A Pricing Mechanism for Digital Content ... - Semantic Scholar

A Pricing Mechanism for Digital Content Distribution over Computer Networks

Karl R. Lang and Roumen Vragov Department of Computer Information Systems Zicklin School of Business Baruch College, City University of New York (CUNY) New York City, NY 10010, USA {karl_lang, roumen_vragov}@baruch.cuny.edu

Abstract This paper uses modified economic growth theory to compare and contrast two currently available ways of digital content distribution; the client-server model and the peer-to-peer model. We describe a monopolistic pricing scheme for distributing digital content over peer-to-peer networks that rewards peer users who actively participate in the distribution process. Our results show that digital distribution through a peer-to-peer network is more profitable and more efficient than in the corresponding client-server setting, if the pricing mechanism used provides strong incentives to users to share content. The basic results hold when the model is extended to include time-variant preferences across generations of consumers, and when the monopolist performs price discrimination based on generations. Some practical implications from the theoretical analysis are also discussed.

Key Words: Client-server networks, content sharing, digital content distribution, information goods, monopolistic seller, peer-to-peer networks, pricing, user participation incentives.

(Revised, April 19, 2005)

Introduction As the media industry has begun shifting its operations from physical to digital distribution models to deliver its content products to consumer markets, it faces the question of whether to adopt a centralized or a decentralized solution [4]. The former approach will typically be implemented as some kind of client-server system where content provision and customer relationships are managed centrally.

Decentralized

distribution, on the other hand, might be most effective when implemented over peer-topeer (P2P) networks where consumers partake in the distribution process by trading information and content files [2, 13]. For media companies, however, adopting P2P distribution generally means trading-off control over content supply and distribution channels for possibly increased distribution efficiencies and service levels [8].

In general, client-server based distribution models provide content providers with several advantages. Since all content product files reside on a centrally-organized server system, content providers to maintain control over content supply and product promotion. Consumers need to connect directly with the provider when looking for a product and download it from its central server site if they decide to purchase a copy. Hence, customer relationships and personalized marketing efforts can be managed centrally. However, centralized client-server distribution also has several limitations.

Besides

potential capacity problems with regard to simultaneously servicing a large number of customers, its hierarchical design also constrains the immediate participation of the consumers in generating additional interest and demand for content products.

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Peer-to-peer consumer networks, on the other hand, are interactive network designs that can serve as effective marketing platforms where any peer can directly and proactively communicate with any other peer, exchange information, promote certain products through word of mouth, develop online communities, and, of course, trade content [7]. Thus, peer nodes can act at the same time as both suppliers and consumers of content products and information.

Moreover, by collectively sharing computing

resources, such as file storage space and communication bandwidth, P2P networks can adapt well to peak demand times and distribute work over the peer nodes in the network and efficiently serve high volumes of content. The higher the demand for a particular content file the more it will be available in the network as peer nodes download copies and become potential suppliers of the same product. If all peer users are permitted to offer original content, the collective supply of a large P2P network can substantially increase product selection in terms of breadth (number of different product offerings) and depth (number of sources for a particular product). Table 1 compares client-server and peer-to-peer distribution and suggests that organizing content distribution over P2P consumer networks could improve service levels in terms of content provision, content delivery, consumer satisfaction, and possibly distribution cost. The potential for piracy presents a big concern in either of the two models.

But technical solutions such as digital rights management and content

encryption methods and legal actions to enforce existing copyright laws apply equally in both situations and can be employed to mitigate piracy problems [3].

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Table 1: A comparison of client-server and P2P distribution models Service Attribute

Client-Server Distribution Model

P2P Distribution Model

organizing principle

centralized

decentralized

user role

passive consumer

active participant

product selection

content provider site

collective user holdings

content search

central product catalog

distributed play lists

content distribution

one to many delivery

user to user exchange

service capacity

centrally allocated resources

distributed, shared resources

piracy threat

leaking products to outside channels sharing without remuneration

Several additional issues need to be addressed before a content provider can successfully implement a digital distribution model over P2P networks. Assuming that providers charge for content and that users value content and are willing to pay for it, there needs to be a mechanism that makes information about costs and values available to participants in the network. The network also needs to provide incentives to users to participate in distributing content through exchanging product files in order to achieve stability, efficiency and effectiveness [16, 17]. In order to optimize service performance it is necessary that the self-interested participants reveal important information concerning the value of demanded products and the costs for sharing resources and

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providing their own content holdings and trade-off information concerning available bandwidth and storage capacities across the network [9].

