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**ASYMMETRIC STORE POSITIONING AND PROMOTIONAL ADVERTISING **
**STRATEGIES: THEORY AND EVIDENCE **
**Marketing Science****, Vol. 21 (2002), No. 1 (forthcoming) **
The authors are listed in reverse alphabetical order and contributed equally to the paper. We thank the Editor, Professor Brian Ratchford, the former Editor, Professor Rick Staelin, the Area Editor and two anonymous reviewers of this journal for their helpful comments and suggestions. We thank Nanda Kumar and Georg Muller for research assistance. This work was partly supported by the Beatrice Companies Faculty Research Fund to the first author. The support from the Kilts Center for Marketing at GSB, University of Chicago to the first and third authors is gratefully acknowledged. The usual disclaimer applies.

**ABSTRACT**
Asymmetrically positioned retailers, who vary in the quality/in-store service offered, are increasingly using promotional advertising – the practice of advertising sale prices on familiar merchandise lines – to compete for customers who are willing to comparison shop. The objective of this paper is to examine the role of promotional advertising for stores that vary in their quality positioning in competing for customers using a game-theoretic model. Our focus is on two key retail promotional advertising decisions – the frequency with which to advertise price reductions and the accompanying depth of discount.
We consider a stylized duopolistic retail market with the two stores that differ in their service
positioning. We assume that each store enjoys a relative advantage in serving a subset or segment of customers who regularly visit it and whom we call “patrons” of the store. It is assumed that it costs more to shop at the less-frequented store. We further assume that consumers are only partially informed about the prevailing retail prices – while they perfectly know the posted price at the store that they patronize, they are uncertain about the price at the other store and have rational expectations about these prices. Consumers in this market differ on three dimensions: preference for service, shopping costs and store switching costs. We explicitly consider two consumer segments differing in their willingness to pay for service. Further, we assume store switching is more costly for the high-valuation segment. We allow for within-segment heterogeneity by assuming that consumers differ in their shopping costs.
Our analysis shows that if promotional advertising is not “too costly”, the equilibrium strategies of
the competing retailers entail occasionally posting its “regular” price but not advertising that price and on other occasions positing its “sale” price and advertising that price. The analysis also suggests that promotional advertising is driven by “offensive” (traffic-building) as well as “defensive” (consumer-retention) considerations. Further, the relative importance of offensive and defensive considerations is influenced by the service positioning of the stores. Specifically, relative to the low-service store, promotional advertising by the high-service store is driven more by offensive consideration than defensive consideration. Finally, a stores' service positioning impacts its frequency of promotional advertising and the depth of discount that it offers during “sale”. Specifically, relative to the low-service store, the high-service store offers advertised sales more frequently but with shallower discounts.
These results follow from the fact that differences in service positioning leads to a natural consumer
“self-selection”. Specifically, the consumer-mix of the high-service store comprises a higher fraction of the high-valuation consumers who are less sensitive to promotional advertising due to their higher store switching costs. Thus, if the low-service retailer were to build store traffic by targeting the customer-mix of the high-service retailer (motivated by offensive consideration), it has to offer deeper discounts and yet the demand enhancement is lower. Thus, relative to the high-service store, promotional advertising is not that attractive for the low-service store. However, the low-service store still relies on offering discounted prices occasionally in order to retain its customer base. Thus when using promotional advertising to attract and retain customers, the high-service store should rely more on the “frequency cue” while the low-quality store should rely more on the “magnitude cue”.
We provide empirical support for the key predictions of our analytical model by collecting and
analyzing retail promotional advertisements for stores that vary in their level of in-store service, published in major newspapers in a large U.S. metropolitan city. We collect data from 813 advertisements across 14 different product groups in the men’s and women’s categories. The data are consistent with the model’s predictions. Our theory and empirical analysis should be of interest to both academics and practitioners, particularly those in the area of channel management and promotional advertising. KEY WORDS:

*Retail Competition; Store Positioning; Promotional Advertising; Shopping Cost; *
*Traffic Building; Customer Retention.*
**1. INTRODUCTION **
In many retail markets, asymmetrically positioned stores provide different levels of service, store
ambiance, convenience while competing for customers who comparison shop for similar merchandise
offered by these stores e.g. Marshall Field's and Filene's Basement in the apparel market, Workbench and
Door Store in the furniture market (Berman and Evans, 1995; Lewison, 1997; Ortmeyer and Salmon,
1989). These asymmetrically positioned stores primarily use promotional advertising – the practice of
advertising sale prices on familiar merchandise lines – in order to attract customers. For instance, in
1990, retailers spent at least 70% of the total $20 billion media expenditures on promotional advertising
(Berman and Evans, 1995). Most of these advertising dollars are used for newspaper advertising
(approximately 75%) that is also rated by consumers to be the most important source of information for
retail prices (Kopp, Eng and Tigert, 1989; Newspaper Advertising Bureau, 1990).
The two key decisions in retail promotional planning are the frequency of advertised sales and the
depth of discount offered (Stern, El-Ansary and Coughlan, 1995). A natural question that arises is
whether the positioning of the store is related to its advertising frequency and depth of discount
decisions? Table 1 below reports the average time interval between advertised sales and the average
depth of discount advertised on men’s dress shirts by both high- and low-service stores. This data is
collected from an overall total of 813 newspaper advertisements over a 6-month period in a major
metropolitan city in the US out of which 133 advertisements related to men’s dress shirts. Based on this
data, we observe that the high-service stores advertise sales more frequently but offer lower depths of
discount than the low-service stores. This pattern is observed for other product groups as well (data for
14 different product groups in both the men’s and women’s departments are reported in Table 3).
TABLE 1: Mean Time Interval & Depth of Discount for High- and
Low-Service Stores for Men’s Dress Shirts
* High-service stores include Marshall Field’s, Bloomingdale’s, Carson Pirie Scott and Lord & Taylor.
** Low-service stores include Filene’s Basement and T.J. Maxx
This empirical observation is particularly intriguing as neither conventional wisdom nor previous
related theoretical research can readily explain this phenomenon. For instance, conventional wisdom
based on the differences in consumers that these store serve would suggest that high-service stores should
advertise sales less frequently as well as offer a lower depth of discount than low-service stores since
high-service stores serve consumers who are less price sensitive than low-service stores. Similarly, these
differences in the promotional advertising strategies for high- versus low-service stores cannot be
explained by the differences in their merchandise margins. Since high-service stores have higher margins
and therefore a higher promotional budget, they may have a greater ability to both advertise sales more
frequently as well as offer higher depths of discount than low- service stores.
The observed empirical differences in the frequency and depth of discount decisions for high-
versus low-service stores are also inconsistent with the predictions for strong versus weak brands in
previous pioneering research on price promotions (Narasimhan, 1988; Raju, Srinivasan and Lal, 1990).
Specifically, Narasimhan (1988) and Raju, Srinivasan and Lal (1990) predict that a brand with a higher
loyal share/strong brand will promote less often than a brand with a lower loyal share/weak brand. Also,
while Narasimhan (1988) predicts that both the strong and weak brand will offer the same expected
discount, Raju, Srinivasan and Lal (1990) predicts that the strong brand will offer a higher average depth
of discount than the weak brand. In a seminal work, Blattberg and Wisniewski (1989) present a rationale
for the empirically observed asymmetry in cross-price elasticities for high- versus low-price tier brands.
This observed asymmetry implies that higher price-tier brands benefit from offering price cuts since it
takes away sales from lower price-tier brands. In contrast, lower price-tier brands will not take away sales
from higher price-tier brands by offering similar price cuts. These findings suggest that higher price-tier
brands derive a higher benefit by offering price cuts relative to lower price-tier brands. However, it is not
immediately obvious as to why this higher benefit for high-service stores should imply only a higher
frequency and not a higher depth of discount as well.
Our objective in this paper is to develop a game-theoretic framework to examine how the
competition between retailers who differ in their level of quality/in-store service influences their
promotional advertising decisions. Our analysis focuses on two key aspects of promotional advertising –
(a) the frequency with which sales are advertised; and (b) the advertised depth of discount. In particular,
we are interested in answering the following questions:
1. What are the strategic considerations that underlie a retailer's decision on the frequency and depth-of-
discount aspects of its promotional advertising strategy?
2. How do differences in the quality positioning of competing stores influence a retailer’s decisions on
the frequency of advertised sales and the depth of discount offered?
3. How do consumer characteristics influence the stores' promotional advertising decisions?
1. In the rest of the paper, we will refer to quality and in-store service interchangeably. 2. A few caveats apply to this statement. Both these papers model inter-brand promotional competition. Hence, the above is based on interpreting high- (low-) service store being the analog of strong (weak) brand in these papers. Further, this statement applies only to the insights from the base models considered in these papers. Both Narasimhan (1988) and Raju, Srinivasan and Lal (1990) also consider several model extensions that yield different
To address these issues, we consider a stylized duopolistic retail market with the two stores that differ
in their service positioning. We assume that each store enjoys a relative advantage in serving a subset or
segment of customers who regularly visit it and whom we call “patrons” of the store. It is assumed that it
costs more to shop at the less-frequented store. We further assume that consumers are only partially
informed about the prevailing retail prices – while they perfectly know the posted price at the store that
they patronize, they are uncertain about the price at the other store and have rational expectations about
these prices. This feature captures the fact that consumers have better price information about stores that
they frequently visit while they have less precise price information about stores only visited occasionally
(say during advertised sale events). Consumers in this market differ on 3 dimensions: preference for
service, shopping costs and store switching costs. We explicitly consider two consumer segments
differing in their willingness to pay for service. Further, we assume store switching is more costly for the
high-valuation segment. We allow for within-segment heterogeneity by assuming that consumers differ in
their shopping costs. These assumptions imply that segment-level demand is finitely elastic.
Our analysis shows that if promotional advertising its not “too costly”, the equilibrium strategies of
the competing retailers entail occasionally posting its “regular” price (that are not advertised) and on
other occasions positing its “sale” price (that are advertised). In addition, the analysis yields the
• Promotional advertising is driven by both “offensive” or traffic-building as well as “defensive” or
• A stores quality positioning impacts the relative importance of offensive and defensive considerations
as drivers of promotional advertising. Specifically, relative to defensive consideration, offensive
consideration plays a more prominent role for the high-service store than for the low-service store; and,
• A stores' service positioning impacts its frequency of promotional advertising and the depth of discount
that it offers during “sale”. Specifically, relative to the low-service store, the high-service store offers
advertised sales more frequently but with shallower discounts.
These results follow from the fact that differences in service positioning leads to a natural consumer “self-
selection”. Specifically, the consumer-mix of the high-service store comprises a higher fraction of the high-
valuation consumers who are less sensitive to promotional advertising due to their higher store switching
costs. Thus, if the low-service retailer were to build store traffic by targeting the customer-mix of the high-
service retailer (motivated by offensive consideration), it has to offer deeper discounts and yet the demand
enhancement is lower. Thus, relative to the high-service store, promotional advertising is not that attractive
for the low-service store. However, the low-service store still relies on offering discounted prices
occasionally in order to retain its customer base.
Our analysis thus suggests that in using promotional advertising to attract and retain customers, the
high-quality store should rely more on the “frequency cue” while the low-quality store should rely more
on the “magnitude cue”. It further shows that the high-service store's reliance on frequency versus
magnitude cues depends on its positional strength on the service dimension as well customer
segmentation characteristics. We offer empirical evidence in support of these findings.

