The Dutch market for telecommunication : a model

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The Dutch Market for

Telecommunication: a Model

Wouter de Waart

11943149

Supervisor: dr. A. Kiss University of Amsterdam Amsterdam School of Economics MSc Economics: Markets and Regulation

July 15, 2018

Abstract

Telecommunication is developing at an ever increasing pace. In the Netherlands, recent innovations have enabled two independent own-ers of cable networks (KPN and ZiggoVodafone) to grow equally large in market share. Although equally large, only one of them is regu-lated in opening up its network for new entrants. This paper analyzes existing literature on network industries, interconnection and access charge regulation. It introduces a model in which two independent, symmetric networks compete and accommodate an entrant. Taking a benchmark model without entry as starting point, it analyzes the effects on welfare when entry is accommodated by either one or both networks. For every scenario, the long-term equilibrium outcome is derived by allowing the process of accommodation to be repeated. It finds that the optimal equilibrium in terms of welfare is achieved in a scenario where entry is accommodated by two networks after a simultaneous negotiation on the terms of access.

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1 Introduction

Connectivity plays an important role in the 21st century. In 1818, Alexan-der Graham Bell invented a way in which two devices could be connected and used for communication. Two centuries later, devices all over the world are connected through an extensive network of cables, wires and satellites. Telecommunication has developed rapidly and impacts live on a daily ba-sis. To ensure these developments enhance welfare rather than decrease it, adequate regulatory policy is needed. Whereas network industries in gen-eral used to be characterized by state-owned monopolies for a long time, the late 20th century witnessed a wave of liberalization. In the Netherlands, liberalization concurred with innovations enabling cable networks to rapidly expand their services. In just two decades, two independent network-giants have emerged: KPN and ZiggoVodafone. Equally large in size, they together serve 80-90% of the Dutch market for fixed internet access, television and wired telephony (ACM (2017)). In terms of regulation, only one of them is required to open up its network for new entrants. As of January 2018, the Dutch situation in the market for telecommunication is being assessed by both the ACM (Autoriteit Consument en Markt) and the EC (European Commission). Together with Dutch stakeholders, they analyze what regu-latory policy would best suit the Dutch situation in terms of welfare. This paper asks itself the exact same question. Absent any data on prices, in-frastructure and costs, we use a Hotelling line model to analyze the effects on welfare in a scenario without entry versus scenarios where an entrant is accommodated by one or both networks. For each scenario, the process of accommodation is allowed to be repeated to derive the long-term equilibrium outcome. We interpret the results and draw five main lessons to be taken into account in constructing the optimal regulatory policy for the Dutch telco sector.

Our model follows the framework of Laffont et al. (1997 and 1998), Arm-strong (1998) and Carter and Wright (1999 and 2003) to describe competition in network industries. Whereas the aforementioned models all contain two players: either two incumbent networks competing directly (using two-way access) or one incumbent network competing with one entrant (using one-way access), our model contributes to the existing literature by allowing compe-tition between three players: two independent networks versus one entrant (using one-way access). We find that if we introduce entry in a benchmark scenario where two networks compete directly, the optimal outcome in terms

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of welfare is a scenario in which the entrant is accommodated in a simul-taneous negotiation on the terms of access. If the process is allowed to be repeated to infinity, the optimal long-term equilibrium is found when two firms offer access to the entrant. In the following section, the context and relevant market are defined by analyzing the history and status quo of the Dutch sector for telecommunication. Section 3 provides a summary and anal-ysis of economic theory and models on the topics of access price regulation, interconnection and network competition. In section 4, we build on existing models and construct a Hotelling line on which two incumbent networks are permanently located. The benchmark scenario analyzes a scenario without entry, followed by two scenarios in which the entrant is accommodated first by one and then by both networks. The results are interpreted and discussed in section 5. In section 6, the limitations of our model are summarized to-gether with further recommendation for economic research.

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2 The Duth Market for Telecommunication

The Dutch market for telecommunication (telco) has developed rapidly in the past two decades. Before analyzing the economic literature relevant for our study, it is useful to provide some context by analyzing the background of the Dutch telco sector.

2.1 History

In 1881, the first Nederlandsche Bell Telephoon Maatschappy (centre for telecommunication) was opened in Amsterdam. During the 20th century, the Dutch market started to develop rapidly. The state owned company PTT (the company for Post, Telegraphs and Telephones) invested in an ex-tensive network of cables and wires, up to the point that the Netherlands became ”one of the most densely ’wired’ countries in Europe” (Tempelman

(1997)). In 1989, the Dutch government decided it was time to erode the the position of incumbent PTT and liberalize the market for telecom. By 1996. the privatized version of PTT (known as KPN) became publicly owned. Meanwhile, the government had started issuing new (national) telecommuni-cation licenses for KPN and its competitors Telfort (a joint venture between the Dutch railway networks and British Telecom) and Enertel (an alliance of Dutch energy- and cable-companies)(van Nieuwstadt (1997)). Following the liberalization of network-industries all across Europe, technological in-ventions like internet and wireless telephones started to reshape the market for telecommunication. van Marrewijk(1997) described the Dutch telco mar-ket as a sector consisting of ”all telecom organizations that offer speech and data carrier services”. In this paper, we restrict the relevant market for telecommunication to only consist of speech and data carrier services pro-vided through cables and wires (copper, fibre and COAX). Examples include but are not limited to: fixed internet connection, television (all except satel-lite) and fixed telephone connection.

2.2 Regulation

To keep regulatory oversight of the vast developments in the first days of telco liberalization, the regulatory authority OPTA (Onafhankelijke Post en Telecommunicatie Autoriteit) was established in 1997. Situated in the de-partment of economics, its main focus was to ensure telco-industry

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compli-ance with Dutch law and protect the privacy of Dutch consumers (van de Coevering and van der Werff (2001)). In 2013, the OPTA was merged with two other independent regulatory agencies to form the Dutch regulatory au-thority ACM. Up to this day, the ACM has been in charge of monitoring and regulating the Dutch telco industry.

Before we analyze the regulatory developments of the past decade, it is important to focus on the market for television. During the privatization of KPN, the market for television was independent and not related to any telco service. Whereas KPN and its adversaries had their core business in providing communication services through its cable network, the market for television provided consumers a television connection using the (COAX) ca-ble for fixed access and satellites for wireless access. Whereas there had been one provider of cable television (Casema) in the Netherlands since 1970, several new companies like Multikabel, @Home and UPC (a joint venture between Philips and American United Holdings) entered the cable television industry during the 1990s and started to build their own cable infrastruc-ture. In 2008, after two decades of bankruptcies, mergers and take-overs, two cable-networks for television remained in the Dutch market: UPC and Ziggo (Kool, Maris, de Munck, and Huveneers (2010)).

Through constant innovation on their cable network, UPC and Ziggo started to provide their customers with internet connections (Arnbak and Lemstra (2006)). As of 2008, fixed internet connection was provided either through the network of KPN (made of copper and optic fibre) or through the COAX-network of UPC and Ziggo. The once separated markets for televi-sion and telecommunication services had become related. Further technolog-ical developments on both network infrastructures allowed the two markets to unify in a market for fixed internet, fixed television and fixed telephone services. Although there are several service providers, there are only three companies that own the infrastructure: KPN’s network of copper and optic fibre versus UPC and Ziggo’s network of COAX. Apart from the different cables, there is one other crucial feature that distinguishes KPN from its competitors UPC and Ziggo: KPN is regulated by the ACM and required to open up its network for new entrants. The following developments have happened since:

• 2012

Several telecommunication providers (KPN, Tele2 and YouCa) accuse the regulatory authority of deliberately not regulating the COAX-cable

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duopoly UPC and Ziggo. The Commission of Appeal rules in favour of the regulatory authority, stating it cannot be accused for measures it did not take (CollegeVanBeroep(2012)).

