le

Marketing impact

Marketing efciencyExclusive sellingCustomer heterogeneity

terume

Intern. J. of Research in Marketing 26 (2009) 2133

Contents lists available at ScienceDirect

Intern. J. of Research in Marketing

l sev ie r.com/ locate / i j resmarincrease in the types of channels where consumers shop, make itincreasingly difcult for marketing managers to achieve measurableimpact with marketing activities. In fact, maintaining impact withmarketing spending is a major challenge for managers. As a result,there are numerous organizations, from marketing agencies to mediaexperts, which offer services to provide clients with a higher level ofimpact from their spending on marketing. The service provided bythese organizations is that of assisting clients to organize andcoordinate marketing activity such that the effective reach of a

Donelley Marketing have databases on millions of households,companies or individuals that can be used to identify high potentialcustomers in many categories.1 For example, ICOM collects informa-tion on the social issues that respondents most identify with (choicesinclude animal welfare, environmental issues, the arts, health andreligious causes). This information is then used by organizations (thesellers of various products and services) to improve the performanceof their spending. To be specic, the symphony orchestra might useICOM to prepare a mailing list based on the level of interest that aclient's marketing activity is increased. A signare potential customers who are a) unawareaware of the product yet lack complete andits characteristics and pricing. In general, mosunless they know what they buying. The s

INSEAD, Boulevard de Constance, Fontainebleau Ce6072 4412; fax: +33 1 6074 5596.

E-mail address: david.soberman@insead.edu.

0167-8116/$ see front matter 2008 Elsevier B.V. Alldoi:10.1016/j.ijresmar.2008.05.003fragmentation and an

Many market research agencies build databases on the behaviorand media habits of consumers that can improve the effectiveness ofmarketing spending. Companies such ICOM, Experian, Acxiom andToday, increased competition, media1.1. Background1. Introductionother due to strong differentiation in the downstream market or a low level of overlap in the customersreached by the marketing of each downstream rm. In contrast, exclusive selling is advantageous when manycustomers have been reached by the marketing of both rms or the level of differentiation between the rmsis low. Surprisingly, in many situations, the seller's prot is inversely related to the level of differentiation.

2008 Elsevier B.V. All rights reserved.market is effectively reached by a rm's marketing effort. My objective is to understand the optimal strategythat marketing agencies, media experts and sales agents should use to sell these services. In particular, Ianalyze how these services should be priced and whether a seller gains by selling such services exclusively.The model consists of a seller of marketing services and two symmetric rms that compete in a differentiatedmarket. A downstream rm that purchases the services reaches a higher fraction of the potential market dueto the efciency provided by the services. The analysis shows that the optimal selling strategy for the servicesis a function of three factors: a) the degree of differentiation between rms, b) the fraction of the target thatis reached by rms (prior to using the seller's services) and c) the increase in reach provided by the seller'sservices. Non-exclusive selling is likely to be optimal, the less that downstream rms compete with each

increase the fraction of the market that has complete and accurateinformation about the rm's product.ReachMedia impactthese organizations offer are to organize and coordinate spending such that a higher fraction of the potentialKeywords:is maximized. There are nagents that promise to deliver more impact for the money a rm allocates to marketing. The service thatMarketing agencies, media experts and saimprove the effectiveness of marketing

David A. Soberman INSEAD, Boulevard de Constance, Fontainebleau Cedex, 77305, FranceRotman School of Management, University of Toronto, Toronto, Canada M5S 3E6

a b s t r a c ta r t i c l e i n f o

Area Editor: Eitan Muller A major challenge for marke

j ourna l homepage: www.eicant problem for rmsof a rm's product or b)accurate information ont customers will not buyervices are assumed to

dex, 77305, France. Tel.: +33 1

rights reserved.s agents: Helping competitive rms

s is how to spend a marketing budget such that the impact on a target marketrous organizations including marketing agencies, media experts and saleshousehold has in the arts. Targeted direct mail campaigns such as this

1 Frequently, market research companies and media experts possess monopoly-likepositions for the type of information that they sell. ICOM is the only market researchcompany in Canada that owns a database containing millions of households. Experianis the only market research company in the US that has an extensive database on thecredit worthiness and nancial status of individuals. Donelley Marketing is the onlyresearch company that possesses information on the characteristics of rms andindividuals based on their involvement in Yellow Pages telephone listings.

ce of marketing efciency Year

tication of UC Admission Service to reach parents whoseren are about to go to university

1995

argeting technology using NY Times database 1997t to Patient media: reaches prospects in physicians' ofces 1999rated DM, e-mail and web communication 2000rgeting technology based on proprietary optimizers 2003rieta

22 D.A. Soberman / Intern. J. of Research in Marketing 26 (2009) 2133have a much higher response rate than standard campaigns based ongeographic targeting. Clients nd that information sold by companieslike ICOM to improve targeting can increase spending effectiveness bymore than 50% (Bush, 1998).

Another important phenomenon is a trend away from integratedadvertising agencies to organizations that specialize in creativedevelopment and media buying respectively (Horsky, 2006). Inparticular, many of the world's largest advertising organizationshave evolved into advertising holding groups comprised of severalcreative shops and a media buying service. The media buying serviceof these groups offer services that assist clients to choose mediavehicles, programmes, and timing that maximize the impact of a givenmarketing budget. Beyond these media buying services, there areconsultants that describe themselves as media experts (see StarTurn, The Economist, March 9, 2000). Examples of media-expertcompanies include Carat, Mediacom and Starcom. These rms commitsignicant resources to collecting information that links the mediahabits of viewers to their consumption patterns and lifestyles.Moreover as media decisions have become more complex, the valueof media experts has risen (see Pfanner, 2005). As noted by Ms.Tassaro of Media Edge, Anyone can come up with a cookie-cuttermedia plan, but leading-edge media planning has become a multi-layered process demanding specialized knowledge and relationships(Fitzgerald, 1999).

In industrial markets, sales agents and manufacturer's repsfrequently offer increased access to a target market: they allow arm to reach customers that are difcult for company's internalsalesforce to reach and inform. Table 1 summarizes several examplesof companies that provide services to increase the impact of a client'smarketing spend.

The one thing these examples have in common is that they allow adownstream rm to get more for its investment in marketing.

I build a model with three objectives in mind. The rst is toincrease our understanding of how the services provided by market-ing agencies, media experts and sales agents affect competition indownstream markets. The second is to provide normative insightabout how these services will be a priced as a function of downstreammarket characteristics. The third is to understand the incentives thatsellers of such services might have to limit their provision within amarket (by granting exclusivity).

Table 1Examples of services that increase the impact of marketing

Marketing experta Target Sour

O&M Direct London, U.K. High potential buyers of phone cards Idenchild

Real Media Inc. New York, NY Men over 40 with income N$90,000 Ad-tOn Target Solutions Cincinnati, OH Families with an asthma sufferer DirecVentureDirect Worldwide New York, NY B2B customers in 23 separate segments IntegStarcom MediaVest Group Chicago, IL Mainstream customers of cars (GM) Ad taMediacom Latino New York, NY Hispanic Media Buying Services Prop

a Sources available on request from the author.1.2. Framework and results

The model consists of a seller of marketing services and twodownstream rms that compete in a differentiated market. In the rststage, the seller offers its services to the downstream rms. Theservices increase the efciency of a rm's marketing effort. Thisimplies that a rm which accepts the seller's offer reaches a higherfraction of the potential target market due to the efciency theservices provide.

After deciding whether to accept the seller's offer, the rms setprices for their products. The marketing of each rm activatescustomers in the target market by informing them of the character-istics and price of the rm's product.2 Marketing thus creates a seconddimension of customer heterogeneity: the degree towhich consumersare informed about products in the market. From the perspective ofeach rm, there are two key groups of consumers created bymarketing: consumers who are aware of both products in the marketand consumers who are only aware of the focal rm's product.Marketing does not guarantee that a customer will buy the rm'sproduct but it does guarantee that a customer will evaluate thecompany's offer and make a decision.

The setting of prices by the seller of these services is notstraightforward. It is driven by how the services ultimately affectcompetition in the downstream market. As expected, the optimalprice for the information is positively related to the added impactprovided by the services. However, the relationship between theoptimal prices and a) the degree of differentiation between thedownstream rms and b) the fraction of the target market that isreached by rms without the seller's services is complex.

In many situations, the seller's price and prot are negativelyrelated to the level of differentiation. One would think thatdifferentiation might limit the degree to which competition dissipatesbenets created by more efcient marketing. For example, there isevidence that increases in category demand, improvements indistribution efciency and product modications are more valuablewhen differentiation insulates rms from each other and allowshigher prices.3 However, in a market where demand is driven byreaching customers with marketing, this is not necessarily the case.

I also examine the seller's incentive to sell its services exclusively.The optimal strategy depends on how the demand-enhancing effect ofthe services compares to their competition-increasing effect. Sinceincreases in efciency invariably lead to higher demand, the naturalstrategy is for the seller to sell to both rms (for exclusive selling to beattractive, the exclusive price must be more than two times the pricethat can be charged when selling to both rms). Non-exclusive sellingis likely to be optimal the less that downstream rms compete witheach other due to a) a high level of differentiation between the rmsand b) a low level of overlap in the customers that are reached by themarketing of each rm. In contrast, exclusive selling is advantageouswhen many customers have been reached by the marketing of bothrms and the level of differentiation between the rms is low. Toimplement an exclusive selling strategy, the seller needs to provide a

ry tools and information on the media habits, culture and language of Hispanics 2003contractual guarantee to the buyer.In the following section, I review the literature that is relevant to

the selling of marketing services that allow rms to increase theimpact of their marketing spend.

