Pricing communication networks P12

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Kết nối Hai bên được kết nối với các mạng khác nhau có thể giao tiếp với nhau nếu có kết nối của hai mạng. Các ngoại mạng mà kết quả tích cực khi các mạng được kết nối là một lực lượng kinh tế kết nối giữa các nhà cung cấp lái xe mạng. Tiếp cận công nghệ hiện đại, tăng cường kết nối internetwork bằng cách cung cấp truy cập phổ cập. Một khách hàng sử dụng hệ thống truy cập không dây có thể truy cập mạng từ bất kỳ vị trí địa lý. Kết nối quan trọng...

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Pricing Communication Networks: Economics, Technology and Modelling. Costas Courcoubetis and Richard Weber Copyright  2003 John Wiley & Sons, Ltd. ISBN: 0-470-85130-9 12 Interconnection Two parties that are connected to different networks are able to communicate with one another if there is interconnection of the two networks. The positive network externalities that result when networks are connected are an economic force driving interconnection between network providers. Modern access technology strengthens inter- network connectivity by providing universal access. A customer using a wireless access system can access the network from any physical location. Interconnection is important if networks are to offer truly global services. Network service providers often negotiate special interconnection agreements and tariffs so they can provide the best service to their end-customers. These play a vital role in ensuring the smooth operation of today’s worldwide Internet. They also provide substantial income for network operators who have invested in building large backbone networks. By buying interconnectivity, a small network can appear larger to its customers, without investing in costly and rapidly changing infrastructure. This helps it to offer services that can compete with those offered by a network that has invested in greater geographical coverage. There are important incentive issues involved in offering interconnection services. Unless prevented by the contract, the network that provides the service may be tempted to discriminate in favour of trafﬁc that originates from its own end-customers and against trafﬁc that originates from end-customers of its ‘customer’ network. If that customer network is a direct competitor in the market for retail services, then the interconnection service provider has an incentive to offer a poorer quality of transport to the interconnection trafﬁc than to his own internal trafﬁc. A carefully chosen interconnection charge can correct this inequality by making transport quality a measured part of the contract. In this chapter we introduce some important concepts in interconnection services. Sec- tion 12.1 reviews types of interconnection agreement and pricing. In Section 12.2 we brieﬂy consider the effect of competition on service differentiation and in Section 12.3 we consider the factors that motivate networks to interconnect or not. Section 12.4 is about the asymmet- ric information problem that can arise when one network buys interconnection service from another. Section 12.5 describes how an incentive contract can be used to solve this problem. 12.1 The market structure 12.1.1 Peering Agreements Once interconnection is in place, a network service provider can use the infrastructures of a number of other networks to provide services to any of his customers. However,
280 INTERCONNECTION it is only reasonable that he should transfer part of the charge that he makes to his customer to those other providers whose networks are used to provide the customer’s service. Traditional telephone networks use the so-called accounting rate system to share charges. Interconnection charges are computed on a per call basis, and the network in which the call originates pays a predeﬁned charge to the network that terminates the call (and possibly to intermediate networks). This is implemented by each carrier computing his ‘trafﬁc balance’ with the other carriers over a certain time period, and then paying in proportion to it. In today’s data networks, things are different. First, since customers are connected to the Internet and data ﬂows in all directions, there is no notion of charging on a per call basis. Second, interconnection is achieved by there being a number of Network Access Points (NAPs), at which many different networks interconnect with each other. As a function of the interconnection agreements between network providers, and routing decisions in the interior of the network (which may depend on how network congestion and topology changes), data can ﬂow unpredictably through intermediate networks. In present Internet practice there are two ways that trafﬁc is exchanged between data network providers. The ﬁrst is peering, in which trafﬁc is exchanged without payment, and the second involves interconnection charges for transit trafﬁc. Peering agreements have some distinct characteristics. Peering partners exchange trafﬁc on the bilateral basis that trafﬁc originates from a customer of one partner and terminates at a customer of the other partner. This allows customers of the two networks to exchange information. Note that peering agreements are only bilateral; so a peering partner does not agree to act as an intermediary to accept trafﬁc from a partner and transmit it to a third network. Peering trafﬁc is exchanged on a settlement-free basis, also known as ‘sender- keeps-all’. The only costs involved in peering arise from the equipment and transmission capacity that partners must buy to connect to some common trafﬁc exchange point. Peering agreements do not specify that a network should provide any minimum performance to the trafﬁc originating from his peer; such trafﬁc is usually handled as ‘best-effort’. Network providers consider several factors when negotiating peering agreements. These include the customer base of their prospective peer and the capacity and span of the peer’s network. Clearly, some providers have greater bargaining power than others. It may be of no advantage for a provider with a large customer base to peer on an equal terms with a provider with a small customer base. The second type of interconnection agreement is a transit agreement. It has important differences with peering. Now one partner pays another partner for interconnection and so becomes his customer. The partner selling transit services will route trafﬁc from the transit customer to its own peering partners as well as to other customers. He provides a clearly deﬁned transport service for the transit trafﬁc of the ﬁrst network, and so can charge for it in a way that reﬂects the service contract and the actual usage. This charge, if rightly set, is billed to the customer of the network in which the trafﬁc originated, and becomes one of the components of his total charge. Observe that transit is not the same service as peering. Refusing peering in favour of transit is not a means of charging for a service that was otherwise provided for free. When regional ISPs pay for transit they beneﬁt from the infrastructure investments of national or global backbones without themselves having to make the same investments. Transit gives an ISP customer access to the entire Internet, not just the customers of its peering partners. To fulﬁl his obligations, a transit provider must either maintain peering arrangements with other backbones or pay for transit to another backbone provider who maintains peering relationships.