This paper presents a monopolistic pricing model based on modified economic growth theory that specifically compares centralized with decentralized digital content distribution. We show that content providers can increase efficiency and profitability by adopting P2P distribution methods without losing profitable pricing capabilities. Incorporating a compensation scheme for uploading and sharing content with other buyers allows the monopolistic provider to delegate a substantial amount of distribution to the P2P network. Self-interested peer consumers collect a discount on purchases of content that they help distribute to other consumers who demand the product after them. This mechanism provides an incentive to downloaders to also upload and share content with other network users. The traditional free-riding problem can be reduced, and theoretically eliminated, if the monopolist sets download and compensation prices properly.

Most previous models for pricing information goods assume that variable production and distribution costs are negligible, so that the sole purpose of any pricing mechanism is to recover the fixed costs involved in production [19]. But when we consider different patterns of distribution of information goods, we have to recognize that variable distribution costs can be significant. While reproduction of content files is easy and cheap, incurring merely quasi-zero marginal production cost, their distribution to the end consumer is actually more complex. Studies of real, large-scale file-sharing environments

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have shown that online distribution of digital content creates long waiting queues that prompt many consumers to abort their download service requests before data transmission has been completed or, in many cases, even started [14]. Free-riding has been identified as the main reason for the formation of distribution bottlenecks in peer-topeer settings [1]. As the traded content files get larger, distribution efficiency becomes even more critical.

1

While early file-sharing systems such as Napster and KaZaa have

been mainly used to distribute relatively small content files like images and songs, newer service systems like BitTorrent are specializing in the distribution of very large content files (e.g. movies, TV shows, games).

2

Co-opting the distribution capacity of the peer

consumers increases efficiency and reduces content providers’ distribution cost if the network users can be motivated to participate in the process [22]. The model presented here includes analysis of the variable distribution costs as well as a discussion on participation incentives.

This paper is organized as follows. In the next section, we develop our theoretical P2P distribution model and pricing mechanism. This mechanism incorporates a userparticipation incentive that allows a monopolistic provider of a digital product to use the advantages of P2P networks while collecting the same revenue as in an equivalent clientserver network, but, importantly, decreasing distribution cost and servicing customers faster on average. Users who share content receive compensation from the network, which motivates them to increase participation. The following section presents a small

1

In a recent study by CacheLogic, an Internet-traffic analysis firm based in Cambridge, UK found that BitTorrent traffic alone accounted for about 35% of all data sent across the Internet [21]. 2 These files are usually hundreds or thousands of times larger than a typical MP3 music file.

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example that illustrates how our basic distribution model applies to the two network settings that are analyzed in this paper. Next, we discuss the implications of relaxing some of the assumptions made in the basic distribution model. In particular, we consider the inclusion of time preferences, and discuss variable bandwidth and competition from other content providers. We then examine limitations of our theoretical analysis as well as some practical implications. We conclude the paper with an outline of some possible future research directions.

The Basic Distribution Model Music, movies and other media products are experience goods for which consumers do not exactly know the value of the good until it is used. Different consumers will have different experiences with media content and most likely differing valuations. Hence, uniform pricing that undercharges some customers while overcharging others may not be optimal. For example, [3] found that music should be priced to incorporate the value of music content to consumers and also address technological factors that affect sharing. Copyright law bestows exclusive reproduction and distribution rights to the creator of original content. In other words, copyright grants monopoly power to original content providers. Hence, we assume a monopolistic, primary seller who knows the distribution of consumers’ prior valuations of available content and sets the selling price based on the

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expected valuations and the volume of content delivered.

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(See Table 2 for modeling

notation used throughout this article.) Table 2. Modeling Notation Price per byte charged in the client-server setting p Download price per byte pd Upload price per byte pu Size of content file f Server bandwidth bs Consumer bandwidth bc Total population of consumers N Number of consumers in generation g Ng Number of consumers in generation g who are willing to download a ng file Total number of generations G Generational index g Monopolist revenue in generation g rg Maximum consumer value of content file v Maximum consumer value of content file in generation g vg

More specifically, we propose that the monopolistic content provider, when using a P2P distribution model, should choose two base prices pd and pu, where pd is the base price per byte of content for every downloaded file and pu is the base compensation price per byte for every uploaded file.4 The idea to charge for volume of content resembles to some degree the concept of content delivery as a service rather than a product-oriented sales business and is similar, for example, to the per-packet pricing scheme that [11] devised for Internet data services. However, in our model it mainly serves to simplify calculating compensations. Conceptually, we need to distinguish between content providers who create and supply original content and network service providers who

3

Intellectual property law grants copyright owners of media products the exclusive right to economically exploit original creations, thus effectively giving them monopoly power in terms of distribution arrangements for their products. 4

A constant membership fee, one-time or monthly, could be added to our model specification. However, for the sake of simplicity and without loss of generality, we assume free membership.