• 2014

Liberty Global (owner of UPC) acquires Ziggo, a take-over that re-sults in a market share of 90% in the market for cable television. The European Commission allows the takeover but states it entails “po-tential risk for the Dutch television sector” (ANP (2014)). The ACM present a report that states it is too complex and costly to regulate the COAX-network. The report refers to EU-guidelines that stipulate it is not allowed to regulate two companies within one market. Only one company per industry can be subject to regulation. In response, KPN requests a definition of the relevant market.

• 2015

Following the 2014 decision, ACM defines the relevant market for telco-regulation as the national market for unbundled access to the networks of copper and fibre, leaving the COAX-network out of regulatory scope (Woudt (2014)).

• 2016

Ziggo and Vodafone announce a merger. In august, the merger is ap-proved by the EC on the condition that Vodafone divests its services for fixed Internet and fixed telephone (Commission(2016)). These services had been offered using KPN’s network. T-Mobile takes over the Voda-fone business parts. ACM re-evaluates the industry and concludes that, although complex, it is possible to access-regulate the COAX-network of ZiggoVodafone. ACM announces the relevant market for regulation now includes the COAX-network.

• 2017

The European High Court reconsiders the 2014 judgment by the EC on the takeover of Ziggo by Liberty Global. It concludes that the takeover allowed for an unfair, dominant position in the Dutch television market (Stibbe (2017)).

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Following the high court’s decision, Liberty Global requests the EC to re-approve the takeover of Ziggo with remedies. In February 2018, the ACM proposed to regulate both KPN and ZiggoVodafone in opening up their network for entrant (ACM (2018)). The telco-industry can respond to ACM’s proposal until May. The EC will give its verdict on the proposal in the summer of 2018.

2.3 Status quo and future developments

KPN and ZiggoVodafone have both responded to the proposal of the ACM. According to ZiggoVodafone, the market for telecommunication is already competitive enough. Further regulation will hinder investments that are necessary for the Dutch telco sector to sustain its innovative edge. KPN, in turn, has proposed an alternative plan for industry-regulation. According to KPN, the new regulation proposed by ACM will lead to uncertainty in the telco-sector which hinders investments. The EC has not officially responded to the request of ACM yet. On the 24th of May, a Dutch newspaper (Finan-cieel Dagblad) reported the first rumours that the EC will honour ACM’s request. Regulation of the European telco sector is currently a topic of a heated debate in Brussels. According to Segenhoudt (2018), the EC will propose new regulatory guidelines for telco-industries in the fall of 2018. If the EC indeed approves the proposal, ZiggoVodafone is given three months to establish a wholesale-department and negotiate fixed rates with competitors. If the agreements are in place, ZiggoVodafone becomes officially regulated. The new regulation is expected to be adopted and implemented by the be-ginning of 2020.

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3 Economic Theory

This section provides the economic context for competition and regulation in network industries. Railways, electricity and telecommunication are all ex-amples of network industries. Network industries are characterized by high sunk costs in infrastructure like rail tracks, power plants and cable networks that are not easily replicated by new entrants. Liberalizing network indus-tries is a complex and difficult task. In 1996,Klein (1996) wrote a policy paper on competition in network industries in which he described the end of the twentieth century as the time in which ”a wave of privatization is sweeping the globe”. Network industries are privatized as well. In 1982, England decides to liberalize its natural gas industry and Chile’s opens up its telco sector for competition. In 1996, California follows suit and liber-alizes its electricity sector. Liberalizing a network industry can be complex process that can have far-reaching consequences (illustrated by the Calfiror-nia electricity crisis in 2001). Armstrong and Sappington (2006) introduce two simple models to describe the trade-off for society between a regulated monopoly and unregulated duopoly. In case costs are correlated and demand is inelastic, unregulated duopoly outperforms regulated monopoly in terms of total welfare.

Since network industries are characterized by complex network infras-tructures with high sunk costs, liberalization policies focus on providing en-trants access to the existing networks while accounting for the investments in (and the maintenance of) the network incurred by the incumbent (Helm and Jenkinson (1998)). Apart from the high investments, network industries like telecommunication and electricity have an additional feature in that they both depend on physical connection. In the case of electricity: there exists a power-plant that generates high power electricity, a network of wires and cables that transports this electricity over land and a distribution centre that transforms the high power electricity to a level where it can be transported into households in a particular neighborhood. For a consumer to be able to turn on the lights, it needs to be connected to the electricity grid. In the case of telecommunication, it works in a similar way. When you call someone using your land-line, there is a cable (COAX, copper or optic fibre) that connects your phone to a local distribution centre. This centre con-nects your call to a national or international network that is connected to the telephone of the person you want to reach. For both industries, if you are not connected to the network, you cannot enjoy any service. As

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Arm-strong (2001) explains in his theory on access pricing, connection can occur in two different ways. During the early liberalization of network industries, competition often occurred in the form of international incumbent A offering services to customers of national incumbent B (and vice versa). In order to provide a service, incumbent A needs to be able to connect its customers to the network of incumbent B and incumbent B needs access to the network of A. This is called two-way access. However, as liberalization progressed, com-petition slowly started to occur in the form of a new firm A (with or without its own network) offering services for customers that are connected to the network of incumbent B. In this scenario, firm A requires one-way access in order to deliver a service. A common example of this one-way practice are local retail sellers that are individually connected to one wholesale network. To stimulate competition within the telco-industry, interconnection between monopolized parts and competitive parts of the sector is key. To organize interconnection, both two-way or one-way, someone has to set the terms for connection. Those terms for interconnection have been the subject of exten-sive economic analysis. The first economists to provide a (famous) article on competition through interconnection were Laffont and Tirole (1996). As they explain, there were two different regulatory policies for interconnection occurring during the 90s:

• Cost-based access charge: Potential entrants made (and still make) a strong case for getting access to network at marginal costs. Australia followed this approach in its regulation of the telco-sector. However, critics claim cost-based access charge restricts incumbents from recov-ering their investments on the network.

• Long-run incremental cost + markup: To allow incumbents to recover their fixed cost of the network, regulators have opted for an alternative where entrants are charged some reflection of long-run incremental costs plus a markup. What the markup should reflect is topic of intense debate. Some economists claim it should account for allocation of the access deficit whereas others claim the markup should be related to the use of the network and therefore be linked to demand considerations. Economists have proposed several methods for long-run incremental cost that allow for a mark up. The most famous one is the Efficient Component Pric-ing Rule (ECPR) which consists of an access charge that is ”equal to the difference between the telephone operator’s price and marginal cost on the

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competitive segment” (Laffont and Tirole (1996)). If costs are known, the ECPR allows the incumbent to recover its investment on the network and the entrant to pay a fair access charge. As Laffont, Rey, and Tirole (1997) analyzed, the optimal regulatory policy depends on how prices are set. In their assessment, they investigate whether freely negotiated access charges between two incumbent networks outperform charges set by a regulator. In case the negotiated access prices work reciprocally, both incumbents have an incentive to ’strike a fair deal’ which, in turn, provides customers with a fair retail price. When access charge are set non-cooperatively, both networks have an incentive to raise access charges to the point where retail prices re-flect monopolistic outcomes due to a double marginalization problem. If a regulator introduces a price ceiling for the access charge, society only bene-fits if both access charges and retail prices are set simultaneously. If access charge are determined before the retail prices are set, both networks use the access charge to reflect a monopoly markup to sustain high retail prices. This conclusion is reinforced by Armstrong (1998), who argues that a reg-ulator should at least have a monitoring rule in order to achieve a socially desirable outcome. In 1998, Laffont, Rey, and Tirole (1998) extend their previous work by introducing a model where two incumbent networks locate on the extreme ends of a Hotelling line and compete a la Bertrand. In this famous article in the Rand Journal of Economics, they investigate the effect on welfare for different (two-way) access pricing policies (among which; the Ramsey benchmark, reciprocal access pricing, non-reciprocal access pricing and ECPR).

