Who are Better off for Higher Platform Protection? Impacts of

Consumer Fairness Concerns

Lina Yao

College of Management and Economics, Tianjin University

linayao@tju.edu.cn

Zhiyong Li

College of Management and Economics, Tianjin University

zhiyongli@tju.edu.cn

Guofang Nan

College of Management and Economics, Tianjin University

gfnan@tju.edu.cn

Minqiang Li

College of Management and Economics, Tianjin University

mqli@tju.edu.cn

Abstract

The threat of piracy and the consumer fairness perception have important effects on

platform protection strategies. The former asks the platform to increase protection,

whereas higher protection has a negative effect on legal consumers. The later asks the

competing platforms to charge fair prices to consumers, which further influences

platform protection strategies. In this study, we use a competitive model to analyze

whether platforms are better off if they provide higher protection in the presence of

the consumer fairness concerns. We find that in the case of the absence of fairness

concerns, platforms and their content providers always have the aligned attitudes

toward platform protection. Interestingly, when the change in content providers’

network externalities with protection is sufficiently small, the platforms and their

content providers will be worse off if the platforms provide better protection.

However, in the case of the presence of fairness concerns, the higher protection

decreases the platforms’ profits and increases the profits of the content providers

when consumer fairness concerns and the change in content providers’ network

externalities with protection are sufficiently large, and misfit cost is sufficiently small.

Moreover, in some scenarios, the higher protection may increase the platforms’ profits

but decrease the profits of the content providers.

Keywords: Two-sided platforms, Platform protection, Fairness, Piracy, Competition

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1. Introduction

Advances in information technology have made platforms be more prevalent. The

typical platforms include Microsoft’s Windows, Amazon’s Kindle, Apple’ iTune, and

Sony’s Playstation. As a result, more and more content providers are centered around

and sell their content on platforms. Unfortunately, piracy has caused huge losses to

the platforms and content providers. For instance, nearly three million people daily

search for unauthorized downloads of the top 90 books on Amazon, which leading to

revenue losses from piracy of approximately $3 billion annually (Digimark, 2014).

Nintendo, the market leader in game platforms, has been reported have lost $41

billion due to illegal online downloads.1 Moreover, a study by 24/7 Wall St. reports

that Apple and the companies that sell software for the iPhone and iPod touch at the

App Store have lost over $450 million to piracy since the store opened in July 2008.2

Finally, Apple, which takes 30% of the revenue generated by downloads at the App

Store has lost about $140 million from piracy. More interestingly, prior to 2009,

Apple’s iTunes Store utilized the FairPlay DRM against illegal copying music,

however, all iTunes music no longer uses DRM since April 2009.3 The reason behind

this industry practice is the topic of this paper.

Some studies have proofed that consumers may not buy products or service sold at

“unfair” prices, even though the material value of products exceeds those unfair prices

(Rabin 1993, Anderson and Simester 2008). The consumers will have negative utility,

if they find that the product purchased on the platform is more expensive than that on

the other platform. Consequently, competing platforms must consider the effect of the

consumer fairness concerns when they decide the prices for consumers, which in turn

further affect the platforms’ pricing strategy for content providers due to the

cross-side network effects. In addition, platform protection has different effects on

content providers and consumers. Higher protection makes a positive effect on

content providers, whereas makes a negative effect on consumers. The joint effects of

consumer fairness concerns and platform protection on content providers and

consumers will further affect the platforms’ equilibrium prices and profits. As a result,

competing platforms need to balance the trade-off between the effect of platform

protection and the effect of consumer fairness concerns. Previous researches

involving the joint effects are rare. In this paper, we attempt to fill this gap by

addressing the following research questions: Does lower platform protection

necessarily hurt platforms and content providers? Is higher platform protection better

off for platforms and content providers? What is the effect of consumer fairness

concerns on platform protection strategy?

We lay out an analytical model in which two competitive platforms provide

platform protection to combat piracy. Comparing the equilibrium outcome in the case

1 See http://www.cpmputerbild.de/areikel/cbs-News-Ds-Nintendo-R4-Kopiermodul-Verbot-5499649. 2 See https://247wallst.com/apps-software/2010/01/13/apple-app-store-has-lost-450-million-to-piracy/ and

https://247wallst.com/apps-software/2010/04/20/apple-app-store-has-lost-450-million-to-piracy-update-what-about

-the-ipad/. 3 See https://opensource.com/life/11/11/drm-graveyard-brief-history-digital-rights-management-music.