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maintain the distribution network that delivers content to peer consumers and collect the upload and download fees. In the main analysis of this paper, however, we assume that the content provider assumes both roles, that is, it creates original content and controls the distribution network (forward integration). 5

To determine the values of our base prices pd and pu, we use a dynamic distribution model, where f denotes the size of a content file in bytes and bs defines the content provider’s server bandwidth. We will first develop a model for a client-server network environment and then compare this with the corresponding peer-to-peer network setting. Demand of content files occurs sequentially over time and is fulfilled in batches. The distribution of files in both network settings occurs in groups of consumers (or batches) who can be serviced simultaneously. That is, consumers demand a product in consecutive groups where the first group is served before the second one and so on. Consumers arrive depending on the time when they discover content they are interested in. Consumers who learn about a product early are also placed in earlier groups than those who learn about it later. We borrow the idea of servicing demand in consecutive groups from generation models in economic growth theory [18], but slightly modify their form to fit the specifications of our model. The idea of generations in economics is mostly used to represent monetary transfers between consumers of different age groups. In our model, the concept of generations represents the sequence of content transfers between groups of consumers and thus organizes how the network processes backlogged demand. We use the subscript g as the generational index. 5

The large record companies, for example, used this structural arrangement, when they created their digital distribution ventures Music Net (EMI, BMG, and Warner) and Press Play (Sony and Universal).

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For the sake of computational convenience, we imagine that the whole consumer population N could be divided into G groups (or generations) of equal size. This also covers the special cases of N=G (i.e., every consumer is served strictly sequentially) and G=1 (i.e., the whole population is served simultaneously). In the basic model, the generations are equivalent in terms of their value for the file to be downloaded. That is, the value for a file is uniformly distributed on the interval [0, v] in every generation. The basic model represents a single product case and is concerned with the distribution of one original piece of content. The size of each generation is marked by Ng where Ng = N/G for all generations. The optimal size parameter depends on network capacities, but is exogenously determined in our model. It helps balancing the distribution workload by protecting the network from serving too many customers in parallel. A customer who appears in the second generation does not participate in the first generation of the distribution process. However, the same customer will remain in the system until the later generations are processed and customers are served.

The Centralized Network Setting (Client-server Architecture) Let us first focus our attention on the distribution model in a client-server setting. Suppose that a monopolist owner of a content file with size f is distributing it over a client server network and is charging a price of p dollars per byte. 6 Only those members whose value for the file is greater than its total price (fp) will decide to download it. The number of people who decide to download the file in each generation follows a binomial

6

Obviously, p would be a very small amount, like a tiny fraction of a cent.

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distribution with probability of success (i.e., the probability that a user wants to purchase a copy of the file) equal to (v - fp) / v for 0 ≤ p
0 ⇔ αf < v . v

(7)

The profit is then ⎛ 1 αf ⎞ vGN g ⎜ − ⎟ , ⎝ 2 2v ⎠ 2

provided that the fixed cost are recovered. In every generation, will be willing to buy the product on average.

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(8)

Ng 2

(1 −

αf 2v

) consumers

The Decentralized Network Setting (Peer-to-Peer Architecture) Let us now suppose that the producer of the file has decided to switch from a clientserver to a P2P distribution system. In this case, every client who has already downloaded a copy of the file becomes also a possible source for uploading the same file and sharing it with all later generations. Peers can choose if they want to offer their copy of the file to future generations. We assume that the P2P network software employed by the service provider optimizes the technicalities of the file sharing process in the sense that all possible sources of a file are used to fulfill a current download request in proportion to their bandwidth. That is, the network decides when and which participating peer nodes are used in the distribution process. 7

Let bc denote the peer upload bandwidth, which we assume to be equal across the network. 8 If the content producer keeps the same pricing scheme as in the client-server model, rational, self-interested consumers will not be motivated to share the file. Without offering an explicit incentive mechanism, which is unnecessary in the centralized setting, the P2P case would degenerate into the corresponding client-server case. Therefore, we propose that the content providers in the P2P case charge two prices, a download price and a compensation price for uploading and sharing content. pd is charged (again per byte of content) to anyone who downloads a copy directly from a peer node and a 7

This is similar to the workload distribution mechanism used in the long-term, large-scale peer-to-peer computing project SET@home conducted by the University of California at Berkeley. Like in our model, users get to decide if they want to join the P2P network and if they agree to participate by sharing their resources. But it is the network that chooses how and when user resources are put to work in the process. ( http://setiathome.ssl.berkeley.edu/) 8 In the real world, available bandwidth varies across consumers, of course. However, low bandwidth users (e.g., dial-up customers) are rare among digital downloaders who have migrated to some form of highspeed Internet access that may vary somewhat but not by orders of magnitude.