Carter and Wright(1999) andCarter and Wright(2003) extend the model ofLaffont et al.(1998) by allowing the two networks to be asymmetric. They reinforce the conclusion of Armstrong(1998) and find that in a deregulated economy, two (incumbent) networks that are asymmetric also have an in-centive to use the two-way access charge as an instrument for collusion and that the level of this access charge is related to the level of symmetry. Peitz

(2003), in turn, also analyzes asymmetric markets, but departs from the typical two-network approach and assumes there is one incumbent network that competes with a new entrant (still on a Hotelling line). For this set-up, welfare is maximized if the entrant is charged an access price that includes a markup over cost-based access pricing. In a later paper, Peitz (2005) an-alyzes competition between a strong and a weak network, simulating the European regulatory guidelines in telco industries. He argues that an asym-metric access charge that is higher for the entrant’s network and lower for the

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incumbent’s network optimizes consumer surplus but lowers general welfare. The majority of the literature on network competition and access charge regulation describes two entities that compete. Either two networks that require two-way access or one new entrant that requires access to one incum-bent. Although the models present valuable insight in promoting competition and regulating the access charge so that welfare is maximized, the above pa-pers do not provide any insights regarding the Dutch situation. There is no model or paper that allows two, independent, incumbent networks opposing one or more entrants. This is understandable in the sense that the process of liberalization in networks industries focused on dismantling the power of a former state-owned incumbent while empowering new entrants to invest and establish a network of themselves. In the Netherlands, labeled the most densely wired country in Europe, innovations to both COAX and copper-networks have (quite suddenly) allowed two incumbent copper-networks to become direct competitors in the industry for internet, television and telephone con-nection. Regulatory guidelines lag behind and only allow one of the two networks to be regulated in opening up its network for entrants. In the next section, the incentives of two networks in the accommodation of an entrant and the effect this accommodation has on welfare is modelled. We follow the framework that was first introduced by Laffont et al.(1998) and further extended by Armstrong (1998) and Carter and Wright(1999) and extend it by introducing an extra player to the game.

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4 Model

Our model follows the framework of a hotelling line where two firms (or networks) are located at the extreme ends of the [0,1] interval and compete a la Bertrand. Both networks are independent and have full coverage of the market. Costs are identical and equal zero. All products are provided through the network of firm 1 or 2. The networks are independent in the sense that they do not need access to the other network to provide a service. If entry occurs, one entrant enters the Hotelling line between network 1 and 2. The entrant does not possess its own network and needs access to either network 1 or network 2 to be able to compete. The entrant acquires access by paying a one-way access charge to one of the two networks. Consumers are of unit mass and uniformly distributed on the [0,1] interval. All consumers consume one product, there is no exclusion. In the following section, a benchmark scenario is introduced without entry. In section 4.2 and 4.3, entry occurs by either one or both networks accommodating the entrant on their network.

4.1 Benchmark scenario

In this scenario, firm 1 and 2 are located on the extreme ends of the hotelling line and compete a la Bertrand. There is no entry. Consumers enjoy indirect utility:

U = r − t(li− x) − Pi (1)

Where i = 1,2 and r is exogenous utility that is sufficiently large, t is the travel cost consumers pay when traveling to a network located at li. Without

entry, network 1 and network 2 compete directly for all consumers. There is an indifferent consumer x for whom:

r − t(x) − P1 = r − t(1 − x) − P2

Which gives demand for product i : Qi(Pi, Pj) =

1 2 +

(Pj − Pi)

2t (2)

Profit for firm i is:

πi = (Pi) 1 2 + (Pj − Pi) 2t

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And its best response function: Pi =

1

2(Pj + t)

Equilibrium price, quantity and profit for firm i can be expressed as:

Pi = Pj = t (3) Qi = 1 2 (4) πi = 1 2t (5)

In order to assess the level of welfare, we assume welfare to be the sum of producer surplus and consumer surplus:

W = P S + CS

Producer surplus equals the sum of all profits. Consumer surplus represents the utility received by consumers. Utility depends on exogenous utility r minus the travel cost and price. The travel cost differ per consumer. In the benchmark scenario, the consumer that is located at l = 0 pays P1 = t for

the service of network 1. On the other end of the interval, the consumer located at l = 1 pays P2 = t for the service of network 2. The indifferent

consumer, located at l = 0.5, has to travel to either one of the networks and pays travel costs of (0.5t) plus price (t ) for either one of the networks.1

Consumer surplus is exogenous utility r minus the sum of all travel costs and prices. If we assume r = 2t, consumer surplus for the benchmark scenario equals: CSbenchmark = 2t − t +1 2 ∗ 0.5t = 0.75t Producer surplus in the benchmark scenario is:

P S = 0.5t + 0.5t = t

Total welfare for the benchmark scenario without entry equals:

Wbenchmark= P S + CS = t + 0.75t = 1.75t (6)

1_{In appendix A, a graphical analysis for calculating the sum of all travel costs and} prices provided

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For the remainder of this section, we are interested in what way accommo-dation of an entrant affects welfare. Therefore, absolute changes in producer and consumer surplus are reported for the two scenarios where entry is ac-commodated compared to the benchmark scenario without entry. The level of r is picked arbitrarily and can be any other number as long as the condi-tion that it is sufficiently large for all consumers to consume is satisfied. For the remainder of this section we assume r = 2t.

4.2 Entry accommodated by network 1

We now introduce an entrant to the benchmark model described above. Net-work 1 and 2 are still located at the extreme ends of the hotelling line. Since the entrant has no network in place, it needs access to either network 1 or network 2 to be able to compete. To acquire access, the entrant pays a (one-way) access charge a. The entrant strives to maximize profits and picks it location accordingly. The location of the entrant is denoted l and lays somewhere between firm 1 and 2 on the [0,1] interval. After the entrant has located, all three firms compete a la Bertrand. In summary, the following three stage game is played:

1. Network 1 sets access charge a

2. Entrant observes access charge a and picks its location l 3. Firms set retail prices and compete a la Bertrand

4.2.1 Quantities, profits and best response functions

Using backward induction, we start in stage 3. The entrant is located between firm 1 and 2 on the [0,1] interval. For some location l, there is an indifferent consumer (y) between network 1 and the entrant for which:

r − t(y) − P1 = r − t(l − y) − Pe or: y = Pe− P1 2t + 1 2l

On the other side, there is an indifferent consumer (z) between the entrant and network 2 for which:

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or:

z = P2− Pe

2t +

1

2(1 + le) Demand for the three firms:

Q1 = y = Pe− P1 2t + 1 2l Q2 = 1 − z = Pe− P2 2t + 1 2(1 − l) Qe = z − y = P2− 2Pe+ P1 2t + 1 2

Network 1 accommodates the entrant and is called the ”accommodating network”. Network 1 enjoys retail profit (P1∗ Q1) through selling to its

customers and wholesale profit (a ∗ Qe) through selling its network to the

entrant. The ”not-accommodating network” (network 2) only enjoys retail profits (P2∗ Q2). The entrant’s profit and best response function are given

by:

πe = (Pe− a)Qe

Pe =

1

4[P2+ P1+ t + 2a] For the accommodating network, firm 1, this is:

π₁acc= P1∗ Q1+ a ∗ Qe

P₁acc= 1

2[Pe+ t ∗ l + a] And for the not-accommodating network, firm 2:

πnot₂ = P2∗ Q2

P₂not = 1

2[Pe+ t(1 − l)] Prices as a function of access charge and location are:

Pe = 1 2t + 5 6a (7) P₁acc = 1 4t + 1 2tl + 11 12a (8) P₂not = 3 4t − 1 2tl + 5 12a (9)