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in the absence of consumer fairness concerns with that in the case in the presence of

consumer fairness concerns, we uncover several interesting results. First, we find

whether platforms and content providers can benefit from the platform protection

depends on which side of the platform has greater network externalities and the unit

misfit cost. Second, in the case in the absence of consumer fairness concerns,

platforms and content providers always have same attitude towards protection. Third,

in the case in the presence of consumer fairness concerns, the platforms’ and content

providers’ profits may have conflicts of interest when the platform protection changes.

The rest of this paper is organized as follows. In section 2, we review the related

literature. In section 3, we analyze the benchmark case of consumers without the

fairness concerns, and address the effects of the platform protection on the platforms

and content providers. In section 4, we solve the equilibrium outcomes for the case of

consumers with fairness concerns, analyze the effect of consumer fairness concerns

on the platform protection. In section 5, concludes the paper.

2. Literature Review

This research is mainly related to three streams of literature, social and economic

impacts of piracy, two sided market and network effects, and consumer fairness

concerns.

The first steam is the work on piracy. We discuss related work on the social and

economic impacts of piracy (Lahiri and Dey, 2013; Sundararajan, 2004). Conner and

Rumelt (1991) establish that protection technology always increase firm profits,

unless the product displays positive network effects. Sundararajan (2004) shows that

the optimal pricing strategy for monopolist is to make all consumers indifferent

concerning pirated versus legal usage by focusing on technology deterrence. Geng

and Lee (2013) show that reducing piracy quality and increasing piracy search costs

are both effective in controlling piracy, which affect consumer surplus differently.

Bhattacharjee et al. (2006) find that retailer profits are maximized with piracy by

modeling consumer search of digital experience goods in emerging markets. Lahiri

and Dey (2013) show that lower enforcement for piracy increases the quality of legal

products in certain situations. A branch of this literature identifies several situations in

which a firm may find it profitable to tolerate or support piracy. In the previous

literature, it is shown that piracy is not definitively bad for firms. Zhang (2018) finds

that removing DRM increases digital music sales by 10%, and it increases the sales of

lower-selling albums significantly. Complementarity between products may lead to

positive effects for firms. Leung (2015) finds that although music piracy decreases

music sales by 24% to 42%, it contributes 12% to iPod sales. On the other hand,

music piracy decreases the record companies’ profits due to lower record sales,

whereas it can also increase revenue for artists from music complements such as

concerts (Gayer and Shy, 2006; Mortimer and Saha, 2012). The above literature all

study piracy from the perspective of the one-sided market and do not address the issue

about piracy from the perspective of the platform protection on the two-sided platform.

Our paper helps to fill this gap in the extant literature by study the platform protection

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strategy of the competing platforms.

Second, our research also contributes to literature on the two-sided markets

(Armstrong, 2006; Rochet and Tirole, 2006; Li et al.). They show the price structure

in two-sided markets depends heavily on the size of indirect network externalities.

There are two main points in the research on two-sided platforms. The first is that

platforms can manipulate both the price level (the price charged to members on both

sides) and the price structure (how the total is split up) (Rochet and Tirole, 2006). The

second is that platforms can implement subsidies or discounts to one side and

determine whether the two sides of the platform are single or multiple (Armstrong,

2006). Anderson and Simester (2010) study the investment trade-offs between

improving technology and increasing its cross-market network effects. The previous

studies on two-sided markets mostly address the optimal pricing. Katsamakas and

Bakos (2008) study the effect of different platform ownership structures (independent,

buyer, or seller owned) on the choice of technology in a monopoly setting. Kim and

Tse (2011) investigates the effect of the complexity of questions, accumulated

knowledge, and the price structure of advertising on two-sided platform of online

knowledge-sharing. Bakos and Katsamakas (2008) show that a platform will focus its

investment and pricing on extracting surplus from one side to make sure the

participation of the other side because of network externalities. Previous articles on

two-sided markets focused on pricing structures and some relevant strategic choices,

but neglect the impact of piracy on the platform. In our paper, we not only examine

the effect of platform protection on platforms’ players, but also investigate the effect

of the consumer fairness concerns.

