a ‘equivalence and non-discriminatory’ standard afterward (CrownFibreHoldings, 2010a). When a LFC only provides Layer-1 service, it must provide it on non-discriminatory terms, which means that given equally specified quality of service for two different RSPs, they must be charged the same price. Non-discrimination here ensures that access seekers – RSPs - are treated in a similar manner as LFCs themselves, and that any differences are objectively justifiable by differences in costs, the access seeker’s needs or the access seeker’s characteristics. It is also essential that any differences in treatment do not harm competition (MinistryofEconomicDevelopment, 2009). The latter would ensure that the LFC does not give itself an unfair advantage (whether explicit or implicit, direct or indirect) when both the LFC and its access seeker customers compete in the marketplace for the provision of Layer-2 services (MinistryofEconomicDevelopment, 2009). In May 2011, CFH separately released two agreements with Enable Networks Limited (ENL) and Chorus on UFB delivery. In these two agreements, CFH covers the delivery of UFB in partnership with ENL and Chorus (CFH, 2011a; 2011d). The two agreements complement the other two agreements that CFH had settled previously with respective partners. Those agreements display prices for wholesale Layer-2 services for three main types of users: home end-users, businesses, and priority users such as schools; such UFB products are the “building blocks” - downstream bandwidth, upstream bandwidth and Committed Information Rate 2 (CIR) (CFH, 2011d) - to be used by RSPs as inputs to provide their products to homes and businesses. Table 1 displays the caps that CHF and its partners have agreed for entry level broadband connection, high-definition video, and entry level business service prices, all of which make up the basic Layer-2 offer. 2
As stated in the agreements: “CIR is a guaranteed minimum rate of data transfer for priority traffic.
EIR, or Excess Information Rate, is the accepted rate of data transfer for low priority traffic.” (CFH, 2011d) 9
Table 1. Products and prices for home/retail customers. Source: (CFH, 2011)
Table 2 shows the monthly prices, upstream and downstream speeds, and additional technical conditions (such as the CIR) for Layer-2 services to be used in the delivery of Business products; Table 3 refers to Layer-2 services for schools, one of the groups considered as priority by CFH.
Table 2. Products and prices for businesses. Source:
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(CFH, 2011)
Table 3. Products and prices for schools. Source: (CFH, 2011)
A regional LFC will provide wholesale Layer-2 services to RSPs but is not allowed to be or directly operate a LFC. For instance, the negotiation process between CFH and Telecom has ended in Telecom committing to divest into two completely independent operators: Chorus, a provider of wholesale communication services and the retail operator Telecom (Telecom, 2011a). Chorus will be a nationwide access network operator that will offer services to RSPs on an open access basis, whereas Telecom will be a retail-focused telecommunications business comprising fixed-line, mobile and other ICT services (Telecom, 2011a). Chorus will deliver wholesale Layer-2 service to interested RSPs in New Zealand in a non-discriminated manner so that they can compete with Telecom in a fair way (Telecom, 2011b). In a recently published document, the Whosale Service Agreement (WSA) currently under discussion, CFH and its partners in the LFC (CFH, 2011c) refer to a Primary Service Provider (PSP) as a provider of a residential service - a bitstream service provided to residential end-users or to resellers for provision to residential end-users - that uses a UFB Standard Wholesale Service as an input – that is, a service of a standard that meets or exceeds the minimum standard for the residential wholesale service (being 30Mbps downstream, 10 Mbps upstream with 2.5 Mbps CIR). Any provider, Primary or not, is responsible for all interactions with resellers and end users (including provisioning, billing, customer services, contact with the police and other government authorities, fault reporting and dispute management) (CFH,
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2011c); in particular if the provider delivers voice services it must provide voice at an “acceptable quality” (clause 9.4; CFH, 2011c), which means that “the Service Provider’s network is to add no more than 40 ms of delay, including any trans-coding delay, and 10 ms of delay variation between an Interconnection Point and the point at which voice calls are handed over to other carrier networks”. The latter is as far as regulations on QoS in the proposed WSA go. In general regulators may either intervene to regulate QoS, such as enforcing Quality and Service Level Agreements on providers or allow providers to introduce discriminatory treatment of traffic and, possibly, of end-users. Any approach would face enormous problems from the parties directly affected. As has been discussed in the literature, discrimination – which would basically manifest in one of four forms in a NGN platform, namely, price discrimination, access tiering, blocking, and service quality discrimination (C.Marsden, 2009) – is seen as a direct threat to network neutrality. In terms of our main concern, service quality discrimination, if network neutrality is fully embraced RSPs might be forced to offer a single level of service quality, which as some argue, (Crocioni, 2011) has the potential to make everyone worse-off. CFH may also allow RSPs respond to different consumers’ tastes with different sets of products, which may include different QoS levels. Consumers may benefit from having a wide variety of products and/or services that closely match their preferences (F.Beltrán & L.M.Gómez, 2010). As hearings and conversations proceed between CFH and its partners in the LFCs, and the parties interested in becoming RSPs, it remains an open question what the landscape for QoS will be in the UFB market.