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Quantities expressed in terms of a and l : Qe = 1 2 − a 6t (10) Qacc₁ = 1 8+ l 4− a 24t (11) Qnot₂ = 3 8 − l 4 + 5a 24t (12)

Which allows us to write profits in terms of a and l : πe = t 4 1 − a 3t 2 (13) πacc₁ = t(l + 1 2) 2 + 11a 12 1 8 + l 4 − a 24t + a 1 2 − a 6t (14) π₂not = t( 3 2 − l 2 + 5a 12 3 8− l 4 + 5a 24t (15)

As can be seen in equation (13), the entrant’s profit does not depend on its locations once the access charge is known. Furthermore, the profit of the entrant decreases as a increases whenever a < 3t, given that:

∂πe ∂a = 1 6 a 3t − 1

As we will see in the remainder of this section, a < 3t always holds for an optimally-set a. In order to maximize its profits, the entrant will want to locate in a place where a is as small as possible. Now suppose the accom-modating network, network 1, can set both the entrant’s location and the access charge. (Given that the entrant does not care about the location, but only about the access charge, this assumption seems reasonable.) Network 1 will do so to maximize profits:

∂π1 ∂a1 = 1 24 29 2 + 5l − 59 6 a t = 0 or: amax₁ = 6t 59 29 2 + 5l ≤ 39 59∗ 3t < 3t (16)

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and: ∂π1 ∂l = t 24 1 2+ l > 0

The profit of firm 1 is strictly increasing in l. The accommodating network would prefer the entrant to locate as far away as possible. It would also charge the entrant more if it was located farther away.2 The entrant only cares about a being minimized in order to maximize its profits. As a result, there is a tension between the entrant’s location decision and the network’s access price. To better understand this tension, we first analyze the scenario where the three stage game is followed step by step. In the second scenario, we allow step 1 and 2 to become a simultaneous negotiation.

4.2.2 Scenario I - Strict timing of the game

If we follow the strict timing of the game, the access charge is set before the entrant picks its location and the firms compete a la Bertrand. In determining its access charge in stage 1, the best network 1 can do is to set the profit maximizing access charge. Since this access charge depends on the location, network 1 will present it as a package deal: for any location l the entrant picks, the access charge will be as described in equation (16). Based on the profit maximizing access charge, profits as a function of l are:3

π₁acc = t 6962(1239l 2 _{+ 3009l + 3318.75)} π₂not = t 13924(12960.5 − 5474l + 578l 2₎ πe = t 6962(50l 2_{− 300l + 450)}

In the second stage of the game, the profits of the three firms are determined by the location picked by the entrant. In the third stage of the game, all three firms set retail prices. Table 1 on the following page shows the access

2 _{Substituting back into the entrant’s profit function, we get Q}

e=₅₉5(3 − l), meaning that the entrant will sell positive quantities for any location between 0 and 1 (in which the type of retail pricing equilibrium we are assuming holds).

3 _{In appendix B, prices and quantities are adjusted for the profit maximizing access} charge

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Location of the entrant 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 amax 1 1.47 1.53 1.58 1.63 1.68 1.73 1.78 1.83 1.88 1.93 1.98 Profits acc. 0.48 0.52 0.57 0.62 0.68 0.74 0.80 0.87 0.94 1.01 1.09 not 0.93 0.89 0.85 0.82 0.78 0.74 0.71 0.68 0.64 0.61 0.58 ent. 0.06 0.06 0.06 0.05 0.05 0.04 0.04 0.04 0.03 0.03 0.03 Prices acc. 1.60 1.70 1.79 1.89 1.99 2.08 2.18 2.28 2.37 2.47 2.57 not 1.36 1.34 1.31 1.28 1.25 1.22 1.19 1.16 1.13 1.11 1.08 ent. 1.73 1.77 1.81 1.86 1.90 1.94 1.98 2.03 2.07 2.11 2.15

Table 1: Profit and prices (in t) for different locations of the entrant charge, the profits and the retail prices for the accommodating firm, the not-accommodating firm and the entrant for different locations of the entrant on the [0,1] interval. As determined above, the closer the entrant locates to network 1, the higher its profits. However, not all locations will yield positive profits for the entrant. To illustrate how, suppose the entrant locates at l = 0. Based on this location, the retail price of the entrant would be 1.73t whereas the price of firm 1 would be 1.60t. The consumer located at 0 would prefer buying at firm 1 instead of buying at the entrant. We know that if the consumer that is located at the exact location of the entrant prefers firm 1 over the entrant, all other consumers of the entrant will do so too. It appears that for l = 0, the entrant does not enjoy any profits. To find out for what location the entrant enjoys profits, we have to find the location of the entrant for which the consumer located at the entrant is indifferent between buying at the entrant and traveling to and buying from network 1:

Pe = P1+ tl 204t 118 + 25tl 59 = 189t 118 + 57tl 59 + tl l ≈ 0.08

For any location between 0 and 0.08, the consumers of the entrant prefer to go to firm 1 instead of the entrant. For any l ≥ 0.08, consumers of the entrant prefer to buy at the entrant instead of traveling to firm 1. If the entrant foresees this, he will locate at l ≥ 0, 08. At the other side, between

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the entrant and firm 2, a similar boundary exists. Suppose the entrant locates at 0.7. In the third stage of the game, firm 2 sets a retail price of 1.16t. The consumer that is located at the location of the entrant has a choice, it could go to the entrant and pay 2.03t, or it could travel to firm 2 and pay:

travelcosts + P2 = 0.30t + 1.16t = 1.46t

Clearly, the consumer located at the location of the entrant would prefer to go to network 2 in order to maximize its utility. The consumer located at the location of the entrant is indifferent between buying at the entrant and buying at network 2 when:

Pe = P2+ t(1 − l) or: 204t 118 + 25tl 59 = 161t 118 − 17tl 59 + t(1 − l) l ≈ 0.37

For any location between 0.37 and 1, all consumers of the entrant prefer buying at network 2 over buying at the entrant. The reason this boundary lays on the side of network 1 on the hotelling line is explained by the fact that network 2 only enjoys retail profit. Absent any additional revenue from wholesale sales to the entrant, it sets a retail price to maximize retail prof-its. Its only competitor is the entrant, whose marginal cost depends on the access charge set by network 1. Having a lower marginal cost than its di-rect competitor, network 2 sets a retail price that ’steals away’ the entrant’s customers, up to the point where the travel costs are such that consumers are indifferent between network 2 and the entrant. Entry by the entrant is only sustained if the entrant can actually sell its service to consumers. The boundaries for entry are:

0.08 ≤ l ≤ 0.37

Within these boundaries, the entrant maximizes profits by choosing a loca-tion close to network 1. Consequently, the equilibrium outcome of the three stage game is the entrant locating at 0.08. Prices and profits are:

Prices Profits Network 1 1.68t 0.51t Network 2 1.34t 0.90t

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Compared to the benchmark scenario, accommodation of the entrant leads to an increased level of prices. In terms of profit, there is a very small increase in the profits for network 1 and a significant increase in profits for network 2. Welfare for this scenario is:

W_network1strict = 1.44t + 0.27t = 1.71t (17)

The accommodation of the entrant by network 1 benefits the firms and hurts the consumer:

∆P S = +0.44t ∆CS = −0.48t

In general, welfare has slightly decreased. If only one network accommodates the entrant and the timing of the game is strictly followed, entry leads to higher profits for both networks and decreased utility for consumers. Al-though an extra firm decreases the average travel cost per consumer, the increased prices offset the reduction in travel costs.

