Pricing peer-produced services: Quality, capacity, and competition issues

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Innovative Applications of O.R.

Pricing peer-produced services: Quality, capacity, and competition issues

Yung-Ming Li

*

_{, Yi-Lin Lee}

Institute of Information Management, National Chiao Tung University, Hsinchu 300, Taiwan

a r t i c l e

i n f o

Article history:

Received 6 December 2008 Accepted 16 June 2010 Available online 22 June 2010 Keywords: Game theory Pricing Web 2.0 Peer production Service quality Competition

a b s t r a c t

Peer production has played an important role in the economics of Web 2.0 related services in which user participation and contribution become the main driving dynamics. However, the quality of peer-pro-duced services is uncertain because of inherently decentralized and heterogeneous participants. In the paper, utilizing reliability and game theoretic models, we develop a QoS measure and pricing schemes for this emerging type of service under various market structures. Our results suggest that a monopolistic platform provider has no incentive to offer multiple quality classes of service. Two competing platform providers may offer identical service contracts but still receive non-negative proﬁt. If they offer hetero-geneous service contracts, the provider with the lower quality service may provide higher quality than he advertises. This research contributes to the literature with a number of unique and interesting implica-tions for the issues of service contract design, capacity planning, and market interacimplica-tions for operaimplica-tions of community-based or peer-produced services.

1. Introduction

In the wave of Web 2.0, the power of online community is ad-dressed and peer production is emerging as a major economic force impacting various industries. Online communities are gaining momentum on the web and are reshaping the way how informa-tion is consumed and produced (Kolbitsch and Maurer, 2006). Companies and consumers had different roles of production and consumption in the traditional value creation process, but peer production creates a new dynamic to the producer/customer rela-tionship. Many initiatives have been launched to deal with this changing world and some have been successful, but it is still pretty new to most companies. Different terms can be found to denote the growing new phenomenon such as peer production (Benkler, 2002; Benkler and Nissenbaum, 2006) and user generated content (Oded, 2007), hereinafter we refer these production types as peer production, and the platforms/systems which support peer-produc-tion processes are named as peer-produced services. There exist many popular realized peer production based services, for exam-ple, information services like Experts-Exchange and Yahoo! An-swers. However, it is still an evolving concept, and there is no single dominate business model at present. We observed that some companies provided similar service, but after years only a few still there.

Booming Web 2.0 services are facing challenges to monetize the success (Höegg et al., 2006), and so are peer-produced

ser-vices. The business models of Web 2.0 related services are becom-ing increasbecom-ingly promisbecom-ing. Since peer production is one of the main distinguishing characteristics of Web 2.0 service, it is desir-able to analyze and extend the knowledge of the peer production based service market. Due to the decentralized and loosely self-enforced contribution, the quality of peer-produced services is uncertain. In contrast with traditional ﬁrm-produced products, the quality of peer-produced services is associated with the con-tribution rate of heterogeneous participants, the number of par-ticipants, and the capacity-limited platform (Agichtein et al., 2008). Product or service differentiation is a common marketing technique exploited for proﬁt improvement. As any pricing schemes should be realized based on the classes of service qual-ity, it is important to develop an appropriate model to evaluate the quality of service (QoS) deliverable to the users before they can subscribe to the services.

In this paper, we propose a general framework for investigating the pricing and quality strategies of peer-produced content ser-vices based on the framework of service-level agreement (SLA) un-der various market structure settings, but do not limit it to speciﬁc business applications. To generalize our research, the services which share the following characteristics are deﬁned as peer-pro-duced services. First, there is a platform which enables users to contribute. Second, the contents within a platform are contributed (produced) and requested (consumed) by the platform users. Third, the users are autonomous and individual contribution is stochastic. Due to the decentralized and self-motivated nature, the quality of peer-production-related service is hard to evaluate. A simple yet feasible way is proposed to measure the quality of peer-produced services, and develop optimal service quality levels, pricing

*Corresponding author. Tel.: +886 3 5712121x57414.

E-mail addresses:yml@mail.nctu.edu.tw(Y.-M. Li),marinerlee@gmail.com(Y.-L. Lee).

Contents lists available atScienceDirect

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schemes, and capacity choice for different market settings. This study has the following salient features that differentiate it from the past literature. First, we combine reliability and game theoret-ical approaches to model the pricing schemes of participant-gener-ated services. Second, we propose a simple but feasible way to set up service-level agreements for participant-generated services. Third, we analyze the implications for service differentiation and competition in the market of participant-generated services. Fourth, we examine the role of platform capacity and the invest-ment issue for participant-generated services.

The main unique findings of this study are as follows. First, we find that the service quality of peer-produced services increases with the heterogeneity of the participants. Second, a monopolistic platform provider will never offer multiple quality classes of peer-produced services and never over-provide a quality level higher than advertised. Third, in a duopolistic market, even when offering identical SLA contracts, each competing provider can still receive non-negative profit. Fourth, in a duopolistic market, the provider with the lower service quality level may offer a quality level higher that it advertises in the SLA contract.