THE MARKET STRUCTURE 281 The Internet connectivity market is hierarchical, with three main levels of participants: end-users, ISPs and Internet Backbone Providers (IBPs), as shown in Figure 3.12. At the bottom of the hierarchy are the end-users, individuals and business customers. They access the Internet via ISPs. At the top of the hierarchy are the IBPs, who own the high speed and high capacity networks which provide global access and interconnectivity. They primarily sell wholesale Internet connectivity services to ISPs. ISPs then resell connectivity services, or add value and sell new services to their customers. However, IBPs may also become in- volved in ISP business activities by selling retail Internet connectivity services to end-users. Two markets can be identiﬁed in the Internet connectivity value chain: the wholesale market, and the retail market for global access and connectivity to end-users. There are two main types of contracts and they can be distinguished by their pricing: contracts for primary Internet access between end-users and ISPs, and contracts for interconnection between ISPs and IBPs. In the early days, when the Internet exclusively served public sector purposes of research and education, interconnection was a public good and its provision was organized outside competitive markets. Today interconnection is primarily commercial, yet its basic architectures remain the same. Network externalities generate powerful incentives for interconnection. They also provide incentives for potential opportunistic exploitation. 12.1.2 Interconnection Mechanisms and Incentives To better understand the difference between transit and peering, let us examine the mechanisms which networks use to exchange trafﬁc. One such mechanism is the routing protocol BGP (Border Gateway Protocol). It is primarily used at the borders of carriers’ networks, i.e. at the gateways (the edge routers) between a carrier’s network and other networks that are attached to it. Consider two networks, A and B, which are connected with a link running BGP. There are two principal types of information carried between the two edge routers of the networks: announcements and withdrawals. Announcements (also called ‘advertisements’) are packets containing lists of new destinations (network addresses) which are reachable via this link. Withdrawals are packets containing lists of destinations which can no longer be reached via this link. In making announcements, one network is soliciting from another network packets whose destination can be reached through the ﬁrst network. So if network A advertises network C to network B, it signals its willingness to receive trafﬁc from network B that is destined for network C. By advertising destination networks, and hence by being willing to receive and forward trafﬁc to these networks, network A is offering a service to network B. This service may be offered for a price. Let us see now the difference between transit and peering. In the case that A offers a transit service to B, network A advertises to B all the destinations he can reach (probably the whole Internet). Such information can be used freely by B and advertised to any other neighbouring network, say network D, that he can also reach all the above destinations (through A). In that respect, this routing information is transitive, since all destinations reachable through A are also reachable through B from any network connected to B (if B allows it). For this service A charges B a fee; in most cases, this charge is based on measuring the volume of data crossing the link AB, having as origin or destination the networks advertised by B. Similarly, B advertises to A all its destinations, so that A can advertise these further and the rest of the world can know how to reach them. In the case of peering between A and B, a similar and bidirectional process takes place, the difference being that routing information is not transitive. This means that B will use the information about the destinations reachable through A only for the beneﬁt of its own customers (and its customers from transit agreements), and will not further advertise these
282 INTERCONNECTION 9 4 peering point (NAP) 1 3 5 8 2 direct peering connection 6 7 Figure 12.1 An example of interconnection agreements. Networks 1, 2, 3, 4 offer transit services to networks 5, 6, 7, 8, 9, and peer at a peering point. A peering agreement must be established between each pair of peering networks. As a provider of a transit agreement a network advertises all networks it can reach (through other peers or customers). In a peering agreement a network advertises only those networks he can reach which are also his customers. If the trafﬁc between networks 5 and 6 is substantial, it may be cost-effective for them to peer and incur the cost of the direct connection 5–6. By doing so, the trafﬁc between 5 and 6 will follow the direct route instead of going through (and hence be charged by) the transit providers 1 and 2. destinations to other neighbouring networks. Observe that B has no incentive to advertise A’s destinations to other than his own customers. To do so would result in B carrying for free trafﬁc that is destined for A’s customers, but which does not beneﬁt B’s customers. Consider the example in Figure 12.1. Four large networks, 1–4, offer transit services to smaller networks, 5–8. For instance, network 2 offers transit service to networks 6 and 7. To do so, networks 1–4 peer at a peering point. Each network must make a peering agreement with each of the other networks. Let us consider networks 1 and 2 and the information exchanged between