Before we turn to the scenario where step 1 and 2 of the three stage game is a simultaneous negotiation, we assess the stability of the equilibrium described above. In setting up the three stage game, the terms for accommodation were assumed to be set once and for all. In reality however, the terms of accommo-dation are (the access charge and the entrant’s location) are negotiated for a predetermined amount of time. Without going into too much detail about the explicit duration of these contracts and the frequency of renegotiation, we are interested in the equilibrium outcome if the process of accommoda-tion is allowed to be repeated. As we have seen, firms set retail prices in the third stage of the game based on the location of the entrant. If the contract for accommodation is known to last for a predetermined period of time, the networks have an incentive to deviate on their promised retail price in order to increase profits for that predetermined period. To illustrate: suppose the entrant locates at 0.1. The access charge set by firm 1 equals 1.53t and prices are P1 = 1.70t, P2 = 1.34t and Pe = 1.77t. The consumer that is located

at 0.1 buys from the entrant for a price of Pe = 1.77t. For every consumer

that pays this price, the entrant has to pay 1.53t to the accommodating network. This is the wholesale profit for network 1. Now if the consumer that is located at 0.1 decides to go the accommodating network instead, it would pay: P1 + travelcosts = 1.70t + 0.10t = 1.80t, which is not a very

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consumer located at 0.1 would pay the same price when traveling to firm 1 as it would when buying at the entrant. Now if the contract for access is set for a predetermined period, network 1 knows it can increase its profits for that period by deviating from its promised retail price in step 3 of the game. By setting a lower retail price, it could persuade all consumers of the entrant to buy from firm 1 instead of the entrant. Network 1 would turns its wholesale profit (selling through the entrant) into retail profit (selling to the consumers directly). This strategy has a cost though, since the price decrease to persuade consumers of the entrant also decreases the initial retail profits of network 1’s own consumers. To analyze for what locations of the entrant this strategy is profitable, it has to be that:

(Pe− tl)(Q1+ Qe) ≥ π1acc t 6962(3825 + 459l + 578l 2_{) ≥} t 6962(1239l 2_{+ 3009l + 3318.75)} l ≤ 0.18

If the entrant locates at l ≤ 0.18, firm 1 can increase its profits by under-cutting the entrant. For all locations between 0.18 and 1, firm 1 is better off accommodating the entrant and earning profits via wholesale access. On the other end of the line, network 2 might find it profitable to undercut the en-trant too. As we have seen, firm 2 already steals all consumers of the enen-trant if the entrant locates anywhere between 0.37 and 1. If the entrant locates at 0 < l < 0.37 and firm 2 knows the contract is set for a predetermined period of time, it can increase its profits during that period by deviating on its retail price and undercutting the entrant. This is profitable if:

(Pe− t(1 − l))(Q2+ Qe) ≥ π2not t 13924(9503 + 16242l − 4536l 2 ) ≥ t 13924(12960.5 − 5474l + 578l 2 ) l ≥ 0.16

So for l ≤ 0.18, network 1 undercuts and for l ≥ 0.16, network 2 undercuts the entrant. We have determined that if the terms for access are set for a predetermined period of time, there is always4 _{one network with an}

incen-tive to deviate from their retail price and increase their profits during the contract-period. If we allow the game to be repeated until infinity, there is no long term equilibrium outcome in which the entrant is accommodated by network 1 following the strict timing of the game.

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4.2.3 Scenario II - Simultaneous negotiation of a and l

Instead of following the strict timing of the game, it makes more sense to think of the process of determining the access charge and the location of the entrant as a simultaneous negotiation between the entrant and the accom-modating network. As described before, the accomaccom-modating firm wants to increase both a and l while the entrant wants to decrease a and does not care about l. Since there are joint (but not mutual) gains from the entrant being far from network 1, network 1 would want to ’bribe’ the entrant to locate far away. If side payments are possible, in the form of firm 1 setting a unit access charge a in combination with a fixed payment A that can be negative, then it makes sense to assume network 1 and the entrant negotiate to maximize their joint profits and divide them between them using the fixed payment A. Put differently:

∂π1+ πe ∂a1 = 1 24 21 2 + 5l − 51a 6t = 0 or: ajoint₁ = 6t 51 21 2 + 5l ≤ 62 102 ∗ 3t < 3t

Based on the joint-profit maximizing access charge, profits described in equa-tion (13)-(15) can be written in terms of l :

π₁acc= t 5202 919l 2_{+ 2289l + 2418.75} π₂not = t 5202 4160.25 − 1677l + 169l 2 πe = t 2601 225 − 150l + 25l 2

In the third stage of the game, all firms set retail prices. Table 2 on the next page shows the access charge, profits and retail prices for the three firms for different locations of the entrant. The profits of the entrant have increased significantly compared to the scenario where firm 1 charges the profit maximizing access charge. Following the same procedure as in scenario I, we calculate for what boundaries the entrant does not loose its customers to either network 1 or network 2. Due to the fact that step 1 and 2 are

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Location of the entrant 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 ajoint₁ 1.24 1.29 1.35 1.45 1.47 1.53 1.59 1.65 1.71 1.77 1.82 Profits acc. 0.46 0.51 0.56 0.65 0.67 0.73 0.79 0.86 0.93 1.00 1.08 not 0.80 0.77 0.74 0.68 0.68 0.65 0.62 0.59 0.56 0.54 0.51 ent. 0.09 0.08 0.08 0.07 0.06 0.06 0.06 0.05 0.05 0.04 0.04 Prices acc. 1.38 1.49 1.59 1.73 1.80 1.90 2.01 2.11 2.21 2.32 2.42 not 1.26 1.24 1.21 1.21 1.16 1.14 1.11 1.09 1.06 1.04 1.01 ent. 1.53 1.58 1.63 1.71 1.73 1.77 1.82 1.87 1.92 1.97 2.02

Table 2: Profits and prices (in t) for ajoint₁

allowed to be a simultaneous negotiation, the boundaries for which entry is accommodated have widened:

0.09 ≤ l ≤ 0.42

To illustrate that both network 1 and the entrant enjoy at least as much profits as in scenario ¨I, suppose the entrant locates within the boundaries at l = 0.1, if network 1 sets ajoint= 1.29t and A = 0.02t, profits are:

π1 = 0.51t + 0.02t = 0.53t > πscenario11

πe = 0.08t − 0.02t = 0.06t ≥ πscenario12

The profits of network 2 decrease:

π2 = 0.77t < πscenario12

If we turn back to the tension between a and l as described before, network 1 can now use the fixed fee A to ’bribe’ the entrant to locate far away. At l = 0.09, the entrant earns 0.081t. To be indifferent about its location, it has to earn at least this profit. Now suppose the entrant locates at 0.42 and network 1 sets ajoint = 1.48t. The profit of the entrant is πe = 0.064t. If

network 1 sets a negative fixed fee of A1 = −0.017t, the entrant is indifferent

between locating close or far away from network 1. Network 1 enjoys a higher profit for l = 0.42:

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π1 = 0.681t − 0.017t = 0.664t

If the network 1 and the entrant can negotiate about a and l and side pay-ments are possible through fixed fee A, the entrant will locate at l = 0.42 for a = 1.48t and A = −0.017t. Prices and profits in this scenario equal:

Prices Profits Network 1 1.82t 0.66t Network 2 1.16t 0.67t

Entrant 1.74t 0.08t

Compared to the benchmark scenario, prices increase. In terms of profit, there is a about a small increase in the profits of network 1 and 2. Welfare for this scenario is:

W_network1negotiation= 1.41t + 0.69t = 2.10t (18)

If the access charge and location are determined in a simultaneous negotia-tion, accommodation of the entrant increases producer surplus and slightly decreases consumer surplus compared to the benchmark scenario without entry:

∆P S = +0.41t ∆CS = −0.06t

In general, welfare increases. The entrant locates close to the middle, de-creasing average travel costs. This benefit is slightly offset by the increased overall price level.

