First-mover disadvantages with idiosyncratic consumer tastes along unobservable characteristics

Regional Science and Urban Economics 36 (2006) 99–117

www.elsevier.com/locate/regec

First-mover disadvantages with idiosyncratic

consumer tastes along unobservable characteristics

Byong-Duk Rhee *

Whitman School of Management, Syracuse University, 721 University Avenue, Syracuse,

NY 13244-2450, United States

Available online 24 August 2005

Abstract

Upon entering a market, a first-mover often preempts the best market location and outperforms

followers in competition. Conversely, late entrants are in better positions to learn more about demand

by adopting a bwait-and-seeQ strategy and then enjoy superior performance. This paper demonstrates

first-mover disadvantage, even in the absence of follower’s informational advantage, by using a

standard spatial competition framework. Specifically, a first-mover gains a substantial advantage

over followers when firms correctly predict individual consumer choices with their market locations.

However, the first-mover obtains lower sales and profit when consumers exhibit large idiosyncratic

tastes along unobservable characteristics.

D 2005 Elsevier B.V. All rights reserved.

JEL classification: L11; L13; L15; M31; R39

Keywords: Location decisions; First-mover disadvantage; Consumer heterogeneity; Unobservable characteristics;

Logit model

1. Introduction

Should you enter a new market before or after your rivals? This is one of the most

fundamental decisions encountered whenever a firm establishes its retail store in a

geographic market segment or when it positions a new product in the characteristics space.

0166-0462/$ -

doi:10.1016/j.

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ress: [email protected].

B.-D. Rhee / Regional Science and Urban Economics 36 (2006) 99–117100

Entry order takes precedence over production and marketing decisions and has significant

consequences for the long-term market performance of a firm. In the last two decades,

numerous empirical studies in marketing have shown that first-movers achieve substantial

competitive advantages and are likely to be market leaders in their product categories

(Robinson and Fornell, 1985; Urban et al., 1986).

Most theoretical literature has addressed the issue of first-mover advantage from the

perspective of firms’ sequential market entry in a spatial competition framework (Prescott

and Visscher, 1977; Lane, 1980; Anderson, 1987; Tabuchi and Thisse, 1995, to mention a

few). When entering a market, a Stackelberg leader anticipates following firms’ reactions

to its strategies and incorporates them into its own decision making. Using such strategic

foresight, a first-mover preempts later entrants by adopting the best market locations

(Tabuchi and Thisse, 1995). Preemptive positioning then enables the first-mover to charge

a premium price, leading to higher sales and profit. In less attractive segments, on the other

hand, later entrants should offer bargain prices in order to compete with pioneering

incumbents and attain lower sales and profits. First-movers may also preempt superior

strategic resources in the factor market (Rao and Rutenberg, 1979). Thus, comparative

advantages in production and distribution enable the pioneer to outperform later entrants in

competition and lead to above normal returns for the first-mover.

Schmalensee (1982) shows that imperfect information on the part of consumers leads to

first-mover advantage as well. If consumers are satisfied with the first brand (or store) in a

new product category, they will favor it over later entrants because they are uncertain that

the followers’ brands satisfy their needs. First-movers will then sustain a high market share

and profits so long as consumer experience remains as a crucial information source of

product quality. In addition, first-movers can increase switching costs by developing

brand-specific user skills and influencing consumers’ evaluation of products (Stigler and

Becker, 1977).

A growing body of recent empirical evidence, however, questions this entry order effect

on the market performance of a product and presents the cases of first-mover disadvantage.

Golder and Tellis (1993), for example, report that only 53% of first-movers survive in the

market. Kalyanaram et al.’s (1995) survey of various industries also shows mixed results

and suggests that the order of market entry does not appear to be related to long-term

market performance. First-movers bear a higher risk of new product failure since it is

unusually hard to forecast sales for a pioneering brand. And, while we have observed a

remarkable progress in research methodology, we still cannot eliminate uncertain

consumer responses to a pioneering innovation (Hamel and Prahalad, 1994). In contrast,

late entrants are in better positions to learn more about consumer demand by adopting a

bwait-and-seeQ strategy. Later entrants may achieve higher sales and profits when their

informational advantage prevails over any first-mover’s advantage arising from

preemption and switching costs.

Gal-Or (1985, 1987) analytically proves the disadvantages of moving first, even when

both pioneer and later entrant are equally able to assess demand through market research.

Gal-Or (1987) models a duopoly where firms choose output quantities under the

assumption of incomplete information regarding stochastic demand. The follower has an

informational advantage not only because it directly observes market conditions, but also

because it makes inferences about market conditions based on the first-mover’s quantity

B.-D. Rhee / Regional Science and Urban Economics 36 (2006) 99–117 101

choice. Thus, informational advantage enables the follower to attain higher market share

and profit.1

This study shows first-mover disadvantage even in the absence of the follower’s

informational advantage. Specifically, we demonstrate consumer heterogeneity as a

determinant of first-mover advantage/disadvantage by using a Hotelling (1929)

framework. This paper, however, differs from previous literature cast in a Hotelling

framework (e.g., Neven, 1987; Tabuchi and Thisse, 1995). The prior research assumes that

consumers differ only in their locations on a market segment along which firms position

strategically, but not in their tastes along characteristics that firms cannot manage due to

their unobservability. In other words, consumer preferences are assumed to be completely

accounted for by firms’ market locations. Thus, consumers patronize the product that is

closer to their locations. Consumers who share the same location always purchase identical

products across various choice occasions.

