PROMINENCE AND MARKET POWER: ASYMMETRIC OLIGOPOLY WITH SEQUENTIAL CONSUMER SEARCH

• Published date: 01 August 2024
• Author: Makoto Hanazono,Noritaka Kudoh
• Date: 01 August 2024
• DOI: http://doi.org/10.1111/iere.12704

INTERNATIONALECONOMIC REVIEW

Vol. 65, No. 3, August 2024 DOI: 10.1111/iere.12704

PROMINENCE AND MARKET POWER: ASYMMETRIC OLIGOPOLY WITH

SEQUENTIAL CONSUMER SEARCH∗

By Makoto Hanazono and Noritaka Kudoh

Nagoya University, Japan

This article presents a new perspective on the nature of market power through the lens of firm prominence.

We build a model of oligopolistic price competition with sequential consumer search, showing that a larger

firm sets a higher price than its smaller competitors. Consumers are more likely to encounter sellers from a

larger firm both immediately and in future interactions, resulting in less-elastic demand for that firm. Small

firms can free-ride on the prominent firm’s market power to raise their prices and earn higher profits. The

Herfindahl–Hirschman Index provides a useful guide for welfare evaluation.

1. introduction

Does firm size matter for market power? This article presents a new theory of market

power that arises from search frictions and differences in firm size. We show that firm size

matters in markets with sequential random search. When search is random, consumers are

more likely to find a larger firm at any time. This fact reduces the consumer’s outside option

of rejecting a trade in response to a price increase. This dynamic consideration generates a

less-elastic demand for a larger firm, subsequently setting a higher price than its smaller com-

petitors.

We seek to understand the retail market for goods and services sold by oligopoly firms with

branches, such as chain stores and insurance sales. Goods and services are largely similar in

these markets, and prices are determined by each firm instead of by individual chain stores.

We explore how the interplay between search frictions and firm size shapes each firm’s market

power in such markets. Consider tourists who find themselves searching for gasoline stations,

taxi rides, coffee shops, specific items at convenience stores, or particular meals at restaurants.

Due to the lack of information, these tourists are unlikely to direct their search toward a

specific brand; thus, they are more likely to encounter a store of a larger brand. Even when

consumers receive information about certain brands, this information is often unevenly dis-

tributed. As a result, a larger firm may have a broader customer reach and thus become more

prominent than its smaller competitors.

In this article, we build a model of oligopolistic price competition among asymmetric firms

selling homogeneous products through their branches. We take a profile of firm size (the

number of each firm’s branches) as given and identify it as the market structure. Consumers

search for a branch from which to purchase a good, and the likelihood of finding a particular

∗Manuscript received July 2020; revised November 2023.

We thank the editor, the associate editor, and three anonymous referees for their insightful comments. We also

thank Jan Eeckhout, Daisuke Oyama, Sandro Shelegia, Takashi Shimizu, Makoto Watanabe, Huanxing Yang, and

the participants of EARIE 2017, Contract Theory Workshop, Search Theory Workshop, the annual conference of

Japanese Society of Mathematical Economics, APIOC 2018, AMES2019, MaCCI Annual 2020, and the seminars at

Nagoya, Tokyo,Yonsei, Keio, Nanjing, Hitotsubashi, Okayama, Doshisha, NHH, Glasgow, and UPF for helpful com-

ments and discussions. Wewould especially like to thank Jose Luis Moraga-Gonzalez for his detailed comments on an

earlier version of this article. Part of this research is financially supported by KAKENHI (20H01476). Please address

correspondence to: Makoto Hanazono, Department of Economics, Nagoya University, Furo-cho, Chikusa-ku, Nagoya

464-8601, Japan. E-mail: hanazono.makoto.y0@f.mail.nagoya-u.ac.jp.

1249

© 2024 the Economics Department of the University of Pennsylvania and the Osaka University Institute of Social

and Economic Research Association.

1250 hanazono and kudoh

firm’s branch is proportional to that firm’s size. We assume that each buyer faces (unobserv-

able) temporary preference shocks to their willingness to pay, reflecting variations in both the

buyer’s mood and the seller’s service quality.1

Given a market structure, we seek a stationary asymmetric oligopoly equilibrium in which

firms commit to prices. We establish that an equilibrium exists and is unique for any given

market structure. We further establish that persistent price dispersion occurs such that a larger

firm sets a higher price than its smaller competitors in pure strategy. As search frictions be-

come negligible, price dispersion vanishes, and all firms set the competitive price; thus, search

frictions are essential for market power.

We show that each firm’s price satisfies a markup pricing, and the markup component (or

the margin) consists of the inverse hazard rate combined with what we term the strategic com-

ponent, through which firms’ prices interact with one another. When a firm raises its price,

two effects are at work. One effect is that the current buyer is less willing to accept a trade.

The other effect reduces the buyer’s value of search by committing to this higher price in the

future, inducing the current buyer to be more willing to accept a trade. The second effect also

makes all buyers more willing to accept trades, which helps competing firms. This effect cre-

ates strategic interactions among firms. Interestingly, the strategic component is greater for a

larger firm, generating asymmetry in market power and hence price dispersion.

To explore the issue of market concentration, we examine an extreme market structure that

consists of one large firm and a multitude of symmetric small firms (Armstrong et al., 2009;

Menzio and Trachter, 2015). Interestingly, as the large firm increases in size (i.e., the mar-

ket becomes more concentrated), small firms can charge higher prices and earn higher profits.

This is because small firms can free-ride on the large firm’s market power through the buyer’s

reduced value of search. We further consider the equilibrium level of market concentration by

examining the model with free entry of small firms to find that the equilibrium prices become

competitive as the entry cost vanishes.