2 Without marketing, consumers are inactive. This representation follows modelsproposed by Butters (1977) and Grossman and Shapiro (1984).

3 As noted by Hermalin (1993) and Cabral and Villas-Boas (2005), there aresituations where differentiated rms are unable to capture the benets of reducedcosts of production or marketing. Nevertheless, in a standard spatial model, higherprices due to higher differentiation make increases in the density of demand morevaluable (Salop, 1979). Iyer and Soberman (2000) also nd that the value of productmodications can be positively related to the level of differentiation.

1.3. Related research

A rich stream of research examines the optimal selling strategiesfor monopolists that are endowed with knowledge or expertise that isvaluable to downstream buyers. This literature has its origins in

innovation literature (Arrow, 1962; Kamien & Tauman, 1984, 1986).However, services that increase the awareness of a rm's offeringare different than innovations that reduce the cost of productionprimarily because marketing itself creates a second dimension of

23D.A. Soberman / Intern. J. of Research in Marketing 26 (2009) 2133nancial markets where an informed agent sometimes has valuableinformation about the uncertain value of a risky asset (such as a stock,bond, or option). The informed agent can sell the information touninformed investors who then use the information to makeadvantageous trades with investors who have not purchased it(Admati & Peiderer, 1986). As demonstrated by Grossman andStiglitz (1980), the problem is interesting because market prices arethemselves informative about the private information of traders.4

These ideas have been extended to the marketing arena wheresellers (or consultants) sell reports that are valuable because theyprovide buyers with better estimates of a stochastic demand param-eter (Sarvary & Parker, 1997). The authors nd that an informationseller can sometimes be better off when he faces competition thanwhen he is the only seller. In fact, when buyers need two reports, arecent study suggests that information sellers will split the market tosell only rst or second opinions to customers (Sarvary, 2002).

There is also literature that considers the selling of syndicatedmarketing information that identies relationships between brandloyalty and the preferences or demographic characteristics ofconsumers. Iyer and Soberman (2000) consider information thatfacilitates targeted product modications. The primary nding of thispaper is that the nature of the information is the main determinant ofthe information seller's optimal strategy. For example, when theinformation seller has information on attractive productmodicationsfor the loyal customers of two competing rms, the information sellerwill sell a complete set of information to both rms. In addition, thevalue of the information is highly dependent on the impact of themodications relative to the level of differentiation between rms.

Several other papers consider the impact or use of information in amarketing context. Shaffer and Zettelmeyer (1999) consider the use ofvalue-adding information in the context of distribution channels. Theauthors study how this information affects the division of prots in amarket with two competing manufacturers and a common retailer.Raju and Roy (2000) consider the value of information on uncertaindemand to rms that are ex ante of different sizes (the authors focuson the value of information and not on its selling or provision). Pasaand Shugan (1996) model expertise as an ability to interpretinformation about demand and they are interested in characterizingthe value of this expertise within companies. Finally, Villas-Boas(1994) studies the transmission of information between competingrms through an advertising agency and proposes an explanation forwhy competing rms might use a common advertising agency. Whilethe context of Villas-Boas is similar to the context of this paper, thefocus is different. In Villas-Boas, the agency is a mechanism for re-ducing rm-specic asymmetric information. In contrast, the servicesprovided by the seller in my analysis are equally valuable to bothpotential buyers: the services of the marketing agencies, mediaexperts and sales agents allow any rm that purchases the services toincrease the impact of its marketing effort.

This leads to the critical element that distinguishes this analysisfrom the existing literature. The services provided by the seller inthis model do not provide a better estimate of a stochastic para-meter. The services allow a client-rm to increase the fraction ofpotential consumers who are fully informed about its productcharacteristics and price. The analysis is related to the diffusion of

4 There are many approaches that an informed agent can use to prot from aninformational advantage in nancial markets. For example, an informed agent can sellinformation directly to uninformed investors, can trade with them or can sell shares ina portfolio of assets that have been constructed using the information (Admati &

Peiderer, 1988, 1990).customer heterogeneity.The article proceeds as follows. The model is presented in the next

section. In Section 3, I analyze the downstream market equilibrium asa function of the level of differentiation and the fraction of thepotential market that is aware of each rm's offer. In Section 4, Idetermine the relationship between the pricing of these services anddownstreammarket differentiation. and examine the incentives of theseller to sell the services exclusively. Finally, I conclude in Section 5.

2. The model

The model consists of a marketing agency, media expert or salesagent that offers services to two potential clients who compete in adownstream market. The game has two stages. The rst stage is theselling of services to the downstream rms. In second stage, thedownstream rms choose prices (these prices depend on thedecisions taken in the rst stage). Finally consumers make decisionswhether or not to buy either of the products offered by the competingrms. I next describe the downstream market and then explain themechanism by which marketing creates demand for products.

2.1. The downstream market

The downstreammarket consists of two rms located at either endof a unitary Hotelling market. The rm at the left end of the market isFirm 1 and at the right end is Firm 2. Each rm sells a single productand the unit cost of production, c, is assumed to be constant. Theproducts differ with respect to an attribute and consumers areuniformly distributed along the attribute with a density of one. Thisimplies that any consumer is identied by an ideal point along theattribute corresponding to her preferred brand.

A consumer buys at most one unit of product and places a value von her ideal product. Because the rms are located at either end of themarket, a consumer does not obtain her ideal product. A consumerlocated a distance x from Firm i (i=1, 2) obtains a surplus v txpi byconsuming Firm i's product, where t is the preference cost per unitdistance and pi is the price charged by Firm i. The parameter tmeasures the sensitivity of consumers to the product attribute(it serves as a measure of the degree of differentiation in the market).Marketing informs consumers about the characteristics and prices ofproducts but does not affect v (the consumer's willingness to pay) or t(the preference cost).5

A consumer only buys if she knows of a product that offers positivesurplus i.e. v txpiN0. Without marketing, consumers are assumedto be uninformed about the characteristics or prices of products; theonly way a consumer becomes informed about a rm's offer (productcharacteristics and price) is through that rm's marketing. As in themodel of Butters (1977), marketing provides truthful informationabout the rm's offer and customers do not experiment with productsthey do not know. If a consumer is aware of more than one productoffering positive surplus, she buys the product offering the greatestsurplus.

This model is a 2-rm version of the model proposed by Grossmanand Shapiro (1984) where marketing activates consumers. The modelhas been used in marketing in papers such as Soberman (2004, 2005),Dukes and Gal-Or (2003), Dukes (2004) and Gal-Or and Dukes (2006).Typically marketing effort is treated as a decision variable in these

5 There is en extensive literature on the numerous paths by which marketing canaffect the behaviour and decisions of consumers (Tirole, 1988). Nevertheless, the ideathat marketing provides information about products and their key attributes is

relatively uncontroversial.

models. Here however, the base level of each rm's marketing effort isassumed to be an exogenous parameter. This allowsme to focus on theupstream selling of marketing services that increase the reach of arm's marketing effort.

2.2. The impact of marketing

The marketing effort of Firm i (i=1, 2) is assumed to reach afraction i of the potential market and this fraction is assumed to beuniformly distributed along the market. This means that marketingcreates a second dimension of consumer heterogeneity based on theinformation consumers have about products. Following the structure

downstream rm cannot tell whether an exclusive agreement hasbeen violated, exclusive selling may not be possible.

The structure of the game is as follows. The seller of marketingservices decides whether or not to offer exclusivity before it contactsdownstream rms. The game tree for the rst stage of the game is

24 D.A. Soberman / Intern. J. of Research in Marketing 26 (2009) 2133described in Fershtman and Muller (1993), 4 distinct groups ofconsumers are formed when the rms market at levels 1 and 2respectively. First, there are consumers who have been reached by themarketing of both rms (a fraction 12 of the market). Second, thereare consumers who were not reached by the marketing of either rm(a fraction (11)(12) of the market). Finally, there are two groupsof consumers been reached by the marketing of one of the twocompeting rms (given by 1(12) and 2(11) respectively).

Without the seller's services, the rms are assumed to besymmetric and their marketing has a base reach of (i.e. 1=2=).In order for the seller to be able to improve the reach of a rm'smarketing effort, I restrict b1.

2.3. Stage one: The selling and buying of marketing services

Before describing the selling stage, I clarify the precise benet thatthe marketing agent, media expert or sales agent offers to down-stream rms. The seller is assumed to possess information orknowledge that allows a rm to obtain a % increase in the effectivereach of its marketing effort. As explained earlier, the services offeredby the seller allow the client to increase the fraction of themarket thathas complete and accurate information about the rm's product: thisincreases the number of customers who seriously consider buying therm's product. In the context of themodel, this implies that a rm thatengages the seller will increase the impact of its marketing effort from to (1+).6

A further issue regards the viability of using an exclusive strategyto sell marketing services. In this model, the seller always has anincentive to violate an exclusive agreement. As a result, the seller mustmake a credible commitment for the exclusive strategy to be viable.This seems reasonable as industry interviews reveal that manymarketing agencies offer category exclusivity for their services (atleast for a specied period of time). For example, the services of ICOMare often sold with category exclusivity for a specic period (between6 months and one year).7 The loss of both reputation and relatedbusiness (many clients use marketing services companies acrosscategories) were the violation of an exclusive contract detectedappears to make exclusivity commitments both frequent and highlycredible. In the game presented here, a violation would be detectedsince the second rm acquiring the services would have marketingimpact in excess of its initial levels. Conversely, in markets where a

6 The analysis will show that different combinations of and t are associated withdifferent types of equilibria. When is high enough, the introduction of the servicescan change the type of equilibrium observed in the market. My analysis focuses onefciency increases that do not lead to a change in the type of equilibrium. Later in thepaper, I discuss how the seller's optimal selling strategy is affected when is highenough to lead to such a change. An interesting extension to this model suggested byan anonymous reviewer would be that of making , a costly decision for the seller ofservices (the impact of the services would be a function of ex ante investment made bythe seller). I do not investigate this idea; nevertheless, the selling sub-game in such anextension would be analogous to the selling game presented here.