The remainder of the paper is organized as follows. In Section2, we review the related literature. The service quality evaluation and the user decision models are described in Section3. In Section4, we analyze the baseline model of price scheme and capacity choice for a monopolistic market and extend the analysis to a duopolistic market in Section5. In Section6, we numerically compare the SLA contracts, capacity, and proﬁt levels under different market scenar-ios. Finally, case study and managerial implications are presented in Sections7 and 8provides concluding remarks and offers future research directions.

2. Literature review

Unlike traditional products, the quality of peer production is associated with the contribution rate of heterogeneous partici-pants, the number of participartici-pants, and the capacity-limited com-munity platform. As any pricing schemes should be realized based on the classes of service quality, it is important to develop an appropriate model to evaluate the quality of service (QoS) deliv-erable to the users before they can subscribe to the services. While extensive existing works on product differentiation and competi-tion are mostly conducted for the tradicompeti-tional ﬁrm-produced prod-ucts, little is targeted to the emerging peer-produced services. 2.1. Peer-produced service

Peer production was introduced to describe the new Web 2.0 model of economic production based on online community activi-ties (Benkler, 2002), and peer participants depend on self-orga-nized communities to produce a shared outcome (Tapscott and Williams, 2006). Although peer production is a new concept, it has been proven to be beneficial. The advantages of peer produc-tion are known from many pieces of research (Benkler, 2002; Schonfeld, 2005), and it has been proven to be efficient (Kogut and Metiu, 2001). According to Linus’s Law (Raymond, 1999), the number of peer participants contributing to specific content pro-vides a useful indication of its quality. Past studies also suggested the importance of peer participants’ contribution to the service quality (Lerner and Tirole, 2002; Lakhani and Hippel, 2003; Höegg et al., 2006). However, the challenges in forming an online commu-nity are the willingness to contribute and the development of peer participants (Koh and Kim, 2004). The contribution behavior of on-line community participants was covered in other researches (Koh and Kim, 2004; Bagozzi and Dholakia, 2006; Baldwin and Clark, 2006), and theories like Social Cognitive Theory, Social Capital

The-ory and Organizational Citizenship Behaviors are applied to help clarify contribution behavior (Koh and Kim, 2004; Chiu et al., 2006). Peer production depends on peer participants’ action that is self-organized and decentralized. However, due to the variety of peer participants and loosely altruistic contribution, the quality of peer-produced services is uncertain and difﬁcult to measure.

The existing works generally do not cover the proﬁtability issue of peer-produced services from the perspective of service platform provider. In our research, we develop peer-produced services busi-ness models (pricing schemes) based on the advertised quality le-vel, which is mainly determined by collective contribution of participants. Rather than controlling the quality, we propose a par-ticipant-based metric to measure the service quality. Furthermore, a QoS-based pricing mechanism is proposed to achieve the purpose of service differentiation.

2.2. Quality, capacity and pricing

Quality can be defined as the ability of a service to meet or ex-ceed customer expectations (Vörös, 2006). It is critical for peer pro-duction to be successful (Benkler, 2002; Benkler and Nissenbaum, 2006), and the issues on quality control/assurance/improvement have been studied (Stviliaet al., 2008; Hütter et al., 2008). Eco-nomic models dealing with price and quality relationships typi-cally take quality into consideration (Karmarkar and Pitbladdo, 1993; Zhang et al., 2009), and it is usually treated as a decision var-iable (Teng and Thompson, 1996). From the viewpoint of potential users, the service quality and price could influence their willing-ness to adopt directly. However, in the real world the information on service quality is hard to measure and rarely revealed to users. QoS is a comparison between what a user feels should be offered and what is provided (Pitt et al., 1995), and beliefs about a service’s perceived quality influence one’s attitude toward using this service (Hwang and Kim, 2007). QoS uncertainty is common for services, and a useful mechanism is the offering of a QoS guarantee ( Bharg-ava and Sun, 2008). A QoS guarantee is a business contract that de-scribes the service-level agreement (SLA) that a provider needs to commit. A SLA is a statement of the expectations and obligations that exist between a service provider and a customer. Within an SLA, pricing should be aligned with service-level priority differen-tials, and with the service provider’s achievement of service-level targets (Fitsilis, 2006).

Many services that exhibit QoS uncertainty are offered under flat-rate pricing, but quality uncertainty reduces the effectiveness of pricing strategy (Bhargava and Sun, 2008). Besides, QoS prom-ises are usually ill-defined. An alternative to solve this difficulty is to monitor long-term QoS and provide a statistical guarantee (Bhargava and Sun, 2008). From the real world cases and past liter-atures, we find something interesting. First, past researches fo-cused mainly on quality control. However, it has never been easy to control various participants over the network. Second, the price of existing services is flat-rate pricing and the quality is ignored. Third, the number of participants within the service platform is crucial to QoS, it would be an important issue for service provider. Nevertheless, it is often ignored.