their edge routers. Network 1 advertises network 5 to network 2, and network 2 advertises networks 6 and 7 to network 1. Similarly, when networks 2 and 3 peer, network 2 advertises networks 6 and 7 to network 3, and network 3 advertises network 8 to network 2. Observe that network 2 does not advertise to network 3 the information obtained from network 1 concerning the reachability of destination 5. To do so would be to invite to carry trafﬁc at no charge from 8 to 5. Thus, under peering, full-meshes of peering relationships must be created between peers even if these are peering at the same peering point. However, as network 2 charges its customers 6 and 7 for transit service, it does advertise to 6 and 7 all the destinations that are advertised through its peers. When should one prefer peering to transit? First, note that peering cannot completely substitute for transit. This is because transit services usually offer global Internet access (advertise all possible destinations), whereas peering is useful for only a ﬁxed set of destinations. Nonetheless, peering relationships can reduce the amount of trafﬁc that is served through transit agreements and so reduce transit charges. Of course there is a cost to establishing a peering relationship. A network provider must decide whether a peering agreement is worthwhile by estimating its effects on the trafﬁc serviced under the transit agreements. Consider again Figure 12.1. Networks 5 and 6 observe that they have substantial trafﬁc between one another. If networks 5 and 6 peer then they can save transit charges that they would otherwise have to pay to networks 1 and 2. But to peer, 5 and 6 must pay for a new connection, either directly connecting them (private peering), or through some peering point. They should decide to peer if the cost of doing so is less than savings they can make because their local trafﬁc no longer needs to ﬂow through the transit providers 1 and 2. After establishing a new peering relationship, the transit contract can continue to act as a backup, to can carry trafﬁc between peers whenever the direct peering connection is out of order. This means that the peering connection can tolerate a certain amount of downtime and so can be safely implemented with inexpensive facilities and technology.
THE MARKET STRUCTURE 283 12.1.3 Interconnection Pricing Much study has been given to interconnection pricing for telecommunications networks and many intricate issues have been identiﬁed. Many of these issues remain equally relevant for communication networks which offer a broader set of services. Let us look as some details. Two common regimes for interconnection pricing are calling-party’s-network pays (CPNP) and bill-and-keep. CPNP regimes presently account for the majority of interconnection agreements for traditional voice trafﬁc. In this regime, the calling party’s local exchange carrier (LEC) or interexchange carrier (IXC) pays the called party’s local network for the cost of processing and allocating resources to terminate the call. More speciﬁcally, the calling party’s LEC collects a charge from the calling party and then pays a transport and termination charge to the called party’s network. In the case of long-distance, the calling party’s IXC collects a charge from the calling party and pays an originating access charge to the calling party’s LEC and a terminating access charge to the called party’s LEC. In ‘bill-and-keep’ regimes the calling party’s carrier does not pay any termination charge to the called party’s carrier. Instead, the termination cost is recovered from the end-customer. This means that an end-customer has the incentive to choose among competing carriers. The resulting competition means that bill-and-keep regimes achieve better economic efﬁciency than do CPNP regimes (where the terminating carrier is a de facto monopolist). ‘Bill-and- keep’ regimes are also fairer. As both the calling and called parties beneﬁt from a call, it is fair that they should share its cost. Of course there are subtleties as to how the cost should be shared. Let us investigate these issues further. As we say, a fundamental problem with CPNP is that the LEC who terminates calls is a de facto monopolist. Because end-customers usually receive their access service from just one provider, any interconnecting LEC or IXC who carries the call prior to it reaching the terminating network has no choice over the terminating carrier. Thus, each terminating carrier, no matter its size, has monopoly power over termination to its own customers. A long distance IXC does not enjoy such a monopoly because there are usually a number of competing IXCs that can carry the call between the LECs of the calling and called parties. The problem with CPNP is that a terminating carrier can safely raise termination prices without losing customers, since the called party does not share any part of the termination charge. Furthermore, there are usually geographic rate-averaging requirements, which mean that call prices cannot depend in a very detailed way upon precisely how they are terminated. For example, calls from Greece to all UK destinations should be priced the same, even though they may be terminated by different local carriers in the UK. If one of such terminating carrier raises his price, then this will raise the average termination price, but his identity will be hidden. Since it is only the average termination charge that affects the bill of the calling party, that party will have little or no incentive to complain to the called party and encourage him to switch to a local carrier with a smaller termination charge. Thus, CPNP denies customers the ability to choose the most cost-efﬁcient network provider. Customers must pay part of the charges of all the networks involved in the interconnection service, even though some of these may be artiﬁcially inﬂated and uncompetitive. By comparison, ‘bill-and-keep’ provides better incentives, because a LEC with high access charges will lose customers when they see those charges in their bills. Another issue with CPNP is that interconnection charges tend to be trafﬁc sensitive, typically being calculated on a per-minute or per-call basis. These inter-network charges are typically reﬂected in the trafﬁc-sensitive retail prices charged to customers. Customers facing such tariffs are given trafﬁc-sensitive incentives to reduce usage, even when the
