Choosing the Quality of the Fit between Complementary Products

• Date: 01 March 2016
• Author: Maxim Sinitsyn
• DOI: http://doi.org/10.1111/jems.12136
• Published date: 01 March 2016

Choosing the Quality of the Fit between

Complementary Products

MAXIM SINITSYN

Department of Economics

University of California, San Diego

La Jolla CA 92093

msinitsyn@ucsd.edu

In this paper, I examine how firms should position their complementary products. I assume that

there are two competing firms, each producing two complementary products. Each firm decides

whether to employ strategies that enhance the quality of the fit (the degree of complementarity)

between its pair of complementary products before competing in prices. The consumers have

heterogeneous tastes for the four possible bundles. They are willing to pay a price premiumin order

to purchase a bundle from the same firm if this firm chose to make such bundle more attractive.

I find that increasing the degree of complementarity between a firm’s complementary products

intensifies price competition and often leads to smaller profits. Only when complementarity-

enhancing strategies significantly increase the demand for a firm’s matching bundle, does the

firm benefit from employing them. The highest profits for both firms are obtained when both firms

do not employ complementarity-enhancing strategies. Deteriorating the quality of the fit between

one’s own and a rival’s complementary products is never profitable.

1. Introduction

One of the major decisions faced by firms producing products in complementary cate-

gories is how to position these products. There are various strategies that can influence

consumers’ perception of the quality of the fit (the degree of complementarity) between a

firm’s complementary products. A firm can assign its complementary products the same

brand name (umbrella branding).1It can adjust the design of its complementary prod-

ucts so that they look more uniform and generate the appearance of a better match.2

A firm can allow for the same accessory to be used with its various complementary

electronic devices 3or make the connection between these devices more convenient.4A

manufacturer can negotiate shelf space with retailers so that its complementary products

are located next to each other, reducing consumers’ search costs (Dawar and Stornelli,

2013). Another option is to run advertisements promoting the joint consumption of its

I thank a co-editor and two anonymous referees for the helpful suggestions on improving the paper.

1. It has been established experimentally and empirically that consumers who purchase a pair of comple-

mentary products receive a larger utility if these products share the same brand name (Simonin and Ruth,

1995; Ma et al., 2012; Sinitsyn, 2012; Rahinel and Redden, 2013).

2. This assumption is a reflection of the Dideroteffect—“a force that encourages the individual to maintain

a cultural consistency in his/her complement of consumer goods” (McCracken, 1988, p. 123). This effect is

named after the French philosopher Denis Diderot (1713–1784). In his essay “Regrets on Parting with My Old

Dressing Gown” he describes receiving a new dressing gown as a present and consequently replacing all the

elements of his study to match the elegance of the gown.

3. For example, one charger can be used for both iPad and iPhone, whereasa tv and a dvd player produced

by the same firm can share a remote.

4. For example, AirDrop allows for convenient file sharing between various Apple devices.

C2015 Wiley Periodicals, Inc.

Journal of Economics & Management Strategy, Volume25, Number 1, Spring 2016, 161–178

162 Journal of Economics & Management Strategy

products5or to make the warranty on one product be conditional on the consumer using

the same firm’s complementary product.6In this paper, I examine how this choice of

the degree of complementarity affects the pricing strategies of the competing firms and

show that increasing the degree of complementarity intensifies price competition and,

under certain conditions, decreases the firms’ profits.

In my model, there are two firms, each selling products in two complementary

categories. The consumers can mix and match between the firms’ products and have

heterogeneous tastes for the four possible bundles, selecting the one that offers them the

highest utility. Following the set-up of network models of Matutes and Regibeau (1988,

1992), I assume that consumers are uniformly distributed on the unit square with one

firm located at the bottom-left corner and another firm located at the upper-right corner.

The firms interact over two periods. In the first period, each firm chooses the degree of

complementarity between its products, and in the second period, they compete in prices.

The degree of complementarity measures the additional utility consumers receive when

they purchase two complementary products that are produced by the same firm.

The framework of my paper also contributes to the large body of literature on

compatibility decisions in networks. It is well established that, even in the absence

of network externalities, when facing a choice between full compatibility and incom-

patibility, the competing firms set higher prices and obtain higher profits under full

compatibility (Matutes and Regibeau, 1988; Economides, 1989). Consistent with these

findings, I employ the model in which the firms operate under full compatibility,that is,

the consumers can assemble their own system by combining the components produced

by the rival firms.

The novel feature of my model is that I allow for the matching system composed of

the components produced by the same firm to be valued higher than the mixed system.

The firm achieves this by either improving the quality of the fit between its components

or deteriorating the quality of the fit between its own and the rival’s components. The

examples of the former strategy are given in the beginning of this introduction. One

example of the latter practice was the effort by Microsoft during the first browser war

to discourage the users of its Windows platform from using the competitor’s Netscape

Navigator instead of Microsoft’s Internet Explorer. Problems experienced by Windows

consumers during the installation of the Netscape Navigator fulfilled the promise of

Microsoft’s vice president “to make the use of any browser other than Internet Explorer

on Windows a jolting experience” (Finding of Facts, United States v. Microsoft Corp.,

No. 172).

I solve for the subgame perfect Nash equilibrium and find that a firm’s decision to

increase the degree of complementarity between its products rests on the relative size of

two effects: a direct effect resultingfrom an increase in consumer demand and a strategic

effect resulting fromthe competitive response of the rival firm, which decreases its prices.

If the increase in consumer utility for a matching bundle is significant (the degree of

complementarity is high), the direct effect dominates, and in equilibrium both firms

employ complementarity-increasing strategies. If, on the other hand, the consumers

do not gain much extra utility from purchasing the matching bundle (the degree of

5. For example, Betty Crocker ran a TV commercial showing a cake made with Betty Crocker’s comple-

mentary products: Devil’s Food Cake Mix and Chocolate Frosting (2009BettyC, 2009).

6. For example, a lifetime warranty on BEHR paint requires applying the product according to the label

directions which, in turn, suggest using BEHR primer beforehand (Premium Plus RInterior Ceiling Paint

n.d.).