**1.1 Li terature Review & Research Contributions: **
This paper builds on and contributes to three research streams. The first stream (e.g., Shilony, 1977;
Narasimhan, 1988; Raju, Srinivasan and Lal, 1990) examines the phenomena of price promotions, both in
the context of brand-level and (grocery) retail-level competition. Assuming perfect consumer knowledge
about prevailing prices of the competing brands/retailers, these papers show that a pure strategy equilibrium
in which manufacturers charge a single price for their brands does not exist because of incentives to
undercut the competitor’s price. The second stream (e.g., Varian, 1980; Banks and Moorthy, 1996)
investigates a market where consumers are uninformed about prevailing prices of all the brands/retailers.
They show that if valuation and search costs are positively correlated, price promotions can be used as a
mechanism to implement price discrimination. We contribute to these research streams by examining a
retail market where consumers have imperfect price knowledge (i.e., they know about prevailing prices at
certain outlets better than others) and highlight the role of promotional advertising as a competitive tool.
The third-stream (e.g. Blattberg and Wisniewski 1989; Allenby and Rossi, 1991) empirically
examines the impact of price promotions on the sales of brands asymmetrically positioned in terms of
quality. They find evidence of asymmetric price elasticity. We contribute to this stream by highlighting the
strategic implications of this asymmetry for retail promotional advertising decisions.
In contrast, a recent set of marketing papers has incorporated varying roles for price advertising in
different retailing contexts. Lal and Matutes (1994), in the context of multi-product retailers (grocery
stores), highlight the commitment role of price advertising. Lal and Rao (1997), again in the context of
multi-product retailers, investigate the role of two different formats of price advertising (viz., EDLP and Hi-
Lo formats) and highlight the dependence between stores’ positioning and pricing strategies. Simester
(1995) investigates the role of advertised prices in influencing consumers’ expectations about the
unadvertised prices, thus highlighting the signaling role of price advertisements. We contribute to this
stream by highlighting the informational role of promotional advertising.
3. Note in Narasimhan (1988), we can also interpret “loyal” consumers as those who lack information on prices of the competing brand. Similarly, Varian (1980) can be interpreted as a model with perfectly informed loyals and switchers. We thank an anonymous reviewer for this interpretation.
The rest of the paper is organized as follows. In Section 2, we present the basic assumptions of our
model and derive analytical expressions for the retail demand. We present the equilibrium analysis in
Section 3 and characterize the optimal retail promotional advertising strategies. We also highlight the
differences in the optimal strategies of the high- and low-quality stores. We discuss the data, empirical
model formulations and results of our empirical analysis in detail in Section 4. In Section 5, we discuss
the conclusions, managerial implications and provide directions for future research.

**2. THE MODEL **
**Retail Structure:** We consider a retail market with two competing stores – store

*H* and store

*L*. We further

assume that the two stores differ in their positioning on the quality dimension: the quality of store

*H* is

*q *
while that of store

*L* is

*q * with

*q*
>

*q *> 0 . This captures the vertical differentiation in the retail market.
The difference in quality could arise due to differences in the level of in-store service, store ambiance,
shopping convenience etc. (Stern, El-Ansary and Coughlan, 1995). For instance, retail chains in the apparel
market can be classified into two major retailer groups – traditional department stores such as Carson Pirie
Scott and Marshall Field’s offer higher in-store service than full-line discount stores such as Filene’s
Basement and T.J. Maxx. We assume that each store enjoys a relative advantage in serving a subset or
segment of customers in this market who regularly visit it and whom we call “patrons” of the store. This
captures the horizontal differentiation in the retail market. A store may enjoy this relative advantage among
patrons due to several reasons: (a) their familiarity with the store in terms of its layout (stores have very
different layouts with several departments spread over multiple floors); (b) knowledge of how to shop at
the store based on their prior experiences (e.g. who to obtain in-store assistance from); (c) familiarity
with the price levels and merchandise sold by the store; (d) geographic proximity with the store etc. We
assume that in the face of uncertainty about prevailing store prices and the absence of a sale from either
store,

*H*-patrons will visit store

*H* and

*L*-patrons visit store

*L*. However, when a sale is offered each store
may also attract the other store’s patrons. These assumptions are consistent with findings based on a
survey conducted with retail managers in the apparel market (Kopp, Eng and Tigert, 1989). The stores are
assumed to sell comparable merchandise that can be considered imperfect substitutes. We assume that
stores have an identical marginal cost of

*c* which, without loss of generality, is set to zero (we discuss this
assumption in section 2.1). This characterization is similar to that of Shilony (1977) and Bester and Petrakis
4. In a survey conducted with high- and low-service stores in our empirical study, we found that for the categories studied, the mix of products – both in terms of breadth of product line and depth of assortment – across different price points are comparable. For instance, both Marshall Field’s (a high-service store) and T.J. Maxx (a low-service store) have roughly 30:70 mix of “better” and “moderate” priced merchandise. Also, while Marshall Field’s has approximately 40,000 SKU’s, T.J. Maxx has about 37,500 SKU’s in men’s categories.

**Consumer Characteristics & Shopping Behavior: **We assume a unit mass of

*H*-patrons and

*L*-patrons.

, , of both

*H*-patrons and

*L*-patrons have a higher valuation
(preference) for quality while the remaining consumers have a lower quality valuation (we discuss this
assumption in section 2.1). We label the former as the

*HV *consumer segment while the latter is referred to
as the

*LV *consumer segment. This captures the vertical heterogeneity across the customers. The consumer
valuations assumed in the analysis are as below.
The parameter θ captures the extent of vertical differentiation in the retail market so that θ = 1 either
denotes a symmetric positioning of stores on the quality dimension or that consumers do not value the
quality differentials across stores. It is instructive to view

*v * as representing the core product valuation
while α represents the extent of heterogeneity in consumers’ preference for in-store service.
We capture the heterogeneity in consumer (unit) shopping costs through the parameter

*s *that is
assumed to be uniformly distributed i.e.