284 INTERCONNECTION network may actually have large amounts of unused capacity and so there is no need for congestion pricing. This may signiﬁcantly reduce the economic efﬁciency of the overall system. To prevent LECs behaving as monopolists, it is common for access charges to be regulated. Typical regulatory frameworks are rather complex and treat different classes of interconnecting parties and types of services in different ways, even when there may be little difference in the costs that they generate. For instance, the regulatory regime can depend on whether the interconnecting party is another local carrier, an interexchange carrier, or a subscriber. This complexity in the regulatory framework creates regulatory arbitrage opportunities that motivate entrepreneurs to invent new ways to provide services. The availability of new services can be highly beneﬁcial unless these are motivated solely by artiﬁcial differences in regulatory rules. For instance, Internet telephony is not subject to LEC access charges (either originating or terminating) for that part of the call that is placed over the IP protocol. In this respect (besides being more cost-efﬁcient), IP telephony is more competitive than traditional long-distance telephony (where the long-distance carrier must pay access charges). Pressure from Internet-based technologies should cause interconnection regimes based on CPNP to collapse. Looked at another way, so long as interconnection regimes based on CPNP continue to exist, they act as a spur to the introduction of new disruptive technologies such as IP telephony. ‘Bill-and-keep’ may be unfair to a large network that interconnects with smaller networks. A smaller network, with smaller operating costs, may be able to offer lower prices to its customers. Yet because of interconnection with the large network its customers can reach the same population of customers as those of the large network. A way to remedy this could be to split the cost of the interconnection facilities so that customer prices are the same for both networks. This is the idea of facility-based interconnection cost sharing, which contrasts with the usage-based prices that CPNP computes on a per call basis. Another interesting idea is to make the calling party’s network pay all the cost of the call up to the point that it reaches the called party’s network, which then does not receive any payment for terminating the call. That ﬁnal part of the cost is paid by the called party. In this scenario, the originating network also pays for the long-distance part of the call, and so has the incentive to choose a lost-cost IXC, since the long-distance charge will be seen in the bills of its customers. The reader may wonder why charging for interconnection has evolved differently in the Internet than in traditional telephony. A principal reason is the difference in the market structure. The market for local Internet service that is offered by ISPs is highly competitive, whereas the market for backbone connectivity is less competitive, reversing to some extent the trends of the telephony market. No ISP can survive by charging high access prices. So peering, which is a type of ‘bill-and-keep’, is widely used. In the market for backbone con- nectivity, competition encourages IBPs to adopt a similar peering strategy for terminating each others’ trafﬁc, except that their customers are now ISPs. The limited competition in the IBP market justiﬁes nonnegligible prices in the transit contracts paid by ISPs to IBPs. Note that ISPs have the incentive to operate as efﬁciently as possible, since they pass on the cost of their local network and its transit agreements directly to their customers, who can easily switch ISP if they feel they are not receiving the best value for money. 12.2 Competition and service differentiation We can use standard models of oligopoly to analyse competition in networks that offer guaranteed services. In these networks, capacity determines the quantity of services that