Third, this paper is also closely related to the growing stream of literature that

incorporates fairness concerns into platforms’ optimal strategies. Consumers’ fairness

concerns have been well documented in the marketing and economics literature

(Rabin 1993; Anderson and Simester 2008; Yi et al. 2018). Fehr and Schmidt (1999)

propose a model of peer-induced “inequity aversion” to capture the notion that

consumers experience a disutility from receiving a payoff that is different from the

others. Cui et al. (2007) find that channel members’ fairness concerns may help

achieve higher coordination for profit maximization in the channel. Guo (2015) shows

that the seller’s ex ante profit may increase as more consumers become inequity

averse, assuming that the firm has exogenous quality and that consumers make

inferences only from the firm’s price. Guo and Jiang (2016) consider that consumers

with fairness concerns care about not only from the price but also from the quality of

the product, and find that inequity aversion may benefit an efficient firm and hurt an

inefficient firm and reduce consumers’ monetary payoffs. Li and Jain (2016) consider

the impact of peer-induced fairness on firms’ behavior-based pricing strategy, where

consumers are mostly concerned about the discriminatory prices they pay in

comparison to prices other consumers pay. They find that consumers’ fairness

concerns reduce inefficient switching and improve social welfare. In contrast to

previous research which study consumer fairness concerns from the perspective of the

one-sided market, we consider the effect of consumer fairness concerns from the

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perspective of the two-sided markets.

3. The Duopoly model without Consumer Fairness Concerns

In this section, we study competition between two platforms in the threat of content

piracy. Content providers and consumers can choose to affiliate with one platform (i.e.,

single-homing), or the two platforms (i.e., multi-homing). Platforms do not incur

marginal costs and their fixed costs for setting up and running the business are

normalized to zero. Platforms generate income from both consumers (by charging an

access fee) and content providers (by charging a license fee). We allow access fee or

license fee to be negative; that is, platforms may subsidize consumer or the content

providers. We start with the case in which consumers do not show fairness concerns.

We use the basic model as a benchmark to examine the effect of consumer fairness

concerns. For ease of exposition, we use subscripts “𝑁𝐹” and “𝐹” on variables to

indicate the context of no fairness concerns and fairness concerns, respectively.

Consumers: Consumers buy a unit of legal contents on the platform. They will join

the platform if the platform provides a nonnegative net utility. Consumers are

heterogeneous with respect to their preferences for the two platforms and are

uniformly distributed over a Hotelling line with range [0,1]. The net utility of a

consumer choosing platform 1 is given by

𝑈𝑁𝐹1 = 𝑉 + 𝑎𝑛𝑁𝐹

1 − 𝑝𝑁𝐹1 − 𝑡𝑥. (1)

The net utility of a consumer choosing platform 2 is given by

𝑈𝑁𝐹2 = 𝑉 + 𝑎𝑛𝑁𝐹

2 − 𝑝𝑁𝐹2 − 𝑡(1 − 𝑥). (2)

where 𝑉 is the intrinsic utility that the consumers obtain form buying access to a

platform, and 𝑡 represents the misfit cost. Moreover, consumers derive utility from

contents provided by content providers. The number of contents 𝑛𝑁𝐹𝑖 (with 𝑖 ∈ {1,2})

is available for this platform, the larger the utility. The benefit from an extra unit of

production is given by 𝑎.

Let 𝑥𝑁𝐹1 be the marginal consumer who is indifferent between accessing platform

1 or not. By setting 𝑈𝑁𝐹1 = 0, we have 𝑥𝑁𝐹

1 =𝑉+𝑎𝑛𝑁𝐹

1 −𝑝𝑁𝐹1

𝑡. In the same way, the

marginal consumer that is indifferent between joining platform 2 or not is given by

𝑥𝑁𝐹2 = 1 −

𝑉+𝑎𝑛𝑁𝐹2 −𝑝𝑁𝐹

2

𝑡. As a result, the market shares of platforms 1 and 2 are 𝑥𝑁𝐹

1

and 1 − 𝑥𝑁𝐹2 , respectively.