In contrast, we explicitly assume that consumers differ both in their bobservableQlocations and in their tastes along unobservable characteristics. Such unobservable

characteristics might include latent attributes of firm-specific associations and unspecified

situational influences (Manski, 1977). For example, consumers may hold different brand

reputations and images, the underlying attributes of which are not fully captured in a

strategy (Broniarczyk and Alba, 1994). Product choice may also be affected by physical

and social surroundings in a specific choice situation such as decor, sounds, aromas,

lighting, or other persons present and their characteristics and roles (Belk, 1975). In this

setting, even consumers with the same location may choose different products due to their

idiosyncratic tastes along the unobservable characteristics. This study also differs from

Gal-Or (1987) because it does not limit the investigation to the case of a single strategic

variable such as output quantity. Instead, we assume each firm strategically chooses its

own location as well as price. Further, we assume inelastic demand and firms’ identical

information sets of consumer tastes in order to eliminate asymmetric market conditions

and informational advantage as possible sources of either first-mover advantage or

disadvantage. Using these assumptions, we isolate the effect of consumer heterogeneity on

first-mover advantage.

The findings of this study are as follows. When consumer heterogeneity in tastes along

unobservable characteristics is small, a first-mover preempts the market center in order to

capture the largest number of consumers. The follower then positions away from the

pioneer in order to avoid cutthroat price competition. Consequently, the first-mover earns

higher sales and profit due to its positional advantage in competition. However, as the

heterogeneity increases along the unobservable characteristics, consumers do not

necessarily patronize the product that is closer to them along the market segment. Hence,

preemptive positioning becomes ineffective in competition. Furthermore, as the increase in

heterogeneity along the unobservable characteristics generates brand switching over the

1 This result occurs when the firms’ reaction functions are upwards sloping (Gal-Or, 1985). Gal-Or (1987)

assumes that firms are exogenously endowed with private information of given precision. Though firms are

allowed to determine endogenously how precisely to conduct their market research, Gal-Or conjectures that the

follower always earns higher profits than the first-mover and that the first-mover may refrain from any market

research in order to eliminate the follower’s indirect inference.


entire market, the follower aggressively approaches the market center in order to capture

more switching customers. Anticipating such an action, the first-mover then reacts

passively by moving away from the center in order to avoid destructive price competition.

In equilibrium, the follower positions itself closer to the market center and attains higher

sales and profits. When consumers exhibit sufficiently large idiosyncratic tastes along the

unobservable characteristics, product differentiation becomes insignificant in competition

and both firms position at the market center.

The rest of the paper is organized as follows. Section 2 clarifies the idea of

unobservable characteristics in consumer choice and their implications for demand and

profit in a formal model. Section 3 derives a pure strategy equilibrium and analyzes the

effect of unobservable characteristics on first-mover advantage. The last section draws

implications and suggests areas for future research.

2. The model

There are two firms considering market entry. Consumers will purchase one unit of

product per period. Assume a continuum of consumers uniformly distributed on a market

segment with unit length [0,1], as in the standard Hotelling paradigm (1929). The location

of each consumer is denoted by xa [0,1]. Further, assume a quadratic transportation cost

as in d’Aspremont et al. (1979).2 When a consumer at x purchases a product from firm i

located at xi on the market segment, the consumer incurs transportation costs d(xi�x)2,

where the transportation coefficient d N0 is the importance weight associated with

shopping distance in product choice.

We also allow consumers to differ in their tastes along characteristics that are not

observable to firms but still affect consumer choices. This reflects the fact that firms may

not have perfect information on an individual consumer’s decisions in each choice

occasion (Manski, 1977). For example, even though products are identical functionally,

they may differ in latent firm- or brand-specific associations, the underlying characteristics

of which are not fully known to the firms. Product choice is also affected by unspecified

situational influences. Consumers exhibit different choices when they have idiosyncratic

preferences along these characteristics. Moreover, the manner in which consumers

evaluate the large number of different latent attributes may not be systematic either

(Anderson and de Palma, 1992). For example, consumer choices may vary due to

temporary changes in their value of time (Becker, 1976). Consumer variety-seeking could

be a source of idiosyncratic preferences, following Pessemier’s (1978) view that

consumers could better handle their uncertain tastes by purchasing a portfolio of products.

Consumer heterogeneity along unobservable characteristics may be viewed as an error

in judgment on the part of consumers (Manski, 1977). When search costs are relatively

high compared to the potential benefit of making a correct decision or when consumers

have difficulty assessing product characteristics, errors in accurately measuring the utility

2 Alternatively, we may assume a linear transportation cost. However, the nature of the problem remains the

same even in the linear case and derives fundamentally identical results. A detailed formal investigation in the

linear case is available from the author upon request.


of a product will generate diverse product choices that cannot be accounted for by firms’

strategic attributes (Hawkins and Hoch, 1992). In addition, such heterogeneity may occur

because current analytical tools cannot predict consumer choices perfectly due to

functional misspecification or measurement error problems. Product choices, therefore,

vary across individuals and purchase occasions due to idiosyncratic tastes along such

unobservable characteristics, even when consumers share identical locations on the market

segment.

Attribute Y represents unobservable characteristics to the firms and captures the

remaining consumer heterogeneity that is unexplained by location X. Though the firms

observe the distribution of differing tastes along the attribute Y, they cannot manage it

strategically because of the intractability of its underlying characteristics. This approach

has been employed in research on price discrimination (Anderson and de Palma, 1988) and

on product differentiation (de Palma et al., 1985; Rhee et al., 1992). de Palma et al. (1985)

use this approach in a simultaneous entry game framework. Firms compete on price and

location in a one-stage game. Rhee et al. (1992) examine the same issue in a two-stage

game of location and price. See Anderson et al. (1992) for a detailed discussion of this

approach and its application to spatial competition.

A consumer of type yaR on the attribute Y has valuation ei ( y) of product i. Assume

that both firms equally assess information regarding consumer tastes and attempt to model

choices in the same manner. This assumption eliminates informational advantage as a

possible source of first-mover disadvantage. Therefore, a consumer of type (x, y) obtains

the following (indirect) utility in consuming product i:

Ui x;yð Þ ¼ V � d x� xið Þ2 � pi þ ei yð Þ; ð1Þ

where V is a positive constant and may be viewed as an average gross benefit that

consumers at x can obtain from consuming a unit of the product, and pi is the price

charged by firm i. Assume that V is large enough for the consumer to buy either product.