*s ~ U*[0

*, *]

*s *. This captures the horizontal heterogeneity across
customers. Further, we assume that a store’s patrons incur a higher shopping cost while visiting the
competing store. This is represented by a scaling factor, β , β > 1. We also assume that

*HV *consumers
incur higher shopping costs than

*LV* consumers. We represent this higher cost by a scaling factor, τ ,
> 1. Thus, an

*L*-patron belonging to the

*LV *segment with a unit shopping cost of

*s *∈ 0,

*s*
shopping cost of

*s* to visit store

*L*, while she incurs a shopping cost of β

*s * to visit store

*H *and vice versa
for

*H*-patrons. On the other hand, an

*L*-patron belonging to the

*HV *segment with a unit shopping cost of
0

*s*] incurs a shopping cost of τ

*s * to visit store

*L*, while she incurs a shopping cost of βτ

*s *to visit
store

*H*. Note that the parameters

*s * and β capture two distinct aspects of horizontal differentiation. While
5. Note that in this formulation,

*HV*
implied by the valuation-for-quality function of the form
willingness-to-pay for quality for consumer

*i* with γ

*j* is the quality of the “augmented” product
(base product + shopping experience) at store

*j* with

*qH*>

*qL*>0 (Moorthy, 1988; Bagwell and Riordan, 1991). 6. Note that our assumption of a positive correlation between consumer valuation for quality and shopping costs (being implied by θ > 1 and τ > 1) is consistent with the literature (Salop and Stiglitz, 1977; Tellis and Wernerfelt, 1987; Banks and Moorthy, 1996; Lal and Rao, 1997) and is justifiable on the ground that consumers with higher valuation for in-store service and ambiance, being higher income consumers, also have a higher opportunity cost of time and hence higher shopping costs (Becker, 1965).

*s * represents the extent of consumer heterogeneity in shopping costs, β captures the magnitude of the
switching cost from the store that the consumer patronizes (Berman and Evans, 1995; Stern, El-Ansary and
Coughlan, 1995). Under this interpretation, a larger value of

*s * would signify greater variations in
consumer shopping costs. Similarly, a larger value of β would imply a higher extent of store loyalty.
Therefore, the consumer surplus function (i.e. valuation less shopping cost and price) is given by
gross willingness-to-pay of consumer

*i*,

*i*∈{

*HV*,

*LV*},

* *at store

*j*,

*j*∈{

*H*,

*L*},
β = β > 1 if consumer

*i* is not store

*j’*s patron;
if consumer

*i* is store

*j’*s patron,

*i *belongs to the

*HV *segment;
if consumer

*i *belongs to the

*LV *segment.

**2.1 Discussion of Key Model Assumptions: **
1. Similar Cost Structure: We assume that stores have an identical marginal cost for model parsimony.
The net effect of this assumption (coupled with the fact that consumers have higher willingness to pay
while buying at the high-service store) is that the high-service store enjoys a higher margin. As we
discuss later in section 3.2, this higher margin forms the basis for the high-service store to offer
advertised sales with a higher frequency than the low-service store. Therefore, even if we allow the
high-service store to have a higher cost, as long as it continues to enjoy a higher margin this result will
2. Same Mix of High- and Low-Valuation Consumers: We assume that the mix of high- vs. low-
valuation customers is the same amongst the patrons of the high- and low-service stores. This is not a
critical assumption for our analysis and is made for analytical simplicity. Allowing the high-service
store to have a higher fraction of high-valuation customers will only strengthen our results.
7. An alternative interpretation is based on consumers’ preference for proximity/convenience in the spirit of Hotelling-type locational models (e.g. Lal and Rao, 1997). If β = 1, there is no store loyalty or switching cost and
the set-up reduces to a pure vertical differentiation model. If both β = 1 and θ = 1, the retail competition reduces to undifferentiated Bertrand competition. 8. An industry study done in 1995 by McKinsey Consultants (cited in Stern, El-Ansary and Coughlan, 1996) suggests that department stores have higher margins than discount stores In addition, we collected data on retail margins from a sample of both high- and low-service stores. On an average, retail margins were 40-50% higher for the high-service stores than discount stores. For instance, the gross profit margins for Neiman-Marcus over the period 1991-95 was 35.5% while that for T.J. Maxx over the same period was 23.2%. We thank the Editor and the Area Editor for suggesting this comparison.
3. Imperfect Price Information: We assume that

*H*-patrons are aware of the prevailing prices at store

*H*
while they are uncertain about the prevailing prices at store

*L*. Similar assumption holds for

*L*-patrons.
This assumption captures the notion that consumers are better informed about prices at stores that they
regularly shop at and are familiar with versus prices at stores that they occasionally visit to take
advantage of the sales offered. Further, this assumption is also consistent with that in Gabszewicz and
Garella (1987) and Bester and Petrakis (1995).
4. Rational Expectations: We assume that consumers form rational expectations about prevailing retail
prices that they are unaware of. In the context of the model, this means that when an

*H*-patron (

*L*--
patron) does not receive a promotional advertisement from store

*L* (store

*H*), she correctly infers that
store

*L* (store

*H*) is not offering a sale. As we discuss in section 2.2, this inference is consistent with
store

*L*’s (store

*H*’s) incentives and equilibrium strategies. Further, the rational expectation assumption
is consistent with the literature (Lal and Matutes, 1994; Bester and Petrakis, 1995; Lal and Rao, 1997).

**2.2 Rational Expectations and Consumer Beliefs about Unadvertised Prices: **
In this section we discuss the rationale underlying consumer inference about stores' unadvertised price.
Recall that as per our assumptions, even when a store does not advertise its posted price its patrons are
aware of it. Thus the problem of inferring the store's unadvertised price is relevant only for the patrons of

*p * be the prices of stores

*H* and

*L*, respectively. Further, define indicator variables
δ

*j *,

*j*∈{

*H*,

*L*}, denoting the advertising decisions of store

*j* such that δ

*j * = 1 if store

*j* advertises its price

**Rational Expectation about Store ***L's ***Unadvertised Price **(

*e*
**: **Since

*L*-patrons are aware of

*p *, we

only need to consider the case of an

*H*-patron. As per our assumption, this consumer is perfectly
informed of store

*H*'s posted price

*p*
irrespective of whether store

*H* advertises this price or not.
However, in order to decide whether to shop at store

*H* or

*L*, she must form an expectation about store

*L*'s
unadvertised price. What should be her belief about the unadvertised price

*p *? She reasons as follows:
If store

*L* had posted a “low” price, it would have the incentive to advertise its price because by doing so,
store

*L* can induce some of the

*H*-patrons (those with low shopping costs) to switch to store

*L*. Thus, if
store

*L* has not advertised its price

*p *, it must be that the price is “high” so that no

*H*-patron would
9. Having said that, we recognize that consumer’s rational expectation implicitly assumes that consumers are reasonably aware of the pricing pattern in the product category. As such, this assumption may be more applicable to items such as apparel that are commonly advertised by retail stores and whose general price levels consumers are typically familiar with at different stores (e.g. men’s white shirts). We thank an anonymous reviewer for alerting us to this issue.
switch even when informed about it. It can be shown that such a “high” price satisfies the condition:

*p *>

*p *−

*v *θ −

**Rational Expectation about Store ***H's ***Unadvertised Price **(

*e*
**: **A similar argument indicates that

when store

*H* does not advertise its price

*p*
, the

*L*-patrons should recognize that this price is “high” i.e.

*p *>

*p *+ α

*v *θ −
. Under this condition, no

*L*-patron would switch to store

*H* even if the store were

**2.3 Characterization of Retail Demand: **
We briefly discuss the logic underlying the demand characterization for store

*H*. We need to consider
demand in the following two situations: (a) Store

*H* charges a “high” price; and, (b) Store

*H* charges a

*H* charges a “high” price: As mentioned earlier, when

*p*
were to advertise its price, it will not induce

*L*-patrons to switch stores. Thus, the demand is
exclusively derived from high- and low-valuation

*H*-patrons and is independent of store

*H*'s
promotional advertising. However, if store

*L* advertises its price, some

*H*-patrons (those with low
shopping costs) will switch to store

*L* thereby reducing the demand at store

*H*.
Aggregating demands from high- and low-valuation

*H*-patrons and adjusting for store
switching in the event of promotional advertising by store

*L* (c.f. footnote

**16**), the demand at store

*H*
θ [

*v*αρ +τ(

*1*− ρ)] −

*p*
10. Note that for any

*H*-patron to switch to store

*L*, she must derive a higher surplus at store

*L*: θ

*v *−

*s *−

*p * <

*v *− β

*s *−

*p *. Thus, she will switch to store

*L* only if

*s *< {

*p *−

*p *−

*v *θ −
β − i.e. her shopping cost is "low
enough". However, shopping cost must be positive i.e.