Section 4: A Simple Model of Competition in the UFB Retail Market In this section we present an analytical model of competition as a game of complete information; the model is used to illustrate several scenarios that correspond to the use of pricing schemes and will allow us to perform a comparative analysis between relative effects of pricing mechanisms on the discussed end-user 12
service markets. Figure 1 exhibits the delivery of end-user services by a RSP that purchases layer-2 services from the LFC; it also highlights the commercial relationships between end-users and RSPS, and RSPs and the LFC. Provision of an open platform and Layer-1 and Layer-2 services is the foundation of the UFB market; RSPs will purchase Layer-1 and Layer-2 services from a regional LFC, offering its services to priority users, homes and businesses. LFC’s service offer and prices are largely dependent on CFH’s regulatory decisions such as wholesale service prices (CFH, 2011c).
Figure 1. Commercial relationships in the broadband supply chain.
In addition to providing network access to end users (such as homes, businesses, health centers, and schools), LFCs will sell Layer-2 services to RSPs. Once a RSP purchases Layer-2 access, it can release its own products to end users, most likely based on a triple play (Internet access, VoIP, IPTV) offer. LFCs are not allowed to trade with end-users directly but only provide wholesale access services, with RSPs selling 13
access service to end-users3 (CrownFibreHoldings, 2011a). As an example CFH’s agreement with Chorus states that “Chorus will contract with RSPs who can then provide services to end users. As per the open access requirements, Chorus will operate only at the wholesale level - it will not sell services directly to end users. In turn, RSPs may use wholesale products from Chorus and the Local Fibre Companies to create retail UFB-based services which are sold to residents, businesses, schools and health premises.” (CFH, 2011d) Consumer derive benefits from the purchased services and their utility is affected by the price paid and the QoS received. In fact, in terms of QoS a NGN promises to deliver services that go beyond the “best effort” approach of Internet. Introduction of a QoS framework is of concern to regulators as efforts to assure quality-based delivery of services may conflict with manifestations of the network neutrality principle (Crocioni, 2011). Our model’s representation of benefits to end-users means that as much as consumers base their purchase decision on price, the expected QoS also influences their decision.
4.1 Model Framework A regional LFC provides Layer-1 and Layer-2 services to RSPs, which in turn compete for customers on the basis of price and quality of service. In our model, monetary cost (the price charged) and a QoS cost (related to the network congestion level) are linearly combined to form the ‘perceived price’ (Maillé, Tuffin, & Vigne, 2011). For convenience, our model assumes every user has a choice between two RSPs, each with its own triple-play offer. End-user’s selections are based on the combination of Quality of Service (QoS) and price level by the service provider. We find conditions for the existence of Nash equilibria in the strategic game between
3
In its 2009 Invitation to Participate, MED says that a LFC can indeed offer end-user services in
competition with RSPs. LFC would have to use a separate subsidiary. The latter contributes to further justify the introduction of non-discriminatory and equivalence principles.