Consequently, the consumer decision is over which product to buy, not over whether to

buy. The assumption of inelastic category demand eliminates asymmetric market

conditions as a possible source of first-mover advantage. If we allow the existence of

consumers who are served by neither firm, some consumers may not purchase either

product if consumption generates negative utility. The resulting asymmetric market

conditions would confound the effect of consumer heterogeneity on first-mover advantage,

which is what we wish to investigate.

Because the firms cannot observe the underlying characteristics of attribute Y, they do

not know the exact value of ei( y) on any given purchase occasion. Thus, from the firms’

perspective, consumer valuations are random along the unobservable attribute. When

estimating sales and profits, the firms treat the valuation, ei( y), as a random disturbance ei.As a result, a firm’s prediction of consumer choice will be probabilistic in nature. The

probability Pri(x) that a consumer at x will purchase product i over j is

Pri xð Þ ¼ Pr ezpi � pj þ d xi � xj� �

xi þ xj � 2x� ��

; ð2Þ

where e = ei� ej. The normal distribution is an obvious candidate for the distribution of eidue to the central limit theorem. However, it does not provide a tractable form for the


choice probability. It is well known that the logistic distribution not only closely

approximates the normal but provides a closed-form expression for the choice probability

as well. Then, assume that e has the logistic distribution with mean zero and standard

deviation pr=ffiffiffi3

p. Anderson et al. (1988) show that the logistic choice model can be

derived from an entropic utility function in the representative consumer approach of

Spence (1976) and Dixit and Stiglitz (1977). Note that parameter rz0 measures the

degree of consumer heterogeneity along the unobservable attribute. It also represents the

importance weight associated with the unobservable attribute.

Each firm offers one product and competes non-cooperatively on price and market

location. Without loss of generality, assume that firm 1 positions to the left of firm 2: i.e.,

x1Vx2. Further, assume that the firms have identical cost structures and that marginal costs

are constant and normalized to zero. Fixed costs are not considered in this study.

Hence, a consumer at x will purchase a product from firm 1 with the probability

Pr1 xð Þ ¼ 1þ exp aþ bxð Þ½ ��1; ð3Þ

where

aup1 � p2 þ d x21 � x22

� �r

and bu2d x2 � x1ð Þ

r:

Fig. 1 illustrates the choice probabilities. Notice that Pr2(x)=1�Pr1(x) under the

assumption of inelastic category demand. The probability monotonically decreases for

firm 1, whereas it increases for firm 2. Furthermore, the inflection point of Pr1(x) occurs at

xx ¼ � a

b¼ x1 þ x2

2þ p2 � p1

2d x2 � x1ð Þ : ð4Þ

Pr1(x) is strictly concave over 0VxV x and strictly convex over xVxV1. Consumers to

the left of x have a higher probability of purchasing a product from firm 1, whereas

consumers to the right have a higher probability of purchasing from firm 2. A consumer at

the inflection point has identical probabilities of purchasing a product from either firm

(Pr1(x)=1 /2).

Fig. 1. The choice probability that a consumer will purchase a product either from firm 1 or 2.


When r =0, the probabilistic choice becomes deterministic as in d’Aspremont et al.

(1979),

Pr1 xð Þ ¼ 1 if 0VxVxx0 if xxVxV1:

�ð5Þ

As shown in Fig. 1, all consumers to the left of x patronize firm 1, whereas all

consumers to the right patronize firm 2. As consumers are increasingly heterogeneous

along the unobservable attribute, their choice probabilities become flatter. When rYl,

consumers will show equal choice probability of either product (1/2), regardless of their

locations on the market segment.

Given the uniform consumer distribution on the market segment, firm 1’s expected

demand is

Q1 p1;p2; x1;x2ð Þ ¼Z 1

0

Pr1 xð Þdx ¼ 1� 1

bln

1þ exp aþ bð Þ1þ exp að Þ

� : ð6Þ

Note that Q2=1�Q1. The expected demands are non-negative for r =0 and strictly

positive for r N0. Under the assumption of constant (zero) marginal costs, the expected

profits are P1=p1Q1 and P2=p2Q2, respectively. The expected profits are continuous

functions of location and price over the strategy set, R2 R2, for any rz0. Although the

firms are uncertain as to a particular consumer’s choice due to heterogeneity along

unobservable characteristics, they know the distribution of e and are then able to compute

their expected sales and profits with certainty. Therefore, the firms have perfect

information regarding expected market demand.

3. Sequential entry under price competition

We model competition in a two-stage sequential entry game as in the prior literature

(Neven, 1987; Tabuchi and Thisse, 1995). In the first stage, a Stackelberg leader chooses a

location first. After observing the leader’s market position, the follower chooses its

location. As in Tabuchi and Thisse (1995), we do not limit the location space to the market

space. For example, a firm may open a retail store or shopping mall away from the

residential area. In the characteristics space, a firm may launch a new product that is quite

different from consumers’ ideals.3 In the second stage, each firm determines its own price

competitively. Consequently, when choosing a location, the firm anticipates the impact of

this decision on price competition. Given any pair of firm locations, we first obtain price

equilibrium in pure strategies.

3 Alternatively, firms’ locations can be restricted to lie within the consumer market, [0,1], as in d’Aspremont et

al. (1979). However, the nature of the problem remains the same even in the restricted case and derives

fundamentally identical results. A detailed formal investigation in the restricted case is available from the author

upon request.


3.1. Price competition

Under the assumption of quadratic transportation cost, consumer utility is linear in eand x for given x1 and x2. The joint density of e and x in the utility function (i.e., the

logistic times the uniform densities) is log-concave. Thus, a unique price equilibrium

exists for any rz0 given any pair of locations x1 and x2 (Caplin and Nalebuff, 1991).