INCENTIVES FOR PEERING 285 can be sold. However, when networks offer elastic services, then we must be more careful in modelling competition, as congestion must now be taken into account. The desire of competing networks to discriminate between consumers who differently value various aspects of the offered services motivates the production of services with different qualities of service. These differing services can be realized by dividing a network into subnetworks with different congestion levels and proﬁt can be increased thereby. However, when more services are offered they will be partly substitutable, and the resulting increase in competition can reduce the proﬁts of all the competing network operators. It is therefore interesting to ask to what extent a competitive market induces service differentiation by making it advantageous for competing networks to offer many types of service. The answer is very sensitive to assumptions. Consider the market for access services. If a customer can subscribe to multiple services, and so beneﬁt from multiple levels of quality, then it is probable that competing networks will wish to provide services at multiple quality levels, i.e. levels of congestion. However, if a customer can subscribe to just one quality level, then competition effects can outweigh service differentiation effects, and each competing network will wish to offer just one class of service, at a price that depends upon its congestion level. Of course this assumes competition. If network operators collude, then they can maximize proﬁts by each producing at multiple quality levels. In any case, if an access network wishes to distinguish itself by a certain quality level, it must guarantee that quality by buying appropriate interconnection agreements. Thus, the intermediate networks’ quality of service can be a constraining factor on the competitiveness of an access network. 12.3 Incentives for peering Whether or not peering between two networks is beneﬁcial depends on how their customers value those things that differentiate the networks, such as size and location. Network size is very important to users who wish to access a large customer base and buy or sell services through the network. Similarly, location is important to customers that ﬁnd it easier to access one network than another. A network provider can make his network look more attractive by providing good performance to the trafﬁc of his own customers, and worse performance to trafﬁc that originates from outside. Simple economic models of competition suggest that, as a function of customer preferences, either all or no competing networks may want to peer, or smaller networks may want to peer while larger ones do not. The case in which no network wants to peer occurs when most customers are more interested in network size than location. Here, the market is modelled by a game whose equilibrium solution is asymmetric, in the sense that competing networks grow to different sizes. However, if customers are more interested in location, then networks may wish to peer, since by increasing their customer bases, they add value to what they provide and can charge more for it. If both size and location are important then peering can beneﬁt smaller networks, but not larger ones. This is because, in a competitive scenario, smaller networks can introduce access charges. Peering eliminates the advantage of network size and can encourage customers of larger networks to move to smaller and cheaper ones. In practice, it is typical for a network provider to specify conditions for peering that depend on the other network’s size and geographic span. He might also specify a ‘peering charge’ that compensates him for his loss of income when he peers with another network. Of course it is very difﬁcult to determine this charge. In practice, it is often made a function of the access speed of the connection between the two networks at the NAP where peering takes place.
286 INTERCONNECTION 12.4 Incentive contract issues Interconnection agreements may not always provide sufﬁcient incentives for partners to collaboratively realize the full potential of positive network externalities. In the present best- effort Internet, interconnection agreements tend to be rather simple, specifying a maximum rate and perhaps a volume charge. However, newer Internet applications increasingly require speciﬁc network performance guarantees, and so new types of interconnection contract are needed that can account for both quality and volume. These contracts must give the peering network the appropriate incentives to allocate the effort required for the contracted quality. This contrasts with the present practice of ﬂat contracts that do not include incentives for effort. It is difﬁcult to devise interconnection contracts because of asymmetric information about variables. We can discuss this using the terminology of the principal-agent model , in which a principal (the contractor who sets the terms of the contract) wishes to induce some action from an agent (the contractee who executes the contract). There are variables, such as peak rate, average throughput and number of bytes, that can be observed and veriﬁed by both principal and agent. However, there are other variables that cannot be observed by the principal. For example, a principal who buys from an agent a contract for interconnection may not be able to tell what minimum bandwidth the agent dedicates to his trafﬁc, or the priority class to which his trafﬁc is assigned. These are variables of the ‘effort’ provided by the agent. It is technology that dictates what is observable and what not. Sometimes, the effort of the agent may be observable, but the context in which this effort is exercised may not be known at the time the contract and the incentives are deﬁned. Information asymmetry can provide signiﬁcant advantage to the contractee, who naturally tends to expend the least effort he can to fulﬁl his contractual obligations. The contractor takes a risk known as moral hazard . There is an adverse selection problem when, at the time the contract is agreed, the agent knows some important information that the principal does not. For instance, if the principal is the provider of the interconnection service and the agent is the network generating the trafﬁc, the agent knows how he values ‘heavy’ or ‘light’ use of the contract. If he intends to make heavy use of the interconnection service, it is to his advantage