When talking about QoS, a large number of users were consid-ered to be a negative factor to service quality because of congestion problem. Past research showed that the quality of service degrades as user increases (Westland, 1992). Nevertheless, in peer-produced services the more the users the better the service quality. QoS of peer-production service is determined by the individual contribu-tion rate and the number of participants. Because contribucontribu-tion rate varies, it is difﬁcult to estimate the exact quality of service level. In the research, a metric is developed to estimate a lower bound of service quality, and SLA business contract can be further be imple-mented. As the service quality level is associated with the available

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number of participants, the price and capacity should be consid-ered. Price level can adjust the number of participants but the number of participants are limited by the available capacity. Capacity is usually considered as a QoS constraint (Song and Jamal-ipour, 2008), and the number of participants is constrained by the capacity. To reflect the real cases and make our model reasonable and feasible, the capacity is assumed to be limited. In a short run, capacity is fixed and treated as an exogenous parameter ( Falk-ner et al., 2000; Rho et al., 2007; Zhang et al., 2009). However, in a long run, considering the capacity size and investment cost, plat-form providers can plan appropriate capacity to improve the profit (Goyal and Netessine, 2007; Anupindi and Jiang, 2008).

3. The model

Our settings follow the techniques commonly used to model the market with price and quality competition (Banker et al., 1998; Zhang et al., 2008). Consider a peer-produced service market that includes the participatory platform (infrastructure) providers and peer participants. We focus on the profit-maximizing platform pro-viders whose revenue is mainly generated from the subscription fee. Conceptually, peer-produced services are created based on the community activities. Peer participants benefit from exploiting the content, knowledge, or computing resource contributed by other participants in the networks. As the participants voluntarily contribute their content, the contribution levels are heterogeneous among different peer participants. As a result, the quality of the service becomes uncertain and is closely associated with the level of individual contribution and the number of peer participants. In the following, we first develop a model to represent the QoS level and potential peer participants decide whether to join the commu-nity after considering the advertised QoS, price, and their own indi-vidual valuation of the service. The notations used are listed in

Table 1and discussed in the corresponding subsections. 3.1. Quality of service

The contribution rate hidenotes the resource (content,

knowl-edge, information, service, etc.) availability of peer participant i, where 0 6 hi61. Since the provision of the resource in a distrib-uted system is stochastic, from the perspective of reliability theory, hican be interpreted as the probability that a given requested

re-source can be found from participant i. Notice that the contribution rate among individuals is independent; therefore, it is possible that more than one peer provider will provide the same resource in the same time. Assume the total potential number of users of the peer-production system is

g

0and the total number of subscribed users is

g

. The exact quality measurement of the peer-production system is

estimated as H ¼ 1 Qg_i¼1ð1 hiÞ. However, it is difﬁcult to

mea-sure hifor individuals in a large community. This makes it hard

for the service provider to set the SLA. To conquer this, we use h the mean of the individual resource availability of peer participants in the peer-production system, to evaluate the lower bound of the QoS. The rationales of this approach can be explained as follows. According to the arithmetic and geometric mean inequality (Alzer, 1996), we have H ¼ 1 Y g i¼1 ð1 hiÞ P 1 1 Xg i¼1 hi !,

g

!g ¼ 1 ð1 hÞg¼ H: ð1Þ

Proposition 1. (i) Given an equivalent mean of contribution rate, the service quality of a peer-production system with heterogeneous peer participants is always better than homogeneous ones. (ii) As a result, the lower bound of service quality can be measured as long as only the average contribution rate is known.

Researches on an electronic-based brainstorming system like a group support system have shown that the diversity of partici-pants may be of little benefit to group creativity (Bantel and Jack-son, 1989). Service quality level of peer-produced service is uneasily to be measured because of uncertain individual contri-bution. As far as we know, peer-produced service providers do not reveal their QoS information. Consequently, it is difficult for users to judge whether to subscribe or not. From the viewpoint of service providers,Proposition 1indicates that the lower bound of service quality is obtainable when the information of the aver-age contribution rate is known. The benefits of this approach are twofold. First, the average contribution rate h is comparatively easy to measure even if the distribution of the individual contri-bution rate is unknown. Second, the lower bound of the service quality ensures the level of quality to be delivered to the subscribers.

3.2. Subscription functions

The peer participants are heterogeneous on the valuation of the service. We assume that consumers have an independent value

vi

for a service that is unknown to providers and uniformly distrib-uted in interval [0, V]. Uiis the utility function, and p is the price

of the service. The utility function of user i can be formulated as

Ui¼

v

iH p if users subscribe;

0 if users do not subscribe:

Table 1 Model parameters.