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RSPs. Equilibrium conditions are studied on the set of retail service prices. Once prices are public information, every customer selects the service provider that best suits him according to his perceived service quality and price levels. We study the latter situation using the Wardrop equilibrium concept (Wardrop, 1952), whose principles can be restated in our model as follows: - every RSP faces positive demand; - the perceived price for any RSP with positive demand is the same; otherwise, some end users would have an interest in churning (Maillé, et al., 2011). In the next stage, customers will select the RSP that best suits their preferences for a combination of service quality and price level. Services include Internet, VoIP, IPTV, and others; RSPs may sell differentiated service packages to end users. To avoid confusion, here the price level refers to the price for the package and the service quality refers to the quality for the package. For this stage we calculate a Wardrop equilibrium and closely observe the equilibrium existence conditions. The two-stage game can be solved by using backward induction. Figure 2 illustrates a market with a regional LFC, and two RSPs that compete for customers on the basis of their price and QoS. End-users are offered a tripe-play bundle and, possibly, other services.
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Figure 2. Detailed UFB Market
Our model explores the regional UFB market; in a given region only one LFC will operate, although users may also have the option of purchasing ADSL broadband services from other providers. The only LFC provides wholesale layer-2 services to RSPs. We assume that two RSPs (RSP1 and RSP2) purchase access from the LFC and make their offers to consumers in the region providing them with triple-play (Internet, VoIP, IPTV) and other services. In the region, there are plenty of end users who want to consume services from either RSP1 or RSP2, but none actually purchase services from both RSPs. 4.2. Solving the model Stage 2: Solving the end-user game This two-level game requires determining how demand distributes between RSPs. We assume prices are fixed and can only be changed in stage 1. The Wardrop principle states that at equilibrium the perceived price at each provider with strictly 16
positive demand is the same. The end-user’s perceived price of services provided by RSP s ( s = 1,2 ) can be written as pps = ps + T(D(ps)) where ps is RSP s service monetary price and Ts(D(ps)) represents a QoS-based cost when demand for RSP s service is D(ps); such cost can be interpreted as that part of the end-user’s utility that she has to give up in order to obtain a desired QoS that overrides network congestion. Any end-user will settle on the minimum perceived price in the market, otherwise she would have an interest in switching providers. In other words the perceived price of any RSP with non-negative demand is necessarily the same. Finally the RSPs’ total joint demand depends solely on the perceived price. The latter observations can be summarized to state the Wardrop equilibrium conditions as follows: (1) for every service with a positive demand, its perceived price must be the minimum among all services. And this perceived price is less than or equals to the perceived price of service with zero demand; (2) the demand of a service is depending on the perceived price of that service; (3) the perceived price and demand must be nonnegative. One interpretation of the resulting UFB competition scenario that helps illustrate the use of the Wardrop equilibrium solution concept is that end-users can be regarded as searching for the best route to satisfy their communications needs. Such route consists of a chosen RSP and the QoS expected. For stage 2 of the game we have the following result: Proposition 1. In the second stage of the UFB game the Wardrop equilibrium among end users in the UFB market exists and is unique. Proof: In our case existence and uniqueness of Wardrop equilibrium are justified by results found in (Aashtiani and Magnanti, 1981), (Roughgarden, 2005) and (Hayrapetyan et al., 2005). Theorem 5.4 in (Aashtiani & Magnanti, 1980) assures the
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existence of Wardrop equilibrium when the demand function and the QoS cost are nonnegative. The second step is to prove the uniqueness of the Wardrop equilibrium. Assume we have two Wardrop equilibriums for one RSP with different perceived price pp and ppˆ and pp > ppˆ. Since the demand function is strictly decreasing on its support, when pp > ppˆ, the total demand for D(pp) is strictly smaller than for D(ppˆ), D(pp) < D(ppˆ). That means the relationship between two congestion costs of such demand function is T(D(pp)) < T(D(ppˆ)). So the perceived price pp is supposed to be less than ppˆ, this is making a contradiction to the assumption (pp > ppˆ), and so the end-user game Wardrop equilibrium is unique. We will call (x, (1-x)) the Wardrop equilibrium to denote how the market has split between RSP1 and RSP2 (0