Again, we are interested what happens if we assume the contract for accom-modation to be negotiated for a predetermined period of time. Network 1 has an incentive to deviate on its promised retail price if:

(Pe− tl)(Q1+ Qe) ≥ π1acc

l ≤ 0.20

Vice versa, network 2 has an incentive to undercut the retail price of the entrant if:

(Pe− t(1 − l))(Q2+ Qe) ≥ π2not

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Contrary to the scenario where the timing of the game is strict, there is a position of the entrant: 0.20 < l < 0.22 for which neither network 1 or network 2 have an incentive to undercut the retail price. If we allow the the terms for accommodation to be set repeatedly, the long-term equilibrium scenario described above is stable. Welfare in this case (l = 0.21) equals:

W_network1negotiation−longterm= 1.49t + 0.28t = 1.77t (19)

In the long term, the entrant locates closer to firm 1. Average travel costs per consumer decrease compared to the benchmark scenario, but not as much as the scenario where l = 0.42. The overall price level is increased, leading to an increase in producer surplus and decrease in consumer surplus. The overall level of welfare is roughly the same as in the benchmark scenario.

∆P S = +0.49t ∆CS = −0.47t

4.3 Entry accommodated by both networks

In the previous subsection, only network 1 was accommodating the entrant. In this subsection, both networks can offer access to the entrant. The three stage game is essentially the same, although now, in stage 1, both network 1 and network 2 simultaneously set an access charge. Again, we compare a scenario where the timing of the three stage game is strict against a scenario where we allow for a simultaneous negotiation about a and l and the use of side payments.

4.3.1 Quantities, profits and best response functions

Previously, the prices, quantities and profits for network 1 accommodating the entrant were calculated. If network 2 accommodates the entrant, equa-tion (7)-(9) are rewritten to:

Pe = 1 2t + 5 6a (20) P₁not = 3 4t − 1 2t(1 − l) + 5 12a (21) P₂acc= 1 4t + 1 2t(1 − l) + 11 12a (22)

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Quantities in terms of access charge and location become: Qe = 1 2 − a 6t (23) Qnot₁ = 1 8 + l 4 + 5a 24t (24) Qacc₂ = 3 8 − l 4− a 24t (25)

And profits in terms of a and l : πe = t 4 1 − a 3t 2 (26) π₁not = t( 1 2 + l) 2 + 5a 12 1 8 + l 4 + 5a 24t (27) π₂acc= t( 3 2 − l) 2 + 11a 12 3 8 − l 4− a 24t + a 1 2− a 6t (28)

4.3.2 Scenario I - Strict timing of the game

If the timing of the game is strict, the best firm 1 and 2 can do is to set the profit maximizing access charge in the first stage of the game. Since the location of the entrant is yet unknown, the access charge is set in terms of l. For network 1, the profit maximizing access charge is described in equation (16). Network 2 maximizes profits with respect to a:

∂π2 ∂a = 1 24 39 2 + 5l − 59 6 a t = 0 or: amax₂ = 6t 59 39 2 + 5l ≤ 49 59∗ 3t < 3t (29)

If network 2 accommodates the entrant for the profit maximizing access charge described in (29), profits are:

π₁not = t 6962(289l 2_{+ 2159l + 4032.25)} π₂acc = t 13924(15133.5 − 10974l + 2478l 2 )

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πe =

t 6962(50l

2_{− 300l + 450)}

In the second stage of the game, the profits of the three firms are determined by the location picked by the entrant. In the third stage of the game, all three firms set retail prices. In table 3 on the following page, the access charges and profits for all three firms are depicted for different locations of the entrant on the [0,1] interval and for different accommodators of the entrant (network 1 and network 2). Network 1 has an incentive to accommodate the entrant if its profits under accommodation are higher than its profits under no accommodation: π₁acc≥ πnot 1 t 6962(1239l 2_{+ 3009l + 3318.75) ≥} t 6962(289l 2_{+ 2159l + 4032.25)} or: l ≥ 0.53

On the other side, network 2 has an incentive to accommodate the entrant if: π₂acc≥ πnot 2 t 13924(15133.5 − 10974l + 2478l 2_{) ≥} t 13924(12960.5 − 5474l + 578l 2₎ or: l ≤ 0.47

In the first stage of the game, both networks quote their profit maximizing access charge for different locations of the entrant. Table 4 on the next page

describes the lowest access charges for different locations observed by the entrant in stage 2. Now that network 2 also offers access, the situation on the left side of the [0,1] interval is mirrored on the right side. Consequently, as can be seen in table 3, it pays off for the entrant to locate near one of the two networks. Although not too close! If its accommodated by network 1, it looses all consumers to network 1 if l < 0.08. On the other end, if the entrant is accommodated by network 2 it looses all consumer to network 2 if l > 0.92. The areas in which the entrant is able to ’maintain’ its consumers are:

0.08 ≤ l ≤ 0.37 and:

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Location of the entrant 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 amax₁ 1.47 1.53 1.58 1.63 1.68 1.73 1.78 1.83 1.88 1.93 1.98 Profits 1 (acc) 0.48 0.52 0.57 0.62 0.68 0.74 0.80 0.87 0.94 1.01 1.09 1 (not) 0.58 0.61 0.64 0.68 0.71 0.74 0.78 0.82 0.85 0.89 0.93 E (acc. 1) 0.06 0.06 0.06 0.05 0.05 0.04 0.04 0.04 0.03 0.03 0.03 amax₂ 1.98 1.93 1.88 1.83 1.78 1.73 1.68 1.63 1.58 1.53 1.47 Profits 2 (acc) 1.09 1.01 0.94 0.87 0.80 0.74 0.68 0.62 0.57 0.52 0.48 2 (not) 0.93 0.89 0.85 0.82 0.78 0.74 0.71 0.68 0.64 0.61 0.58 E (acc. 2) 0.03 0.03 0.03 0.04 0.04 0.04 0.05 0.05 0.06 0.06 0.06 Table 3: Profits (in t) for two accommodators of the entrant

Location of the entrant

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

a 1.47 1.53 1.58 1.63 1.68 1.73 1.68 1.63 1.58 1.53 1.47

network 1 1 1 1 1 1/2 2 2 2 2 2

Table 4: Access charge observed by entrant in stage 2

Since the profits of the entrant are mirrored too, the entrant is indifferent between locating at l = 0.08 or l = 0.92. Prices and profits for either one of these locations are:

Prices Profits

Accommodating 1.68t 0.51

Not accommodating 1.34t 0.90

Entrant 1.76t 0.06

In terms of welfare we find that:

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If we introduce predetermined contract periods into the three stage game, both network 1 and 2 again have an incentive to undercut the entrant in the third stage of the game and increase their profits during the contract period (either when they accommodate the entrant or when they do not accommodate the entrant)5_{. For the access charge described in table 4, there}

is no long-term equilibrium in which the entrant is accommodated by both networks following a strict timing of the game.

However, there is an long-term equilibrium for different access charges. If the game is played an infinite amount of times, the networks have an opportunity to tacitly collude on the access charges in the first stage of the game. If network 2 repeatedly observes the access charges set by network 1, it can benefit from artificially increasing its own access charges up to the point where a2 ≥ 1.73t (for every location of the entrant). In this scenario,

the entrant is accommodated by network 1 and locates on the left side of the [0,1] interval. Network 2 benefits since:

πnot−lef tside₂ > π₂acc−rightside

After network 1 has observed the increased access charges of network 2, it has an incentive to follow suit and also increase its access charge up to the point where a1 ≥ 1.73 (for every location of the entrant). The two networks

now use their access charges as a tool to increase retail prices. The entrant will observe access charges as described in table 5.