7 This information is based on personal interviews with the managers of ICOM.Violating an exclusive contract is easy to detect since many of ICOM's clients are

competitors in multiple categories.shown in Fig. 1. The downstream prots are denoted by y and y=a, d,b, n (a implies the rm is the sole purchaser of the marketing services,d implies that the rm faces a competitor that has purchased themarketing services, b implies that both rms have purchased theservices and n refers to the situationwhere neither rm has purchasedthem).

The left side of the tree represents the choice of exclusive selling.The prices Px1 and Px2 are chosen by the seller in the context ofexclusive selling. Second, Fig. 1 shows that Firm 1 receives theexclusive offer rst; however, this is arbitrary since the downstreamrms are ex ante symmetric. If Firm 2 is contacted by the seller, Firm 2knows that Firm 1 has rejected the seller's offer. However, when anexclusive strategy is chosen this does not happen. The seller chooses aprice Px1 such that Firm 1 is strictly better off by accepting the seller'soffer. The right side of the tree represents the choice of non-exclusiveselling and Pb is the non-exclusive price chosen by the seller. Thedownstream rms are assumed tomake simultaneous decisions aboutaccepting the seller's offer under non-exclusive selling.

Several comments are worth noting. On the one hand, there aremany ways to model exclusive selling: the services could be soldthrough an auction, buyers could be asked to submit two bidssimultaneously for the services or, in contrast to Fig. 1, the price for thesecond buyer could be chosen a priori and announced to the rst rm.On the other hand, the steps shown in Fig. 1 are a straightforward wayto represent a process where a) the seller of marketing services hasmarket power (the seller moves rst) and b) the exclusive offer hasbite (a rm that refuses the seller's exclusive offer knows that it willprobably a face a competitor who accepts a similar offer from theseller). One could also model the selling of services as independentnegotiations between the seller and each rm (as a bargainingprocess). However, the optimal downstream arrangement (non-exclusive or exclusive selling) would not be affected because a) thegame is one of complete information and b) there is no coordinationproblem.8

2.4. Stage two: Competition between downstream rms

The second stage of the game entails the simultaneous pricingdecisions by downstream rms and nally those of informed con-sumers. The prot of a candidate rm is a function of the price that itcharges and the demand that it realizes from the two segments itserves (consumers who are aware of the candidate rm xi andconsumers who are aware of both rms yi).

1 = p1 1 12 x1 + 12y1 1

2 = p2 2 11 x2 + 12y2 2

These functions represent the prots net of expenditures onmarketing. I use these functions because the role of the seller'sservices is to provide more impact for the money that each rmallocates to marketing (the amount each rm allocates is assumedidentical).

The demand from each segment follows the reasoning ofSection 2.1. In the group of consumers who have been reached by

8 When coordination is important, cooperative or non-cooperative bargainingprovide insight into the types of arrangements that are observed empirically. Forexample, in vertical channels when manufacturers set wholesale prices and retailerschoose retail prices, there is a coordination problem (Dukes, Gal-Or, & Srinivasan,

2006; Iyer & Villas-Boas, 2003).

25D.A. Soberman / Intern. J. of Research in Marketing 26 (2009) 2133Firm i's marketing only and not the competitor's, demand isdetermined by individual rationality i.e. all consumers in the segmentwho obtain positive surplus in the segment from Firm i's product willbuy from Firm i. This implies that demand from this segment is xi =

vpit

except if vpiN t in which case xi=1. The derivation of demand fromconsumers who have been reached by the marketing of both rmsdepends on the location of the indifferent consumer given prices p1and p2. It is straightforward to show that y1 = p2p1 + t2t and y2 =

p1p2 + t2t

.

Fig. 1. Stage oneThese expressions hold except when p2p1N t or p1p2N t. In thesecases, Firm 1 or Firm 2 respectively capture the entire group of fullyinformed consumers.

The extensive form of stage two is summarized as follows:

Step 1: Firms choose prices pi (i=1, 2) as a function of the fractionof the market that is reached by each rm's marketingi (i=1, 2).

of the game.

Step 2: If a consumer has been reached by the marketing of one ormore rms, she purchases the product that provides her withmaximum surplus assuming that her participation constraintis satised.

3.1.1. Strong differentiation: Symmetric competitorsThe downstream rms are symmetric in terms of marketing reach

when a) neither rm accepts the seller's offer 1=2= or b) both of

26 D.A. Soberman / Intern. J. of Research in Marketing 26 (2009) 2133To simplify the analysis, I make two normalizations. The actuallevel of differentiation between downstream rms is a function ofthe total surplus created when a consumer consumes her idealproduct (vc) relative to the level of differentiation t. Thus, withoutloss of generality, I set the marginal cost equal to zero and thereservation utility to 1. This allows me to analyze a complete range ofdifferentiation conditions by varying t.

In addition, I restrict the analysis to conditions where all con-sumers are potential customers of either rm tb1

2

. When all

consumers in the market have been reached by the marketing ofboth rms, the equilibrium price is t. When tb1

2and p1=p2= t, any

consumer in the market realizes positive surplus from either rm'sproduct.9

I now proceed to the analysis of the downstream game. Thisprovides the basis for determining the optimal selling strategy for theseller in Section 4.

3. The downstream market and equilibrium decisions

Given the range of conditions I examine tb12

, the analysis reveals

that there are two distinct regions based on the types of equilibria that

occur in the downstream market. The rst region is ta 15;12

which I

call strong differentiation. The second region is ta 0; 15

which I call

weak differentiation. I rst present the equilibrium outcomes for theregion of strong differentiation.

3.1. Strong differentiation: ta 15;12

The objective functions for the downstream rms when they bothchoose prices less than 1 t are a function of demand from the twogroups of consumers that have been reached by each rm'smarketing.

1 = p1 1 12 + 12p2p1 + t

2t

3

2 = p2 2 11 + 12p1p2 + t

2t

4

In contrast, when the prices are marginally greater than 1t, thedemand from consumerswhohave only been reached by themarketingof one rm is downward sloping in the price that the rm charges (therst term in large parenthesis in Eqs. (5) and (6) is negatively related top1 and p2 respectively).

1 = p1 1 12 1p1t

+ 12p2p1 + t

2t

5

2 = p2 2 11 1p2t

+ 12p1p2 + t

2t

6

Both sets of objective functions are needed to identify theequilibrium outcome in the downstream market. First, I consider thecase where 1=2.

9 This assumption ensures fully competitive conditions between the downstreamrms. When tN1

2, the externalities between the downstream rms are reduced andwhen tN1, there is no interaction between the rms.them do 1=2=(1+). Proposition 1 summarizes the downstreamequilibrium as a function of (the marketing reach of the rms whenthey are symmetric). All proofs are provided in Appendix A.

Proposition 1.

1. When b2t, p1=p2=1 t and rms earn prots of 12 1t 2 .2. When N2t, p1 = p2 = 1 2tt and rms earn prots of 12t 2

2.

When b2t Proposition 1 shows that each rm sets price such theinformed consumer at the maximum distance from the rm isindifferent between buying and not buying. Firms effectively chargethe maximum feasible price to the market: were rms to raise priceabove 1t, then the captive consumer located at themaximumdistancewould nd the product too expensive.10

In essence, rms choose not to compete for consumers who areaware of both rms (demand from this segment is evenly splitbetween the rms). The potential gain in demand from a pricereduction is less than the loss in prot created by giving existingconsumers a subsidy.11 In this situation, prices and prots arenegatively related to the level of differentiation because a higher treduces the prot earned from each consumer (i.e. p=1 t). Inaddition, prots are positively related to the marketing reach of therms A

A= 1t 1 N0

.

When there are enough customers in the market who are aware ofthe offerings of both rms, the rms have an incentive to deviate fromthe equilibrium strategies described in Proposition 1. When N2t,each rms sets price in order to a) extract prot from the consumerswho are reached by its marketing effort (and not the competitor's)and b) compete for the consumers who are reached by the marketingof both rms. This leads to an equilibrium in pure pricing strategies

where prices are positively related to the level of differentiationApAt= 2

N0

. Prots are also positively related to the level of differen-

tiation AAt

= 122 2N0

. In contrast, prots are negatively related to

the reach delivered by each rm's marketing AA= t 2 b0

. These

relationships are the opposite of those observed when b2t.

3.1.2. Strong differentiation: Asymmetric competitorsThe downstreamrms are asymmetricwhenonly onerm engages

the seller of marketing services. If only Firm 1 accepts the offer of theseller, this implies that 1=(1+) and 2=. Proposition 2 sum-marizes the downstream equilibrium as a function of and .

Proposition 2.