Though it is difficult to find closed-form solutions for the equilibrium prices in the general

case, we can obtain the closed-form solutions in the two cases of r =0 and symmetric

locations (i.e., x2=1�x1).

When consumer tastes are completely homogenous along unobservable characteristics

(r =0), the firms’ demands defined in Eq. (6) become

Q1 ¼x2 þ x1

2þ p2 � p1

2d x2 � x1ð Þ and Q2 ¼ 1� Q1: ð7Þ

Given Pi =piQi, the first-order conditions yield the following closed-form solutions:

p14 ¼ d x2 � x1ð Þ x2 þ x1 þ 2ð Þ3

and p24 ¼ d x2 � x1ð Þ 4� x2 � x1ð Þ3

: ð8Þ

If x2=1�x1, the first-order conditions provide a symmetric price solution p1*=p2*=p*

satisfying

1þ 1

2hln

1þ exp hð Þ1þ exp � hð Þ

� � p

2hrexp hð Þ � 1

exp hð Þ þ 1

� ¼ 0; ð9Þ

where h =d(1�2x1)/r. Hence, the symmetric equilibrium prices are

p4 ¼ p14 ¼ p24 ¼ rhexp hð Þ þ 1

exp hð Þ � 1

� ¼ rh coth

h2

�: ð10Þ

The comparative statics in these two cases are consistent with intuition. We obtain

Bpi* /Bxd N0, where xd =x2�x1, in the case of r =0 and Bp* /Bx1b0 in the case of

symmetric locations. Firms lower their prices in equilibrium due to intense price

competition as their locations get closer along the market segment. Moreover, Bpi* /Bd N0in the case of r =0 and Bp* /Bd N0 and Bp* /Br N0 in the case of x2=1�x1. Hence, firms

have more leeway to post higher prices in equilibrium as either d or r increases. This is so

because price competition is alleviated as consumers assign more weight in product choice

to shopping distance (i.e., increasing d) or their tastes along the unobservable

characteristics (i.e., increasing r). The reduced intensity in price competition leads to a

price increase.

As r increases, consumers are more concerned about their preferences along the

unobservable characteristics in making their choices. Thus, pricing becomes increasingly

dependent on idiosyncratic consumer tastes along the unobservable characteristics, but

relatively less on the firms’ locations. When rYl, equilibrium prices are invariant,

regardless of locations. The firms charge identical prices ( p*c2r) and earn identical

profit margins for any pair of locations x1 and x2 (see Appendix for a formal proof).


3.2. Positioning competition

The previous section shows that a unique price equilibrium exists given any pair of

locations x1 and x2. In that equilibrium, p1*(x1, x2) and p2*(x1, x2) are functions of these

locations. When we substitute prices in the profit functions with the equilibrium prices,

we obtain profits that depend solely on each firm’s location, x1 and x2: P1(x1, x2) and

P2(x1, x2). Without a loss of generality, it is assumed that firm 1 positions before firm 2 in

the sequential entry game. The Stackelberg equilibrium is, therefore, derived from

following first-order conditions:

dPP1

dx1¼ BPP1

Bx1þ BPP1

Bx2

dx2

dx1V0; ð11Þ

BPP2

Bx2z0; ð12Þ

where dx2/dx1 is equal to �(B2P2/Bx2Bx1)/(B2P2/Bx2

2) using the implicit function theorem

under the first-order condition dP2/dx2=0. Note that the second term in Eq. (11)

represents the effect of the first-mover’s location on its profit via the follower’s positioning

strategies.

The complexity of the problem, however, makes it difficult to find closed-form

solutions for the equilibrium locations in the general case. Thus, we obtain closed-form

solutions in the two extreme cases of r =0 and rYl. By using numerical computations,

we show changes in equilibrium locations as r increases from zero to a sufficiently large

number that yields the same solutions as in the case of rYl.

When consumer tastes are identical in the unobservable characteristics (r =0), the

model is the same as Tabuchi and Thisse (1995). We obtain the following profits by

substituting prices in P1 and P2 with p1* and p2*, given in Eq. (8):

PP1 ¼d x2 � x1ð Þ 2þ x2 þ x1ð Þ2

18and PP2 ¼

d x2 � x1ð Þ 4� x2 � x1ð Þ2

18: ð13Þ

Firm 2’s reaction function, x2*=(4+x1) /3, is derived from the first-order condition,

BP2 /Bx2=0. With perfect foresight, the first-mover takes into account the follower’s

reactions and maximizes the profit:

PP1 ¼4d243

50þ 15x1 � 12x21 � 4x31� �

: ð14Þ

As shown in Tabuchi and Thisse (1995), the first-order condition, BP1 /Bx1=0,

produces the following Stackelberg equilibrium locations and prices:

x14; x24� �

¼ 1

2;3

2

�and p14; p24

� �¼ 4d

3;2d3

�:

Given r =0, the first-mover takes a substantial advantage. The first-mover preempts the

market center and attracts the largest number of consumers. The follower then positions


itself away from the first-mover in order to avoid cutthroat price competition.

Consequently, the first-mover attains higher market share and profit, Q1*=2/3 and

P1*=8d / 9, than the follower’s Q2*=1 /3 and P2*=2d / 9.

Proposition 1. When rYl, there exists an agglomerated equilibrium at the market

center, x1*=x2*=1/2, and corresponding equilibrium prices are p1*=p2*=2r.

Proof. See Appendix. 5

When consumer tastes are very heterogeneous along unobservable characteristics, their

product choices are almost completely determined by their idiosyncratic preferences along

the characteristics. Hence, as shown in the previous section, both firms earn identical profit

margins in the price equilibrium given any pair of locations x1 and x2. Consequently, entry

order and competitive positioning along the observable dimension decline in importance.

Firms merely search for the location which appeals to the largest number of consumers.