*s* > 0. For this condition to hold for any

*H*-patron, we must
have

*p *≤

*p *−

*v *(θ − )
1 . However, when

*p *>

*p *−

*v *θ −
no

*H*-patron (with a positive shopping cost) will
find it optimal to switch to store

*L*. 11. The analytical details underlying the demand derivations are given in the Technical Appendix that is available from the authors on request. 12. Note that it is not optimal for store

*H* to offer a price in the “intermediate” range such that

*p *+ α

*v *(θ − )

*p *>

*p *+

*v *(θ − )
1 . The store can always increase its profit by reducing its price further (i.e., to “low” price range)
and attract low-valuation

*L*-patrons as well.
13. Specifically, the consumers who switch are low-valuation

*H*-patrons with

*s *≤ {

*p *−

*p *−

*v *(θ − )
high-valuation

*H*-patrons with

*s *≤ {

*p *−

*p *−α

*v *(θ − )

*H* charges a “low” price: This is the price range when, if store

*H* advertising its price, it attracts
both the high- and low-valuation

*L*-patrons who have low shopping costs. Specifically, we have
+ θ −1 . Further, in this range, even if store

*L* were to advertise its price, it would not
induce any

*H*-patron to switch to store

*L*. Thus, store

*H*’s demand is independent of store

*L*'s
Aggregating demands from the high- and low-valuation

*H*- and

*L*-patrons, the demand at store
θ [

*v*αρ +τ(

*1*− ρ)] −

*p*

*v*(θ − )

*1*[αρ +τ(

*1*− ρ)] +(

*p *−

**Demand at Store ***L***:** As above, the demand at store

*L* is obtained by aggregating demand from four

consumer segments: the high- and low-valuation

*L*-patrons as well as the high- and low-valuation

*H*-
patrons. It can be shown that store

*L*’s demand when it charges “high” price is given by

*v*[αρ + τ (

*1 *− ρ )] −

*p *ρ + τ − ρ
1 [αρ +τ (1− ρ )]+ (

*p *−

*p*
Similarly, store

*L*’s demand when it charges “low” price is given by

*v*[αρ +τ (1− ρ )]−

*p *ρ +τ 1− ρ
+ ( − )]−

*v*( − )[ + ( − )]

**Properties of Retail Demand Functions: **Having characterized the retail demand, it is instructive to

a) How sensitive is a store's demand to its own promotional advertising? Does this own “promotional
advertising sensitivity” differ across stores

*H* and

*L*?
14. Note that if

*LV* *L*-patrons find it optimal to switch to store

*H*, so will

*HV* *L*-patrons because of store

*H*'s higher quality. For any

*LV L*-patron to switch to store

*H*, she must derive a higher surplus at store

*H*: θ

*v *− β

*s *−

*p * >

*v *−

*s *−

*p *. Thus, she will switch to store

*H* only if

*s *< {

*v *(θ − )
β − i.e. her shopping cost is "low
enough". However, shopping cost must be positive i.e.

*s* > 0. For this condition to hold for any

*H*-patron, we must
have

*p *≤

*p *+

*v *(θ − )
b) How sensitive is a store's demand to its competitor's promotional advertising? Does this cross-
promotional advertising sensitivity differ across stores

*H* and

*L*?
Note that answers to these questions sheds light on a store's frequency of advertised sales: The higher a
store's own promotional advertising sensitivity, the greater is the retailer's incentive to offer more
frequent advertised sales motivated by traffic-building considerations. Similarly, the higher a store's cross
promotional advertising sensitivity, the greater is the retailer's incentive to offer more frequent advertised
sales motivated by customer-retention considerations.
Now, in equations (3) and (5), the second term captures the expansion in store

*H*’s and

*L*’s demand
respectively as a result of its own promotional advertising. Thus, this captures the “traffic building”
effect of promotional advertising – the extent to which a store is able to induce store switching by the
competing store’s patrons. Holding the relative price advantage enjoyed by a store the same across the
in case of store

*L*)

*, *we find that by engaging in
promotional advertising, store

*H* is able to attract more

*L*-patrons as a result of its superior quality
positioning. We summarize this insight in the following lemma:

**LEMMA 1: ***Due to its superior quality positioning, promotional advertising by store H induces *

more L-patrons to switch to store H. Thus, relative to store L, store H enjoys more “clout”.
This suggests that from a purely offensive or traffic-building consideration, store

*H* would have a higher
incentive to engage in promotional advertising relative to store

*L*.
Further note that in equations (2) and (4), the second term captures the reduction in store

*H*’s and

*L*’s demand respectively as a result of promotional advertising by the competing store. Thus, this
captures the “lost customer” effect of competitive promotional advertising – the extent to which a store
stands to lose its own patrons due to store switching induced by promotional advertising by the
competing store. Holding the relative price disadvantage the same across the two stores –

*p *−

*p*
−

*p * in case of store

*L*, we find that store

*L*’s demand is more susceptible to
promotional advertising by store

*H*. This reflects the inferior quality positioning of store

*L*. We
summarize this insight in the following lemma:

**LEMMA 2: ***Due to its inferior quality positioning, store L stands to lose more of its patrons in *

the event of promotional advertising by store H. Thus, relative to store H, store L is more

“vulnerable” to competitive promotional advertising.
This suggests that, relative to store

*H*, defensive or customer-retention consideration would be more
salient for store

*L* while deciding on its promotional advertising strategy.
We now investigate the “promotional price elasticity” of retail demand by addressing the following
a) Given that a store has decided to advertise its “low” price in order to attract the competing store's
patrons, how elastic is this incremental demand to changes in its (advertised) discounted price? Does
this “own promotional price elasticity” differ across the two stores?
b) Given that a store has decided to advertise its “low” price in order to attract the competing store's
patrons, how do changes in its (advertised) discounted price affect the competitor's demand? Does
this “cross promotional price elasticity” differ across the two stores?
Observe that answer to these questions shed light on the depth-of-discount decision of a retailer: The
higher a store's own promotional elasticity, the greater is the retailer's incentive to offer deeper price
discounts motivated by traffic-building considerations. Similarly, the higher a store's cross promotional
elasticity, the greater is the retailer's incentive to offer deeper price discounts motivated by customer-
Comparing equations (3) and (5), we observe that the incremental change in retail demand from
price change is the same for both stores

*H* and

*L* i.e.
This is the incremental effect on the retail demand from the patrons of the competing store due to an
increase in the advertised depth of discount offered by the store. However, as noted earlier, the
incremental store traffic (the competing store's patrons who switch) due to promotional advertising is
more for store

*H* than store

*L* (c.f. Lemma 1). Thus, the % change in retail demand is more for store

*L*
than store

*H* thereby implying a higher “own promotional price elasticity”. We summarize this

**LEMMA 3: ***The “own promotional price elasticity” – incremental % change in retail demand *

due to change in (advertised) depth of discount (originating from the patrons who switch from

competing store) – is higher for store L than store H.
This suggests that, relative to store

*H*, during advertised sales store

*L* will tend to offer deeper discounts
Finally, comparing equations (3) and (5), we observe that the incremental change in retail demand
due to changes in the (advertised) depth of discount offered by the competing store is the same for both
15 It is important to note that incremental traffic at store

*H *depends both on its promotional advertising (i.e., whether

*H * is 0 or 1) and the level of advertised discounted price (

*p*
given that it is “low” i.e.

*p*
Thus, the sensitivity of retail demand to competitor's price (slope) is the same across the stores. However,
as noted earlier, the reduction in store traffic due to promotional advertising (because of the store's
patrons switching to its competitor) is less for store

*H* than store

*L* (c.f. Lemma 2). Thus, the % change in
retail demand as a result of competitive price cut is more for store

*L* than store

*H* thereby implying a
higher “cross promotional price elasticity”. We summarize this conclusion in the following lemma:

**LEMMA 4: ***The “cross promotional price elasticity” – incremental % change in retail demand *

due to change in (advertised) depth of discount offered by the competing store (resulting from its

patrons switching to the competing store) – is higher for store L than store H.
This suggests that, relative to store

*H*, during advertised sales store

*L* will tend to offer deeper discounts
To ensure that the demand functions facing stores

*H *and

*L *is elastic even for low prices, in the
following analysis we assume that the parameters satisfy the following conditions:

*v *<

*s * and β > θ . The
first condition implies that some consumers will derive negative surplus even at very low prices so that a
price cut will have a demand expansion effect for all positive prices. Similarly, the second condition
ensures that store

*H* (with higher quality) cannot force store

*L *to exit by undercutting.

**3. ANALYSIS **
As mentioned earlier, a store's equilibrium promotional advertising strategy is driven both by offensive or
traffic-building and defensive or customer retention motivations. Before analyzing the equilibrium
promotional strategies, we first analyze a store's incentive to initiate price promotion (i.e, discount and
advertise its sale price even when its competitor is charging an unadvertised "high" price). We then
characterize the mixed strategy promotional pricing equilibrium.

