Competitive pricing strategies in social networks

• Author: Ying‐Ju Chen,Junjie Zhou,Yves Zenou
• DOI: http://doi.org/10.1111/1756-2171.12249
• Published date: 01 September 2018
• Date: 01 September 2018

RAND Journal of Economics

Vol.49, No. 3, Fall 2018

pp. 672–705

Competitive pricing strategies in social

networks

Ying-Ju Chen∗

Yves Zenou∗∗

and

Junjie Zhou∗∗∗

We study pricing strategies of competing firms selling heterogeneous products to consumers.

Goods are substitutes and there are network externalities between neighboring consumers. In

equilibrium, firms price discriminate based on the network positions and charge lower prices

to more central consumers. We also show that, under some conditions, firms’ equilibrium prof-

its decrease when either the network becomes denser or network effects increase. In contrast,

consumers always benefit from being more connected to each other. We determine the optimal

network structure and compareuniform pricing and discriminatory pricing from the perspectives

of firms and consumers.

1. Introduction

The past decade has witnessed an emerging role of social networks in shaping individ-

ual choices. Consumers now make consumption decisions largely based on whether their close

friends, neighbors, and celebrities also adopt the same products. In economic terminology, these

social goods provide network externalities to connected consumers.1Various sources of network

externalities have been documented in economics. For telecommunication devices, these exter-

nalities are generated via physical connections. For operating systems and software packages,

∗The Hong Kong University of Science and Technology; imchen@ust.hk.

∗∗Monash University, IFN, and CEPR; yves.zenou@monash.edu.

∗∗∗National University of Singapore; zhoujj03001@gmail.com.

We would like to thank the Editor, three anonymous referees, Rabah Amir, Masaki Aoyagi, Francis Bloch, Ozan

Candogan,Yi-Chun Chen, YongminChen, Gabrielle Demange, Itay Fainmesser, Jacob Goeree, Ben Golub, Ben Hermalin,

Bruno Jullien, Alessandro Lizzeri, Alessandro Pavan, Cheng-Zhong Qin, John Quah, Andrew Rhodes, Chris Shannon,

Adam Szeidl, Satoru Takahashi, Guofu Tan, Curtis Taylor, Julian Wright, Jidong Zhou, and conference and seminar

participants at Stockholm University, Singapore Management University, the Johns Hopkins Carey Business School,

National University of Singapore, Universityof Technology Sydney,University of Southern Califor nia, CUHK, SHUFE,

UIBE, 2014 Workshop on Industrial Organization and Management Strategy (The University of Hong Kong), 2015

POMS-HK Conference at Guangzhou, and 2017 AMES for valuable comments. The usual disclaimers apply.

1Network externalities exist if the value of a product increases when there are more users joining the network.

Here, we are focusing on local network externalities, wherethe value of consuming a product for a given agent increases

when others directly connected to this agent consumethis product.

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CHEN, ZENOU AND ZHOU / 673

the externalities come from compatibility concerns. Network externalities may also arise because

people want to conform to the behavior of their peers. The successes of Facebook, LinkedIn,

Twitter, WhatsApp, WeChat, and variousonline game producers have confirmed the high poten-

tial of market profitability in the social networking business.

These social interactions create abundant opportunities for service providers and thereby

lead to intense competition among them. For instance, in the mobile and data services market,

consumers can choose among AT&T, Verizon, T-Mobile, and other operators in the United States.

In the market for mobile messaging apps, WhatsApp, Line, and WeChat are fighting for market

shares. In such a scenario, consumers are confronted with various options to stay connected

with their friends, and service providers strive to induce the consumers to lean toward their own

products rather than their competitors’ products.

Tobetter understand these issues, we provide a frameworkthat examines product competition

between firms when products are differentiated and exhibit local networkeffects. Each consumer

has access to two products, which are offered by two firms. Within each product there are local

network externalities among the consumers in terms of their consumption utilities: a consumer

pays more attention to her close friends’ decisions than to others’ choices. As in Ballester,

Calv´

o-Armengol, and Zenou (2006), we develop a model with strategic complementarities in

consumption choices so that more consumption from a consumer reinforces other consumers’

decisions to consume the same good. In contrast, to capture the competition between firms, the

products are assumed to be substitutable.2The firms incur heterogeneous costs of serving different

consumers and are allowed to charge discriminatory prices to these consumers.

We show that there is a unique subgame perfect equilibrium where, first, firms choose

the prices of each good for each consumer, and, then, the individuals decide their consumption

levels of the two goods. We provide a full characterization of the equilibrium prices, which

can be decomposed into two parts. The first term corresponds to the monopoly price, which is

independent of the network configuration. The second term is proportional to the Katz-Bonacich

centrality measure of a consumer (Katz, 1953; Bonacich, 1987). Thus, contrary to the monopoly

case (Bloch and Qu´

erou, 2013), the equilibrium prices exhibit strong network dependence, where

more central consumers obtain a larger discount because of their impact in terms of consumption

on their neighbors.