not to reveal this to the principal. He would rather be charged the cost of a contract that is targeted at the average customer. In practice, there are many important ways that information asymmetry can occur and can inﬂuence the performance that is obtained from an interconnection contract: ž Perhaps an ISP signs an interconnection agreement, but subsequently does not maintain or upgrade his network capacity. The result is that the interconnection trafﬁc receives poor service. As peering agreements are presently based on best-effort services, one party cannot easily tell whether or not the other party is properly managing his network. ž An ISP carrying a high load of local trafﬁc might actively discriminate against packets that enter his network from an interconnected partner. The damaging effect of the discrimination may be camouﬂaged as natural congestion, and it can be hard for his partner to detect the true cause. ž A client party cannot easily predict the trafﬁc load that a network offering interconnection service carries on its backbone. It is hard for that party to know the other party’s available spare capacity, his resource allocation and routing policies, or whether he effectively uses statistical multiplexing and overbooking. Resource allocation and trafﬁc multiplexing can strongly affect network performance. In negotiating peering or transit agreements, all the above are critical. However, information about these issues is not readily available, and ISPs have little incentive to reveal it. Present market practices only partly address the problem. Large ISPs exert their
MODELLING MORAL HAZARD 287 bargaining power to extract information from smaller partners. However, the requirements and terms of their agreements are private and undisclosed to third parties. 12.5 Modelling moral hazard To model asymmetric information problems in the market for Internet connectivity, three fundamental parameters must be deﬁned: effort, outcome, and the cost of providing effort. The effort of a network service provider is deﬁned in terms of how he treats his client’s trafﬁc; e.g. how an IBP treats the trafﬁc of client ISPs. Quantitatively, it can be described in terms of the resources that he allocates and the scheduling policies he applies to serving the client’s trafﬁc. When multiplexing trafﬁc from different sources and applications, the network manager can assign different priorities to different ﬂows of packets according to subjective criteria, such as the type of application being served (e.g. email vs. videoconferencing), the identity of the sender or recipient, and the revenue generated by the trafﬁc transferred. The dangers inherent in being unable to verify the level of effort can be reduced by using pricing mechanisms that provide the IBP with suitable incentives to exert the effort required to ensure the required performance. In effect, such mechanisms make the IBP responsible for the effort he provides by making his proﬁt depend upon the outcome, after accounting for uncertain conditions. Performance indicators, such as average delay or packet loss, could be used to measure the observable outcome in an interconnection agreement. Effort has a cost. This cost could be deﬁned as the opportunity cost of not serving (or reducing the quality of service for) other client ISPs of the same network. An alternative but equivalent deﬁnition of this cost is based on the negative externality (congestion) imposed on the network and its other users. It is quite difﬁcult to estimate this cost, as it depends on parameters that an IBP may not reveal. Often, a key component in the cost of serving the interconnection trafﬁc is the load of ‘local trafﬁc’ in the network, i.e., the trafﬁc that originates from the network’s other customers and which it is already contracted to carry. Information about this load may be available to the network provider before he must decide how to treat transit trafﬁc from an ISP with whom he peers. The cost of allocating effort to the trafﬁc of the new contract is negligible when the local trafﬁc load is small, but increases quickly as the local load becomes greater and exceeds a certain threshold. This threshold may depend upon the total available capacity, the multiplexing algorithms used, and the burstiness of the trafﬁc. In principle, the greater the amount of effective bandwidth that is allocated to the speciﬁc contract, the less bandwidth is available for the rest of the trafﬁc, resulting in some opportunity or congestion cost. For an incentive contract to be successful, one must be able to quantify reasonably well the expected cost to the contractee of the required effort, and the value of the resulting quality to the contractor. These issues are illustrated in the following example. There is information asymmetry at the time the contract is established. A rational service provider will provide the minimum possible effort, unless he is given appropriate incentives. In our simple model, we assume that some network conditions are unobservable (implying an unobservable cost to the agent), but that the provider’s effort is observable. The latter assumption is reasonable since interconnection contracts are typically of long duration, and so a customer ISP should be able to rather accurately estimate the parameters that he needs to infer the effort allocated by the contracted ISP. Only if contracts were of short durations, say a connection’s life, might such estimation be inaccurate and effort unobservable. For simplicity, we focus on the modelling issues and the resulting optimal incentive schemes, omitting the complete analysis.