Parameters Description

hi Individual contribution rate of peer participants i, hi2 [0, 1]

h Average contribution rate of peer participants, h 2 ½0; 1

g0 Total number of potential users,g0P0

g Subscribed users of peer-production systema

,gP0 ^

g Minimum number of subscribers to ensure the advertised quality, ^gP0

gk Service quality capacity of the platform,gkP0

H Service quality of the peer-production systema

, H 2 [0,1]

H Lower bound of service qualitya

, H 2 ½0; 1

vi Valuation of peer participant i,vi2 [0, V], where V > 0 is the upper bound

p Price of the peer-production system related servicesa

Ui Utility function of a typical peer participant i

K(gk) Platform investment in peer-production system with capacitygk

p The proﬁt of service platform providera

a

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In equilibrium, only the customers with utility UiP0 will subscribe

to the system. That is, the total demand comes from those partici-pants with value

vi

P ^

v

¼ p=H (Shy, 1995) and the number of sub-scriptions is derived as

g

¼ 1 p VH

g

0: ð2Þ 4. Monopolistic market

The objective of the monopolistic service provider is to choose an SLA and price to maximize the profit. The detailed enforce-ment of the SLA agreeenforce-ment is beyond the scope of the paper. Here, we assume the penalty for violating the service quality guarantee is huge, such that the firm definitely commits to the advertised SLA. A platform provider may provide services with differentiated QoS levels. Q denotes the set of all differentiated QoS levels offered by the platform providers and q a typical SLA level. K(

g

kq) is the cost of infrastructure that affords the

accom-modation of

g

kqnumber of users at the same time for the service

with QoS level q.

q 2 Q: ð3Þ

In the following, we ﬁrst discuss a baseline model in which only a single SLA level is offered by the monopolistic provider and then discuss the feasibility of offering multiple SLA levels.

4.1. Single service class

If only a single service quality level is provided, the objective function becomes

MaxH;p

p

m¼ p

g

Kð

g

kÞ

s:t: H 6 H;

g

6

g

k:

k6

g

0. Solving the

ﬁrst-order condition o

p

m/@p = 0, we obtain the optimal price

p*_{= VH/2 and the subscription demand}

_g

0/2. Thus, to ensure the

satisfaction of the SLA, the total number of all the potential partic-ipants of the system should be large enough to satisfy the condi-tion

g

0P2^

g

. Obviously, if the potential market is too small

, the optimal number of

sub-scribed users is

g

m¼ ^

g

and the SLA is promised. If the market

keeps growing to the interval 2^

4.1.2. Choice of QoS level

In the above analysis, the service quality level H is assumed to be exogenous and proposed by the industry standard. If the mar-ket is not perfectly competitive, the service quality level should be one of the decision variables. From (7), we can straightfor-wardly observe that the revenue is positively related to the qual-ity level. In order to maximize proﬁt, the platform provider should improve its service quality as much as possible. However, higher quality desires larger subscribers and higher individual contributions, which requires the reduction of the price. The deci-sion problem the platform provider faces is to choose an appro-priate SLA that generates the maximum revenue. According to

_k: ð8Þ

We ﬁrst derive the optimal service quality level under the condition that the capacity constraint is not binding, bH, by solving @

p

m/@H = 0.

b

H can be obtained from the following equation:

lnð1 hÞ

g

0 2 lnð1 HÞ

ðlnð1 hÞ

g

0 lnð1 HÞÞ lnð1 HÞ

¼1 H

H : ð9Þ

Proposition 2. For a monopolistic service provider offering a single service class, the optimal SLA contract is developed as

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SLA H m;pm ¼ min 1 ð1 hÞgk_{; b}_H_;_VH m 1

g

m=

g

0 ; where

g

m¼ min

g

k; lnð1 bHÞ lnð1 hÞ ! : ð10Þ

Inevitably the QoS is restricted by the number of participants. Price can be used to adjust the number of participants but the max-imum QoS is still limited by the platform capacity. Therefore, the importance of capacity planning cannot be overemphasized.

4.1.3. Choice of capacity investment

The above QoS choice is evaluated after the infrastructure has been constructed. The capacity is treated as an exogenous param-eter as in a short run; we cannot adjust the capacity. In a long run, capacity planning can be considered and capacity becomes an endogenous variable. To avoid unused capacity, the platform pro-vider will choose the capacity that just equals the subscription de-mand ð

g

k¼ ^

g

Þ. The decision problem is rewritten as

g

kbe the optimal capacity that maximizes proﬁt. ^

g

kis given by

kÞ ¼ 0: ð12Þ

Notice that if

p

m< 0, then ^

g

k becomes zero and no service will be

provided.

4.2. Multiple service classes

Now, we analyze the scenario in which multiple service levels are offered. Assume the platform provider offers two classes of ser-vice quality level: a high class of serser-vice with quality level Hhand

price ph, and a low class of service with quality level Hland price pl.

The utility function of user i subscribing to class q is Ui=

vi

Hq pq

where q 2 Q = {h,l}. The customers choose a better service to sub-scribe to if his/her utility UiP0. Let ^

v1

be the value of a marginal

2 ½^

v1

g

h¼

g

0=2;

g

l ¼ 0. The result shows that the platform will never

of-fer multiple classes of service and only a high-quality service is provided.

Proposition 3. A monopolistic provider never provides multiple differentiated SLA contracts.