**3.1 Stores’ Incentives to Initiate Promotional Advertising:*** *
As noted earlier, when consumers are imperfectly informed about retail prices, if store

*H *(store

*L*) does
not advertise its price, it would attract

*H*-patrons (

*L*-patrons) alone. As such, in the absence of
advertising, the two stores would be localized monopolies. Now, if stores

*H* and

*L* were to serve only
their own patrons, it can be shown that the optimal monopoly prices, retail demand and profits for the
_________________________________________________________________________
_________________________________________________________________________
Consider the incentive of the two stores to unilaterally offer a price discount and advertise it in
order to induce store switching from the patrons of the competing store. The optimal prices, retail
demand and profits for the two stores are as given in Table 2 where

*k* refers to the advertising cost.
Comparing the monopoly profits of the two stores with their corresponding profit when they
initiate price promotion, we find the incremental profits from advertised promotion to be more for store
This is due to the fact that relative to store

*L*, store

*H* generates higher incremental sales due to the
advertised price cut, while at the same time it does not need to offer as deep a discount as store

*L* (cf.
Lemma 1 and 3). This suggests that from a purely offensive consideration, store

*H* has an incentive to
We summarize these insights in the following lemma.

**LEMMA 5: ***The potential gains from attracting the competing store’s customers through *

promotional advertising are higher for store H than for store L. Further, store L needs to offer a

steeper discount in order to attract store H's patrons.
From equation (8), it is evident that if advertising is "too costly" i.e. if
neither of the stores will offer advertised discounted price. However, if the advertising cost is sufficiently
both the stores will have an incentive to advertise. Finally, in the case when % <

*k*
has the incentive to offer advertised promotion.
it is easy to see that an equilibrium wherein both the stores always
advertises their prices to attract the competing store’s patrons can never arise. The rationale is as follows.
Since store

*H* advertises its price to attract

*L*-patrons, it must be that its equilibrium price is “low

*p** * are the equilibrium prices for stores

*H* and

*L*,
respectively. But this implies

*p** *>

*p** *−

*v *θ −

*1 * i.e. store

*L*’s equilibrium price is “too high” and it
will not advertise its price thereby leading to a contradiction. We summarize this insight in the following

**PROPOSITION 1: ***If the marginal cost of advertising is not “too high” i.e. k *<

*~*
*pure strategy equilibrium in which both stores either always post “high” prices and not advertise or always post and advertise “low” prices does not exist. Thus, the only equilibrium when k *< ~

* must entail random promotional advertising by the competing stores i.e., store j *
*randomizes between posting a non-discounted price (and not advertising it) and posting a *
*discounted price (and advertising it). *
The proof is given in the Technical Appendix. In the subsequent analysis, we characterize the
promotional advertising equilibrium under the assumption that

*k *< ~

**3.2 Characterization of the Promotional Advertising Retail Equilibrium: **
The unique mixed strategy equilibrium of the pricing game entails store

*j*,

*j*∈{

*H*,

*L*}, randomizing
between its “sale” (discounted) price,

*s*
*f *) and its “regular” (non-discounted)

*f *). Consistent with the literature (Shilony, 1977; Rao, 1991; Raju,
Srinivasan and Lal, 1990), we interpret the mixed strategy equilibrium in a temporal context so that

*f *
denotes store

*j*’s frequency of advertising sale prices.
The promotional advertising (PA) equilibrium is a 2-support point mixed strategy equilibrium. This
is distinct from the mixed strategy equilibria in Narasimhan (1988) and Raju, Srinivasan and Lal (1990)
which entail a continuous distribution over a range of prices. The difference arises due to the fact that in
Narasimhan (1988) and Raju, Srinivasan and Lal (1990), all the switchers have an identical valuation for
the product, while in the proposed framework consumers are heterogeneous in their willingness-to-pay
(due to heterogeneity in their shopping costs). Our discrete 2-price mixed strategy equilibrium is
consistent with prior research in economics and marketing (Salop and Stiglitz, 1982; Banks and Moorthy,
16. The rationale for the non-existence of an equilibrium wherein the stores charge “low” price and always promote
is that the profit functions of stores

*H *and

*L *are not jointly concave in (

*p ,*δ .
17. The continuity of the retail profit functions ensures the existence of a mixed strategy equilibrium in which stores randomly offer and advertise “sale” prices (Dasgupta and Maskin, 1986). Please see Raju, Srinivasan and Lal (1990) for a detailed discussion on this issue. 18. This temporal interpretation is based on a result due to Benoit and Krishna (1985) that states that a unique Nash equilibrium of a constituent sub-game is also a unique sub-game perfect equilibrium of the (finitely-repeated) super-game. See Raju, Srinivasan and Lal (1990) for additional details. 19. In fact, if all consumers had identical shopping costs, the mixed-strategy equilibrium in our framework would also have a continuous distribution over a range of prices. While a continuous mixed strategy equilibrium allows for a range of depths of discount, it comes at the cost of a more restrictive consumer model.

**Solution Procedure to derive Promotional Advertising Equilibrium:** Our approach to solving the

discrete 2-point equilibrium differs from the "text book" approach in one important way. In the standard
approach, the support points (i.e. the underlying pure strategies) are exogenously given. In our setting,
this would imply that the stores do not select their "regular" and "sale" price but only choose their
promotional frequencies. In contrast, our analysis requires characterizing both the support points (which
determines the depth of discount) and the mixing distribution (which determines the frequency of
advertised sale). This poses an additional challenge since in our formulation the support points (i.e. the
"regular" and "sale" prices) are dependent on the mixing distribution and thus, have to be derived
Appendix gives an outline of the solution procedure. This essentially entails 3 steps:
• Step 1: Characterizing the support points of the discrete distribution for both stores

*H* and

*L*, given
the support points and the mixing distribution of the other store i.e. ˆ

*r*
• Step 2: Deriving the stores' reaction functions for frequency of promotional advertising (i.e.,
for store

*H* and

*f L*(

*f H*) for store

*L*) recognizing that the store must earn the same profits
when charging unadvertised “regular” price and advertised “sale” price.
• Step 3: Simultaneously solving the 2 reaction functions to obtain the Nash Promotional Advertising

**Features of the Promotional Advertising Equilibrium:** As mentioned earlier, the inter dependence

between the support points and the mixing distribution makes our computation task harder unlike
previous formulations. While we are unable to obtain closed form expressions for the equilibrium
promotional advertising frequencies, we verified through extensive simulations that for a wide range of
• NE frequencies lie in the unit simplex i.e. { *
• Store

*H*'s promotional frequency is higher than that of store

*L* i.e.
Further, we analytically demonstrate that if

*f*
>

*f *, the % depth of discount offered by store L is
higher. We illustrate the property of the promotional advertising equilibrium through a numerical
example with the following parameter values viz.

*v* = 1; θ = 1.1; α = 1.5; τ = 1.5; β = 1.25;

*s * = 1; ρ =
0.4. For these parameter values, the cost-of-advertising thresholds for stores

*H* and

*L* are:

*~*
20. This is analogous to deriving the support of the continuous distribution in Narasimhan (1988) and Raju, Srinivasan and Lal (1990). However, in their model, the support is independent of the mixing distribution. 21. We have done extensive simulations over the entire parameter space where prices are positive.
= 0.1637 (cf. Proposition 1). We let

*k* = 0.05 so that both stores have the incentive to advertise.

*f * * are 0.3796 and 0.1550 respectively i.e. in equilibrium store

*H* offers an
advertised sale with probability 0.38 while store

*L* offers an advertised sale with probability 0.16. Thus,
>

*f *. Further, at these equilibrium frequencies, the optimal regular and sale prices of store

*p*$ = 0.3438, while the corresponding prices for store

*L* are:

*p*$ = 0.2658. Thus, the equilibrium % depth of discount offered by store

*H* is

*%*
32.29%. In contrast, the % depth of discount for store

*L* is

*% *∆

*L *= 40.23%. Therefore, we find that
∆

*L *. These findings reinforce the intuition from Lemma 5.
We summarize this discussion in the following proposition.

**PROPOSITION 2: ***The optimal frequency of advertised sales is higher for store H than for *

store L. However, the optimal depth of discount (expressed as a % of regular price) offered by

store H is lower than that for store L.
**Relative Drivers of Promotional Advertising:** Since the equilibrium promotional strategies are driven

by both traffic building (offensive) and customer retention (defensive) considerations, we attempt to
disentangle the relative impact of the two effects and assess any systematic differences across the stores.
To do so, we compare a store's equilibrium frequency with the frequency it will choose if its competitor

*f *(

*f *= 0 , is 0.2705. Said differently, even
if store

*L* were not to offer advertised sales, store

*H* will offer an advertised sale with probability 0.27
driven by traffic-building motivation alone. Recall that store

*H*'s equilibrium frequency is 0.38. Thus,
store H's promotional advertising is mainly motivated by traffic building considerations (i.e., 71%
(0.27/0.38) vs. the balance 29% for customer retention consideration). In contrast, for store L, the
customer retention consideration is relatively more important (i.e., 53% (0.08/0.15) accounted for by
traffic building motivation vs. the balance 47% for customer retention consideration).
The intuition for this finding follows directly from Lemma 1 and 2 where we note that the own
promotional advertising elasticity is higher for store

*H*, its cross-promotional advertising elasticity is
We summarize this intuition in the following lemma.