Content providers: Content providers with a unit mass are multi-home and can

offer contents for both platforms. They are heterogeneous with respect to the fixed

costs, 𝑓, of providing their contents through the platform. A content provider can earn

an expected amount of 𝑏 from a consumer when he sells his content on a platform.

Thus, the profit of a content provider producing for platform 𝑖 is

𝜋𝑁𝐹𝑖 = 𝑏𝑠𝑁𝐹

𝑖 − 𝑙𝑁𝐹𝑖 − 𝑓𝑁𝐹, (3)

where 𝑠𝑁𝐹𝑖 denotes the number of consumers at platform 𝑖 and 𝑙𝑁𝐹

𝑖 denotes the

license fee charged by platform 𝑖. A provider offer his content for platform 𝑖 as long

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as he do not incur a loss, i.e., 𝜋𝑁𝐹𝑖 ≥ 0 ⟺ 𝑓𝑁𝐹 ≤ 𝑏𝑠𝑁𝐹

𝑖 − 𝑙𝑁𝐹𝑖 = 𝑓𝑁𝑑 . Thus, all

providers with 𝑓 < 𝑓𝑁𝑑 enter and the amount of providers on platform 𝑖 is given by

𝑛𝑁𝐹𝑖 = 𝑏𝑠𝑁𝐹

𝑖 − 𝑙𝑁𝐹𝑖 ， (4)

where 𝑠𝑁𝐹1 = 𝑥𝑁𝐹

1 and 𝑠𝑁𝐹2 = 1 − 𝑥𝑁𝐹

2 .

Platforms: Platforms choose prices on both sides simultaneously to maximize total

profits of

𝛱𝑁𝐹𝑖 = 𝑠𝑁𝐹

𝑖 𝑝𝑁𝐹𝑖 + 𝑛𝑁𝐹

𝑖 𝑙𝑁𝐹𝑖 . (5)

Effects of platform protection and piracy: Suppose the parameter 𝑘 measures

the level of platform protection and higher level of 𝑘 denotes higher platform

protection. Different from most two-sided market models, the magnitude of network

externalities is not fixed exogenously but depends on the level of platform protection.

We denote 𝑎(𝑘) as the utility of a consumer from the interaction with an

additional content provider. The higher protection creates greater experience disutility

(e.g., more restrictions on the flexibility of usage) and/or the paying a higher

purchasing fee to content providers. Thus, the benefit a consumer deriving from an

additional content provider decreases with the level of platform protection. Formally,

𝑎′(𝑘) < 0. In addition, we denote 𝑏(𝑘) as the revenue of a content provider from the

interaction with an additional consumer. Higher platform protection is enable to more

consumers to consume the legal contents. Thus, the benefit a content provider

deriving from an additional consumer is positively affected by platform protection.

Formally, 𝑏′(𝑘) > 0.

To guarantee that all optimization problems with competing platforms are well

behaved, we make the following assumption:

Assumption 1: 𝑡 >(𝑎+𝑏)2

4.

The assumption states that the indirect network effect must be relatively small

compared to the degree of horizontal differentiation on both sides of the markets. This

assumption is standard in two-sided market models with cross-group externalities and

is needed to ensure concavity of the platforms’ profit functions.

The time line of the game is as follows. In the first stage, competing platforms set

prices simultaneously. In the second stage, content providers and consumers make

purchasing decisions, respectively. Table 1 summarizes the main notations used in the

paper.

Table 1. Summary of notations

Notation Description and Comments

𝑖 Index for platform, 𝑖 ∈ {1,2}.

𝑗 Index for setting type, 𝑗 ∈ {𝑁𝐹, 𝐹}.

𝑘 Level of platform protection.

𝑟 Degree of fairness concerns.

𝑡 Unit misfit cost.

𝑈𝑗𝑖 A consumer’s utility derived from platform 𝑖 in setting 𝑗.

𝑉 Intrinsic value.

𝑎(𝑘) Benefit a consumer deriving from an additional content provider.

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𝑏(𝑘) Benefit a content provider deriving from an additional consumer.

𝑥 Location of a given consumer.

𝑝𝑗𝑖 Price for consumers of the platform 𝑖 in setting 𝑗.

𝑙𝑗𝑖 License fee charged by platform 𝑖 in setting 𝑗.

