Social learning with differentiated products

• Date: 01 March 2019
• DOI: http://doi.org/10.1111/1756-2171.12268
• Author: Arthur Campbell
• Published date: 01 March 2019

RAND Journal of Economics

Vol.50, No. 1, Spring 2019

pp. 226–248

Social learning with differentiated products

Arthur Campbell∗

Learning from friends is a key process by which consumers acquire information about avail-

able products. This article embeds social learning in a model of firms producing differentiated

products. I consider how the structureof social relationships between consumers influences pric-

ing and welfare. In particular, how a variety of characteristics of social networks - distribution

of friendships, homophily, clustering, and correlations between an individual’s preferences and

number of friends - influence these outcomes. I also find conditions under which consumer aware-

ness and the sensitivity of demand to prices are useful measures of the informational efficiency

of markets.

1. Introduction

An important aspect of competition in differentiated product markets is how informed

consumers are about their available choices. In addition, consumers’ lack of information is

commonly identified as an important source of inefficiency in markets, and information provision

policies are often used to ameliorate it.1Learning from friends is one of the most significant

sources of information for consumers in making purchase decisions.2The objective of this article

is to study the role that social learning through a social network playsin determining both the nature

of competition between firms and the welfare of participants in a differentiated product market.3

I develop a model of differentiated Bertrand competition, on a line, where awarenessof each

firm’sproduct diffuses through friendships. An individual becomes aware of a product if a friend

∗Monash University; arthur.campbell@monash.edu.

I would like to thank Andrea Galeotti, Florian Ederer, Kristof Madarasz, Mushfiq Mobarak, and seminar participants at

EUI and LSE for their helpful comments.

1Examples of policies include agricultural outreach programs, energy auditing, and financial planning services. See

also academic studies such as Miller and Mobarak (2014) and BenYishay and Mobarak (2018) that attempt to leverage

information provision through social networks.

2Word of mouth has been shown to affect purchasing behavior in restaurant choices (Luca, 2016), book sales

(Chevalier and Mayzlin, 2006), banking (Keaveney, 1995), entertainment (Chintagunta, Gopinath, and Venkataraman,

2010), and technological products (Herr, Kardes, and Kim, 1991), as well as appliances and clothing (Richins, 1983).

The Word of Mouth Marketing Association has been acquired bythe Association of National Advertisers and this is no

longer freely available online. Also, Bughin et al. (2010) observe “Word of mouth is the primary factor behind 20 to 50

percent of all purchase decisions.”

3Grossman and Shapiro (1984), in their influential model of advertising and competition in a differentiated product

market, observe that “[t]he absence from our model of search, word-of-mouth and experience as sources of information

is an important omission.” One contribution of this article is to incorporate and analyze word of mouth in a differentiated

product market.

226 C2019, The RAND Corporation.

CAMPBELL / 227

has previously purchased it. My baseline model with two firms is very tractable, allowing one to

analytically derive solutions to the question of how a wide range of network characteristics affect

pricing and welfare.

In the baseline model with two firms, consumers are uniformly located on a line, and the

firms are located at opposite ends of the line. A unit mass of consumers must choose a product

to purchase. I assume that individuals learn about the available products from a second mass

of individuals who have previously purchased one or other of the products. A product is in a

consumer’s choice set if they have a friend who purchased that product. The intensity of price

competition is determined by the prevalence of consumers who are aware of both products and

may therefore respond to a change in price by either firm. In a symmetric equilibrium, these

will be individuals who are located equidistant from either firm and find out about the existence

of both firms from their friends. The social network influences price competition through its

effect on the probability that a marginal consumer will find out about both products. In my

model, inefficiencies arise due to individuals not buying from the firm located closest to them.

The welfare loss that results from buying from the wrong firm is largest for individuals located

close to one of the firms. Hence, the social network influences welfare through the likelihood

that individuals receive information about the firm located closest to them. My analysis finds the

characteristics of social networks that influence prices and welfare through these channels.

I find that increasing the number of friendships reduces prices and improveswelfare, whereas

a mean preserving spread in the distribution of friendships will increase prices and reduce welfare.

When individuals are more likely to have friends with similar product preferences, prices are

unaffected, but welfare is improved. I consider how correlation between a consumer’s product

preferences and their number of friends may influence prices and welfare. I show that when

individuals located further from marginal consumers (i.e., those closer to one of the firms) are

more likely to have more friends, welfarewill be higher. Furthermore, when marginal consumers

(individuals located furthest from any firm) have fewer friends, prices increase.

I also consider two common measures of how wellinfor med consumers are: average aware-

ness of products and sensitivity of demand to price. I study how these are related to welfare.

Intuitively, these measures will be positively correlated with the efficiency of consumer decision-

making. I find conditions under which the naive use of these metrics will correctly identify

markets with higher welfare and conditions under which they either cannot be distinguished (i.e.,

the metric is uncorrelated with welfare) or are misleading as to the efficiency of a market (i.e., the

metric is negatively correlated with welfare). In particular, when the distribution of friendships

through First Order Stochastic Dominant (FOSD) or Second Order Stochastic Dominant (SOSD)

(less dispersed) changes, these metrics move in an intuitive manner. However, when comparing

markets with different levels of homophily, the market with higher welfare will also exhibit lower

consumer awareness and the same sensitivity of demand. Also, when comparing two markets

with different correlations between an individual’s number of friends and product preference, a

market where demand is more sensitive to prices may have lower welfare than a market where

demand is less sensitive.

The rest of the paper is organized as follows. In the next section, we discuss the related

literature. Section 3 develops the baseline model of social learning with differentiated products.

Section 4, we analyze the baseline model. In Section 5 weextend the model to consider homphily.

In Section 6 we consider a setting where there is correlation between an individual’s valuation

and connectedeness. We discuss further extensions to the model in Section 7. We conclude in

Section 8.

2. Related literature

I believe this article is the first to characterize how features of a social network between

consumers influence welfare and price competition in a differentiated product market. The article

is broadly related to a large body of literature in industrial organization that studies settings where

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The RAND Corporation 2019.