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compensation price pu (per byte) is offered to reward peers who help distributing by sharing their own copy with other peer consumers.

It is easy to see that in our model it is optimal for every peer to offer her copy of the content file to all other peers as long as Pu > 0 and her computer resources and bandwidth can not be used for other, alternative purposes. A peer can therefore receive compensation larger or smaller than fpu. Obviously the amount of maximum compensation for a peer will also depend on her generation.

In the first generation, the producer’s server is the only source for downloading the file. Thus every peer from the first generation who decides to download the file incurs a cost of fpd. Let us keep the notation from the client-server distribution case and use ng to denote the number of users who decide to download the file in generation g. The decision to download the file in the P2P distribution system is more complicated because peers have to evaluate the expected future streams of revenue when they share their copy with future generations. The n2 f total demanded bytes by the second generation peers will be supplied by the main server and the first generation peers who are willing to share. The revenue share for each source will depend on its bandwidth. Each first generation peer will contribute

n2 fbc bytes to the peers in the second generation and the level of bs + n1bc

individual peer compensation will be

n fb n2 fbc pu . The original owner will contribute 2 s . bs + n1bc bs + n1bc

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Similarly, each first-generation peer can expect compensation from the third generation peers equal to

n3 fbc pu . Note that compensation decreases because the bs + (n1 + n2 )bc

number of available copies increases and individual peers can only supply progressively smaller shares. The total compensation for the first generation peers from all future generations can be expressed as G ngbc . fpu ∑ g−1 g=2 bs +bc ∑ni

(9)

i=1

Balancing the compensation for sharing and the cost of buying the file, each first generation peer will eventually be charged an amount equal to G

fpd − fpu ∑ g =2

ng bc g −1

bs + bc ∑ni

.

(10)

i =1

We can generalize this formula to calculate the expected compensation per byte of a peer in any generation g as G

c g = pu ∑ g +1

n g bc g −1

bs + bc ∑ ni

.

(11)

i =1

We should note here that cg = 0 since there will be no more future generations after generation g.

A peer in this P2P distribution system will decide to download a file only if his value for the file is greater than the net price that the peer has to pay. This happens when

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v i − fp d + fc

g

≥0

. Given the value distribution for the file in each generation we find

that the number of people who will purchase and download a copy of the content file is n g = N g (1 −

f f pd + c g ) , v v

(12)

and hence, the total revenue for the monopolistic file provider is G f ( p d − c g )⎤ ⎡ Total _ Re venue = ∑ fN g ⎢1 − ⎥( pd − c g ) . v g =1 ⎣ ⎦

(13)

The variable cost in the P2P setting is calculated in a slightly different way as before. The variable cost in the first generation is Variable _ Cost1 = αfn1 and in every subsequent generation Variable _ Cost g =

αfn g bs g −1

bs + bc ∑ n k

. The variable cost decreases with

k =1

every generation and becomes negligibly small as the number of generations goes to infinity. This means that the variable cost is only significant in the beginning of the distribution process when the content provider is most actively involved.

By including the variable cost into the revenue equation (13) we derive the profit for the monopolist who charges prices pd and pu.

G

π =∑ g =1

⎞ ⎛ ⎟ ⎜ α bs f ⎡ ⎤⎜ ⎟ fN g ⎢1 − ( p d − c g )⎥ p d − c g − g ⎜ f ⎡ ⎤⎟ ⎣ v ⎦ bs + bc ∑ N i ⎢1 − ( p d − ci )⎥ ⎟ ⎜ ⎣ v ⎦⎠ i =1 ⎝

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(14)

Because of the complex form of cg, it will be hard to calculate an optimal pricing strategy with optimal values for pd and pu. However, we can derive a pricing strategy that allows the monopolist to keep the same revenue as in the client-server model and, at the same time, decrease variable costs. The monopolist can vary pu through all the generations in such a way that cg and ng are kept constant. Using equation (11), we can calculate pu for every generation as Pu, g =

G

∑b g +1

s

cg ng bc

1≤ g ≤ G .

(15)

+ ng gbc

Based on our assumptions we can now prove the following proposition. The proof is shown in the appendix.

Proposition 1 (The Monopolist’s Pricing Strategy Proposition): Using the pricing strategy described above, in (15), the monopolist‘s profits are higher in the P2P network setting than in the corresponding client-server network setting.

If the monopolist uses this pricing strategy, the number of served peers in every generation will be ng =

Ng 2

(1 −

αf 2v

) . Notice that in this case the compensation per byte

the last generation receives is not zero, which clearly indicates that the strategy is suboptimal. Yet, using the proposed pricing mechanism the monopolist will eventually earn the same revenue in the peer-to-peer model as previously in the client-server model. In

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addition, the variable costs will be smaller because the monopolist effectively delegates some distribution work to peer consumers.