The result mainly comes from the signiﬁcant externality effect of the users on the service quality and the effect overweighs the market segmentation effect. Therefore, a better business strategy for a monopolistic provider is to offer single class of service as developed. In reality, at the time when there were no other com-petitors, Experts-Exchange and Mininova provided two types of service. Basic service allowed users to access limited contents (low quality), whereas premium service can search whole website database (high quality). But due to the nature of peer production, it is hard to control the contribution of self-organized participants and make two types of service quality feasible. After running for a period of time, basic service was revoked. This phenomenon is consistent withProposition 3, implying that service differentiation of peer-produced service in a monopolistic market is infeasible. 5. Duopolistic market

In this section, we extend our model to discuss the quality and price competition of two independent service providers. The sce-nario that both platform providers conduct price competition for providing identical SLA contracts is ﬁrst discussed. Then, heteroge-neous SLA contracts are provided by the two competing platform providers. First, we consider that there are two identical symmetric service providers.

5.1. Homogeneous SLA contract 5.1.1. Choice of SLA contract

As the service quality levels of the two systems are identical, users always choose the cheaper one. For the sake of price compe-tition, the providers will reduce their price to attract the users from their opponent. The number of subscriptions is increasing as the competing service providers continue to drop their price. The pro-cess will not cease until one of two situations occurs: the number of subscriptions reaches the capacity limit of the infrastructure or the providers make no profit. In the first scenario, both competing providers received non-negative profit. The price and the number of subscribers are

p

0 q ; ð17Þ

where Hk¼ 1 ð1 hÞgkand bH is a solution of lnð1 HÞ lnð1 hÞ¼

g

0 4 1 þ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 8Kð

g

kÞ=ðVH

g

0Þ q : ð18Þ

And each provider receives proﬁt

p

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Proposition 4. For homogeneous service providers, higher capacity may improve the QoS but is never beneficial to homogeneous providers because of higher intensive competition. Furthermore, both providers receive zero profit if the capacity is higher than specific threshold.

In reality, Experts-Exchange and Google Answers provided com-parable service quality to the public. Google Answers started with small capacity and was very popular (West, 2002). It was full of users and very busy and Google did make proﬁt. ThusProposition 4is evidenced when the demand is limited by the capacity. Similar scenario can also be observed in P2P resource sharing service pro-viders like Pirate Bay and Mininova.

In a long run, providers set up an appropriate capacity invest-ment to ensure a non-negative proﬁt. The proﬁt function for each platform provider is written as

g

kbe the optimal capacity that maximizes proﬁt. ^

g

kis given by

kÞ ¼ 0: ð21Þ

Notice that if

p

c< 0, then ^

g

k becomes zero and no service will be

provided. Comparing(12) and (21), we can ﬁnd that the levels of the capacity and service quality in a competing market are smaller than in a monopolistic market.

5.2. Heterogeneous SLA contracts

Next, we consider two competing providers offering heteroge-neous SLA contracts with high quality Hh and low quality Hl,

respectively.

5.2.1. Choice of SLA contract

The timing of the game stage is as follows. In the ﬁrst stage, the competitive providers choose the quality level simultaneously; in the second stage, the providers choose the price for their service simultaneously. Finally, after observing the SLA contract, the cus-tomers choose a better service if UiP0. From(13), the proﬁt

g

klÞ: ð24Þ

Since @

p

h/@Hh> 0, the best response quality strategy of the high

ser-vice provider is to set the quality as high as possible, calculating his opponent’s strategy. The best response quality strategy of the pro-vider with a lower quality level can be obtained by solving @

p

l/

@HlP0. Here, we have Hl ¼ /Hh, where / 6 4/7 and the price can

thus be obtained as ph¼ 2VHhð1

u

Þ 4

u

; pl¼ VHlð1

u

Þ 4

u

: ð25Þ

The demand for a high- and low-quality service can be obtained as

g

h¼ 2g0 4/

g

l¼ g0 4/ 8 > < > : if Hl–0;

g

h¼ g0 2

g

l¼ 0 ( if Hl¼ 0: ð26Þ

Similarly, the proﬁts for the two providers with differentiated ser-vice quality can be obtained as

p

h¼

4VHhð1

u

Þ

g

0

ð4

klÞ: ð27Þ

From(27), we know that both service providers will set their quality as high as possible, satisfying the condition H

l ¼ /Hh. / is

k¼

maxð4

g

0=minð

g

kh=2;

g

klÞ; 0Þ. In addition, the demand for each

type of service will be sufﬁciently large to ensure the SLA adver-tised.

r

¼ ð1 ð1 hÞgl_{Þ=ð1 ð1}_hÞgh_{Þ denotes the ratio of the}

ac-tual lower quality level to the higher one. It can be easily veriﬁed that @

r

/@/ < 0. Since the service providers can advertise their ser-vice with a quality level not larger than the actual quality level and the high-quality provider can set his/her quality as high as possible regardless of the level of the lower quality one, we have / 6 /g,

where /gis the value of / that satisﬁes / =

r

. Finally, we obtain

the equilibrium SLAs for both providers:

Hh¼ 1 ð1 hÞgh; Hl¼

u

Hh; where

u

¼ minð4=7;

u

k;

u

gÞ:

ð28Þ

Finally, these heterogeneous SLA contracts SLA H h;ph

and SLA H l;pl

are described inEqs. (25) and (28).