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

a 1.98 1.93 1.88 1.83 1.78 1.73 1.78 1.83 1.88 1.93 1.98

network 2 2 2 2 2 1/2 1 1 1 1 1

Table 5: colluded access charge observed by entrant

The entrant locates where the access charge is the lowest. In theory this would be at l = 0.5. In reality however, the entrant would loose all its customers to the not-accommodating network. The best it can do is to locate at the boundaries l = 0.37 or l = 0.63. For these locations, prices and profits are:

5_{As explained in the previous section, if network 1 accommodates the entrant, it has} an incentive to undercut the retail price when l < 0.18. The not accommodating network has an incentive to undercut when l < 0.16 In a scenario where both networks access, these incentives are mirrored for the other side of the [0,1] interval.

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Prices Profits

Accommodating 1.96t 0.66t

Not accommodating 1.26t 0.79t

Entrant 1.89t 0.05t

Welfare in this scenario equals:

W_bothnetworksstrict−longterm= 1.50t + 0.26t = 1.76t (31)

If contracts for accommodation are renegotiated repeatedly, the long-term equilibrium outcome of entry accommodated by two firms and following a strict timing of the three stage game benefits the firms and hurts the con-sumer compared to the benchmark scenario without entry:

∆P S = +0.50t ∆CS = −0.49t

4.3.3 Scenario II - Simultaneous negotiation of a and l

We relax the timing of the game and allow step 1 and step 2 to become a simultaneous negotiation between the entrant and the two networks. Again, we allow for side payments through the fixed payment A which can be nega-tive. If network 1 accommodates the entrant in a simultaneous negotiation, it sets an access charge that maximizes joint profits. For network 2, the access charge that maximizes joint profits is:

ajoint₂ = 6t 40 8l − 24 2

For the simultaneous negotiation, network 1 and network 2 set access prices (a and A) to maximize their joint profits with the entrant. For different accommodators of the entrant, profits are described in table 6 on the next page. The profits for accommodating and not accommodating the entrant follow a mirrored pattern for network 1 and 2. In the previous scenario we have seen that if the entrant is accommodated by network 1, it ’maintains’ its customers after retail prices set if it its located between:

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Location of the entrant 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 ajoint₁ 1.24 1.29 1.35 1.45 1.47 1.53 1.59 1.65 1.71 1.77 1.82 Profits 1 (acc) 0.46 0.51 0.56 0.65 0.67 0.73 0.79 0.86 0.93 1.00 1.08 1 (not) 0.51 0.54 0.56 0.59 0.62 0.65 0.68 0.68 0.74 0.77 0.80 E (acc. 1) 0.09 0.08 0.08 0.07 0.06 0.06 0.06 0.05 0.05 0.04 0.04 ajoint₂ 1.82 1.77 1.71 1.65 1.59 1.53 1.47 1.45 1.35 1.29 1.24 Profits 2 (acc) 1.08 1.00 0.93 0.86 0.79 0.73 0.67 0.65 0.56 0.51 0.46 2 (not) 0.80 0.77 0.74 0.68 0.68 0.65 0.62 0.59 0.56 0.54 0.51 E (acc. 2) 0.04 0.04 0.05 0.05 0.06 0.06 0.06 0.07 0.08 0.08 0.09 Table 6: Profits (in t) for two accommodators of the entrant

In the case the entrant is now accommodated by network 2, these boundaries are mirrored:

0.58 ≤ l ≤ 0.91

In the first two stages of the game, network 1 and 2 negotiate with the entrant to determine the optimal location and access charge package. Now suppose network 1 and 2 do not care about the entrant having any consumers or not, but only care about accommodating the entrant as long as its far away. Suppose network 1 offers the entrant ajoint₁ = 1.71t and A1 = −0.03t for

l = 0.8. If the entrant would accept this offer, it would not sell any products. In stage 3 of the game, network 2 sets P2 = 1.06t whereas the entrant sets

Pe = 1.92t (table 3 on page 29), all consumers of the entrant will go to

network 2. The profit of the entrant solely consists of the (negative) fixed fee A1 it receives from network 1: πe = 0.03t. For network 1 however, this

equilibrium outcome is not profitable at all. If it sets its optimal retail price in stage 3, P1 = 2.21t, it would loose all its consumers to network 2, whose

price is more than twice as low. In order for network 1 to reap the benefits from accommodating the entrant, it has to be that the entrant is actually in business (in other words: the entrant has its own customers). More generally: for an accommodating network to benefit from accommodation, the entrant has to have its own customers.

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Now within the boundaries where entry is accommodated, profits for the accommodating network are maximized if the entrant locates as far away as possible. For network 1, this is at l = 0.42 (with a1 = 1.48t and A1 =

−0.017t, as described in the previous section). For network 2, this is at l = 0.58 (with the same a and A as network 1). The entrant is indifferent between the two offers. For either location, prices and profits are:

Prices Profits

Entrant 1.74t 0.08t

Welfare in this scenario equals the welfare level described in (18):

W_bothnetworksnegotiation = W_network1negotiation = 1.41t + 0.69t = 2.10t (32)

Introducing predetermined contract periods into the simultaneous nego-tiation, we have seen that neither network 1 nor network 2 has an incen-tive to undercut the entrant if it is accommodated by network and locates 0.20 < l < 0.22. Now if it is accommodated by network 2, there is no incen-tive to undercut the entrant if 0.78 < l < 0.80. For these locations of the entrant, there exists a long-term equilibrium in which the entrant is accom-modated by one of the two networks following a simultaneous negotiation. Welfare in this equilibrium equals the welfare described in equation (19).

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

a 1.82 1.77 1.71 1.65 1.59 1.53 1.59 1.65 1.71 1.77 1.82

network 2 2 2 2 2 1/2 1 1 1 1 1

Table 7: colluded access charge observed by entrant

There is an additional risk of the two networks interacting repeatedly. Following the same reasoning as in the previous scenario, network 1 and 2 can use the access charge as instrument to increase retail prices. The entrant will observe access charges as described in table 7. The best the entrant in maximizing its profits is to locate on the boundaries l = 0.42 or l = 0.58. For these locations, prices and profits are:

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Prices Profits

Entrant 1.58t 0.06t

Welfare in this scenario equals:

W_bothnetworksnegotiation−longterm= 1.42t + 0.43t = 1.85t (33)

In general, welfare is slightly higher than the benchmark scenario without entry but significantly lower compared to W = 2.10t. This is explained by the colluded access charge that drives up prices. If contracts for accommo-dation are renegotiated repeatedly and firm collude on the access charge, the long-term equilibrium outcome of entry accommodated by two firms after a simultaneous negotiation benefits consumers and hurts consumers compared to the benchmark scenario without entry:

∆P S = +0.42t ∆CS = −0.32t

4.4 Results

Our model showed that in the benchmark case without any entry, welfare equals:

Wbenchmark= P S + CS = t + 0.75t = 1.75t

By introducing an entrant to the benchmark model using a three stage game, different effects on welfare are reported. Assuming the entrant picks its location after the access charges are set (a strict timing of the three stage game), we found that that the entrant locates at a distance of 0.08 from the accommodating network. The effect on welfare is:

W_bothnetworksstrict = W_network1strict = 1.44t + 0.27t = 1.71t

Following the strict timing of the game, the equilibrium outcomes for one network offering access or both networks offering access are exactly the same. Although an extra firm that locates in between network 1 and 2 decreases average travel cost per consumer, the location in this scenario is still very close to the accommodating network, yielding the consumers almost zero

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benefits. The increased price level hurts the consumers and benefits the firms. The overall level of welfare slightly increases.