An Illustrative Example In this section, we provide an example to illustrate how content is distributed in the two network settings and how revenue and profit accrues, based on our theoretical distribution model presented in the previous section. Let us suppose the case where a content file of size 1Mb is to be distributed over a network with five nodes. Node 1 is the original producer of the content. Nodes 2 through 5 are the peer consumers in the network. In this example, v = $1.00 and the individual values for content are $0.70 for Node 2, $0.80 for Node 3, $0.90 for Node 4 and $0.65 for Node 5. Nodes 2 and 3 form Generation 1, and Nodes 4 and 5 form Generation 2. The ratio between the server bandwidth and the client bandwidth (bs:bc) is 3:1. Remember that all consumers have the same bandwidth. In the client-server setting, depicted in Figure 1, no files are shared, and all demanded content is provided directly by the producer. Suppose there is a small but positive variable distribution cost factor α = 0.00000001. Then total price for the content file fp = 0.505 and the monopolist profit is 2.02 – 0.04 = 1.98.

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Figure 1: Illustrative Example for the Client-server Setting

Next, let us consider the distribution mechanism for the corresponding peer-to-peer network setting, shown in Figure 2. The producer of the file in this case provides a total of 3.2 MB content. Then fpc = 0.505, fpu,1 = 0.20, fpd = 0.585, and fpu,2 = 0.08. The monopolist profit in this case is $2.02 – $0.032 = $1.988, higher than in the client-server case.

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Figure 2: Illustrative Example for the Peer-to-peer Setting

Model Extensions In this section, we point out some limitations of our basic model and explore implications of relaxing some of the modeling assumptions made in the previous section. In particular, we discuss issues concerning time, bandwidth, and competition more thoroughly. We extend our model to incorporate time preferences in the form of decreasing consumer valuations for content over generations. We show that, in this case, the monopolist can employ a pricing strategy based on the mechanism proposed in Equation (15) and again reap higher profits in the peer-to-peer setting. Introducing timevariant content valuations allows the monopolist to exercise generation-based price discrimination, which further increases profits in the P2P case.

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Time Considerations It is obvious that some of the costs and values in the model described above could be affected by time. In the case of distributing media products, it is common that the bulk of total demand occurs within days, weeks, or perhaps months of the original release. In our model, we do not specify the length of time within or between generations. Hence we can determine only relative but not actual distribution times. This is sufficient as long we compare distribution efficiency and profitability between the two alternative distribution settings (client-server and peer-to-peer).

However, it is unrealistic to assume that it doesn’t matter at all to the peer consumers when their demand occurs and gets served. In order to allow for time-variant consumer preferences we relax our previous assumption of a constant ceiling for content valuations and now stipulate that they are uniformly distributed on the interval [0, vg] where vg can vary across generations. The optimal price in the client server model is then p=

G G

2 f ∑ vg

+

α 2

.

(16)

g =1

We can show that using the same principle pricing mechanism as in Equation (15) and in the Monopolist’s Pricing Strategy Proposition (Proposition 1) will guarantee the monopolist achieves higher profits in the P2P network setting than in the corresponding client-server setting.

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Proposition 2 (The Peer Consumer’s Compensation Proposition): If the monopolist uses the pricing strategy put forth in Proposition 1 and he pays the expected total compensation to each consumer at the end of the download time then monopolist’s profits will be higher in the P2P setting compared to the corresponding client-server setting. The proof for the proposition can be found in the Appendix.

If the monopolist is aware of the pattern in which vg changes over time, she might be able to exercise price discrimination based on generations. She can choose to maximize the profit in each generation individually. In that case, the monopolist will construct a modified pricing schedule p g =

vg 2f

+

α 2

. Our pricing mechanism has to be adapted to

accommodate price discrimination on the part of the monopolist based on generations. The monopolist needs to set pd,g - cg = pg . The calculation of pu,g , however, will be more complex and computationally more intensive. Using this slight modification in the pricing mechanism we offer Proposition 3, As follows:

Proposition 3 (The Generation-Based Price Discrimination Hypothesis):

The

monopolist can use price discrimination based on generations and still get more profit in the P2P setting than in the corresponding client-server setting with a slight modification of the pricing strategy described in Proposition 1.

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Time is important if there is delay between the payment for downloading and the payment of the compensation for sharing. Including the delay only complicates the calculation of the amount of compensation and also requires additional knowledge on the part of the monopolist of the consumers’ applicable discount factors.