Therefore, as in the case of simultaneous market entry (Rhee et al., 1992), both firms

position at the market center in equilibrium and charge identical prices, 2r. Neither firmhas an advantage based on order of entry. Both firms have identical sales, Q1*=Q2*=1 /2,

and profits, P1*=P2*=r.We resort to a numerical method in order to track changes in equilibrium locations if r

is greater than zero, but less than a sufficiently large number that yields an agglomerated

equilibrium at the market center. The profits are computed with a grid size of 10�2 for

0Vr/dV1.4 Note that r/d represents the relative importance of taste along the

unobservable characteristics compared to shopping distance in product choice. We obtain

the following results through numerical computations:

Proposition 2.

(a) When 0Vr /db0.38, there are dispersed equilibria,5 in which x1* is closer to the

market center than x2*.

(b) When 0.38Vr /db0.76, there are dispersed equilibria, in which x2* is closer to the

market center than x1*.

(c) When r /dz0.76, there exists an agglomerated equilibrium at the market center.

Fig. 2 illustrates changes in equilibrium locations with respect to r/d. Figs. 3 and 4

describe the effect of r/d on first-mover advantage in terms of market share and profit.

4 For each case of r/d, equilibrium prices are computed with a grid size of 10�3 for �2Vx1Vx2 and x1Vx2V2.Specifically, given x1 and x2, price equilibrium is obtained from the simultaneous first-order conditions using the

Newton–Raphson method. In order to check the second-order conditions, we fix p1 ( p2) at the equilibrium level

and change p2 ( p1). We confirm that C2 (C1) is decreasing as p2 ( p1) moves away from the equilibrium level.

Taking the equilibrium prices into account, we obtain x2* that generates the largest profit for each given x1. Then,

we choose x1* that provides firm 1 with the largest profit.5 There are two dispersed equilibria for firm 2’s position to the right or to the left of firm 1. We assume x1Vx2 in

the analysis. The equilibrium in the case of x2Vx1 is the mirror image of the one in the case of x1Vx2 with respectto the market center.

Fig. 2. Equilibrium locations with respect to r/d.


Note that the firm that positions itself closer to the market center charges a higher price and

obtains higher market share and profit.

As r/d increases in the interval of 0Vr /d b0.38, x1* moves away from the market

center, whereas x2* moves toward the center. This is consistent with intuition because we

view a large r as assigning more weight to preference along unobservable characteristics

in product choice. As consumer choices increasingly depend upon their idiosyncratic

preferences along unobservable characteristics, they become less loyal to the product

closer to their locations and may switch to the competing product. As shown in Fig. 1,

the inflection point x is on the right segment of the market at a lower level of r, givenx1Vx2. The increase in r enables the follower to take more customers away from the

Fig. 3. Equilibrium market shares with respect to r/d.

Fig. 4. Equilibrium profits with respect to r/d.


first-mover. Since the increase in r also makes preemptive positioning less effective in

competition, the follower (which positions itself far away from the center) moves

aggressively toward the market center in order to capture more switching customers over

the entire market. Anticipating the follower’s approach, the first-mover insulates itself

from intense price competition by moving away from the market center. By doing so,

however, the first-mover erodes its initial strategic advantage. Thus, its sales and profit

decrease. Nevertheless, since x1* is closer to the center than x2* in the interval of 0Vr /

d b0.38, the first-mover still obtains higher sales and profit: i.e., Q1*zQ2* and P1*zP2*.

When r/d=0.38, these two firms, which have evolved in opposite directions, are

equidistant from the center. The symmetric positions then produce identical sales and

profits.

The choice variation arising from idiosyncratic tastes along the unobservable

characteristics leads not only the follower, but also the first-mover, toward the market

center where demand is greatest. As shown in the second term of Eq. (11), however, the

first-mover should take the follower’s approach into account in its positioning, whereas the

follower takes the first-mover’s location as given. Consequently, the follower is more

aggressive in capturing switching customers. When 0.38br /d b0.76, anticipating the

follower’s aggressive positioning, the first-mover realizes that its positioning for a higher

market share would generate destructive price competition. Hence, the first-mover

positions farther away from the center and leaves more consumers for the follower to

capture. The follower, therefore, obtains greater sales and profits under its positional

advantage: i.e., Q2*zQ1* and P2*zP1*.

Note that x1* moves back to the market center as r/d increases over 0.47. As consumer

choices depend increasingly on their different tastes along the unobservable character-


istics, proximity in distance becomes ineffective in attracting consumers and the firm’s

incentive for product differentiation decreases. When r/d N0.47, the incentive for greater

demand prevails over the incentive for product differentiation. Thus, the first-mover

gravitates toward the market center. When r/d exceeds 0.76, both first-mover and follower

position themselves at the market center as shown in Proposition 1.

4. Conclusion

The late mover’s informational advantage has been advanced as a source of first-mover

disadvantage in previous game-theoretic literature (Gal-Or, 1985, 1987). This paper,

however, presents consumers’ idiosyncratic tastes along unobservable characteristics as

another source and shows the disadvantage of entering a new market first even in the

absence of informational advantage.

The spatial location model in this paper can be generalized to a situation in which two

product attributes form the characteristics space: a strategic attribute, which firms observe

and control such as market location or product features, and an unobservable attribute,

which firms cannot manage strategically due to its intractability. Consumers are

heterogeneous along both attributes, whereas each firm sequentially chooses its position

on the strategic attribute only.

Given the sequential entry, this paper shows that market preemption is not always a

consequence of moving first. The degree of first-mover advantage is determined by how

much consumer heterogeneity is accounted for by dimensions on which a first-mover can

preempt strategically. When their tastes vary mainly along the strategic attribute,

consumers invoke their judgments along the strategic attribute in making their choices.

Thus, a later entrant is sensitive to the pioneering incumbent’s strategic positioning and

strives to move away from the incumbent in order to avoid cutthroat price competition.

Anticipating the later entrant’s defensive positioning, the first-mover preempts the best

market position and earns higher sales and profit.