**LEMMA 6: ***Relative to store L, promotional advertising by store H is influenced more by traffic *

building than customer retention considerations.
**Intuition for Results: ** Recall that relative to

*LV* consumers,

*HV* consumers incur a higher cost to

switch stores (τβ

*s * for

*HV* consumers vs. β

*s * for

*LV* consumers). Thus, the

*HV* segment is less sensitive
to promotional advertising. Since the retailers draw both the

*HV* and the

*LV* consumers, the effective
“promotional advertising sensitivity” of retail demand depends on the mix of customers that a retailer
draws. Because of asymmetric quality positioning, consumer “self-selection” implies that under
competitive promotional advertising, relative to store

*L*, store

*H* draws a higher fraction of

*HV*
consumers. This implies that while store

*H*'s demand is less vulnerable to store

*L*'s promotional
advertising (cf. Lemma 2), it also means that store

*H* stands to attract more customers were it to advertise
its “sale” targeted at store

*L*'s customers (cf. Lemma 1). Thus, defensive or customer retention
considerations is more salient for store

*L* while store

*H* is driven primarily by offensive or traffic-building
The aforementioned difference in the stores' promotional advertising sensitivities also explains
why store

*H* offers more frequent advertised sales. Note that higher the promotional advertising
sensitivity of the target customers (i.e., the competing store’s customer-mix), the greater is the incentive
to offer such advertised sales. Since the target customers of store

*H* are more sensitive to promotional
advertising, store

*H* has incentive to offer advertised sale more frequently.
Finally, the intuition behind differences in the depth of discount is as follows. As mentioned
earlier, store

*H*'s customer-mix comprises a higher fraction of

*HV *customers relative to that for store

*L*.
Given the higher store switching costs for

*HV *consumers, store

*L* needs to offer deeper discounts to
overcome this (cf. Lemma 3). This difference in customer-mix also implies that store

*L* needs to offer
deeper discounts to retain its customer (cf. Lemma 4).

**Comparison with Prior Models: **Note that findings in Proposition 2 are distinct from those in

Narasimhan (1988) and Raju, Srinivasan and Lal (1990). Both these models imply a lower promotional
frequency for the high-quality store. While the former predicts the two stores should offer the same
depth of discount, the latter suggests the high-quality store should offer deeper discounts.
22. Even though the model structure appears complex due to 3 sources of consumer heterogeneity and 2 sources of retail differentiation, they constitute the minimal sufficient set of assumptions needed to obtain these results. The parameters characterizing vertical heterogeneity (viz., α and ρ ) and differentiation (θ ) are necessary for consumer “self-selection”. As stated earlier, it is horizontal heterogeneity (

*s *) that results in a 2-support point mixed strategy equilibrium. This also leads to market expansion as a result of price promotions (unlike e.g., Narasimhan 1988; Raju, Srinivasan and Lal 1990). Further, unlike the extant models, it also implies differential expansion in retail demand across the two stores. The horizontal differentiation ( β ) parameter corresponding to switching costs makes it imperative for the stores to offer price cuts for traffic building. In technical terms, β >1 creates the requisite discontinuity in stores' profit function to have a mixed strategy NE. Finally, the second source of vertical heterogeneity (τ ) leads to differential switching costs across

*HV* and

*LV* segments and is necessary for differences in stores' promotional frequencies and depths-of-discount offered. 23. Note both Narasimhan (1988) and Raju, Srinivasan and Lal (1990) deal with manufacturer/brand-level
The intuition for the contrasting results is as follow. In both these models, the incremental traffic is
the same across the two stores because of identical consumer valuation. Further, in both these models, the
losses occurring from subsidizing “loyal” customers are higher for the high-quality store. Thus, the net
gains to the low-quality store from price promotions are higher than that for the high-quality store. In
contrast in our model the net gains to high-quality store from promotional advertising are higher (cf.

**3.3 Consumer Characteristics, Store Positioning and Reliance on Frequency Cues: **
In the previous section, we showed that in using promotional advertising, the high-quality store relies
more on the “frequency cue” while the low-quality store relies more on the “magnitude cue”. We discuss
below how this relative emphasis is influenced by consumer characteristics and stores' positioning.
To do so, we focus on the difference in the frequency of advertised promotions across the two
∆

*f *≡

*f *−

*f *). Note that as
∆

*f *increases, store

*H* relies increasingly on the frequency cue,
while store

*L* relies increasingly on the magnitude cue. The following proposition summarizes the key

**PROPOSITION 3: ***The difference in the frequency of advertised sales across the high- and low-*

quality stores increases with increase in α

*, *θ

* and *ρ

* while it decreases with increase in *β

* and *
The intuition behind these results is as follows. As noted above, it is consumer “self-selection” that leads
to differences in the stores' promotional advertising strategies. Increases either in vertical differentiation
( θ ) or vertical heterogeneity ( α ) as well as the relative size of the

*HV* segment ( ρ ) leads to sharper
consumer “self-selection”. Note that sharper the consumer “self-selection”, the greater is the difference
in the customer-mix across the two stores. Specifically, store

*H* predominantly attracts

*HV* customers
while store

*L* mainly serves

*LV* customers. Since the switching costs of the

*LV* customers is lower, this
mix implies that store

*H* can attract these customers even by offering a shallower discount, thereby
making promotions more attractive. This accounts for store

*H* placing a higher emphasis on frequency
cue than magnitude cue. In contrast, an increase either in horizontal heterogeneity ( β ) or horizontal
differentiation (

*s *) blurs this process thereby reducing the differences across the two stores in their
competition between “strong” and “weak” brands. In this comparison, we consider “strong” and “weak” brands as analog of high- and low-service stores, respectively. Further, this section compares our results to insights from the base models considered in these papers. In addition, both these models assume that consumers are perfectly aware of the posted prices; as such, there is no role of price advertising in these models.

**4. EMPIRICAL VALIDATION **
In this section, we examine whether market data are consistent with our model's key predictions. However,
since secondary data were not available, we collected our own data by coding information from newspaper
price advertisements for both high- and low- service level stores in product groups that mirror our model
assumptions. To test whether the model predictions are consistent with empirically observations, we focus
1. Other things being equal, the frequency of advertised sales increases with the service positioning of a
2. Other things being equal, the depth of discount decreases with the service positioning of a store.

**4.1 Description of the Data Set:*** *
Our empirical analysis focuses on the apparel market. Traditional department stores and off-price discount
stores are the two major retailer groups in this market. Mirroring our model assumptions, stores across these
two groups differ in their quality positioning providing customers with different levels of in-store service,
sales assistance, and shopping convenience. Similar to our model, stores in both these groups periodically
advertise sales in newspaper advertisements in order to compete for customers (Kopp, Eng and Tigert
1989). A sale advertisement typically features several product groups including discount information on
each of these groups. In order to determine the appropriate unit of analysis i.e. the level at which to code the
sale information from these advertisements, we conducted interviews with approximately 50 shoppers
asking them how they made their store selection decision. Consumers stated that in deciding among
competing stores, promotional advertisements was an important factor and that they evaluated and
compared savings at the product group level (e.g., men’s dress shirts).
Using information obtained from interviews conducted with 10 retail managers, we selected only
those product groups in which (a) comparable product lines were both stocked and advertised by the two
store groups; and (b) items do not have a fashion orientation so that they do not have any temporal variation
in prices. This led to a total of 14 product groups – 7 of them were men's products (dress shirts, sports shirts,
neck ties, casual pants, boxer shorts, tee shirts and shorts) and the other 7 were women's products (tee
shirts/tank tops, knit top vests, blouses, knit separates, shorts, shoes, bras). As stores typically advertised
chain-wide sales in a given geographic area, we focus our study on a major metropolitan city in the U.S.
In this market, traditional department stores and off-price discount stores comprise about 76% of the
apparel market. We included the following four leading (in terms of market share) department store chains –
Carson Pirie Scott, Marshall Field's, Lord & Taylor and Bloomingdale's – accounting for about 85% of the
department store market; and the following two leading discount store chains – Filene's Basement and T.J.
Maxx – accounting for about 80% of the discount store market. By collecting data from multiple chains in
each of the two retailer groups, we minimize the impact of retailer-specific effects in our analysis.
Newspaper advertising account for about 75% of the total advertising dollars spent on promotional
advertising for the chains included in our analysis. Furthermore, by restricting our analysis to retailers in the
same geographic area, we ensure that the same retail advertising regulations govern the advertising practices
for our sample of retailers (Ortmeyer, 1991).
We obtained data from two different sources. First, for the retail chains included in our analysis, we
collected all promotional advertisements published in the two leading newspapers in the city over a 6-
month period. This led to a total of 813 promotional advertisements across the six stores from which we
coded information on the 14 product groups that were included in our study. In addition, we obtained
consumer ratings data on in-store service and sales assistance for each of the six chains from a survey
published in

*Consumer Reports *(1994).