Bandwidth Considerations Under the assumptions of this model, server bandwidth is only part of the fixed costs of the content producer. Clearly, investing in server bandwidth in order to speed up distribution will increase the producer’s fixed costs. Such an increase would be the same in both the client-server and the P2P setting, so that the monopolist’s incentive to increase bandwidth should not differ in the two settings. The case is different for client bandwidths. In the client-server model a client who has higher bandwidth will take less time to download a file than another client. In the P2P setting, peers will not only take less time to download a file but can also receive relatively more compensation. That is why peers in the P2P setting may have a stronger incentive to increase their bandwidths. As mentioned earlier, we assume in our analysis that all peer consumers subscribe to some kind of high-speed Internet access that puts them in a roughly equivalent category. Low-speed Internet users are discouraged from using download services for large content files. Conceptually, our constant consumer bandwidth can be viewed as an average of the actual consumer bandwidth values.

Another limitation in our treatment of consumer bandwidth concerns the possibility that users may actually incur disutility as a form of opportunity costs when using

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bandwidth for sharing content with others. Hence, the compensation that they receive for sharing may be offset by the disutility that sharing imposes by limiting how else they can use their resources. Incorporating disutility into the model would affect whether users decide to share content.

Monopolistic Competition Setting When a particular market segment becomes more competitive and generates a range of similar content offerings that are available through large-scale P2P networks, the assumption of monopolistic sellers may, at some point, no longer adequately reflect market realities. The pricing mechanism from Proposition 1 and its price discrimination version in Proposition 3 above can be used in exchange environments for multiple files when files are not substitutable from a consumer point of view. When the monopolist faces competition from producers of similar content, he will need to lower pc or pc,g to more competitive levels, but the way to calculate pu,g could stay the same. Again, there is no substantial difference in principle between the client/sever and the P2P setting.

In order to implement the pricing mechanism developed above, the monopolist needs to have information about its customers. We know that download and upload speeds differ across platforms and computers, so the monopolist has to use estimated averages instead of actual values. The same limitation in our theoretical model applies to different discount factors in the utility of consumers as well as opportunity costs of resources.

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Practical Implications Distributing digital content over large-scale P2P networks exhibits characteristics of Internet access and data services, as well as what is involved with selling information products. Traditionally, media content providers like the music industry have been product-oriented and focused on selling individual copies of content. But in an age where information content is ubiquitous, selling content like music becomes much more service –oriented, so pricing should depend more on volume rather than particular content. Hence, two streams of pricing literature are relevant for our pricing mechanism, pricing for network traffic and pricing for information goods. The latter generally suggests differential pricing as the best strategy for selling information products when the seller can offer different quality versions for different prices to different consumer segments [19, 20].

The literature on data and voice communication services distinguishes between flatrate and usage-based pricing schemes. Usage-based pricing is economically most efficient, at least from a theoretical perspective, in achieving optimal bandwidth allocation and reducing network congestion and overuse [5, 6, 11]. But there is also ample evidence that consumers of telecommunication and Internet-based services prefer simple, flat-rate pricing schemes [12]. As technology matures, quality rises, prices decrease, and overall usage increases and generates increased total revenues. The need for market segmentation lessens and simple pricing plans based on flat rates begin to dominate [2]. Flat rates encourage usage, but also over-use and waste, and lead to economically inefficient subsidies of heavy users. Usage-based pricing, on the other

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hand, allows providers to more effectively implement quality of service differentiation and price discrimination, but discourages usage when the unit price is high. P2P service environments will thrive when they have a large user base and high levels of peer participation.

In an effort to balance the need to provide users with participation incentives and service providers with profitable margins, we suggest the adoption of a hybrid pricing mechanism for P2P networks that is file-specific. The mechanism is closer in theory to usage-based pricing strategies and reflects the value of content and the way it is distributed. The theoretical pricing mechanism proposed in this paper, which depends on both content value and content volume, could serve a basis for developing a flat-rate strategy as well. For example, service providers could sell monthly plans for a flat fee that would allow peer users to download a maximum amount of content (measured in bytes). Each piece of content could be priced based on our pricing mechanism. The price for each download would be deducted from the monthly allowance purchased. This would be somewhat analogous to cell phone service plans.

Conclusion This paper has described a monopolistic pricing scheme for distributing digital content over peer-to-peer networks that rewards music consumers who actively participate in the distribution process. This participation incentive leads to increased profits and faster content distribution than in equivalent client-server settings. The basic

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results hold when the model is extended to include time-variant preferences across generations of consumers, and when the monopolist performs price discrimination based on generations.

The formal analysis presented in this paper requires a number of modeling assumptions that should be further relaxed in future research. For example, the P2P pricing schedule that we suggest combines in one price, pd - cg, the content and distribution value of a file. It could be useful in practice if prices were explicitly divided to account separately for both. In another paper [10], the authors pilot-tested in a laboratory setting a pricing mechanism that attempts this division. There, monopolist owners are allowed to sell two types of licenses: a view license and a distribution license. The price of a viewing license is strictly under the control of the monopolist throughout the distribution process. The distribution licenses are sold in a public auction at the beginning of the distribution process and are then freely traded on a “digital distribution exchange.” The results of that study indicate that peer consumers are able to discern the market mechanism and find efficient prices for trading digital content.