However, as consumer choices increasingly depend on their idiosyncratic tastes along

the unobservable attribute, the later entrant moves aggressively to the center in order to

capture increasing choice variations over the entire market. Moreover, preemptive

positioning on the strategic attribute becomes an ineffective means of competition. Thus,

anticipating the later entrant’s aggressive approach, the first-mover passively positions

farther away from the center in order to alleviate destructive price competition and attain

lower sales and profit. In other words, when a large portion of consumer heterogeneity

cannot be identified along strategic dimensions, this study recommends a wait-and-see

strategy because a later entrant obtains greater demand and profit, even in the absence of

informational advantage.

First-mover disadvantage arises when consumer heterogeneity along unobservable

characteristics is large (but not so large as to lead to the agglomeration at the market

center). It results from a random component of consumer utility from firms’ perspectives:

e.g., consumers’ idiosyncratic valuations of diverse firm-specific characteristics and brand

associations, etc. When consumers show different preferences for a product along these

firm- or brand-specific attributes, the intractability of the underlying characteristics enables


late movers to attain a comparative advantage in competition. This finding prescribes that

a first-mover should not only preempt the best market location, but should also maintain

consistent and positively evaluated brand associations across consumers in order to sustain

their pioneering advantages.

The random component may also be attributed to errors in judgment on the part of

consumers. Such errors may occur when the effort associated with an information search is

relatively costly compared to the potential benefit of making a correct decision. It is well

known in marketing that consumer purchases in many product categories are not very

involved, either situationally or on an enduring basis (Hawkins and Hoch, 1992).

Judgment errors will be prevalent in such low involvement decision making. We would,

therefore, expect a higher possibility of later entrants outperforming first-movers in such

consumer markets.

Alternatively, the random component may be the result of not being able to conduct

market research that uncovers all factors contributing to consumer preference. During the

last several decades, much progress has been made in research methodology. As the

sophistication of research methods and related information technology improves, firms

will become more proficient in countering consumer heterogeneity through a more

accurate understanding of consumers’ true preferences. This leads us to expect that firms

will have more leeway in adopting a pioneering strategy.

We employ the logistic distribution of e because it produces a tractable form for the

choice probability. We conjecture that we would obtain the fundamentally consistent

results and implications with any symmetric unimodal distribution of log-concave

density.6 Given the uniform consumer distribution on the market segment X, a symmetric

unimodal distribution of e will lead to the similar choice probability presented in Fig. 1.

Sufficiently high probability of choosing a remote product due to the idiosyncratic

preferences along unobservable characteristics results in the disadvantage of positioning

first on observable dimensions. For example, when we assume a triangular distribution of

e with density f (e)= (1/a)� (jej/a2), where �aV eVa, we obtain the similar choice

probabilities and findings that the first-mover earns greater sales and profit if a is less than

1.3, but lower sales and profit if a is greater than 1.3. In an extreme case of the uniform

distribution, the choice probability becomes linear and both pioneer and follower always

locate at the market center.7

This study derives the results under somewhat restrictive assumptions of inelastic

demand and uniform taste distribution in order to focus on the causality between

idiosyncratic tastes along unobservable characteristics and first-mover disadvantage. An

extension would be to relax these assumptions in order to check whether the causal

relationship would be generalized to other settings. We conjecture that idiosyncratic tastes

along unobservable characteristics will lead to first-mover disadvantage even under the

relaxation. However, the first-mover disadvantage will occur at higher levels of

heterogeneity along unobservable characteristics than in the current model because of

6 Function f(x) is log-concave in x if ln[ f(xE)]zE ln[ f(x0)]+ (1�E) ln[ f(x1)], where xE=Ex0+ (1�E) x1 and0VEV1. A group of log-concave densities includes the normal, uniform, logistic, Laplace, Dirichlet, exponential,

gamma, and beta distributions.7 A detailed formal proof and numerical computations are available from the author upon request.


local monopoly under finite reservation prices and a concentrated mass of consumers with

similar locations (Tabuchi and Thisse, 1995). In addition, this study assumes a duopoly.

We would extend this research to examine the effect of a potential entrant’s threat on the

findings by increasing the number of competing firms in the market.

Another extension would be the case of a quality-type attribute. Rhee (1996)

examines the effect of consumer heterogeneity along unobservable characteristics on

firms’ quality decisions in a simultaneous entry framework and derives the same results

as in the case of spatial competition. Drawing upon Rhee’s (1996) findings, we

conjecture that a sufficiently large heterogeneity along unobservable characteristics

would lead to first-mover disadvantage even when each firm chooses a level of product

quality in a sequential entry game. Multi-dimensional competition would be an

interesting extension as well. Furthermore, as the results generate testable hypotheses,

careful empirical studies should be called for in order to gain real-life insights about the

critical values of r/d.

Acknowledgement

The author wishes to thank Eunkyu Lee, Jae-Hyeon Pae, Andre de Palma, Julie Ruth,

and Jacques-Francois Thisse for their helpful discussions and comments. The author also

gratefully acknowledges funding from the Hong Kong Polytechnic University Research

Grant G-T439.