Proposition 5. If two competing service providers offer heteroge-neous SLA contracts,

(i) the demand, price, and proﬁt of high-quality service are more than those of low quality;

(ii) the low-quality provider advertises a lower SLA than he/she can actually offer.

As Proposition 5 suggests, the low-quality provider should advertise a lower SLA than he/she can actually offer. By doing this the users enjoy higher quality than advertised, and a sufﬁcient number of users required to maintain SLA is kept. Thus the low-quality provider can compete with its opponent and sustain. Evi-dence can be observed from the competition of Pirate Bay and Torrentz. The former one is the leading company while the latter one provides lower quality of service. But the resources found in Torrentz are more than expected, which makes its subscribers en-joy better quality. By advertising a lower SLA, Torrentz maintains sufﬁcient subscribers and survives in the competition with Pirate Bay.

0 4Hh Hl : ð29Þ

Because the capacity levels of two platforms,

g

khand

g

kl,

be-come functions of the Hh and Hl, the objective function of the

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klÞ; s:t: Hl61 ð1 hÞgkl: ð31Þ

Without regarding the advertised quality agreement, the high-qual-ity platform provider’s best response function bH

hðHlÞ is given by

solving @

p

h/@Hh= 0, which can be rewritten as 4 bH hðHlÞ 2 3 bH hðHlÞHlþ 2H2l 4 bH hðHlÞ Hl 2V bH hðHlÞ þ K0 2 bH hðHlÞ

g

0 4 bH hðHlÞ Hl ! Hl¼ 0: ð32Þ

However, if the advertised quality cannot be satisﬁed, the high-quality platform provider has to reﬁne its advertised high-quality to sat-isfy the SLA. Hence, its best response function eH

hðHlÞ is given by

solving Hh¼ 1 ð1 hÞgkh when the case arises, which can be

rewritten as 4 eH hðHlÞ Hl ln 1 eH hðHlÞ 2 eH hðHlÞ ¼ lnð1 hÞ

g

0: ð33Þ

As a result, the high-quality platform provider’s best response func-tion is given by H hðHlÞ ¼ b H hðHlÞ; if bHhðHlÞ 6 1 ð1 hÞgkh; e H hðHlÞ; if bHhðHlÞ > 1 ð1 hÞgkh: ( ð34Þ

Similarly, the low-quality platform provider’s best response func-tion is given by H lðHhÞ ¼ b H lðHhÞ; if bHlðHhÞ 6 1 ð1 hÞgkl; e H lðHhÞ; if bHlðHhÞ > 1 ð1 hÞgkl; ( ð35Þ where bH

kÞ ¼ k

g

2k, where k is a non-negative constant and

g

kis the

number of users the service platform can serve. The parameter for investment function is k = 0.000001. As peer production producing high-quality results from small contributions by numerous

inde-pendent volunteers (Benkler, 2002; Benkler and Nissenbaum,

2006). So we assume the average contribution rate h ¼ 0:00005 , which appropriately describes the characteristic of small individual contributions. The number of users and the capacity should be large. Therefore, in the short-term scenario, the number of potential users is

FromFig. 1, it is observed that the service quality of the short-term scenario increases with capacity, except in homogeneous competing providers. For the monopoly provider (Hm) and

homo-geneous competing providers (Hc), if the capacity is not large

en-ough to service the number of subscribers required to achieve optimal quality, the quality is bounded by capacity and both mar-kets provide an identical service quality. If the capacity is large en-ough, Hmis kept but Hcdecreases as the capacity increases. The

intuition is because homogeneous providers compete with each other on price and the price undercutting continues. Finally, it de-clines to cover just the investment cost. The cost is increased with capacity and thus the price is also increased. However, a higher price results in fewer subscribers, and consequently the quality is decreased. As for heterogeneous competing providers, the optimal quality of the lower one is proportional to that of the higher one and the ratio is constrained by capacity. The ratio becomes zero if both capacities are low and Hlis set to 0. As both providers

in-crease their capacity, the ratio also rises and is becoming closer to the optimal rate 4/7. Finally, both platforms can serve more than the optimal subscribers and the quality is ﬁxed.

Observation 1. The effect of capacity on service quality of homogeneous competing providers is non-monotonic (positive if capacity is small but negative if large). However, in other market settings, the effect of capacity on service quality is always non-negative.

Competition generally results in a lower price and higher QoS. However, for homogeneous providers, intensive competition may force the providers set higher price to cover the investment as the capacity becomes sufﬁciently large. Consequently, users will

30000 40000 50000 60000 70000 80000

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not be willing to subscribe because of high price and the service quality cannot be improved since there is no enough subscribers. As for the other market structures, the monopolistic provider serve only one type of quality, whereas the heterogeneous providers pro-vide different service quality to different types of users. In these settings more users can be served by way of improving capacity and the service quality can be improved.