𝑛𝑗𝑖 Number of content providers at platform 𝑖 in setting 𝑗

𝑠𝑗𝑖 Number of consumers at platform 𝑖 in setting 𝑗

Π𝑗𝑖 Profit of platform vendor i in setting 𝑗.

π𝑗 Content provider 𝑗’ profit.

𝑓 A fixed investment cost for content providers.

Using the first-order conditions (FOCs), we can derive the equilibrium outcomes,

which are summarized by the following proposition.

Proposition 1 (Equilibrium Outcomes without Consumer Fairness Concerns)

Without fairness concerns, the equilibrium prices are

𝑝𝑁𝐹1 = 𝑝𝑁𝐹

2 = 𝑝𝑁𝐹 =2𝑡−𝑎𝑏−𝑏2

4𝑡−(𝑎+𝑏)2,

𝑙𝑁𝐹1 = 𝑙𝑁𝐹

2 = 𝑙𝑁𝐹 =𝑉(𝑏−𝑎)

4𝑡−(𝑎+𝑏)2,

the content providers’ equilibrium profits are

𝜋𝑁𝐹 =𝑉(𝑎+𝑏)

4𝑡−(𝑎+𝑏)2 − 𝑓,

and the profits of content providers and platforms are given by

𝛱𝑁𝐹1 = 𝛱𝑁𝐹

2 = 𝛱𝑁𝐹 =𝑉2

4𝑡−(𝑎+𝑏)2.

Proof. All proofs are omitted because of the page limit and are available upon

request.

Next, we analyze the platforms and content providers’ attitudes towards protection.

For the platforms and the content providers, are they always better off from a higher

platform protection? Proposition 2 summarizes their attitudes towards platform

protection.

Proposition 2 (Attitudes towards Platform Protection without Fairness Concerns)

If the change in legal sales (i.e., 𝑏′(𝑘)), is large (small) compared to the change in

consumers’ expect revenue form a content provider (i.e., |𝑎′(𝑘)|), both platforms and

content providers prefer higher (lower) protection.

For platforms, there are two reasons to explain for their preferences. On the

positive effect, platforms benefit from increased platforms protection because they are

able to charge higher license fees to content providers or access fees to consumers in

the case of certain conditions. One the downside, higher platform protection may

decrease the numbers of consumers and content providers to lower revenues. When

the change in content providers’ expected revenue form additional consumer with

protection is large, the positive effect dominates, thus platforms may actually be better

off from higher platform protection.

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For content providers, although content providers obviously benefit from high

protection through the cross-side network effects, they are also hurt by the increasing

of the license fees. In addition, higher protection affects the number of consumers

which further influences content providers’ revenues from consumers. When the

change in content providers’ expected revenue is large, content providers’ expected

revenue increases with higher protection more quickly. The positive impact from the

cross-side network effects dominates the negative effect from the increasing license

fee, thereby content providers benefit from higher protection.

The intuition is that content providers prefer higher protection while platforms may

not always be better from the higher platform protection. However, Proposition 2

uncovers an interesting result about the content providers’ and platforms’ attitudes

toward platform protection. That is, content providers and platforms have an aligned

attitude toward platform protection.

4. The Duopoly model with Consumer Fairness Concerns

In the benchmark model, we address the effect of platform protection on the profits

of the platforms and the content providers in the absence of consumer fairness

concerns. However, as the public becomes increasingly concerned about fairness of

price, platform owners cannot be blind to such concerns. When they purchase a

content in a platform, consumers would intentionally compare the payoffs with that of

other platforms. Consumers who pay a higher price than the other platform may also

be reluctant to buy when the business transaction is deemed to be inequitable (Li and

Jain, 2015; Guo, 2015; Guo and Jiang, 2016).