Appendix A

Proof of Proposition 1. This proof shows an equilibrium when r approaches. Given the

firms’ demands in Eq. (6), we obtain following first-order conditions:

BP1

Bp1¼ Q1 þ p1

BQ1

Bp1¼ 0 and

BP2

Bp2¼ Q2 þ p2

BQ2

Bp2¼ 0: ðA:1Þ

From Eq. (A.1), we obtain

p24 ¼ � Q2

BQ2

Bp2

� �1

¼ r1þ exp að Þ½ � 1þ exp aþ bð Þ½ �

exp að Þ � exp aþ bð Þ½ � ln1þ exp að Þ

1þ exp aþ bð Þ

� :

ðA:2Þ

Note that

limrYl

p24 ¼ limrYl

r1þ exp að Þ½ � 1þ exp aþ bð Þ½ �

exp að Þ � exp aþ bð Þ½ � ln1þ exp að Þ

1þ exp aþ bð Þ

�

¼ r limrYl

1þ exp að Þ½ � 1þ exp aþ bð Þ½ � limrYl

ln1þ exp að Þ

1þ exp aþ bð Þ

�

1

exp að Þ � exp aþ bð Þ½ � ¼ 2r; ðA:3Þ


because

limrYl

1þ exp að Þ½ � 1þ exp aþ bð Þ½ � ¼ 4; ðA:4Þ

limrYl

ln1þ exp að Þ

1þ exp aþ bð Þ

� 1

exp að Þ � exp aþ bð Þ½ � by l;Hospital

;s rule

¼ limrYl

exp aþ bð Þ � exp að Þ½ �aþ exp aþ bð Þ 1þ exp að Þ½ �b1þexp að Þ½ � 1þexp aþbð Þ½ � exp aþbð Þ�exp að Þf gaþexp aþ bð Þb½ � ¼

1

2:

ðA:5Þ

Hence, p2*c2r when r is sufficiently large. With the same procedure, we obtain

p1*c2r.At p1* and p2*, the second derivatives of P1 and P2 with respect to prices are

non-positive,

B2P1

Bp21¼ exp að Þ � exp aþ bð Þ½ � 2þ exp að Þ þ exp aþ bð Þ½ �

d x2 � x1ð Þ 1þ exp að Þ½ �2 1þ exp aþ bð Þ½ �2V0 ðA:6Þ

B2P2

Bp22¼ exp að Þ � exp aþ bð Þ½ � 2exp að Þexp aþ bð Þ þ exp að Þ þ exp aþ bð Þ½ �

d x2 � x1ð Þ 1þ exp að Þ½ �2 1þ exp aþ bð Þ½ �2V0

ðA:7Þ

because exp(a +b)z (a). Thus, the second-order conditions are satisfied.

As rYl, equilibrium prices approach 2r, regardless of x1 and x2. Thus, the first-ordercondition of P2 with respect to x2 (given x1) becomes

BPP2

Bx2c2r

BQQ2

Bx2¼ 2r

1

b x2 � x1ð Þ ln1þ exp aVð Þ

1þ exp aVþ bð Þ

� �þ 1

x2 � x1ð Þ

�

x2 exp aVð Þ� exp aVþ bð Þ½ � þ exp aVþ bð Þ 1þ exp aVð Þ½ �1þ exp aVð Þ½ � 1þ exp aVþ bð Þ½ �

� �¼ 0;

ðA:8Þ

where aVud(x12�x2

2)/ r. From the above first-order condition, we obtain

x2 � x1 ¼ � r2d

ln1þ exp aVð Þ

1þ exp aVþ bð Þ

�

1þ exp aVð Þ½ � 1þ exp aVþ bð Þ½ �x2 exp aVð Þ � exp aVþ bð Þ½ � þ exp aVþ bð Þ 1þ exp aVð Þ½ � : ðA:9Þ

The right-hand side of Eq. (A.9) approaches zero as rYl because

limrYl

ln1þ exp aVð Þ

1þ exp aVþ bð Þ

� ¼ 0: ðA:10Þ


This ensures that, given x1Vx2, firm 2’s best reaction is positioning as close to x1 as

possible.

When r is sufficiently large, the first-order condition of P1 with respect to x1becomes

BPP1

Bx1c2r

BQQ1

Bx1¼ 2r

1


1þ exp aVþ bð Þ

� �þ 1

x2 � x1ð Þ

�

x1 exp aVð Þ�exp aVþ bð Þ½ �þ exp aVþ bð Þ 1þ exp aVð Þ½ �1þ exp aVð Þ½ � 1þ exp aVþ bð Þ½ �

�� ¼ 0:

ðA:11Þ

From the above first-order condition, we obtain

1


1þ exp aVþ bð Þ

� þ exp aVþ bð Þ

x2 � x1ð Þ 1þ exp aVþ bð Þ½ �

þ x1 exp aVð Þ � exp aVþ bð Þ½ �x2 � x1ð Þ 1þ exp aVð Þ½ � 1þ exp aVþ bð Þ½ � ¼ 0: ðA:12Þ

As x2Yx1, the first term in Eq. (A.12) becomes

limx2Yx1

1


1þ exp aVþ bð Þ

�

¼ limx2Yx1

r2d x2 � x1ð Þ lim

x2Yx1

1

x2 � x1ð Þ ln1þ exp aVð Þ

1þ exp aVþ bð Þ

�

by l;Hopital

;s rule

¼ limx2Yx1

r2d x2 � x1ð Þ

limx2Yx1

� 2dr

��x2 exp aVð Þ � exp aVþ bð Þ½ � þ exp aVþ bð Þ 1þ exp aVð Þ½ �

1þ exp aVð Þ½ � 1þ exp aVþ bð Þ½ �

�

¼ limx2Yx1

r2d x2 � x1ð Þ � d

r

�¼ � lim

x2Yx1

1

2 x2 � x1ð Þ : ðA:13Þ

The last term in Eq. (A.12) becomes

limx2Yx1

x1 exp aVð Þ � exp aVþ bð Þ½ �x2 � x1ð Þ 1þ exp aVð Þ½ � 1þ exp aVþ bð Þ½ �

¼ limx2Yx1

x1

1þexp aVð Þ½ � 1þexp aVþbð Þ½ � limx2Yx1

exp aVð Þ�exp aVþbð Þx2�x1

by l;Hopital

;s rule

¼ limx2Yx1

x1

1þexp aVð Þ½ � 1þ exp aVþbð Þ½ � limx2Yx1

2dr

exp aVþbð Þ x2�1ð Þ�exp aVð Þx2½ ��

¼ limx2Yx1

2dx1r 1þ exp aVð Þ½ � 1þ exp aVþ bð Þ½ � : ðA:14Þ


Hence, as x2 approaches x1, Eq. (A.12) becomes

limx2Yx1

exp aVþ bð Þ � 1

2 x2 � x1ð Þ 1þ exp aVþ bð Þ½ � � limx2Yx1

2dx1r 1þ exp aVð Þ½ � 1þ exp aVþ bð Þ½ �

¼ 1

4limx2Yx1

exp aVþ bð Þ � 1

x2 � x1

� � dx1

2rby l

;Hopital

;s rule

¼ 1

4limx2Yx1

2d 1� x2ð Þexp aVþ bð Þr

� � dx1

2r¼ d 1� x1ð Þ

2r� dx1

2r¼ d 1� 2x1ð Þ

2r¼ 0:

ðA:15Þ

Therefore, Eq. (A.15) leads to the following Stackelberg equilibrium locations:

x14;x24� �

¼ 1

2;1

2

�:

Consequently, under sufficiently large s, two firms position themselves at the market

center with an infinitesimal distance between them. In equilibrium, they charge identical

prices, p1*=p2*=2r, and obtain identical demands and profits: Q1*=Q2*=1 /2 and

P1*=P2*=r. 5

References

Anderson, S.P., 1987. Spatial competition and price leadership. International Journal of Industrial Organization

5, 367–398.

Anderson, S.P., de Palma, A., 1988. Spatial price discrimination with heterogeneous products. Review of

Economic Studies 55, 573–597.

Anderson, S.P., de Palma, A., 1992. The logit as a model of product differentiation. Oxford Economic Papers

44, 51–67.

Anderson, S.P., de Palma, A., Thisse, J.-F., 1988. A representative consumer theory of the logit model.

International Economic Review 29, 461–466.

Anderson, S.P., de Palma, A., Thisse, J.-F., 1992. Discrete Choice Theory of Product Differentiation. The MIT

Press, Cambridge.

Becker, G.S., 1976. The Economic Approach to Human Behavior. University of Chicago Press, Chicago.

Belk, R.W., 1975. Situational variables and consumer behavior. Journal of Consumer Research 2, 157–164.

Broniarczyk, S.M., Alba, J.W., 1994. The importance of the brand in brand extension. Journal of Marketing

Research 31, 214–228.

Caplin, A., Nalebuff, B., 1991. Aggregation and imperfect competition: on the existence of equilibrium.

Econometrica 59, 25–59.

d’Aspremont, C., Gabszewicz, J.J., Thisse, J.-F., 1979. On Hotelling’s stability in competition. Econometrica 47,

1145–1150.

de Palma, A., Ginsburgh, V., Papageorgiou, Y.Y., Thisse, J.-F., 1985. The principle of minimum differentiation

holds under sufficient heterogeneity. Econometrica 53, 767–781.

Dixit, A.K., Stiglitz, J.E., 1977. Monopolistic competition and optimum product diversity. American Economic

Review 67, 297–308.

Gal-Or, E., 1985. First mover and second mover advantages. International Economic Review 26, 649–653.

Gal-Or, E., 1987. First-mover disadvantages with private information. Review of Economic Studies 54, 279–292.

Golder, P.N., Tellis, G.J., 1993. Pioneer advantage: marketing logic or marketing legend? Journal of Marketing

Research 30, 158–170.


Hamel, G., Prahalad, C.K., 1994. Competing for the Future. Harvard Business School Press, Boston.

Hawkins, S.A., Hoch, S.J., 1992. Low involvement learning: memory without evaluation. Journal of Consumer

Research 19, 212–225.

Hotelling, H., 1929. Stability of competition. The Economic Journal 39, 41–57.

Kalyanaram, G., Robinson, W.T., Urban, G.L., 1995. Order of market entry: established empirical generalizations,

emerging generalizations, and future research. Marketing Science 14 (Part 2), G212–G221.

Lane, W.J., 1980. Product differentiation in a market with endogenous sequential entry. The Bell Journal of

Economics 33, 237–260.

Manski, C.F., 1977. The structure of random utility models. Theory and Decision 8, 229–254.

Neven, D.J., 1987. Endogenous sequential entry in a spatial model. International Journal of Industrial

Organization 5, 419–434.

Pessemier, E.A., 1978. Stochastic properties of changing preferences. American Economic Review 68, 380–385.

Prescott, E.C., Visscher, M., 1977. Sequential location among firms with foresight. The Bell Journal of

Economics 8, 378–393.

Rao, R.C., Rutenberg, D.P., 1979. Preempting an alert rival: strategic timing of the first plant by analysis of

sophisticated rivalry. The Bell Journal of Economics 10, 412–428.

Rhee, B.-D., 1996. Consumer heterogeneity and strategic quality decisions. Management Science 42, 157–172.

Rhee, B.-D., de Palma, A., Fornell, C., Thisse, J.-F., 1992. Restoring the principle of minimum differentiation in

product positioning. Journal of Economics and Management Strategy 1, 475–505.

Robinson, W.T., Fornell, C., 1985. Sources of market pioneer advantages in consumer goods industries. Journal

of Marketing Research 22, 305–317.

Schmalensee, R., 1982. Product differentiation advantages of pioneering brands. American Economic Review 72,

349–365.

Spence, M., 1976. Product selection, fixed costs, and monopolistic competition. Review of Economic Studies 43,

217–235.

Stigler, G.J., Becker, G.S., 1977. De gustibus non est disputandum. American Economic Review 67, 76–90.

Tabuchi, T., Thisse, J.-F., 1995. Asymmetric equilibria in spatial competition. International Journal of Industrial

Organization 13, 213–227.

Urban, G.L., Carter, T., Gaskin, S., Mucha, Z., 1986. Market share rewards to pioneering brands: an empirical

analysis and strategic implications. Management Science 32, 645–659.

Documents

First-mover disadvantages with idiosyncratic consumer tastes along unobservable characteristics