1. Whenb 2t

1 + , p1=p2=1t. Firm 1 earns prots of 12

t1

2

+ 1 and Firm 2 earns prots of 12 t1

+

2

.

2. WhenN 2t

1 + , p1 = 6t3t + 4t3t3

1 + and p2 =

6t3t + 2t3t

3 1 + . Firm 1 earns

prots of34 + 3

6 2t

18 1 + and Firm 2 earns prots of32 + 3

6

2t18 1 + .

Proposition 2 demonstrates that the equilibria when the compe-titors are asymmetric (in terms of marketing reach) follow a similarpattern to those observed for the symmetric case. For example, whenthe level of marketing reach is sufciently low, the pricing equilibriuminvolves both rms choosing the maximum feasible price. Notsurprisingly, the rm with higher marketing reach earns higherprots. Proposition 2 also shows that Firm 2 prices more aggressively

10 Captive consumers have only been reached by a focal rm's marketing i.e., eitherthey buy from the focal rm or not at all.11 This outcome is competitive even though it looks collusive.

than Firm 1 whenN 2t

1 + . The explanation for this is that when Firm 1's

marketing reach is higher than Firm 2's, a greater fraction of Firm 2'sdemand comes from consumers who have been reached bymarketingfrom both rms. Thus, Firm 2 has a stronger incentive than Firm 1 tochoose a price that is close to the optimum for the competitivesegment. This means that Firm 2's price is lower than Firm 1's.

Proposition 3.

1. When b2t, p1=p2=1 t and rms earn prots of 12 1t 2 .2. When a 2t; 1 + t

6t + 5t2 + 1

p

2t

p1 = p2 = 1 2tt and rms earn prof-

its of 12t 2 2.

3. When a 1 + t6t + 5t2 + 1

p

2t; 1 + t +

6t + 5t2 + 1

p

2t

, the equilibrium entails

mixed pricing strategies and rms earn prots of 1t 1 +122t.

4. When a 1 + t +6t + 5t2 + 1

p

2t;1

, p1 = p2 = 1 2tt and rms earn

prots of 12t 2 2.

Note that the interval 1 + t6t + 5t2 + 1

p

2t; 1 + t +

6t + 5t2 + 1

p

2t

exists if an only

if tb15. In other words, the level of differentiation between rms needs

to be sufciently low for mixed pricing strategies to be possible. Thepattern of outcomes for the feasible range of when t = 1

6is shown in

27D.A. Soberman / Intern. J. of Research in Marketing 26 (2009) 2133Surprisingly, Firm 2 captures more than 50% of the competitivesegment in spite of having less effective marketing x = 12

2b12

.12

3.2. Weak differentiation: ta 0;15

When the level of differentiation is sufciently low, the cost tocompete for consumers who have been reached by marketing fromboth rms increases. The reason the cost is higher is that thecompetitive price for consumers who are informed about the productsof both rms is t and the monopoly price for consumers who haveonly been reached by one rm is 1 t.13 As the level of differentiationincreases, the difference between these two prices increases. Whentb1

5, the equilibrium where rms price at 1 t (when marketing reach

levels are low) and the equilibrium where prices are a function ofmarketing reach (when the levels of marketing reach are higher) areobserved. However, for a range of , the equilibrium in pure pricingstrategies breaks down. I examine this issue for symmetric compe-titors and then for asymmetric competitors.

3.2.1. Weak differentiation: Symmetric competitorsWhen the levels of marketing reach are either too high or too low,

the rms have an incentive to defect from the competitive price of12tt to the highest feasible price 1 t in order to charge the maxi-

mum price to consumers who have only been reached by one rm'smarketing (these consumers do not make a comparison between therms). However, if Firm 1 increases price to 1 t then Firm 2 has anincentive to increase its price to 12t and earn higher prot on allconsumers who have seen Firm 2's advertising. But when Firm 2chooses a price of 12t, Firm 1 has an incentive to undercut Firm 2 andchoose a price of 13t.

Similar to Shilony (1977) andNarasimhan (1988), this implies thenon-existence of anequilibrium inpure strategies. This game (with continuousaction spaces) also has discontinuous payoffs (when |p1p2|Nt, the rmwith a lower price obtains the entire segment of consumers who havebeen reached by the marketing of both rms). In games such as this theexistence of amixed strategy equilibriumdepends on two theorems fromDasgupta and Maskin (1986). The model satises the conditions for amixed strategy equilibrium and this is discussed in Appendix A.

Undercutting for the fully informed segment does not reduceprots from the fully informed segment to zero: a rmwill not reduceits price such that it earns less than it would earnwere the competitiveprice of t charged to the fully informed segment. This implies thatthe guaranteed prot that either rm can earn by selling to thefully informed segment is 12t

2. The outcomewhen rms are symmetric

and a pure strategy equilibrium does not exist is summarized inLemma 1.

Lemma 1. When a 1 + t6t + 5t2 + 1

p

2t; 1 + t +

6t + 5t2 + 1

p

2t

, the equilibrium in-

volves mixed pricing strategies. The rms earn prots of 1t 1 + 122t.

Using Lemma 1, I derive Proposition 3 which identies theequilibria for the feasible range of when differentiation is weak.

12 The feasibility condition on x implies that must be less than 12 for the equilibriumto hold.13 The monopoly price when tN1

2is 12, however, when tb

12, a monopoly maximisesprot by charging the reservation price to the most distant consumer.Fig. 2. Fig. 2 shows that as increases from 0 to 1, the type of equilibriaobserved changes three times. Moreover, because prots are nega-tively related to differentiation A

At= 1

2 32

when b2

3and price

strategies are mixed, the relationship between prots and differentia-tion changes three times as increases from 0 to 1. At low levels of ,the relationship is negative, it then becomes positive, it then becomesnegative and then positive again.

Whenprice strategies aremixed, the relationship betweenmarket-ing reach and prots depends on the level of marketing reachAA= 3t2t + 1

. When the level of reach is less than 1t

23t, the rela-

tionship is positive and when the level of reach is greater than 1t23t

, therelationship is negative. The relationship changes because increasingmarketing reach has two effects. Therst is to raise the level of demandfor each rm (this has a positive effect on prots). The second is toincrease the fraction of consumers reached by the marketing of bothrms. These consumers compare the offers from each rm and thiscreates an incentive for rms to cut prices (this has a negative effect onprots). When the level of marketing reach exceeds 1t

23t, the second

effect is larger. This explains why the relationship between marketingreach and rm prots is negative when N 1t

23t.

3.2.2. Weak differentiation: Asymmetric competitorsAs earlier, I assume that Firm 1 accepts the offer of the seller. This

implies that 1=(1+) and 2=. Similar to the case of symmetricrms, when the levels of marketing reach are either too high or too low,the pure price strategy equilibrium breaks down and the pricing equi-librium is in mixed strategies. The outcome when rms are asymmetricand a pure strategyequilibriumdoes not exist is summarized in Lemma 2(the prots of Firm 1 and Firm 2 are summarized as a function of afunction of and ).Fig. 2. Different equilibrium zones for the entire range of .

Lemma 2. Whena 1 + t

6t + 5t2 + 1

p

2t; 1 + t +

6t + 5t2 + 1

p

2t

, and only Firm 1

accepts the seller's offer, the prots earned by Firms 1 and 2 respectively

are 1 = 1 + 1

1t +

2 1 + t2

and 2 =1

1t +

2t2.

Using Lemma 2, I derive Proposition 4 which identies theequilibria for the feasible range of and when differentiation isweak.

Proposition 4.

1. Whenb 2t

1 + , p1=p2=1 t. Firm 1 earns prots of 12

t1

2

+ 1 and Firm 2 earns prots of 12 t1

+

2

.

2 . Whena 2t

1 + ; 1t2

t +6t + 5t2 + 1

p1

, p1 =

6t3t + 4t3t

3 1 + and

p2 =6t3t

+ 2t3t

3 1 + . Firm 1 earns prots of

34 + 3

6

2t18 1 + and Firm 2

earns prots of 32 + 36 2t

18 1 + .

3. Whena 1 + t

6t + 5t2 + 1

p

2t; 1 + t +

6t + 5t2 + 1

p

2t

, the equilibriumentailsmixed

pricing strategies and Firms 1 and 2 earn prots of 1 + 1

4. Optimal pricing and selling strategies for marketing services

First, I examine how the optimal price is determined when the

28 D.A. Soberman / Intern. J. of Research in Marketing 26 (2009) 2133 1t +

2 1 + t2 and

1

1t

2t2 respectively.

4. Whena 1 + t +

6t + 5t2 + 1

p

2t;1

, the outcome is identical to that

described in point 2 (above).

The equilibria described in Proposition 4 show that the patternand relationships observed for asymmetric rms are similar to thoseobserved for the symmetric case. In particular, the relationship be-tween differentiation and prots is negative when price strategies aremixed and marketing reach is low and becomes positive at higherlevels of marketing reach. The relationship between marketing reachand prots depends on the level of marketing reach (detailedcomparative statics are provided in Appendix A). Fig. 3 is a convenientsummary of the equilibrium conditions derived in Sections 3.1 and 3.2.Note that in all cases, I assume that (the efciency increase providedby the seller of marketing services) is sufciently low such that afterthe services are introduced, the equilibrium type is unchanged. It isinteresting to note that in some parameter conditions, the prots ofthe downstream rms are inversely related to the level of differentia-tion between rms.