Consumers: With the fairness concerns, if an consumer at 𝑥 purchases a content

from platform 1 at price 𝑝𝐹1, his utility in that period is

𝑈𝐹1 = 𝑉 + 𝑎𝑛𝐹

1 − 𝑝𝐹1 − 𝑡𝑥 + 𝑟 · 𝑚𝑖𝑛{0, (𝑝𝐹

2 − 𝑝𝐹1)}. (6)

If the consumer purchases a content from platform 2 at price 𝑝𝐹2, his utility is

characterized as follows:

𝑈𝐹2 = 𝑉 + 𝑎𝑛𝐹

2 − 𝑝𝐹2 − 𝑡(1 − 𝑥) + 𝑟 · 𝑚𝑖𝑛{0, (𝑝𝐹

1 − 𝑝𝐹2)}. (7)

The first formula is the utility of buying from platform 1 at the price 𝑝𝐹1. If this

customer access fee is higher than the price 𝑝𝐹2 that buy form platform 2, paying the

price premium of (𝑝𝐹2 − 𝑝𝐹

1) induces negative feelings of unfairness, and the

magnitude of disutility is 𝑟 · 𝑚𝑖𝑛 {0, (𝑝𝐹2 − 𝑝𝐹

1)}. And if he pay lower than price 𝑝𝐹2,

we assume he does not have a negative utility because the price is unfair, which is

same as Li and Jain (2015). The parameter 𝑟 represents the degree of consumers’

fairness concerns and ranges from [0,1]. If 𝑟 = 0, fairness concerns do not exist and

consumption utility is not affected by price differential relative to other platforms.

Following previous literature (Li and Jain, 2016; Guo and Jiang, 2016), all consumers

share the same 𝑟, i.e., consumers are homogeneous in their concerns about price

fairness.

Content providers: The net revenue of a content provider associated with platform

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𝑖 is given by

𝜋𝐹𝑖 = 𝑏𝑠𝐹

𝑖 − 𝑙𝐹𝑖 − 𝑓, (8)

Platforms: Platform 𝑖 faces the problem of choosing 𝑝𝐹𝑖 and 𝑙𝐹

𝑖 to maximize its

profit,

𝛱𝐹𝑖 = 𝑠𝐹

𝑖 𝑝𝐹𝑖 + 𝑛𝐹

𝑖 𝑙𝐹𝑖 . (9)

Similarly, we make the following assumption in order to guarantee that all

optimization problems with competing platforms are well behaved.

Assumption 2

𝑚𝑎𝑥 ((𝑎+𝑏+𝑏𝑟)2

4(𝑟+1),

(𝑎+𝑏+𝑏𝑟)(𝑎+𝑏)

2(𝑟+2)) < 𝑡 <

(𝑎+𝑏+𝑏𝑟)(𝑎+𝑏)+4𝑉(𝑟+1)

2(𝑟+2). (10)

and

𝑉 >(𝑎+𝑏+𝑏𝑟)(𝑏+𝑏𝑟−𝑎)𝑟

8(𝑟+1)2 . (11)

To ensure concavity of the platforms’ profit functions and entering into platform of

consumers and content providers, the degree of horizontal differentiation on both

sides of the markets must be midterm compared to the indirect network effect and the

degree of the consumer fairness concerns.

There may be two kinds of price schemes, one is symmetric (i.e., 𝑝𝐹2 = 𝑝𝐹

1) and the

other is asymmetrical (i.e., 𝑝𝐹1 ≠ 𝑝𝐹

2 ). We show that the later situation is not

established. Thus, we summarize the equilibrium prices of the former in the following

proposition.

Proposition 3 (Equilibrium Outcomes with Consumer Fairness Concerns)

The optimal prices are:

𝑝𝐹 = 𝑝𝐹1 = 𝑝𝐹

2 =𝑉(𝑏2𝑟+𝑎𝑏+𝑏2−2𝑡)

(𝑎+𝑏)(𝑎+𝑏+𝑏𝑟)−2𝑡(𝑟+2),

and

𝑙𝐹 = 𝑙𝐹1 = 𝑙𝐹

2 =𝑉(𝑏𝑟−𝑎+𝑏)

2𝑡(𝑟+2)−(𝑎+𝑏)(𝑎+𝑏+𝑏𝑟),

the content providers’ equilibrium profits are

𝜋𝐹 =𝑉(𝑎+(𝑟+1)𝑏)

2𝑡(𝑟+2)−(𝑎+𝑏)(𝑎+𝑏+𝑏𝑟)− 𝑓.

and the platforms’ equilibrium profits are:

𝛱𝐹 = 𝛱𝐹1 = 𝛱𝐹

2 =((𝑟+1)2𝑏2−2(𝑟+1)𝑎𝑏−𝑎2+4𝑟𝑡+4𝑡)𝑉2

((𝑎+𝑏)(𝑎+𝑏+𝑏𝑟)−2𝑡(𝑟+2))2 .