Under our simplifying assumption of search with buyer replacement, a new buyer enters

the market after each transaction, complicating welfare evaluation. To explore the welfare

implications of our model, we consider an alternative environment in which a fixed number

of buyers switch their shopping status between active and inactive. Using this framework, we

conduct a numerical analysis to uncover the relationship between the Herfindahl–Hirschman

Index (HHI) and welfare. We randomly generate market structures (firm size distributions)

and calculate the associated equilibrium variables. We then find that the correlation between

the HHI and welfare is nearly −1, suggesting that the HHI, a conventional index for market

concentration, is useful for welfare evaluation (with the obvious caveat that the scope of the

market must be clearly defined).

This article contributes to the vast literature on price dispersion, which dates back at least

to Axell (1977) and Reinganum (1979). Our analysis complements the literature on firm size

as the determinant of meeting probabilities in random search models. Menzio and Trachter

(2015) study a consumer search model without temporary preference shocks, in which one

large firm and a continuum of small firms compete in a homogenous-product market. Al-

though their model generates price dispersion as in our model, the relationship between firm

size and market power is not easily defined in their mixed-strategy equilibrium. Jarosch et al.

(2019) show that a larger firm pays a lower wage because workers, once separated, are more

likely to encounter larger firms. Their equilibrium builds on the firm’s history-dependent strat-

egy, whereas ours builds on history-independent pricing. Arnold and Saliba (2011) present

findings that complement ours, using a directed-search model with capacity constraints. Since

product availability correlates with firm size, larger firms have the potential to attract more

buyers, allowing them to set higher prices.

1It is widely acknowledged that for a consumer search model to be useful, it requires a distribution of trade valua-

tions to motivate consumers to search for a better deal (Diamond, 1970). One approach to address this crucial issue in

markets with homogeneous products is to make each buyer’s willingness to pay stochastic.

prominence and market power 1251

This article also contributes to the growing literature on the prominence of firms in con-

sumer search. We focus on prominence in random consumer search, meaning consumers are

more likely to encounter a larger (i.e., more prominent) firm. Our approach contrasts sharply

with the model of prominence in ordered consumer search, in which prominent firms are sam-

pled earlier. Arbatskaya (2007) explains that search order enables otherwise homogeneous

firms to coordinate their prices, sorting consumers by varying search costs. She finds that a

prominent firm sets a higher price than its less-prominent competitors by serving customers

with higher search costs (see Wilson, 2010, for a model with endogenous search order). In

these models, the relationship between market shares and prices is ambiguous. Armstrong

et al. (2009) study prominence in a differentiated product market, showing that a promi-

nent firm charges a lower price because it faces a more elastic demand than nonprominent

firms.2See Moraga-González and Pertikait˙

e (2013), who consider endogenous prominence by

merger, and Zhou (2011).3

Our theory complements the literature on firm heterogeneity in meeting probabilities

through the choice of advertising intensity.4Haan and Moraga-González (2011) consider a

differentiated product market and find a case in which a more prominent firm in advertising

charges a lower price as seen in Armstrong et al. (2009). Ireland (1993) and McAfee (1994)

study static advertising models of homogeneous products in the spirit of Butters (1977) to

consider asymmetric advertising intensity.5They demonstrate that a mixed-strategy equilib-

rium exists, where products with higher advertising intensity tend to have higher prices on

average. Although our model and theirs share the property that a market share-like variable

positively affects prices, notable differences exist with distinct empirical implications. First, the

mixed strategy reflects temporary discounting whereas the pure-strategy equilibrium in our

model reflects persistent price dispersion. Second, prices in our model can exceed the static

monopoly price because firms internalize future profits when setting their prices. In Ireland

(1993) and McAfee (1994), firms charge prices up to the static monopoly price in mixed strate-

gies.

There is a growing empirical literature on persistent price dispersion. For example, Moen

et al. (2020) study store-level data for the Norwegian retail market, finding that store hetero-

geneity accounts for about 50% of the observed price variation. Berardi et al. (2017) inves-

tigate price dispersion among French supermarkets, concluding that the permanent compo-

nent of price dispersion dominates the temporary component. From household-level scanner

data, Kaplan and Menzio (2015) provide evidence in favor of models of intertemporal price

dispersion; however, they also find that store heterogeneity accounts for 10% of the variance

of prices. Haucap et al. (2017) empirically study fuel prices across all gasoline stations in Ger-

many, finding that “brand recognition” is a factor influencing price dispersion.

The organization of the article is as follows: Section 2 presents our basic model, and Sub-

section 2.4 discusses the key assumptions of the model. Section 3 establishes the existence

and uniqueness of stationary asymmetric oligopoly equilibrium. Section 4 considers a case in

which one large firm competes with a continuum of small firms to determine the equilibrium

level of market concentration through firm entry. Section 5 relaxes the buyer replacement as-

sumption to explore our model’s welfare implications. Section 6 concludes. Proofs of many re-

sults are presented in the Appendix, and a separate Online Appendix provides further details

and additional results.

2Carrasco and Yañez (2022) consider a random search model in which the degree of firm prominence is heteroge-

neously distributed. They show that a prominent firm charges a lower price only when the firm is significantly more

cost-efficient than its less-prominent competitors.

3Other approaches to firm prominence include Moraga-González et al. (2021, section 4) and Myatt and Ronayne

(2019).

4Similarly, Fishman and Levy (2015) and Moraga-González and Sun (2019) consider vertical quality differences

across firms in a random search environment to investigate price dispersion and incentives to invest in quality.

5Armstrong and Vickers (2022) explore patterns of competitive interactions in homogeneous product markets

where each consumer’s consideration set of firms is exogenously given (say, by advertising reach). They provide a

comprehensive analysis encompassing existing research, including Ireland (1993) and McAfee (1994).