This completes Section 3 where the outcomes in the downstreammarket as a function of the possible marketing reach levels that rmshave (depending on whether they buy services from the marketingagency or not) are derived. These outcomes are the raw materialsneeded to solve the rst stage of the game, that of determining theoptimal strategy for the marketing agency.Fig. 3. The downstream equilibrium as a function of and t.seller would like to sell to a) both rms (non-exclusively) or b) just onerm (exclusively). I then determine which of these strategies is goingto optimize the seller's prot for the parameter regions shown inFig. 3.

4.1. Key comparisons for the seller of marketing services

A rst challenge for the seller who wishes to sell the marketingservices non-exclusively (i.e. to both rms) is to identify the highestprice at which both rmswill engage the seller. Referring back to Fig.1,aPbn and bPbd are necessary conditions for both down-stream rms to accept the seller's offer. This implies that Pbmin(an, bd). In other words, the maximum price must lead toan increase in prot for a rm when neither rm has access to theservices and a rmmust also realize an increase in prot by purchasingthe services to compete with a competitor that already has them. Theprot earned by the seller of marketing is 2Pb.

In order to maximize the prot associated with selling the servicesto only one downstream rm, the seller needs to provide the solebuyer with a guarantee of exclusivity. The guarantee is requiredbecause in all conditions, the services have value for the rm that didnot engage the seller. When the guarantee is provided, Fig. 1 showsthat themaximumprice the seller can charge is the difference in protthat the marketing services ad create ex post. As long as aNn, anyPx2 (acceptable to Firm 2) is sufcient to ensure that Firm 1 accepts theseller's offer.14

4.2. Optimal action for the seller when differentiation is strong: ta 15;12

n o

Because there are two regimes when the differentiation betweenrms is strong, I present the optimal selling strategy for bothsituations in Proposition 5. As noted earlier, is assumed smallenough such that a regime change does not occur.

Proposition 5.

1. When b2t, the optimal strategy for the seller is to sell the servicesnon-exclusively at a price of Pb = 12

1t 2 1 +

Prots are

(1 t)(2(1+)).2. When N2t, the optimal strategy is to sell the services exclusively at a

price of Px1 = 2t3 1 + 2 + 1 +

.

Proposition5underlineshowthenature of downstreamcompetitionaffects the optimal strategy for the seller.WhenN2t, the fraction of themarket that is has been reached by the marketing of both rms issignicantly higher. As a result, a greater fraction of potential consumersmake direct comparisons of the surplus offered by the products in themarket. When the marketing services are acquired by both rms,the fraction of consumers making comparisons increases further. Thecompetition-increasing effect of these comparisons outweighsthe increase in demand generated by the marketing services. Accord-ingly, the seller of services extracts higher rents from the downstreammarket when she offers a contract of exclusivity to one rm. In thissituation, the sellermaximizes the increase in demand generated by themarketing services (for one rm) but limits the degree to which themarketing services exacerbate the level of competition in themarket. Incontrast, when b2t, the fraction of potential consumers making directcomparisons of the surplus offered by the competing products issignicantly smaller. In addition, there are more consumers in themarketwho have not been reached by themarketing of either rm. As a

14 If abn, Firm 1 can refuse the seller's offer and make itself better off (Firm 2 will

also refuse the offer for any Px2N0).

level of differentiation between the rms is low for a signicantfraction of the parameter space. This can be the case when the size ofthe segment reached by the marketing of both rms (relative to thefraction of the potential market reached by the marketing effort of atleast one rm) is either low or high.When the size of the segment thathas been reached by the marketing of both rms is low, the prots ofthe seller are negatively related to differentiation. Here, the equili-brium price is determined by the maximum price that can be chargedto captive consumers: this price is negatively related to the level ofdifferentiation. In contrast, when the size of the segment that has beenreached by the marketing of both rms is high, the equilibrium is inmixed strategies. Here, the prots of downstream rms are affected bythe maximum prot that can be earned from captive consumers. Thistoo is inversely related to the level of differentiation in the market. Infact, there are only two situations in which the relationship betweenseller prots and the level of differentiation is positive. The rst iswhen the equilibrium outcome involves pure price strategies. In thissituation, equilibrium pricing is driven by the desire of the down-stream rms to compete for customers who are reached by the

29D.A. Soberman / Intern. J. of Research in Marketing 26 (2009) 2133result, the optimal strategy for themarketing agency is to sell its servicesto both downstream rms. In this way, it is able to capitalize on theprimary effect of the marketing services in this situation, that ofenhancing primary demand for both rms.

4.3. Optimal action for the seller when differentiation is weak: tb15

When differentiation is weak, there are three regime changes as increases from zero to one. The optimal strategy for each regime isdescribed in Proposition 6.

Proposition 6.

1. When b2t, he optimal strategy for the seller is to sell the servicesnon-exclusively at a price of Pb = 12

1t 2 1 +

.

2. Whena 2t; 1 + t

6t + 5t2 + 1

p

2t

, the optimal strategy is to sell the

services exclusively at a price of Px1 = 2t 2 + 1 + 3 1 + .

3. Whena 1 + t

6t + 5t2 + 1

p

2t; 1 + t +

6t + 5t2 + 1

p

2t

and

(a) N2t + 69t26t4

, the optimal strategy is to sell exclusively at aprice of

1t 1

+ 1

2t2.

(b) b2t + 69t26t4

, the optimal strategy is to sell non-exclusively at

a price of 6t

4

2t2

+ 3t

+ 2

2 . This is only pos-

sible if t0.14777.4. When

a 1 + t +

6t + 5t2 + 1

p

2t;1

, the optimal strategy is to sell the

services exclusively at a price of Px1 = 2t 2 + 1 + 3 1 + .

When differentiation is low, exclusive selling is more likelybecause the level of competition between rms is high. Nevertheless,Proposition 6 shows that the optimal strategy does not have a simplerelationship to the level of marketing reach. When the level ofmarketing reach is low (b2t), it always better for the seller ofmarketing services to sell non-exclusively. Conversely, at high levels ofmarketing reach (i.e.

N22t

69t), it is optimal for the seller to sell the

services exclusively. However, when the levels of marketing reach arein an intermediate range, i.e.

a 1 + t

6t + 5t2 + 1

p

2t; 1 + t +

6t + 5t2 + 1

p

2t

, a seller

may earn higher prot by selling non-exclusively. In this region, whenthe impact of the services, , is below the threshold of 2t + 69t2

6t4, non-

exclusive selling is optimal. Above the threshold, exclusive sellingyields higher prots.

The analysis shows that the optimal strategy depends on howercely the downstream rms compete with each other. Whencompetition is erce, it is better to sell exclusively. In contrast, whencompetition is muted, it is better to sell the services non-exclusively.Most importantly, the level of competition is not a simple function ofhow differentiated the downstream rms are. It also depends on themarketing reach of rms. The level of overlap in the consumersreached by the marketing of the two competitors is as important adeterminant of competitive intensity as differentiation. When there isa high level of overlap in the consumer groups reached by each rm, aseller will nd that exclusive selling yields higher prots.

A second point relates to the relationship between seller protsand the exogenous parameters (, and t). Invariably, the prots theseller earns are positively related to the efciency () provided by theservices. Whether the services are sold exclusively or to both down-stream rms, the more impactful the services are, the more prot thatis earned. The relationship between prots and the base level ofmarketing reach is more nuanced. When the base level of marketingreach is low, prots are positively related to the base level of mar-keting reach. However, when the regime involves a) pure pricingstrategies that are a function of marketing reach or b) marketing reachlevels that are high; the seller's prots are negatively related to thebase level of marketing reach.

What is most interesting is the relationship between the seller's

prot and differentiation. The seller makes more money when themarketing effort of both rms. This is the regime that is similar to thestandard price equilibrium in a spatial model where consumers havefull information. The second is when the equilibrium entails mixedpricing strategies and the levels of reach are high

N2

3

.

4.4. Optimal selling strategies when the services lead to a regime change

The results of Section 4.3 relate to services where the efciencyincrease associated with the services do not change the equilibriumoutcome. However, a seller's service will change the type ofequilibrium observed in the market when is high enough. To obtain,a qualitative idea of how regime-changing services would be sold, Isummarize the strategy prescriptions for low levels of in Fig. 4. Fig. 4reveals information that is useful to infer the optimal strategy forselling marketing services that lead to a regime change. Independentof the level of differentiation in the market, as one moves from the leftto the right (as is the case with increases in ), one moves from zoneswhere non-exclusive selling is optimal to ones where exclusive sellingis optimal. As argued earlier, high levels of marketing reach increasethe level of competition between downstream rms. This favoursexclusive selling. If the base level of marketing reach is such that therms are in a region where non-exclusive selling is optimal (forsufciently low levels of ), a higher level of will ultimately push theequilibrium into a region where exclusive selling is optimal. In otherwords, while a regime change does not automatically imply a changein the optimal selling strategy (from non-exclusive to exclusive), once is above a threshold, the optimal selling strategy is exclusive selling.Fig. 4. Summary of the optimal strategies for the seller without regime changes.

30 D.A. Soberman / Intern. J. of Research in Marketing 26 (2009) 2133As one moves from the left side of Fig. 4 to the right side, the maineffect of higher symmetric levels of marketing reach changes fromdemand enhancement to exacerbating competition. When theefciency gain is sufcient to move the symmetric equilibriumsignicantly to the right, the seller limits the exacerbation ofcompetition by selling the services exclusively.