If we allow the terms of access to be negotiated for a predetermined pe-riod of time and, consequently, the process of accommodation to be repeated. We find that there is no long-term equilibrium in which the entrant is accom-modated by one network. In the case that two networks offer access to the entrant, repeated interaction between firms provides them with the opportu-nity to use the access charge as an instrument of collusion. In the long-term equilibrium outcome with colluded access charges, welfare equals:

W_bothnetworksstrict−longterm= 1.50t + 0.26t = 1.76t

If we allow the terms for entry to be set in a simultaneous negotiation, we found that the entrant is ’bribed’ to locate far away from the accommodating network, at a distance of 0.42. The effect on welfare is:

W_bothnetworksnegotiation = W_network1negotiation = 1.41t + 0.69t = 2.10t

Following a simultaneous negotiation, the equilibrium outcomes for access by one network or both networks are again the same in terms of welfare. The entrant locates closer to the middle, reducing the average travel cost per consumer significantly. The higher price level slightly offsets this benefit for consumers. Firms increase their profits after entry. The overall level of welfare increases compared to the benchmark scenario.

If we allow the terms of access to be negotiated for a predetermined period, we find that there is a long-term equilibrium in which the entrant is accommodated by one network. The entrant locates at l = 0.21, welfare is slightly higher than the benchmark scenario:

W_network1negotiation−longterm= 1.49t + 0.28t = 1.77t

In the case that both networks offer access to the entrant, the access charge functions as an instrument of collusion sustaining high retail prices. The entrant locates at distance 0.42 from the accommodating network. Welfare equals:

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5 Interpretation of results

The results in the previous section describe the effects entry has on welfare. In the benchmark scenario, two networks compete directly without entry. If entry is accommodated, welfare is maximized in a scenario where the entrant is accommodated through a simultaneous negotiation on the terms of access. If the process of accommodation is repeated, the long-term equilibrium out-come for two firms offering access outperforms the scenario where one firm offers access. Based on our results, we can draw five main lessons that have to be taken into account in constructing the optimal regulatory policy for the Dutch telco sector.

• Entry increases the level of retail prices

In every scenario for entry, producer surplus increased compared to the benchmark scenario. Once the entrant is accommodated, the av-erage price level increases. Network 1 and network 2 are located on the extreme ends of the [0,1] interval. In the benchmark scenario, they compete directly and divide the market equally. As soon as one of the networks accommodates the entrant, the direct competition between networks disappears. Both networks now have a new direct competi-tor: the entrant. Since the entrant has to pay an access charge, its marginal costs are higher than those of the networks. The introduction of one, direct competitor with higher marginal costs allows the net-works to raise prices. The overall price level is increased due to entry. In reality, entrants without a network are accommodated for prede-termined access prices. The accommodating network (now: KPN) is capable of increasing the marginal cost of these entrants through this access price. As illustrated by our model: the retail price level increases together with the access charge. In short: More entrants in the telco sector might not lead to a socially desired outcome in terms of prices. However, it has to be acknowledged that contrary to our model, in re-ality networks will not stop competing directly as soon as an entrant is accommodated. In the next section, we provide a solution for this shortcoming of our model. If the networks will continue to compete di-rectly, they will be limited in their ability to increase the level of retail prices because of entry.

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If an entrant is accommodated between network 1 and 2, the average travel cost per consumer is reduced. If the entrant is accommodated after a simultaneous negotiation, this reduction is significantly large. In terms of travel cost, it would be optimal if the entrant locates at the centre of the [0,1] line. As we have pointed out, this solution is not a sustainable equilibrium. The closest the entrant gets is l = 0.42. In reality, travel costs can be seen as a measure for product differentiation. Telco providers offer a wide array of services to different customer groups to ensure that consumers that are far away still ’travel’ in order to buy their product. An entrant without its own network can increase its market share by providing a specific service or targeting a particular group of customers. In this sense, more entry in the telco industry diversifies the market (in other words: consumers have to ’travel’ less). As long as the reduction in travel costs outweighs the increased retail prices, entry benefits consumers.

• Networks prefer entrants to locate far away

In our model, accommodating networks prefer the entrant to locate as far away as possible. Following the analogy of travel costs above, the accommodating networks does not want the entrant to start competing in the network’s own customer base. On the contrary, the accommo-dating network wants the entrant to target the customer base of the not-accommodating network. As we have seen, the accommodating network is prepared to pay the entrant a fixed fee for doing so. Al-though it is hard to proof in reality, it makes sense to think of an accommodating network like KPN setting a lower access charge for entrants (like Tele2) if they promise to target Ziggo-consumers. Fol-lowing this line of thought, it would be beneficial for consumers if both networks accommodate entry instead of one.

• Incentives for undercutting the entrant

As explained, contracts for access are often negotiated for a predeter-mined period in time. Our model shows that as long as one network offers access, there is a strong incentive for to undercut the retail price of the entrant in order to increase profits. In reality, this incentive is a bit ambiguous. On the one hand, the accommodating network (say KPN) is ’free’ to determine its (profit maximizing) access charge. As soon as an entrant (say Tele2) pays this access charge, the wholesale

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profits of KPN depend one-on-one on the consumers of Tele2. In such, KPN does not want to undercut Tele2. On the other hand, Tele2 is serving consumers that are connected to the network of KPN. If KPN prefers to increase its retail profits, it can easily undercut Tele2 and start serving those consumers directly. For the not accommodating firm (ZiggoVodafone), the incentive to undercut an entrant is ambigu-ous too. On the one hand, the retail price of Tele2 increases the overall price level and thus Ziggo’s own retail profits. On the other hand, since the retail price of Tele2 depends on an access charge that ZiggoVoda-fone does not have, it can easily undercut Tele2 and increase its retail profits by stealing Tele2 customers.

• Collusion on access charge

If two networks offer access to the entrant, the incentive to undercut the entrant decreases. However, if contracts are negotiated repeat-edly, frequent interaction provides the networks with an opportunity to use the access charge as an instrument for collusion. This result corresponds to prior work of Laffont and Tirole(1996) and Carter and Wright (2003). To prevent the two networks from using the access charge as an instrument for collusion, it is better if one network is regulated to accommodate the entrant instead of two.

6 Shortcomings and recommendations

The aim of this paper is to analyze what regulatory policy would best suit the Dutch situation in terms of welfare. Our model follows the framework described by Laffont et al.(1998),Armstrong(1998) andCarter and Wright

(1999). It introduces an extra player to the game and analyzes the effect on welfare if two independent networks with identical costs accommodate one entrant. In assessing the results, we acknowledge the fact that the model as described in this paper features some important shortcomings. The three main shortcomings of our model are:

1. No direct competition between the networks after entry

In reality, an entrant does not prevent network 1 from competing di-rectly with network 2. An extension to our model would be to adapt it to a Salop model where network 1 also competes with 2. The hotelling

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line would become a circle of length 1. If the network’s locations are fixed and opposite of each other, there are two segments in which the networks compete directly with another. If we then allow an entrant to locate somewhere in between the networks on one segment and still control for direct competition in the other segment, the increase in re-tail prices is moderated. It would be interesting to see what incentives the networks have for accommodation if entry does not take away the effect of direct competition.

2. Zero costs

In our model, we assumed network 1 and network 2 to have identical cost structures and that all cost equal zero. The result of this assump-tion is that the entrant’s costs, reflected in the access charge, are always higher than the networks’ costs. Since the entrant competes directly with both networks on the hotelling line, it will have a difficult time in serving its own consumers. This is why the boundaries for entry are relatively small. If we would follow Armstrong (2001) and introduce a cost structure that entails operating cost (for the networks), service cost (for the network and the entrant) and the access charge (only for the entrant), the equilibrium outcome would be more balanced.

3. One entrant

One of the basic assumptions of our models is that there is one entrant without its own network. In section 4.3, both networks offer access to the entrant. If the entrant is presented with equal options, it is just indifferent and picks one. In reality however, there are more entrants. If we would introduce a second entrant into our model and two networks offer access to two entrants on similar terms, both entrants can pick one network and locate on it. If both networks accommodate an entrant on their side of the hotelling line, this has a big influence on the average travel cost and price level and will possibly reshape the incentives for accommodation.

The Dutch market for telecommunication : a model