In the real world,fir ms do price discriminate consumers based on their location or centrality

in their networks. This is often done through digital marketing, which is an important aspect of

firms’ strategy. A key aspect of digital marketing is influencer marketing.3Firms are gathering

and using data on users’ social media activity (social media platforms such as Facebook, Twitter,

and Google+; and by consultancy firms such as Klout.com and Ammo Marketing)4to identify

influencers of a specific market segment and then orienting marketing activities around them.

After acquiring this information, firms do price discriminate consumers, offering discounts to

customers depending on their influence. For example, Microsoft, Sony, and Samsung have in-

fluencer campaigns via Klout. In 2011, Microsoft increased its marketing efforts to promote the

Windows Phone 7.5 by working with Klout and offering a free phone to users who had a high

“Klout” score. More recently,highly influential Klout users received a free Sony NEX-3N camera

and Sony Action Cam.

There are many other examples of price discrimination based on the degree of influence

of consumers. For example, providing price discounts to communications between “friends and

family” members has become an increasingly popular practice in the telecommunication industry.

2In the online web Appendix C.3, we also consider the case of complementary products.

3Influencer marketing (also influence marketing) is a form of marketing in which the focus is placed on influential

people rather than the target market as a whole. It identifies the individuals that haveinfluence over potential buyers and

orients marketing activities around these influencers.

4Forexample, Klout.com provides social media analytics to firms to measure a user’sinfluence in her social network

(see Rao et al., 2015). The service uses social network data (such as Twitter, Facebook, Google+, LinkedIn, YouTube,

Instagram, and Wikipedia) and assigns individuals a “Klout” score, which presumablyreflects their influence.

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A prominent example was MCI’s Friends and Family Program, which offered price discounts

to long distance communications between consumers and their preselected friends and family

members. Sprint offered a similar plan that applied discounts automatically to those telephone

numbers connected most frequently with consumers during a billing period. Both examples can

be seen as price discrimination based on strength of callers’ social ties (Shi, 2013).

Building upon the equilibrium price discrimination in this competitive setting, we also show

that increasing network externalities among consumers or having a denser network pushes the

equilibrium price downward. Indeed, stronger network effects or a denser network influence

profits in two ways. On the one hand, they tend to increase firms’ profits because they enhance

demands due to higher utility externalities for consumers. On the other hand, they can lead to

price reductions because stronger network effects or denser networks lead to fiercer competition

between firms. The former effect is dominated by (dominates) the latter when products are close

substitutes (sufficiently differentiated). By contrast, a monopoly firm always obtains a higher

profit under the same circumstances. Therefore, competition can lead to substantially different

implications in terms of prices and profits.

We find that consumers always benefit from being more connected to each other because

this increases their consumption utilities and, at the same time, intensifies firms’ competition.

This suggests that the complete network maximizes consumer surplus. In contrast, firms may

either prefer the complete network or the empty network, depending on the degree of product

substitution. Finally, we compare uniform pricing and discriminatory pricing from the perspectives

of firms and consumers. We showthat when the network is not regular, firms obtain higher profits

under uniform pricing when the products are sufficiently differentiated. In contrast, consumers

are better off under uniform pricing than under discriminatory pricing when the products are

highly substitutable. We articulate how these contrasting preferences arise from the firms’ salient

incentives to compensate or discriminate against players that are more central.

The remainder of this article unfolds as follows. Section 2 reviews some relevant literature.

Section 3 describes the model. Section 4 determines the equilibrium outcomes both in the second

stage (consumers’ consumption stage) and in the first stage (firms’ pricing strategies), derives

some comparative statics results on equilibrium prices, and extends the model for the case when

consumers only consume one good in equilibrium. Section 5 determines the welfare of this econ-

omy both for consumers and firms and derives some comparative statics results. Section 6 gives

the optimal network structure for both consumers and firms and examines the policy implication

of uniform pricing rule. Finally, Section 7 concludes. In the Appendix, we provide the proofs of

all our results in the main text. In the online web Appendix, we derive some matrix operations

and define the Katz-Bonacich centrality (online web Appendix A), deal with the single represen-

tative consumer case (online web Appendix B), provide additional results for the duopoly case

(online web Appendix C), illustrate our results for specific networks (online web Appendix D),

characterize the total welfare of the economy (online web Appendix E), and provide the proofs

of all the results in the online web Appendix (online web Appendix F).

2. Related literature

A large literature in economics has investigated the issue of network effects/externalities.

The classical articles primarily focus on the aggregate level of network externalities (e.g., Rohlfs,

1974; Katz and Shapiro, 1985; Farrell and Saloner, 1986). Monopoly pricing of network goods is

modelled and analyzed in various articles such as Cabral, Salant, and Woroch(1999), Dybvig and

Spatt (1983), and Ochs and Park (2010).5The competitive pricing problemis mostly studied in the

context of two-sided networksin which players on one side care about the aggregate contributions

of those on the other side (see, e.g., Armstrong, 2006; Caillaud and Jullien, 2003; and Rochet and

5See Economides (1996) for an extensive survey of this literature.

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