6.1.2. Price

Ideally, the service quality is increased with subscribers. Never-theless, this condition holds only if there is no capacity constraint. If this is not the case, the quality will not increase with the number of subscribers after the capacity limit has been reached. InFig. 2, for the monopoly provider (pm), when the capacity is small, he/she sets

a higher price to restrict the amount of subscribers. The price is then reduced to attract more users as the capacity increases until the optimal quality is reached, and the price is ﬁxed. For the homoge-neous competing providers (pc), there is a bit different.

Interest-ingly, the price first decreases and then increases. The reason for the decreasing part is the same as that of the monopoly provider, while the increasing part results from the effect of price competi-tion and increasing capacity investment cost. If the capacity is large enough, the process of price undercutting won’t stop until both pro-viders make no profit. Then, the price has to cover their capacity investment cost to ensure they receive non-negative profit, and this is the reason the price increases with capacity. The effect of capacity on the price decision in two heterogeneous competing providers (ph

and pl) could be in opposite directions. The price of a high-quality

service (ph) increases with the capacity when the capacity is small,

because it improves the quality level. However, because of the emergence of a competing low-quality service, the price decreases with the capacity until the optimal quality is reached. After that, the price is a ﬁxed value. In contrast, the price of a low-quality service (pl) shows different result. In the beginning, the low-quality service

is not provided since its quality is 0 and no price can be charged. The price is then increasing as the service quality keeps improving. Fi-nally, the optimal quality level results in a ﬁxed price.

Observation 2. The effects of capacity on price level with re-spect to various market settings are signiﬁcantly different.

(1) The effect of capacity on the service price of a monopolistic provider is always non-positive. However, the effect of capac-ity on the service price of homogeneous providers is non-monotonic (negative if capacity is small but positive if large).

(2) The effect of capacity on the service price of the high quality provider is non-monotonic (positive if capacity is sufﬁciently small or large but negative if in some middle interval). How-ever, the effect of capacity on the service price of the low-quality provider is always non-negative.

Overloading occurs when the capacity is small, thus the monop-olistic provider utilizes price as a controlling tool to avoid this problem. For heterogeneous providers with small capacity, the high-quality provider can set a higher price since the opponent can not commit the SLA because of the shortage of users. But by providing more capacity the low-quality provider can service more users and thus the SLA can be committed. To maintain the service quality the high type provider has to lower the price to keep a suf-ﬁcient number of users to guarantee the quality advertised. 6.1.3. Proﬁt

FromFig. 3, we observed that all the proﬁt levels decrease as the capacity becomes large enough because of the convexly increasing capacity cost. For the monopoly provider (

p

k

η

m π c

π

h π l

π

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(2) The effect of capacity on the proﬁt of the high-quality pro-vider is always negative. However, the effect of capacity on the service price of the low-quality provider is non-mono-tonic (negative if capacity is sufﬁciently small or large but positive if in some middle interval).

The emphasis of peer-produced service is on the power of com-munity and network externality. Ideally, the more participants, the better the service quality; however, the quality is bounded by the installed capacity and capacity investment is costly. For a monopo-listic provider, balancing the capacity investment and service qual-ity is the main issue, which inherently should be resolved in a long-term scenario. The impact of capacity on the profit of homogeneous competing providers is always negative as a larger capacity only re-sults in higher competition. The capacity effect on the profit of the low-quality provider is similar to that of the monopolistic provider. However, the high-quality provider has less incentive to expand its capacity. As we can observe, homogeneous competing providers re-ceive higher profit than low-quality providers. That is, only the high-quality provider benefits from differentiation.

6.2. Long-term scenario

As observed fromFigs. 4–7, in the long run, all the providers provide increasing service quality and receive more proﬁt as the po-tential user population (market size) grows. However, the market size does have an impact in some ways. When the market size is small, we can ﬁnd that the monopoly provider provides higher quality and establishes larger capacity than the high-quality pro-vider. The low-quality provider serves users with higher quality and larger capacity than homogeneous providers. Although the quality ranks in third place for the low-quality provider, he/she charges the lowest price. If the market size is large enough, the monopoly provider would provider lower quality than the high-quality one, but homogeneous providers are better than that of the low-quality one. However, fromFig. 6, we know that the low-quality provider does not invest less in capacity than homogeneous providers even if the quality is not as good as theirs. As for the price, the homogeneous providers charge more than the high-quality pro-vider even though they do not provide better quality.