Next, we analyze the platforms and content providers’ attitudes towards protection.

Proposition 4 summarizes their attitudes towards platform protection.

Proposition 4 (Attitudes towards Platform Protection with Fairness concerns)

(1). When consumers’ fairness concerns are sufficiently strong (i.e., 𝑟 >𝑎−𝑏

𝑏) and

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misfit cost is sufficiently small (i.e., 𝑡 <(𝑎+𝑏+𝑏𝑟)3

2(𝑟+1)(2𝑎+2𝑏+𝑎𝑟+𝑏𝑟−𝑏𝑟2))

i. If 𝑏′(𝑘) >𝑀|𝑎′(𝑘)|

𝑀−2𝑡𝑟2(𝑎−𝑏−𝑏𝑟), content providers prefer higher, whereas higher

protection will decrease the platforms’ profits.

ii. If 𝑊|𝑎′(𝑘)|

𝑊+2𝑟𝑡(𝑡+2)< 𝑏′(𝑘) <

𝑀|𝑎′(𝑘)|

𝑀−2𝑡𝑟2(𝑎−𝑏−𝑏𝑟), both platforms and content

providers prefer higher protection.

iii. If 𝑏′(𝑘) <𝑊|𝑎′(𝑘)|

𝑊+2𝑟𝑡(𝑡+2), platforms prefer higher protection, whereas content

providers prefer less protection.

(2). When consumers’ fairness concerns are sufficiently strong (i.e., 𝑟 >𝑎−𝑏

𝑏) and

misfit cost is large (i.e., 𝑡 >(𝑎+𝑏+𝑏𝑟)3

2(𝑟+1)(2𝑎+2𝑏+𝑎𝑟+𝑏𝑟−𝑏𝑟2)) or consumers’ fairness

concerns are sufficiently small (i.e., 𝑟 <𝑎−𝑏

𝑏)

iv. If 𝑏′(𝑘) >𝑊|𝑎′(𝑘)|

𝑊+2𝑟𝑡(𝑡+2), both platforms and content providers prefer higher

protection.

v. If 𝑀|𝑎′(𝑘)|

𝑀−2𝑡𝑟2(𝑎−𝑏−𝑏𝑟)< 𝑏′(𝑘) <

𝑊|𝑎′(𝑘)|

𝑊+2𝑟𝑡(𝑡+2), platforms prefer higher protection,

whereas content providers prefer less.

vi. If 𝑏′(𝑘) <𝑀|𝑎′(𝑘)|

𝑀−2𝑡𝑟2(𝑎−𝑏−𝑏𝑟), higher protection will decrease the platforms’

and content providers’ profits.

where 𝑀 = (𝑏𝑟 + 𝑎 + 𝑏)3 − 2𝑡𝑎(3𝑟 + 2) − 2𝑏𝑡(𝑟 + 2)(𝑟 + 1) < 0 and 𝑊 =

(𝑏𝑟 + 𝑏 + 𝑎)2 + 2𝑟𝑡 + 4𝑡 > 0.

According to Proposition 2, we have known that, in the absence of fairness

concerns, platforms and content providers always have the same presence for

protection. However, Proposition 4 shows that, in the presence of fairness concerns,

there are some scenarios in which platform and content providers have different

presences for protection.

The first scenario is that the higher protection decreases the platforms’ profits and

increases the profits of the content providers when the change in content providers’

expected revenue form a consumer with protection is sufficiently large compared to

the change in consumers’ expected revenue, consumers’ fairness concerns are large,

and misfit cost is sufficiently small. There are two effects at work for content

providers’ profits with stricter protection. On the downside, license fees arise in this

context. However, on the positive side, the protection increases content providers’

revenue from the additional consumer more quickly, which compensates for the

negative utility caused by raised license fees.