5. Conclusion

The major message of the analysis is that the optimal strategy for aseller of marketing services depends on how ercely the downstreamrms compete with each other. When competition is erce, it is betterto sell exclusively. This echoes the nding of Goldfarb and Yang (2007)who suggest that a B2Bmarketer can benet by targeting just one rmwhen the rms are sophisticated and competition between them isintense.

In contrast, when competition is muted, a seller earns more byselling her services non-exclusively. It is important to note that thelevel of competition is not a simple function of the level ofdifferentiation between the potential buyers of the services. It alsodepends on how extensive the marketing reach of rms before theseller's services are used. The analysis shows that the level of overlapin the consumers reached by the marketing of the two rms is a keydeterminant of competitive intensity. The model thus providesguidance about the type of contracts a seller of marketing servicesshould use. For example, over a period of two years, Otis SauterPartners Inc. (a marketing agency in Toronto, Canada) developed anelectronic list of tea drinkers using information collected throughseveral consumer contests. The marketing agency then sold the listexclusively to Red Rose (Unilever) as a basis to conduct directmarketing with high potential tea drinkers (the main competitors inthe Canadian teamarket are Unilever and Tetley). The list is valuable toa teamarketer like Red Rose because it allows Red Rose to increase theimpact of its marketing by reaching tea drinkers for whom Red Rose isnot top of mind. Note that the mainstream tea market in Canada ischaracterized by low differentiation and frequent price promotions.These observations explain the exclusive arrangement that wasnegotiated between Otis Sauter Partners and Red Rose.

Another important message of the analysis is to clarify therelationship between a) the prots of the seller of marketing servicesand b) the level of differentiation in the downstream market.Surprisingly, for a signicant fraction of the parameter space, themodel shows that differentiation is negatively related to seller prots.This has an important implication for marketing agencies, mediaexperts and sales agents. A key decision for these organizations is tochoose where to focus their own marketing efforts. Given the well-accepted belief that differentiation is a strong indicator of prots,these organizations might gravitate towards categories whereproducts are well differentiated. The model shows that marketswhere products are not well differentiated can be just as attractive (ifnot more protable) for sellers of marketing services. In other words,it may be a mistake to only look at the degree to which rms aredifferentiated from each other as a basis for deducing the value ofservices that increase the impact of marketing effort.

Two limitations of the analysis need to be highlighted. A rstlimitation relates to the assumption of independence for the incre-mental reach added to the base level of marketing reach for eachdownstream rm when the marketing agency contracts with bothrms. When additional reach provided by a seller is not independent(for example, the additional customers are disproportionately custo-mers who are reached by neither rm's marketing activity), thendings would be different. A lack of independence in the incrementalreach provided by the marketing agency would increase the competi-tion-exacerbating effect of the marketing services. This would causeexclusive selling to bemore attractive at higher levels of differentiation

and lower base levels of marketing reach.A second limitation of this study relates to the types of marketingservices that are represented by the model. As noted earlier, this modelapplies to those services forwhich theeffect is to increase in thenumberofcustomers reached effectively by a rm'smarketing effort. Clearly, thereare marketing services that do more than increase a rm's effectivemarketing reach. For example, internet serviceswhich allow baseball fansto purchase and print their tickets online domore than increase the reachof a baseball team's marketing effort. They also increase the value ofattending the baseball game: baseball fans appreciate how the onlineprinting of tickets eliminates the need to queue at the ticket counter toobtain reserved tickets. Similarly, a recent promotion developed inToronto involved making a beer brand the title sponsor for Hip-Hop/Rapbars in the trendyQueen StreetWest corridor. The promotion appealed tobreweries because it was a vehicle to increase distribution and presencefor a beer brand in Toronto. But the promotion also allowed a beer brandwith tired positioning to refresh its image and improve itstwithyoungwhite collar beerdrinkers. Some agencies also sell information that allowsa rm to implement consumer addressability such that individualconsumers can be offered customized products and pricing (Blattberg &Deighton,1991; Chen & Iyer, 2002). Themodel I present does not addresssituations where a marketing service repositions a product, adds value tothe consumption experience for the customer or allows a rm toimplement consumer addressability. Services that have these effects areimportant and need to be explored in future research.

Appendix A

Proof of Proposition 1. When ta 15; 12

, the objective functions

when prices are marginally less than 1 t are:

1 = p1 1 12 + 12p2p1 + t

2t

i

2 = p2 2 11 + 12p1p2 + t

2t

ii

The rst order conditions for prices are:

A1Ap1

= 1212t + 2t2p2 + 2p12

t= 0 iii

when p1 = p2 = 1t Z A1Ap1

= 121

2t + 2t

A2Ap2

=122

2t1t + 1p12p21t

= 0 iv

when p1 = p2 = 1tZ A2Ap2

= 122

2t1t. Therefore A1

Ap1; A2Ap2

N0 for sufcientlylow. The objective functionswhenprices aremarginally greater than 1tare:

1 = p1 1 12 1p1t

+ 12p2p1 + t

2t

121 v

2 = p2 2 11 1p2t

+ 12p1p2 + t

2t

222 vi

The rst order conditions for prices are:

A1Ap1

=121

24p122 + 2p12 + 2p2 + 2tt

= 0 vii

A2Ap2

=122

24p221 + 2p21 + 1p1 + 1tt

= 0 viii

when p1 = p2 = 1tZA1Ap1 = 121

24t2 + 22tt

. It is straightforward to showthat 1

21

24t2 + 22tt

b 0 for all t b 12. As long as is low enough and

p1=p2=1t, AAp

+b0 and A

Ap

N0.

payoffs not jump down in the limit of the equilibrium strategies.15

Second, the individual payoff functions need to be weakly semi-continuous. Both of these properties are satised. Thus, amixed strategyequilibrium exists where the two rms undercut each other to capturedemand from the fully informed segment.

However, undercutting for the fully informed segment does notreduce prots earned from the fully informed segment to zero (in thesymmetric model of Narasimhan, 1988, the prot earned from theswitching segment in a mixed pricing equilibrium is zero). A rm will

31D.A. Soberman / Intern. J. of Research in Marketing 26 (2009) 2133For a corner solution, A1Ap1

= 121

24t2 + 22tt

N0. For A1Ap1N0when1=2,

I need (2t)N0 which implies that b2t. Therefore the equilibriumwhen b2t is p1=p2=1 t and rms earn prots of 12 1t 2 .

However, when b2t, the equilibrium price is less than 1 t andusing Eqs. (iii) and (iv), I have two equations and two unknowns (p1and p2). Solving the equations yields the symmetric solution ofp1 = 1 2tt and p2 = 1 2tt . At these prices, rms earn prots of12t 2 2.

Proof of Proposition 2. When only Firm 1 engages the seller, thederivatives with respect to price for the two rms (at prices slightlyless than 1 t) must be positive for the corner solution of p1=p2=1 tto be an equilibrium. The derivatives when 1=(1+), 2= andp1=p2=1 t are ( is an arbitrarily small number):

A1Ap1

=12t

2t + 2t

2

2

ix

A2Ap2

=12t

2t

2

2

x

Therefore A1Ap1A2Ap2

= 2tN0. This implies that A1Ap1

NA2Ap2

and the rstcondition to be violated will be A2

Ap2N0. This occurs when 2t

1 + b0Z

b 2t

1 + . When this condition is satised, the prots obtain

easily by substituting, the values for i and p into the rm objectivefunctions. When

N 2t

1 + , both rms set prices at the maximum which

occurswhen A1Ap1

= A2Ap2

= 0. Substituting into Eqs. (ix) and (x), two equationsin two unknowns are obtained.

12t

2tt2

p1 +

p2

+ 1

= 0 xi

12t

t2t + t

p1 + 2

p2

p1 + 2

p2

= 0 xii

Solving the equations yield the equilibrium prices of

p1 =6t3t

+ 4t3t

3 1 + and p2 =

6t3t + 2t3t

3 1 + xiii

The prots of Firms 1 and 2 obtain easily by substituting theequilibrium prices into the objective functions for Firms 1 and 2.

Proof of Lemma 1. In order for the pure strategies to constitute anequilibrium, the prots earned by choosing the pure price strategymustexceed the prots that can be earned by defecting to 1 t. At a price of1 t, the rms would sell to consumers who were reached by itsmarketing and not by that of the competitor.When themarketing reachof bothrms is, prots are 1

2t 2 2 as per Proposition 1. The prots for

a rms that defect are (1)(1t). These prots are equal when

= 1t2

tF6t + 5t2 + 1

p1

. This implies that the defect prots are

greater thanpure strategy prots when a 1 + t6t + 5t2 + 1

p

2t; 1 + t +

6t + 5t2 + 1

p

2t

.

This interval exists if an only if tb15because

6t + 5t2 + 1

phas real roots

if and only if (5t1)(t1)N0. When the defect prots are greaterthan the prots fromchoosing aprice of 1

2tt , suppose Firm1defects

to 1t. Then Firm 2 will have an incentive to increase its price to 12tand earn higher prot on all consumers who are reached by Firm 2'smarketing. But when Firm 2 chooses a price of 12t, Firm 1 has anincentive to undercut Firm 2 and choose a price of 13t (each rmeffectively faces demand from two discrete groups of consumers withdifferent reservation prices). In this game, the existence of a mixedstrategyequilibriumdepends on twoexistence theorems fromDasguptaand Maskin (1986). First, the sum of the payoff functions needs to be

upper hemi-continuous. This implies that the sum of the individualnot reduce its price such that it earns less than it would earnwere thecompetitive price of t charged to the fully informed segment (whenboth rms charge the competitive price, the prots earned from thefully informed segment are 12t

2). This implies that the guaranteed

prot that either rm can earn by selling to the fully informedsegment is 12t

2. Therefore, the guaranteed prots for rms in this

region are 1t 1 + 2t2.

