Competition in the presence of individual demand uncertainty

• Date: 01 May 2016
• Author: Marc Möller,Makoto Watanabe
• DOI: http://doi.org/10.1111/1756-2171.12127
• Published date: 01 May 2016

RAND Journal of Economics

Vol.47, No. 2, Summer 2016

pp. 273–292

Competition in the presence of individual

demand uncertainty

Marc M¨

oller∗

and

Makoto Watanabe∗∗

This article offersa tractable model of (oligopolistic) competition in differentiatedproduct markets

characterized by individual demand uncertainty.The main result shows that, in equilibrium, firms

offer advance purchase discounts and that these discounts are larger than in the monopolistic

benchmark. Competition reduces welfare by increasing the fraction of consumers who purchase

in advance, that is, without (full) knowledge of their preferences.

1. Introduction

In many markets, firms offer advance purchase discounts (APDs) to early customers. For

example, automobile companies often announce special introductory prices that apply to buyers

who sign up prior to the launch of a newmodel. Similarly, conferences and sports events frequently

offer reduced participation fees to those participants who register before a certain deadline. Finally,

airlines increase their ticket prices as the date of travel approaches or require an early booking to

qualify for a low fare category.

A common feature of these markets is the presence of individual demand uncertainty. At

the time of purchase, a test drive, the conference program, or the traveler’s schedule might

be unavailable, leaving consumers with imperfect knowledge about the match between their

preferences and the product’s characteristics. Consumers choose between an early, uninformed

purchase at a low price and a late, informed purchase at a high price.

An emerging literature has shown that in the presence of individual demand uncertainty,

an APD may constitute a firm’s optimal selling strategy. An APD induces consumers with weak

preferences or low degrees of uncertainty to purchase in advance, while deferring the purchase of

consumers with strong preferences or high degrees of uncertainty. An APD thus enables a firm to

price discriminate between consumers of different types. Although the existing literature focuses

on the case of a monopolistic seller, a tractable model of competition is still missing. This article

fills this gap by considering a duopoly.

∗University of Bern; marc.moeller@vwi.unibe.ch.

∗∗FEWEB, VU University Amsterdam, Tinbergen Institute; makoto.wtnb@gmail.com.

Wethank Marc Armstrong, Volker Nocke, two anonymousreferees, and par ticipants at variousseminars and conferences

for valuable discussions and suggestions.

C2016, The RAND Corporation. 273

274 / THE RAND JOURNAL OF ECONOMICS

In our model, two differentiated products are sold during two periods, an advance purchase

period 1 and a consumption period 2. A continuum of consumers with unitary demands know

their preferences in period 2 but face uncertainty in period 1. We model this uncertainty, by

assuming that in period 1, each consumer receives only an imperfect (private) signal about the

identity of his preferred product. The signal’s precision is identical across consumers, that is, all

consumers face the same degree of uncertainty. Consumers are also identical with respect to their

average valuation of the two products. However, consumers differ in their “choosiness.” More

choosy consumers derive a higher consumption value from their preferred product and a lower

consumption value from their nonpreferred product. We compare the case in which products are

sold by twocompeting fir ms with the monopolistic benchmark, in which both products are offered

by a single seller. Our main analysis assumes that firms are able to commit to a price schedule in

advance and focuses on the case in which market structure has no influence on the total quantity

supplied.

We first show that, in equilibrium, firms offer APDs, thereby extending the insights of the

existing literature to the case of competition. Our main result shows that, in any (symmetric

pure-strategy) equilibrium, competing firms must offer larger APDs than a monopolist, inducing

a greater fraction of consumers to purchase in advance. This result is driven bythe fir ms’ incentive

to capture those consumers in advance who might become their rival’scustomers in the future.1It

holds under the fairly weak restriction that the distribution of consumer types has an increasing

hazard rate.2

Price commitment turns out to be essential for the occurrence of intertemporal price discrim-

ination. We show that without commitment, intertemporal price discrimination ceases to occur.

However, though competing firms serve all of their customers in advance, a monopolistic supplier

maximizes profits by selling exclusively after demand uncertainty has been resolved. Hence, our

main result about the increase in advance sales becomes amplified in the absence of commitment.

The influence of competition on the intertemporal allocation of sales has an interesting

welfare implication. Because advance purchases are subject to the risk of a consumer-product

mismatch, an increase in the number of advance sales has a negative effect on total surplus.

Generally, this negative effect of competition might be compensated by an increase in the total

quantity sold. Extending our analysis to the case where individual demand is elastic, we show

the perhaps surprising result that competition can lead to a reduction in welfare even when it

increases the total quantity sold. To the best of our knowledge, we are the first to point out these

negative welfare consequences of competition for markets characterized by individual demand

uncertainty.

One may argue that, though detrimental for overallwelfare, competition should be beneficial

for consumers. We show that, for a uniform distribution of types, competition leads to a price

decrease in the advance-selling period but may result in a price increase in the consumption

period. Hence, competition benefits the “unchoosy” consumers who purchase early but may harm

the “choosy” consumers who purchase late. We show that the aggregate effect of competition on

consumer surplus can be negative.

The plan of the article is as follows. Section 2 introduces the model. In Section 3, we

consider the case of a monopoly, which serves as a benchmark for our subsequent analysis.

Section 4 contains our main results about competition. Our final Section 5 considers the issue of

price commitment. The more technical proofs are relegated to the Appendix. Web Appendix B,

available online, contains our extensionto the case of elastic demand and the rather lengthy proof

of equilibrium existence for a uniform distribution of consumer types.

1This is similar to the occurrence of customer poaching in markets with switching costs (Chen, 1997; Villas-Boas,

1999; Fudenberg and Tirole, 2000) with the difference that consumers are captured ex ante rather than ex post.

2Weprove the existence of a pure-strategy equilibrium for two cases: an equilibrium exists, (i) if individualdemand

uncertainty is sufficiently strong, or (ii) if the distribution of types is uniform. In the general case, existence may require

further restrictions on the distribution of types.

C

The RAND Corporation 2016.