6.2.1. Discussion (the role of market size)

In a large market, the high-quality provider establishes the larg-est capacity and provides the highlarg-est service quality, but does not

Long Term 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Potential Users Quality 0

η

η

η

π

m π c π h π l π

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charge the highest price. In contrast, the monopoly market sets the highest price and receives the highest proﬁt. The homogeneous competing providers set up the smallest capacity, but charge a good price even though the quality is not good enough. The low-quality provider invests in capacity greater than that of homogeneous pro-viders, but the quality, price, and proﬁt rank the lowest. In a small market, the quality of competitive markets (homogeneous and het-erogeneous) is lower than the monopoly market. From the view-point of potential users, they can enjoy high-quality contents from differentiated services if the market size is large enough. 7. Managerial implications

Our research provides useful insights for developing business strategies of peer-produced services to enhance the proﬁt of a plat-form provider under various market settings. From our analytical and numerical ﬁndings, we have several implications, described as follows, for those who intend to operate peer-produced service platforms.

First, SLA based contracts for peer-produced services can be fea-sibly deployed. While service quality level of peer-produced ser-vice is uneasily to be measured because of uncertain individual contribution, we show that it is possible to obtain the lower bound of service quality. When service quality information is available, users would also benefit from choosing the appropriate service as needed and the service provider can further develop SLA based service pricing schemes. Second, although product versioning or differentiation is a popular business strategy for profitability improvement, our results reveal it is infeasible for a monopolistic peer-produced service provider. The phenomenon mainly comes from there exists significant positive externality on the peer-pro-duced services. Furthermore, in a duopolistic market, the benefit from service differentiation becomes effective only when the pop-ulation of users is sufficiently large. Third, the effect of the critical mass should be considered in a competition market. According to our findings, for a low-quality provider in a heterogeneous compe-tition environment, only when the number of users reaches the critical mass will it make profit. Besides, by maintaining the users to ensure the suitable quality, the low-quality provider can differ-entiate itself from the high-quality one. Therefore, the provider positioned as a low-quality service provider should focus its strat-egy on attracting the critical mass. However, it would not be necessary to control the contributions of users. Since the heteroge-neity of users help improve the quality of peer-produced service (Stviliaet al., 2008), service providers can focus on attracting users rather than filtering individual contribution rate. Fourth, under-standing the market structure and position is essential before investment. The same capacity would have very different impacts on quality, price and profit in various market structures. Intui-tively, the providers should attract as many users as possible by building up sufficient large capacity. If a service provider expands capacity unceasingly, the result could possibly have exactly oppo-site effect. A duopolistic market, even when offering identical ser-vice quality level, each competing provider can still receive non-negative profit. For the homogeneous competitors, the profit will be corroded completely if they have to raise the price to cover the capacity cost. Consequently, no profit can be gained. These im-ply that if a company plans to operate a service platform, by under-standing the competitors in the market a better investment decision can be made.

8. Conclusions

Pricing based on SLA have become increasingly promising in IT related services. Peer-produced services are a new types of services

in which service quality is determined by the participants. While the service platform providers do not need to provide the service, the quality is uncertain. Guaranteed service quality level is an essential component for SLA based pricing. In this research, we show that an SLA lower bound can be obtained by simply measur-ing the average contribution rate of participants. We utilize a game theoretical approach to study price, quality and capacity decisions of service providers. SLA based pricing strategies and capacity investments under various market structures can be further devel-oped. The proposed approach can feasibly used to support the operations of peer-produced services.

Our results show that in a monopolistic market, the service pro-vider should provide only single SLA since no users would sub-scribe to low quality service. For a competitive market with homogeneous providers, the market is equally divided and both providers can make profit constrained by capacity, or make no profit because of competition. As a result, their profits decrease with the capacity. For a market with heterogeneous providers, the demand, price, and profit of high-quality service are more than those of low quality and the quality provider advertises a low-er SLA than he/she can actually offlow-er. In addition to the market structure, capacity plays a significant role in developing service quality and pricing strategy. In most of the marketing settings, the service quality increases as the capacity becomes larger; how-ever, the result could be opposite in a market with homogeneous providers. For a monopolistic provider, a higher capacity never raises the service price of a monopolistic provider. However, the ef-fect of capacity on the service price of homogeneous providers or a high-quality provider is non-monotonic. Contrary to other sce-nario, a higher capacity will generally raise the service price of a low-quality provider.

The main unique contributions of this study are as follows From the theoretic perspective, this paper utilizes reliability model based on a simple average contribution rate to measure the lower bound SLA, which conquer the quality uncertainty of peer-pro-duced service and incorporate game theory optimization model develop competition models with quality and capacity constraints in the context of peer-produced services. From the practical per-spective, our research suggests a feasible business model (SLA based pricing and competition strategy) to support the operations of peer-produced services. Various market structures are investi-gated to completely reveal the business model, and managerial implications are provided to practitioners for better decision making.

There are several directions for future research. First, the aver-age contribution rate is used to set the lower bound of the SLA, but the mechanism of measuring is not explicitly discussed. Sec-ond, the individual contribute rate is treated as an exogenously random variable; the incentive for contribution can be further developed as the quality is directly associated with the contribu-tion rate. Third, the participants and contribucontribu-tion rate change from time to time. It would be valuable to study the dynamic SLA mech-anism and pricing strategies. Finally, in addition to the resource availability, the service quality evaluation can be extended to in-clude more performance factors, such as resource freshness and popularity and retrieval delay.

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