The equilibrium pricing strategy entails the rms randomizingover an interval between (p , 1 t): p is the minimum price and 1 t isthe maximum price in the support for the mixed strategy.

Note that F(p) and f(p) be the c.d.f. and p.d.f. respectively of thesymmetric mixed pricing strategy. The objective functions for eachrm are:

1 = p1 1 12 + 12 p1 + t

p1tp2p1 + t

2tf p2

dp2 + 12 1F p1 + t

xiv2 = p2 2 11 + 12

p2 + t

p2tp1p2 + t

2tf p1

dp1 + 12 1F p2 + t

xv

Themixed strategywhich cannot be described analytically satisesEqs. (xiv) and (xv).

Proof of Proposition 3. Part 1 of the proposition follows thereasoning of Proposition 1. Parts 2, 3 and 4 follow the reasoning ofLemma 1. When N2t and the mixed price strategy is not an

equilibrium i.e. g 1 + t6t + 5t2 + 1

p

2t; 1 + t +

6t + 5t2 + 1

p

2t

, the equilibrium is

that both rms choose a price of 12tt .

Proof of Lemma 2. Whena 1

t2t +

6t + 5t2 + 1

p1

;

1t2

t6t + 5t2 + 1

p1

and Firm 1 accepts the seller's offer (but notFirm 2) such that

1 + b 1

t2t

6t + 5t2 + 1

p1

, then the equili-

briumwill be in mixed strategies.16

In this situation, the group of consumers reached by Firm 1'smarketing effort, 1(12), is larger than the group of consumersreached by Firm 2, 2(11). In fact, the group of customers reachedby Firm 1 is (1)(+1) whereas for Firm 2, it is (1(1+)).Following the reasoning of Narasimhan (1988), Firm 1 has lessincentive to reduce price from 1 t than Firm 2 because it losesmore guaranteed prot than Firm 2. Firm 1's guaranteed prot is

1t 1 + 1

+

2 1 + t2 . As a result, Firm 1's pricing strategy

includes a mass point at 1 t and Firm 2's equilibrium prot exceedsthe prot it earns by serving its captive segment at a price of 1 t andcapturing half of the segment that has been reached by the marketing

15 In this game, where the payoffs are the sum of prots from a Hotelling game andtwo discrete segments (reserved for each of the two players respectively), thisproperty is satised.16 I present sufcient conditions for the equilibrium to be in mixed strategies whenthe rms are asymmetric. Because I focus on levels of that do not lead to a change inregime, this is sufcient to characterize the equilibrium zones. It is straightforward tocalculate necessary conditions for the equilibrium to be in mixed strategies bydetermining the point at which Firm 1 (the rmwith an advantage) has an incentive todefect to a price of 1 t. I do not present this condition because it is long and does not

yield additional insight.

of both rms. Letw be the probability that Firm 1 sets price at 1 t andlet F(p) and f(p) be the c.d.f. and p.d.f. of Firm 1's mixed pricingstrategy. Conversely let G(p) and g(p) be the c.d.f. and p.d.f. of Firm 2'smixed pricing strategy. It proves useful to dene F(p) and f (p) as the

32 D.A. Soberman / Intern. J. of Research in Marketing 26 (2009) 2133c.d.f. and p.d.f. of Firm 1's mixed pricing strategy conditional on notchoosing a price of 1 t.

The objective functions for the rms are:

1 = p1 1 12 + 12 p1 + t

p1tp2p1 + t

2tg p2

dp2 + 12 1G p1 + t

xvi

Firm 2's objective function if p2 (12t, 1 t) is:

2 =wp2 2 11 + 121p22t

+ p2 1w

2 11 + 12 p2 + t

p2tp1p2 + t

2tf p1

dp1 + 12 1 F p2 + t

xvii

When p2b12t, Firm 2's objective function is:

2 =wp22 + p2 1w 2 11 + 12 p2 + tp2t

p1p2 + t2t

f p1

dp1

+ 12 1Fp2 + t xviii

Let W p = 12 p1 + t

p1tp2p1 + t

2tg p2

dp2 + 12 1G p1 + t . Using

Eq. (xvi) and the guaranteed prot of the rm, it is straightforwardto show that:

W p = + 1 3t

2

2t2p + 2

p + 2

2p

xix

Following Narasimhan (1988), the conditional distributions of thetwo rms will be identical because the only difference between thetwo rms is the size of the captive segment. I then rewrite Eq. (xviii)replacing for W(p).

2 =wp2 + p2 1w

1 1 +

+

+ 1 3t2

2t2p2 + 2

p2 + 2

2p2

xx

Because the support for p2 is continuous, is constant so A2Ap2

= 0.17

A2Ap2

= w +w = 0Zw =

1 +

I now substitute into Eq. (xx) and evaluate at a price in the sup-port (p2=12t) to identify Firm 2's equilibrium prots: 2 = 1t

1

+ 1

2t2.18 I cannot explicitly identify the mixed pricing strategy;

however, the prots earned by Firms 1 and 2 respectively are

1 = 1 + 1

1t +

2 1 + t2 and 2 =

1

1t +

2t2 .

Proof of Proposition 4. Part 1 of the proposition follows thereasoning of Proposition 1. Parts 2, 3 and 4 follow the reasoning ofLemma2.When

N 2t

1 + and themixed price strategy is not an equilibrium

i.e.g 1 + t

6t + 5t2 + 1

p

2t; 1 + t +

6t + 5t2 + 1

p

2t

, the equilibrium is that the rms

choose prices of p1 = 6t3t + 4t3t3 1 + and p2 =

6t3t + 2t3t

3 1 + .

17 The support for Firm 2's pricing strategy does not include the segment (12t, 1 t)when Firm 1 chooses 1 t with positive probability. Thus the condition A2

Ap2= 0 holds for

p2b12t.18 As noted earlier, Firm 2 (the weaker rm) benets from Firm 1's reduced incentive

to reduce price. Recall that Firm 2's captive segment is (1 (1+)) and not (1).A.1. Comparative statics for the asymmetric case when pricing strategiesare mixed

A1At

=12 3

2

+ 1 b0 if

b

23

xxi

A2At

=12 3

2

b0 if

b

23

xxii

Eqs. (xxi) and (xxii) show that the relationship between prots anddifferentiation depends on the initial level of marketing reach.

A1A

= 3t2

t + 1

+ 1 xxiii

A2A

= 3t2

t + 1 xxiv

Eqs. (xxiii) and (xxiv) show that the relationship between protsand the base level of marketing reach is positive for

b 1t

23tand negative

whenN 1t

23t.

Proof of Proposition 5. When ta 15; 12

n oand b2t, Propositions 1

and 2 imply that n = 12 1t 2

; b = 12

t1 + 1

+

2

;

a = 12 t1

2

+ 1 and d = 12 t1

+

2

. As discussed in

the paper, the exclusive payoff is equal to Pexc=ad= (1 t).The non-exclusive price is the minimum of (bd, an). b

d = 12 t1

+

2

and an = 12

t1

2

. bdbanbecause bd an = 122

2 t1 b0. Therefore bd is the

maximumpriceallowed forrms to sell non-exclusively. This implies thatthe seller's prots are 2(bd) if she sells non-exclusively. As a result,non exc= (t1)(+2) andexc=(1t).

non excexc=(t1)(+1)N0 because a) t1b0 and b) +1b0 since (1+)b1 (the seller cannot offer an efciency gainthat leads to reach level that exceeds 1). Therefore, when marketingreach levels are low and the efciency gain is relatively small i.e.b2 t

1, the seller earns more by selling non-exclusively. The prot of

the seller is (t1)(+2).When ta 15 ;

12

and 03D5N2t, Propositions 1 and 2 imply that

n = 12 t2 2

;b = 12 t +

2

2;a =

34 + 3

6 2t

18 + 1 and d =32 + 3

6 2t

18 + 1 . The prot earned from exclusive selling in this situationis ad =

2t3 1 + 2 + 1 +

.

As discussed in the text, the non-exclusive price is the smaller oftwo differences:

bd =118

+ 1 1 92424

24

+ 18

2 + 9

22 + 12

t

an =118

+ 1 1 162424

+ 9

2 + 9

2 + 12

t

bd an = t2

18 1 + 92 + 9

220

b0 because a) the rst

term is positive and b) the second term is negative (even at themaximum (= 1) andmaximum (= 1), the second term equals 2 b 0).Thus, the maximum price that can be charged for non-exclusiveselling is b d. Summarizing, exc = 2t3 1 + 2 + 1 +

and

non exc = 19 + 9 12t24t4t224t

2 + 9t

2 + 18t

22 + 9t

23

.

This implies that excnon exc = 19

+ 1 1 921018

18

+

18

2 + 9

22t. The rst term 1

9

+ 1 1t is negative. The rst

derivative of the second term is:

A

A921018

18

+ 18

2 + 9

22

= 18

2

18 + 18

210 xxv

The second derivative of the second term is:

A

A18218 + 18210

= 182N0 xxvi

References

Admati, A. R., & Peiderer, P. (1986). A monopolistic market for information. Journal ofEconomic Theory, 39(2), 400438.