The second case is that the higher protection increases the platforms’ profits but

10

decreases the profits of the content providers. This happens in three cases. The first

circumstance is when the change in content providers’ expected revenue form a

consumer with protection is sufficiently small compared to the change in consumers’

expected revenue, consumers’ fairness concerns are large, and misfit cost is

sufficiently large. In this context, platforms get higher fees by charging higher fees to

consumers. However, content providers get less revenue due to the lower revenue

from the additional consumer and the fewer consumer demand. The second

circumstance is when the change in content providers’ expected revenue form a

consumer with protection is medium, and consumers’ inequity aversion and misfit

cost are sufficiently large. In this context, the change in content providers’ expected

revenue from consumers with protection is medium, which results that the positive

effect from the increased license fee dominates the negative effect from the reduced

access fees. Consequently, the overall profits of platforms increase. However, content

providers are hurt due to the increased license fee. The third circumstance is when the

change in content providers’ expected revenue form a consumer with protection is

medium and consumers’ inequity aversion is sufficiently small. When consumers are

not sensitive for the price, platforms can charge consumers more fees, whereas

content providers are worse off from the reduced number of consumers.

5. Conclusion

The threat of piracy and the consumer fairness perception have important effects on

platform protection strategies. Higher protection makes a positive effect on content

providers, whereas makes a negative effect on consumers. In addition, competing

platforms must consider the effect of the consumer fairness concerns when they

decide the prices for consumers, which in turn further affect the platform protection

strategy. We lay out an analytical model to address the effect of the consumer fairness

concerns on duopoly platform protection strategies in the presence of piracy.

We find that in the absence of fairness concerns, there is no case in which platform

and content providers have different presences for protection. When the change in

content providers’ expected revenue form a consumer with protection is larger than

that of consumers’, both platforms and content providers prefer higher protection.

However, when consumers exhibit fairness concerns, there are some scenarios in

which platform and content providers have different preferences to platform

protection. In particular, the higher protection decreases the platforms’ profits and

increases the profits of the content providers when the change in content providers’

expected revenue form a consumer with protection is sufficiently large compared to

the change in consumers’ expected revenue, consumers’ fairness concerns are large,

and misfit cost is sufficiently small. Moreover, the higher protection increases the

platforms’ profits but decreases the profits of the content providers (1) when the

change in content providers’ expected revenue form a consumer with protection is

sufficiently small, consumer fairness concerns are large, and misfit cost is sufficiently

large; (2) when the change in content providers’ expected revenue form a consumer

with protection is medium, consumers’ inequity aversion and misfit cost are

11

sufficiently large; (3) when the change in content providers’ expected revenue form a

consumer with protection is medium and consumers’ inequity aversion is sufficiently

small.

Our findings have significant implications for the platforms. In the absence of

consumer fairness concerns, whether higher protection is beneficial to platforms or

not depends on the changes in network externalities with protection. When platform

protection has a large impact on the content provider’s expected revenue from

consumers, the platform should provide higher protection to maximize its profit. In

the presence of fairness concerns, platforms are better off for the higher protection in

three cases. The first case occurs when relatively high fairness concerns, sufficiently

small unit misfit cost and relatively small the changes in content providers’ expected

revenue from the additional consumer with protection. The second case occurs when

high fairness concerns, sufficiently large unit misfit cost and sufficiently large the

change in content providers’ expected revenue from a consumer with protection. The

third case occurs when relatively small fairness concerns and sufficiently large the

change in content providers’ expected revenue. Beyond these three cases, lower

protection may be better for platform.

Our findings also have significant implications for the content providers. Content

providers may not necessarily benefit from higher protection although content

providers’ network externalities increase with the level of platform protection. When

the change of content providers’ network externalities on protection is sufficiently

large compared to the change of consumers’ network externalities, content providers

prefer higher protection. When the change of content providers’ network externalities

is sufficiently small, higher protection will decrease the profits of content providers.

This paper suggests a few directions for future research. First, in our theoretical

analysis, we only consider that the qualities of two platforms are exogenous. It’s

interesting to consider the case in which the qualities are endogenous. Second, this

paper does not consider the effect of content provider fairness concerns. It is also of

interest of study a model where both content providers and consumers exhibit fairness

concerns. Finally, future work might relax the static pricing strategy and allow some

consumers to switch from a platform to its rival under dynamic pricing (Li et al.

2018).

6. Acknowledgement

This research is partially supported by research grant from the National Science

Foundation of China (No.71471128) and the Key Program of National Natural

Science Foundation of China (No.71631003).

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