**4.2 Variable Operationalization:*** *
(a) Frequency of Advertised Sales (

*TDAYS*): This refers to the time interval in days (

*TDAYS*) from the last
promotional advertisement in the product category. The longer the time interval, the lower the
(b) Depth of Promotional Discount (

*DISCOUNT*): This measure represents the percentage reduction in
price offered on the advertised merchandise. We computed this by determining the fraction of the
advertised regular price that the offered price reduction (difference in advertised regular and sale prices)
represented. While the FTC guidelines and state statutes/regulations prevent retailers from artificially
inflating the “regular” price, we also use actual transacted prices (both “observed” regular and sale) to
develop an alternate measure of the depth of discount offered.
For each of the product groups included in our study, we tracked the actual transacted prices for
identical merchandise sold by a high-service store (Marshall Field's) and a low-service store (Filene's
Basement) for a 6 week period. By tracking specific items that both stores sell, we are able to ensure
that we have the same basis of comparison in terms of the specific brands and type of merchandise sold
by the two stores. This provides a robustness check of our results independent of the operationalization
of “regular” price. This also helps to directly eliminate any items where we observe any temporal
variation in regular prices (as seen for fashion items).
(c) In-Store Service (

*SERV*): This measure is based on

*Consumer Reports* (1994) that provides summary
consumer ratings on in-store service and sales assistance for different chains based a survey of 50,000
consumers. In this survey, respondents rated each store on a five-point scale with 1 being “excellent
sales help” and 5 being “poor sales help”. Both Filene's Basement and T.J. Maxx were given a rating of
24. We thank the Area Editor for this suggestion.
5; Carson Pirie Scott and Lord & Taylor were given a rating of 3; and, Bloomingdale’s and Marshall

**4.3 Empirical Analysis at the Product Group Level:*** *
For each of the 14 product groups, Table 3 reports the mean values of

*DISCOUNT *and

*TDAYS *for the high-
service traditional department stores (Marshall Field's, Carson Pirie Scott, Lord and Taylor, Bloomingdale's;
Mean

*SERV*=2.5) and the low-service off-price discount stores (Filene's Basement and T.J. Maxx; Mean

*SERV*=5). First, we individually compare the mean values of the variables across the two types of stores
_________________________________________________________________________
_________________________________________________________________________
Comparing the differences in the mean values of

*DISCOUNT *across the two store types for each
product group, we find that in all the 14 product groups, the low-service stores offer a higher advertised
depth of discount than the high-service stores (all p-values <0.01). The results are similar when we use the
actual depth of discount computed from transacted prices for the identical merchandise sold by the two store
types. Also, for each product group we find that the mean time interval between advertisements is higher for
high-service stores than low-service stores (in 12 of the 14 product groups, p<0.01; in the remaining 2,
p<0.05). These findings provide support for Proposition 2.

**4.4 Empirical Analysis with Data Pooled across Product Groups:*** *
We also conduct a pooled analysis of the observations across the 6 stores and the 14 product groups by
relating the two dependent variables (

*DISCOUNT *and

*TDAYS*) to

*SERV *separately while controlling for the
confounding effect of covariates. In order to include covariates, we need to conduct the analysis at the
disaggregate level with a store’s promotional advertisement at the product group level being the unit of
analysis. Pooling observations across product groups as well as across stores also helps us improve the
statistical efficiency of the parameter estimates.
In conducting the disaggregate analysis, we need to be careful about a few important econometric
issues. Since we have multiple observations for a store in a product category, there could be a possibility of
serial correlation. However, the conceptualization of sales promotions as mixed strategies (e.g. Narasimhan
1988, Raju, Srinivasan and Lal 1990) implies that different observations from a store correspond to the store
independently drawing from its equilibrium promotional strategies. Empirical support for the lack of serial
correlation among posted prices was shown in Rao, Arjunji and Murthi (1995). It is important to point out
that serial correlation could still exist due to store-specific unobserved factors that are not explicitly
modeled in our analysis. Since we are also pooling data across product groups, we need to also control for
product group-specific unobserved heterogeneity. To account for unobserved heterogeneity on two
dimensions – viz., store and product group – we use the latent class approach (Kamakura and Russell,
1989). We also recognize that while the frequency of a promotional advertisement (

*TDAYS*) and the depth
of discount (

*DISCOUNT*) are jointly determined and ideally should be estimated in the context of SUR
system, due to the discrete/continuous nature of the dependent variables and the non-linearity of the model
specification, we are unable to implement this and recognize it as a potential limitation of our analysis.

**4.4.1 Covariates Operationalization: **
We used the following two covariates in our analysis.
(a) National Brand Advertised (

*NAME*): Based on findings in previous research (e.g. Gupta and Cooper,
1992), consumers do not discount advertised savings for name brands as much as for store brands.
Consequently, offering the same discount on a name brand has more impact on consumers' intention to
buy than a similar discount on a store brand. This may lead retailers to offer lower depth of discounts
when advertising name brands. To control for the possibility, we included an indicator variable,

*NAME*,
with

*NAME *= 1 when national brands are advertised for the product group;

*NAME *= 0 otherwise.
Further, the lower average discount when name brands are advertised may make it optimal for retailers
to reduce the time between advertised sales thereby increasing the frequency (Achabal, McIntyre and
(b) Special Sale (

*SALE*): Retailers hold special holiday sales (e.g. Memorial Day sale; Fourth of July sale)
or limited-time sales (e.g. 13 Hour sale, 2 Day sale). During these sales, retailers may be more likely to
offer a higher depth of discount to build traffic. To control for these effects, we include an indicator
variable,

*SALE*, with

*SALE *= 1 when the advertisement is for a special holiday or limited-time sale;

*SALE *= 0 otherwise. Furthermore, the incidence of a special holiday may reduce the normal time
interval between consecutive promotions for retailers.

**4.4.2 Modeling Relationship between ***TDAYS*** and ***SERV***:*** *
Since the variable

*TDAYS *can only take positive values, using a linear model is inappropriate and hence we
use the proportional hazard function approach (e.g. Jain and Vilcassim, 1991) with a baseline exponential
hazard. In order to control for unobserved heterogeneity, we use the latent class random effects specification
25. We thank the Editor, the Area Editor and an anonymous reviewer for alerting us to this concern. 26. To test for temporal dependence in the frequency of promotion (

*TDAYS*), we also estimated the model with baseline Weibull hazard. However, the likelihood ratio test failed to reject the nested exponential hazard specification (equation 11), thus suggesting lack of duration dependence. We thank an anonymous reviewer for
(

*Xijk*) { (

*i j*)

*g*(

*Xijk*)

*TDAYSijk*}

*m*

*l*
where subscripts

*i*,

*j* and

*k* stand for store, product group and promotional advertisement, respectively.

*Kij*
denotes the number of promotional advertisements for product group

*j*,

*j* = 1, …, 14, and store

*i*,

*i* = 1, …, 6.
We define η and ζ to represent the support points for the store-specific (set

*S*) and product group-
specific (set

*P*) random component, respectively, with corresponding probability masses of γ and ω .
The proportionality function

*g*(

*X ijk*) is given by
The results for the ML estimation of the hazard function with 2-support distribution for store- and product
specific random heterogeneity components are reported in Table 4. Likelihood ratio tests failed to reject the
2-support model in favor of 3-support models.

*SERV *was negative and statistically significant (

*p* < 0.01).
_________________________________________________________________________
_________________________________________________________________________
This is consistent with the prediction of our analytical model that the time between advertised sales is
shorter for high quality stores than for lower quality stores (please note that the

*SERV *variable is reverse
coded with higher

*SERV *ratings for lower service stores and vice versa). In addition, the parameter for

*NAME *is significant (

*p* < 0.01) but the direction is contrary to our hypothesis. We conjecture that it could be
due to the fact that stores in our sample seem to mainly use name brands during major holiday seasons,
offering deep advertised discounts in order to build traffic. In any event, it does not invalidate our main
prediction. The parameter for

*SALE *is significant (

*p* < 0.01) and in the expected direction.

**4.4.3 Modeling Relationship between ***DISCOUNT*** and ***SERV***: **
Since the variable

*DISCOUNT *can only take values between 0 and 1, using a linear model is inappropriate
and hence we use the two-limit probit approach. Note that the two-limit probit model represents a
generalization of the Tobit model (Heckmann, 1979) and controls for both upper and lower truncation of
the dependent variable (for additional details, please see Datar, Jordan, Kekre, Rajiv and Srinivasan
1997). In order to account for unobserved store- and product-specific heterogeneity, we develop the
sample likelihood function using an approach analogous to that for modeling

*TDAYS*.
The relationship between the (latent) depth of discount offered is given by
alerting us to this issue. Details of the hazard function model along with a description of our approach for incorporating unobserved store- and product-specific heterogeneity components are given in the Technical Appendix. 27. We acknowledge that, while the equilibrium is a 2-support point discrete mixing distribution, the 2-limit probit

*y* * = β + β ×

*SERV ijk *+ β ×

*NAME ijk *+ β ×

*SALE ijk *+ ε
where subscripts

*i*,

*j* and

*k* are as defined in equation (11) above.
The results for the ML estimation of the two-limit probit model with 2-support distribution for store-
and product specific random heterogeneity components are reported in Table 5. Likelihood ratio tests failed
to reject the 2-support model in favor of 3-support models. The coefficient for

*SERV* was positive and
statistically significant (

*p* < 0.01). This is consistent with the prediction of our analytical model that lower
_________________________________________________________________________
_________________________________________________________________________
quality stores offer a higher discount than higher quality stores. In addition, the average depth of discount
(a) is lower when advertisements include name brands (

*p* < 0.05); and (b) is higher when the advertisement
is for a special sale (

*p* < 0.01).