288 INTERCONNECTION x aC a ∈{aL, aH} y (1 − a)C y ∈{y1, y2} Figure 12.2 A model for an agent’s effort. He operates a link serving two queues: one for the transit trafﬁc and the other for his internal trafﬁc. The effort given to the transit trafﬁc is measured by the fraction of capacity Þ dedicated to serving the ﬁrst queue. The rate of internal trafﬁc at the time the contract is instantiated is random, taking values y1 , y2 with probabilities p1 , p2 , respectively, with y1 < y2 . Example 12.1 (A principal-agent problem) Consider a transit agreement between two network service providers, using the formulation of the principal-agent model. Suppose a principal, P, contracts with an agent, A, for transport of a packet ﬂow through A’s network. We model A’s network by two queues; one is dedicated to A’s internal trafﬁc and the other is dedicated to P’s transit trafﬁc (see Figure 12.2). The service capacity of the network is C, of which ÞC is allocated to the P’s transit trafﬁc. For simplicity, we restrict the choice of Þ to two values, Þ L , Þ H , where Þ L < Þ H . Thus, Þ is the effort that is provided by A in the context of his contract with P. We suppose that A has no control over the rate of his internal trafﬁc at the time he begins serving P’s trafﬁc. He can control the fraction of his capacity that he will allocate to it, and he knows the distribution of the future rate of his internal trafﬁc at the time he agrees the contract with the principal. These are reasonable assumptions for many practical situations. The contract deﬁnes a service to be provided at some later point in time, and statistical information is available on the future state of the network. Let us denote the rate of the internal trafﬁc by y, and suppose that it is known that it will take one of the two values y1 and y2 , with probabilities p1 and p2 D 1 p1 , respectively, where y1 < y2 . The cost of allocating capacity to P’s ﬂow is the extra delay experienced by packets of A’s internal ﬂow. Assuming, for simplicity, that this is a M=M=1 queue, we can calculate the cost using the fact that if a ﬂow of rate y is served at rate C then the average packet delay is 1=.C y/. Taking as the monetary value of the cost of one time unit’s delay, this implies a rate of delay cost of y=.C y/ per unit time. Thus, the cost of allocating a fraction Þ of the available effort to the contract with P is Ä ½ 1 1 c.y; Þ/ D y .1 Þ/C y C y Let c.i j/ denote c.yi ; Þ j /, i 2 f1; 2g, j 2 fL ; H g. It can be proved that c.2H / c.2L/ > c.1H / c.1L/ > 0 In other words, a change from low to high effort is more costly to A when the system has a greater internal load. Of course, such a change beneﬁts P, since it reduces the average delay of his packets. Denote by r L and r H respectively the monetary value of the service received by P when the effort levels are low and high. Our task is to design an incentive contract in which P pays A an amount w.Þ/. This payment is determined after the completion of the service and depends on the level of effort Þ allocated by A, which we suppose P can estimate both accurately and incontestably. Perhaps P measures the average delay of his trafﬁc and then uses the delay formula for the M=M=1 queue to compute the effort that was provided by A.
MODELLING MORAL HAZARD 289 Let the contract specify that P pays A amounts w L or w H as A provides low or high effort respectively. Once these are known, A needs to decide whether or not to accept the contract. His decision is based on knowledge of the distribution of the rate of the internal trafﬁc at the point that service will be instantiated. At that point, he observes the rate of internal trafﬁc and decides what level of effort to provide to P’s trafﬁc. This decision is rational, and is based on the information available. He maximizes his net beneﬁt by simply computing the net beneﬁt that will result from each of his two possible actions. This is easy to ﬁnd for any given w L and w H . First, observe that if the value of the state is i, the rational action for A is j D arg max` fw` c.i`/g, and the payoff is w j c.i j/. Thus, the sign of w L w H [c.i L/ c.i H /] determines the most proﬁtable action for the agent. The participation condition (i.e. the condition under which A will agree to accept P’s trafﬁc) can be written as p1 maxfw L c.1L/; w H c.1H /g C p2 maxfw L c.2L/; w H c.2H /g ½ 0 Depending upon the parties’ risk preferences, different incentive schemes can result. For example, P might be risk-averse, while A is risk-neutral. This could happen if A, who is perhaps a backbone provider, has many customers and so can spread his risk. His expected utility is then the utility of his expected value. The ideal contract for P is one that induces A to choose the efﬁcient