This suggests that implementing other market mechanisms that remove some of the restrictive constraints that are necessary for model-based analysis and for computing optimal pricing schedules may be workable options. For example, the monopolist could create a market in which to auction the right for a peer to be placed in a particular generation.

The monopolist would choose the number of permits to sell to each

generation with a fixed reservation price per permit, which should be equal to the per unit

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cost of production. Afterwards, he can let the peers bid for the right to become a member of a certain generation. Such an auction-based scheme will be an effective way to let the market determine consumer time preferences. Various auction formats may be employed for this purpose [15].

More research needs to be done in order to fully explore the implications of competition among the different types of agents. For example, one could introduce independent intermediaries and examine the strategic options that arise from this modified setting. This might include investigating strategic options that an independent network service provider has in response to pricing strategies set by the content providers. Investments in bandwidth by competing network service providers or competing peer consumers present other interesting scenarios that could be further explored as well. Another open question concerns the competition among several independent P2P network service providers across competing networks for content suppliers and customers. The inclusion of more versatile consumer preferences and more dynamic P2P community activities is worthwhile. Finally, the fefects of advertising and other promotional efforts, including viral marketing methods, present further interesting possibilities for further research.

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References 1. Adar, E., and Huberman, B. Free riding on Gnutella. First Monday 5, 10 (2000). 2. Anania, L., and Solomon, R.J. The Minimalist Price. In L.W. McKnight, and J.P. Bailey, (eds.), Internet Economics, Cambridge, MA: MIT Press, (1997), 91-118. 3. Bhattacharjee, S.; Gopal, R.D.; and Sanders, G.L. Digital music and online sharing: Software piracy 2.0? Communications of the ACM, 46, 7 (July 2003), 107-111. 4. Bockstedt, J.; Kauffman, R. J.; and Riggins, F.J. The move to artist-led online music distribution: Explaining structural changes in the digital music market. In R. Sprague (Ed.), Proceedings of the 38th Hawaii International Conference on System Sciences, Kona, HI, January 2005, IEEE Computing Society Press, Los Alamitos, CA, 2005. 5. Gupta, A.; Stahl, D.O.; and Whinston, A.B. Streamlining the digital economy: How to avert the tragedy of the commons. IEEE Internet Computing, 1, 6 (December 1997), 38-46. 6. Gupta, A.; Stahl, D.O.; and Whinston, A.B. The economics of network management. Communications of the ACM, 42, 9 (1999), 57-63. 7. Hughes, J., and Lang, K.R. If I had a song: the culture of digital community networks and its impact on the music industry. Journal on Media Management, 5, 3 (2003), 180-89.

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8. Kwok, S.H.; Lang, K.R.; and Tam, K.Y. Peer-to peer technology business and service models: Risks and opportunities. Electronic Markets, 12, 3 (2002), 1-9. 9. Lai, K.; Feldman, M.; Stoica, I.; and Chuang, J. Incentives for cooperation in Peer-toPeer networks. In First Workshop on the Economics of Peer-to-Peer Systems, Berkeley, CA, June 2003. 10. Lang, K.R., and Vragov R. Pricing services in peer-to-peer networks: Aligning theory and practice with the use of experimental economics. Working paper, Zicklin School of Business, Department of Computer Information Systems, Baruch College, The City University of New York, March 2005. 11. MacKie-Mason, J., and Varian, H.R. Pricing the Internet. In B. Kahin, and J. Keller (eds.), Public Access to the Internet, Cambridge, MA: MIT Press 1995, 269-314. 12. Odlyzko, A. M. Internet pricing and the history of communications. Computer Networks, 36, 2001, 493-517. 13. Parameswaran, M.; Susarla, A.; and Whinston, A.B. P2P networking: an informationsharing alternative. IEEE Computer, 34, 7, 2001, 1-8. 14. Pavlov, O.V., and Saeed, K. A resource-based assessment of the Gnutella filesharing network. In S.T. March, A. Massey and J.L. DeGross (Eds.) Proceedings of the Twenty-Fourth International Conference on Information Systems, Seattle, USA, December 2003, 85-95. 15. Porter, D., and Vragov, R. An experimental examination of demand reduction in multi-unit versions of the uniform-price, vickrey, and English auctions. Working paper, Department of Economics, University of Arizona,, 2001.