**5. CONCLUSIONS & MANAGERIAL INSIGHTS **
In this paper, we examine the strategic considerations underlying a retailer's promotional advertising
decisions – the frequency of advertised sales and the depth of the discount offered. Our analysis suggests
promotional advertising is motivated by both traffic building as well as customer retention
considerations. The relative importance of these considerations is related to the store's service
positioning. Our analysis indicates that compared to the low-service store, the high-service store offers
more frequent advertised sales albeit with shallower discounts. We provide empirical support for the key
predictions of our analytical model by collecting and analyzing data from retail promotional
advertisements for stores (which vary in their level of in-store service) published in major newspapers in
Our analysis thus suggests that in using promotional advertising to attract and retain customers, the
high-quality store should rely more on the “frequency cue” while the low-quality store should rely more
on the “magnitude cue”. Further, these actions by the high-service store are motivated mainly by traffic
building consideration. In contrast, the customer retention considerations are relatively more salient for
Our results further suggest that the high-service store's reliance on frequency versus magnitude
cues depends on its positional strength on the service dimension as well customer segmentation
characteristics. Specifically, the high-service store needs to consider the consumer heterogeneity in (a)
corresponds to a continuous mixing distribution. To test if the depth of discount in the current period

*k* depends on the past realizations, we added lagged depth of discount (during the

*k*-1th sale) as an additional covariate in equation (13). However, likelihood ratio test failed to reject the nested specification (equation 13), thereby suggesting a lack of temporal dependence. We thank an anonymous reviewer for alerting us to these issues. Details of the two-limit
willingness-to-pay for service (mix of high- and low-valuation consumers as well as differences in their
intensity of preference for service); and, (b) shopping costs.
The key managerial insights from our analysis are summarized in Figure 1 below. While designing
their promotional advertising strategy, key questions for the high-service store to resolve are: Who are
the customers being served at regular price? Who are the customers being targeted through advertised
Figure 1(a) shows how the design of its promotional advertising strategy is influenced by the
positional advantage enjoyed by the high-service store as well as consumer shopping costs. The store
needs to recognize that when its positional advantage is high and consumers do not differ substantially in
their shopping costs, it predominantly serves the high-valuation customers with its regular price while
attracting primarily the low-valuation customers through advertised sales. In this situation, the store is
better off relying mainly on the frequency cue. In contrast, when its positioning is not distinct and
consumer heterogeneity is substantial, it is difficult to use the regular and advertised sales to distinctly
target the different segments. In this case, the store should rely more on the magnitude cue.
Similarly, Figure 1(b) shows how the high-service store's promotional advertising strategy is
influenced by its positional advantage as well as customers' preference for service. The store needs to
recognize that a high positional advantage coupled with substantial differences in consumers' preference
for service allows it to achieve distinct targeting through its regular and sale prices. Specifically, its
regular price primarily caters to the high-valuation segment while its advertised sales are meant to attract
mainly low-valuation customers. In this situation, the store is better off by relying mainly on the
We consider this paper as an important first attempt to study the effect of promotional advertising
on retail competition between stores that differ in their positioning. Having said that, we realize the
limitations of the theoretical and empirical components of our analysis. For instance, our analysis does
not relate to fashion-oriented products where the dynamics of competition between the two kinds of
stores may be somewhat different from that in our model. We also recognize the shortcomings of our
empirical analysis, primarily due to data limitations. For instance, being limited to data coded from
advertisement, we were not able to identify exogenous variables to control for potential endogeneity
among the covariates and the dependent variables.
probit model are given in the Technical Appendix.

**TABLE 2: Retail Equilibrium with and without Advertising **
*4*τ [

*s*ρ + τ(

*1 *− ρ)]

*4*τ [

*s*ρ + τ(

*1 *− ρ)]

**TABLE 3: Comparison of Mean ***DISCOUNT ***and ***TDAYS*** for High- and Low-Service Stores **
28. The comparison of mean uses pooled variance. In effect, it is assumed that the variance of

*TDAYS *and

*DISCOUNT *is the same for all the six stores.

**TABLE 4: Empirical Results - Time Between Advertised Sales**
1st SUPPORT (γ)

* *PRODUCT-SPECIFIC RANDOM ERROR
** : significant at α = 0.01 *** : significant at α = 0.05

**TABLE 5: Empirical Results - Depth of Discount**
1st SUPPORT (γ)

* *PRODUCT-SPECIFIC RANDOM ERROR
** : significant at α = 0.01 *** : significant at α = 0.05

**Heterogeneity in Shopping**
*s ***)**
**Positional**
**Strength on**

Service (θ

**)**
Figure 1(a): Promotional Advertising Strategy for High-Service Store

**Heterogeneity in Preference**
**for Service (**α

** )**
**Positional**
**Strength on**

Service (θ

**)**
Figure 1(b): Promotional Advertising Strategy for High-Service Store

**APPENDIX **
**Derivation of Promotional Advertising Equilibrium **
**Step 1: Derivation of Support Points of the Mixing Distributions **ˆ

*r*
** and **ˆ

*r*
Program 1 characterizes store

*H*'s choice of “regular” and “sale” prices i.e.,

*pr*
(

*H*)

*H*[

*LDH*(

*H L *) (

*L*)

*DH*(

*H L *)]
refers to store

*H*’s demand when both stores advertise and can be
obtained from equation (3). Similar interpretations hold for
. The implied optimality conditions are:
[

*v f *(θ − )1 +θ(β − )1]{αρ +τ(1− ρ)}+

*f ps *{ρ +τ(1− ρ)}−

*2 pr *β −1+ ρ +τ 1− ρ =
+ (1− )} −[2

*ps *−

*f ps*
Similarly, the pricing problem faced by store

*L* is modeled as program P2 below:
(

*L*)

*L*[

*HDL*(

*H L *) (

*H*)

*DL*(

*H L *)]
(

*L*)

*L*[

*HDL*(

*H L *) (

*H*)

*DL*(

*H L *)]
+ (1− )} −[2

*ps *−

*f ps*
Simultaneously solving equations (A.1)-(A.4), the support points of the mixing distributions are obtained as:
)

*f L*(

*f H*)][ (

*f H *)

*f H*(

*f L*)]

*f H f L*(

*f L *)(

*f H *)
29. Additional details are given in the Technical Appendix.
)(

*f H *) (

*f L*){ (

*f L *)

*f L*(

*f H*)}] ( )

*v*η 4 2β2 −

*f *β + −1 β + −1 − 1−
)

*f L*(

*f H*)][ (

*f H *)

*f H*(

*f L*)]

*f H f L*
)

*f L*(

*f H*)][ (

*f H *)

*f H*(

*f L*)]

*f H f L*(

*f L *)(

*f H *)
β +

*f *− 1 β +

*f *− 1 + θ 1−

*f*
β +

*f *− 1 −

*f *1 −

*f*
)

*f L*(

*f H*)][ (

*f H *)

*f H*(

*f L*)]

*f H f L*(

*f L *)
where η = [αρ + τ(1 − ρ)] [ρ + τ(1 − ρ)].

**Step 2: Derivation of Stores' Reaction Functions ***f*
** and ***f L*(

*f*
For store

*H* to randomize between posting an unadvertised “regular” price and an advertised “sale” price
= 1 , its profits at the “regular” price must be the same as its profits at
the “sale” price (net of advertising costs):
where

*k* is the marginal cost of advertising. Substituting from support points above, we obtain store

*H*'s (implicit) reaction function

*F*
*L*, the requisite randomization condition is:
As above, substitution from support points above yields store

*L*'s (implicit) reaction function

**Step 3: Derivation of Promotional Advertising Nash Equilibrium **{

** **
*f L *}

**: **
The NE is obtained by simultaneously solving the 2 (implicit) reaction functions

*F*
Due to the high order polynomials, we are unable to obtain closed expressions for the promotional frequencies. However, we ran extensive simulations over a range of parameter values for which the
support points were positive (i.e. ˆ

*r*
fo

*j *∈

*H L ***. **For all these values, results enumerated in

the Proposition 2 hold. Details of the numerical simulations are given in the Technical Appendix.

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Source: http://bschool.nus.edu/Staff/bizsr/PDF_Files/asymmetric.pdf

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