action, so maximizing total surplus from the interconnection agreement; and then extracts this entire surplus from A. (Note that A has to be willing to sign the contract – the participation condition must be satisﬁed – so that this is the best that P can achieve.) Simple convexity arguments suggest that a franchise contract is best for P. He keeps a constant amount F for himself, regardless of the outcome, and offers the surplus from the interconnection relationship minus the franchise payment F back to A. F is set so that A receives zero expected net beneﬁt (or some tiny amount). Suppose our risk-averse principal has a utility function of the form U .r w/, where U is assumed concave, and the random variables r and w are respectively the value obtained by the principal and the value of his payment to A. These are well-deﬁned for each pair w L ; w H . The principal’s problem is to maximize E[U .r w/] over w L ; w H , subject to A’s participation, and we know that this is achieved using a franchise payment F to P. For instance, if both actions L ; H are enabled by the optimal incentive scheme, w L ; w H must satisfy r L w L D r H w H D F for some F which should be equal to the difference between the average value generated for the principal and the average cost to the agent as a result of the incentive scheme w L ; w H . Observe that there are ﬁnitely many candidate Fs, since the number of different incentives provided by any choice of w L ; w H is ﬁnite (in our case four). This suggests that we ﬁrst compute all possible values for F and then choose w L , w H to realize the largest. This optimal F will depend on the values of the parameters r L , r H , c.1L/, c.1H /, c.2L/, c.2H /. There are four cases to consider: 1. Always select high effort. Then FH D r H [ p1 c.1H / C p2 c.2H /]. 2. Always select low effort. Then FL D r L [ p1 c.1L/ C p2 c.2L/]. 3. In state 1 select high effort, and in state 2 select low effort. Then FH L D p1 r H C p2 r L [ p1 c.1H / C p2 c.2L/]. 4. In state ð select low effort, and in state 2 select high effort. Then FL H D p1 r L C 1 Ł p2 r H p1 c.1L/ C p2 c.2H / . Let us restrict attention to the interesting case, r L < r H and determine the optimal value of F as a function of r L and r H . In the region marked FH in Figure 12.3, where r H r L ½
290 INTERCONNECTION rH FH FHL c(2H) − c(2L) FL 45° c(1H) − c(1L) 0 rL Figure 12.3 Optimal franchise contracts. There are three regions in which the principal’s optimal franchise contract is different. Here r L and r H are the monetary value of the service received by P when the effort levels are, respectively, low and high, r L < r H . c.2H / c.2L/, FH is the best franchise contract and w L D 0, w H D p1 c.1H / C p2 c.2H /. In the region marked FL , where r H r L Ä c.1H / c.1L/, FL is optimal and w H D 0, w L D p1 c.1L/ C p2 c.2L/. In the region marked FH L , where c.1H / c.1L/ Ä r H r L Ä c.2H / c.2L/, FH L is optimal, and w L D p1 .r H r L / C p1 c.1L/ C p2 c.2L/, w H D p2 .r H r L / C p1 c.1L/ C p2 c.2L/. The intuition is that, given r L , when r H is sufﬁciently large we would like to provide incentives so that high effort is always used. As r H decreases, it becomes economically sensible to use high effort only when the cost of providing it is not too great, which is when the system is in state 1. If r H decreases even further and becomes close to r L , then the greater cost of high effort does not justify its choice, regardless of the state of the system. It is only when c.1H / c.1L/ Ä r H r L Ä c.2H / c.2L/ that one needs to design a nontrivial incentive contract, i.e. one in which the provider’s effort depends on network conditions. 12.6 Further reading The interconnection issues addressed in the ﬁrst part of this chapter are covered by Huston (1998), Huston (1999a), Huston (1999b) and Metz (2001). The web site of EP.NET (2002) provides information regarding Internet NAPs. Atkinson and Barnekov (2000) address facilities-based interconnection pricing issues. Mason (1998) discusses the international accounting rate system and the reasons this may be affected by Internet telephony. An interesting discussion of ISP interconnection agreements and whether regulation should be government-led or industry-led is given by Cukier (1998). The ideas about competition and service differentiation in interconnected networks at the end of Section 12.2 are pursued by Gibbens, Mason and Steinberg (2000), Cremer, Rey and Tirole (2000) and Lafont, Marcus, Rey and Tirole (2001). The information asymmetry issues in Section 12.4 and Example 12.1 were introduced by Constantiou and Courcoubetis (2001). The book of Macho-Stadler and Perez-Castillo (1997) is also a good source on asymmetric information models for incentives and contracts.