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16. Rangananthan, K.; Ripeanu, M.; Sarin, A.; and Foster, I. ‘To share or not to share.’ An analysis of incentives to contribute in collaborative file sharing environments. In First Workshop on the Economics of Peer-to-Peer Systems, Berkeley, CA, June 2003. 17. Samant, K. Free-riding, altruism, and cooperation on peer-to-peer file-sharing networks. In S.T. March, A. Massey and J.L. DeGross (Eds.), Proceedings of the Twenty-Fourth International Conference on Information Systems, Seattle, WA, December 2003, 914-920. 18. Samuelson, P.A. An exact consumption loan model with interest with or without the social contrivance of money. Journal of Political Economy 66, 6 (December 1958), 467-481. 19. Shapiro and Varian, H.R. Versioning Information Goods. In B. Kahin and H.R. Varian (Eds.), Internet Publishing and Beyond, Cambridge, MA: MIT Press, 2000, 190-234. 20. Snir, E.M. The record industry in an era of file sharing: Lessons from vertical differentiation. In S.T. March, A. Massey and J.L. DeGross (Eds.), Proceedings of the Twenty-Fourth International Conference on Information Systems, Seattle, WA, (December 2003), 72-84. 21. Thomas, C. The BitTorrent effect, Wired Magazine, 13, 1 (2005), 50-153. 22. Vishnumurthy, V.; Chandrakumar, S.; and Sirer, E.G. KARMA: A secure economic framework for peer-to-peer resource sharing. In First Workshop on the Economics of Peer-to-Peer Systems, Berkeley, CA, (June 2003), pp 6.

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Appendix I. Proof of Proposition 1 We mark the constant total compensation per peer per byte, pd-cg, as pc. From (1) we have ⎛ ⎞ ⎜ αbs f . π = ∑ fN g (1 − pc )⎜⎜ pc − g v f g =1 bs + bc ∑ N k (1 − pc ) ⎜ v k =1 ⎝ ⎠ G

(A1)

The above expression can be rewritten as ⎛ ⎞ ⎜ αbs f f π = ∑ fN g (1 − pc )(pc − α ) + ∑ fN g (1 − pc )⎜⎜α − g v v f g =1 g =1 bs + bc ∑ N k (1 − pc ) ⎜ v k =1 ⎝ ⎠ G

G

⎛ 1 fα ⎞ The first term of the expression attains a maximum of vGN g ⎜ − ⎟ ⎝2 2 ⎠

pc =

(A2)

2

when

v α + . This is equivalent to the profit collected in the client server setting. The 2f 2

value of the second member is strictly greater than zero for any pc for which the nondegenerate solution criteria, which are applied in Equation (7), apply. Therefore the monopolist’s profit under the proposed pricing mechanism in a P2P network is always greater than the one gained under the client-server setting.

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II. Proof of Proposition 2 The profit under the assumptions of Proposition 1 for the P2P network monopolist producer is ⎛ ⎞ ⎜ αbs f . π = ∑ fN g (1 − pc )⎜⎜ pc − g vg f g =1 ⎜⎜ bs + bc ∑ N k (1 − pc ) vk k =1 ⎝ ⎠ G

(A3)

Using the same methods as in Proposition 1, we can rewrite the above expression as ⎛ ⎞ ⎜ αbs ⎜ f . π = ∑ fN g (1 − pc )(pc − α )+ ∑ fN g (1 − pc )⎜α − g vg f g =1 g =1 ⎜ bs + bc ∑ N k (1 − pc ) ⎜ vg k =1 ⎝ ⎠ G

G

(A4)

As long as the monopolist does not use price discrimination based on generations, the first term in Equation (A4) is equivalent to the profit in the client-server setting and that the second term is always positive. Therefore, the monopolist’s profit, under proposition 2, in the P2P setting is always greater than the one in the client-server setting. Note that if price discrimination is not used there might be generations in which ng = 0, i.e., no consumers in these generations might be willing to buy the product at the posted price.

III. Proof of Proposition 3 Let us pick any generation g ∈ [1, G ] , and mark the variable total compensation per peer per byte as pc,g. Then the monopolist profit in generation g is

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fN g (1 −

f p c , g )( p c , g − vg

α bs g

f bs + bc ∑ N i (1 − p c ,i ) vi i =1

),

(A5)

which can be rewritten as fN g (1 −

f f p c , g )( p c , g − α ) + fN g (1 − p c , g )(α − vg vg

α bs g

f bs + bc ∑ N i (1 − p c ,i ) vi i =1

).

(A6)

The first term of Equation (A6) shows the monopolist profit in the client-server setting for Generation g and the second term of the expression is strictly positive. This means the profit in period g in the P2P setting is larger than in the client-server setting. Since this is true for any generation g, it is also true for the sum of profits from all generations.

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