Admati, A. R., & Peiderer, P. (1988). Selling and trading on information in nancial

33D.A. Soberman / Intern. J. of Research in Marketing 26 (2009) 2133result, the maximum value of the function is found at one endpoint ofthe allowable interval for . The minimum endpoint is =0. At theminimum endpoint, the second term equals 9(2)b0. Themaximum endpoint occurs at the maximum value for which is 1

1

since (1+)1. At = 1 1, the second term equals 1

10

b0. Since the

rst term and the second term are negative, excnon excN0 and theoptimal strategy in these conditions is exclusive selling. This implies thatthe seller's optimal prot isexc = 2t3 1 + 2 + 1 +

.

Proof of Proposition 6. The proof of Parts 1, 2 and 4 (the regionswhere the pricing strategies are pure) are identical to the proofprovided for Proposition 5.

Whena 1t2 t +

6t + 5t2 + 1

p1

; 1t2 t

6t + 5t2 + 1

p1

;

n = 1t 1

+

2t2 ;b =

1t + 1 1

1 + + 1 + 2

2

t2 ; a =

1 + 1

1t +

2 1 + t2 and d =

1

1t +

2t2 . This implies

thatexc =ad = 1t 1

+ 12 t

2.

As discussed in the text, the non-exclusive price is the smaller oftwo differences:

1. bd = 1t + 1 1

1 + + 1 + 2

2t

2 1

1t

2t2 =

12

6t

42t2

+ 3t

+ 2

2 . an = 1 + 1

1t +

2 1 + t2 1t

1

+

2t2

=

12

3t

2

2t + 2

bd an = 12

2 3t2 + 1 b0 because tb 15. Thus, the

maximum price that can be charged for non-exclusive selling is bd. This implies that the prots under non-exclusive selling are nonexc=(6t42t2+3t+2). To determine the optimal strat-egy, I examine the difference between exc and non exc.

excnon exc = 12

9t

6

2t4

+ 6t

+ 2

Note that 12

b0. When

b 1t23t 2 + 3 ; 9t

6

2t 4

+

6t + 2N0 and when

N 1t23t 2 + 3 ; 9t

6

2t4

+ 6t

+ 2b0.

Thus for low levels of , non-exclusive selling is optimal and forhigh levels, the optimal strategy is to sell exclusively.

For non-exclusive selling to be optimal, 9t62t4+6t+2N0. This implies that both and need to be sufciently small; infact,

b 22t69t is a necessary condition for the inequality to be satised

since 0 is the minimum value for . However, these conditions mustoccur when a) the corner solution of 1 t is not the equilibrium (N2t)and b) the pure strategy pricing is not an equilibrium. Since themaximum value of for exclusive selling to be possible is22t69t ;

N2t = 0:4 implies that tb 118

13

p 718 0:18858 is a necessary

condition for non-exclusive selling to be optimal. Second

N 1t2 t +

6t + 5t2 + 1

p1

and

b 22t69t must also be satised for

non-exclusive selling to be possible:

1t2

t +6t + 5t2 + 1

p1

b22t69t

Z4 t2 40t98t2 + 71t34 N0

Numerically, this condition is satised if and only if t 0.14777 (thepolynomial has two real roots). Because 0.14777b0.18858, the limitingcondition for non-exclusive selling to be optimal is t 0.14777. Tosummarize, when

a 1t2 t +

6t + 5t2 + 1

p1; 1t2 t

6t + 5t2 +

p11 and 9t

6

2t4

+ 6t

+ 2b0, exclusive selling is optimal

and the seller earns exc = 1t 1

+ 12 t

2. If falls in the

allowable range and 9t62t4+6t+2N0, non-exclusiveselling is optimal and the seller earns non exc=(6t42t2+3t+2). This is only possible if t0.14777. markets. American Economic Review, 78(2), 96103 (Papers and Proceedings).Admati, A. R., & Peiderer, P. (1990). Direct and indirect sale of information. Econome-

trica, 58(4), 901928.Arrow, K. J. (1962). Economic welfare and the allocation of resources for invention. In R.

Nelson (Ed.), The rate and direction of inventive activity Princeton: PrincetonUniversity Press.

Blattberg, R., & Deighton, J. (1991). Interactive marketing: Exploiting the age ofaddressability. Sloan Management Review, 33(1), 514.

Bush, M. (1998). Nonprots nd donor Names with survey/coupon database. DirectMarketing News, November 9, www.dmwnews.com.

Butters, G. R. (1977). Equilibrium distributions of sales and advertising prices. Review ofEconomics and Statistics, 44, 465491.

Cabral, L., & Villas-Boas, J. M. (2005). Multiproduct oligopoly and Bertrand supertraps.Management Science, 51(4), 599613.

Chen, Y., & Iyer, G. (2002). Research note: Consumer addressability and customizedpricing. Marketing Science, 21(2), 197208.

Dasgupta, P., & Maskin, E. (1986). The existence of equilibrium in discontinuouseconomic games. 1: Theory. Review of Economic Studies, 53, 126.

Dukes, A. J. (2004). The advertising market in a product oligopoly. Journal of IndustrialEconomics, 52(3), 327348.

Dukes, A. J., & Gal-Or, E. (2003). Negotiation and exclusivity contracts for advertising.Marketing Science, 22(2), 222245.

Dukes, A., Gal-Or, E., & Srinivasan, K. (2006). Channel Bargaining with RetailerAsymmetry. Journal of Marketing Research, 45(1), 8497.

Fershtman, C., & Muller, E. (1993). The benets of being small: Duopolistic competitionwith market segmentation. Review of Industrial Organization, 8, 101111.

Fitzgerald, K. (1999). Kraft quiet shift of print makes noise outside. Advertising Age, 70(32), s6.

Gal-Or, E., & Dukes, A. J. (2006). On the protability of media mergers. Journal ofBusiness, 79(2), 489525.

Goldfarb, A. & Yang, B. (2007). Are all managers created equal, mimeo, Rotman Schoolof Management, University of Toronto, Toronto.

Grossman, G. M., & Shapiro, C. (1984). Informative advertising with differentiatedproducts. Review of Economics Studies, 51, 6381.

Grossman, S. J., & Stiglitz, J. E. (1980). On the impossibility of informationally efcientmarkets. American Economic Review, 70(3), 393408.

Hermalin, B. (1993). Notes in microeconomics. mimeo, University of California,Berkeley.

Horsky, S. (2006). The changing architecture of advertising agencies.Marketing Science,25(4), 367383.

Iyer, G., & Soberman, D. A. (2000). Markets for product modication information.Marketing Science, 19(3), 203225.

Iyer, G., & Villas-Boas, J. M. (2003). A bargaining theory of distribution channels. Journalof Marketing Research, 40, 80100.

Kamien, M. I., & Tauman, Y. (1984). The private value of a patent: A game theoreticanalysis. Journal of Economics, Supp. 4, 93118.

Kamien, M. I., & Tauman, Y. (1986). Fees versus royalties and the private value of apatent. Quarterly Journal of Economics, 101(3), 470491.

Narasimhan, C. (1988). Competitive promotional strategies. Journal of Business, 61(4),427449.

Pasa, M., & Shugan, S. M. (1996). The value of marketing expertise.Management Science,42(3), 370388.

Pfanner, E. (2005, June 20). Advertising andmedia redraw the lines. International HeraldTribune, 9.

Raju, J. S., & Roy, A. (2000). Market information and rm performance. ManagementScience, 48(8), 10751084.

Salop, S. C. (1979). Monopolistic competition with outside goods. Bell Journal ofEconomics, 10, 141156.

Sarvary, M. (2002). Temporal differentiation and the market for second opinions.Journal of Marketing Research, 34, 129136.

Sarvary, M., & Parker, P. M. (1997). Marketing information: A competitive analysis.Marketing Science, 16(1), 2438.

Shaffer, G. & Zettelmeyer, F. (1999). Bargaining, third party information and the divisionof prot in the distribution channel. mimeo, University of California, Berkeley, CA.

Shilony, Y. (1977). Mixed pricing in oligopoly. Journal of Economic Theory, 14, 373388.Soberman, D. A. (2004). Research note: Additional learning and implications on the role

of informative advertising. Management Science, 50(12), 17441750.Soberman, D. A. (2005). Questioning conventional wisdom about competition in

differentiated markets. Quantitative Marketing and Economics, 3(1), 4170.Tirole, J. (1988). The Theory of Industrial Organization (pp. 277295). Cambridge,Mass:MIT

Press.Villas-Boas, J. M. (1994). Sleeping with the enemy: Should competitors share the same

advertising agency. Marketing Science, 13, 190202.This implies that with regards to , the second term is convex. As a

Marketing agencies, media experts and sales agents: Helping competitive firms improve the effec.....IntroductionBackgroundFramework and resultsRelated research

The modelThe downstream marketThe impact of marketingStage one: The selling and buying of marketing servicesStage two: Competition between downstream firms

The downstream market and equilibrium decisionsStrong differentiation: t∈(15,12)Strong differentiation: Symmetric competitorsStrong differentiation: Asymmetric competitors

Weak differentiation: t∈(0,15)Weak differentiation: Symmetric competitorsWeak differentiation: Asymmetric competitors

Optimal pricing and selling strategies for marketing servicesKey comparisons for the seller of marketing servicesOptimal action for the seller when differentiation is strong: t∈{15,12}Optimal action for the seller when differentiation is weak: t