generic n brand strategies

8/6/2019 Generic n Brand Strategies

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Vol. 24, No. 4, Fall 2005, pp. 556568issn 0732-2399 eissn 1526-548X 05 2404 0556

informs

doi 10.1287/mksc.1050.0119 2005 INFORMS

Generic and Brand Advertising Strategies

in a Dynamic Duopoly

Frank M. BassSchool of Management, The University of Texas at Dallas, Richardson, Texas 75083-0688,

[email protected]

Anand KrishnamoorthyCollege of Business Administration, University of Central Florida, Orlando, Florida 32816-1400, [email protected]

Ashutosh Prasad, Suresh P. SethiSchool of Management, The University of Texas at Dallas, Richardson, Texas 75083-0688

{[email protected], [email protected]}

To increase the sales of their products through advertising, firms must integrate their brand-advertisingstrategy for capturing market share from competitors and their generic-advertising strategy for increasingprimary demand for the category. This paper examines whether, when, and how much brand advertising versusgeneric advertising should be done. Using differential game theory, optimal advertising decisions are obtainedfor a dynamic duopoly with symmetric or asymmetric competitors. We show how advertising depends on thecost and effectiveness of each type of advertising for each firm, the allocation of market expansion benefits,and the profit margins determined endogenously from price competition. We find that generic advertising isproportionally more important in the short term and that there are free-riding effects leading to suboptimalindustry expenditure on generic advertising that worsen as firms become more symmetric. Due to free-riding

by the weaker firm, its instantaneous profit and market share can actually be higher. The effectiveness of genericadvertising and the allocation of its benefits, however, have little effect on the long-run market shares, which aredetermined by brand-advertising effectiveness. Extensions of the model show that market potential saturationleads to a decline in generic advertising over time.

Key words : advertising; generic advertising; differential games; dynamic duopoly; optimal control

History : This paper was received March 11, 2004, and was with the authors 3 months for 2 revisions;processed by J. Miguel Villas-Boas.

1. IntroductionFrom the relationship product sales = categorysales market share, it follows that marketing deci-sions can increase sales only by increasing categorysales volume, i.e., primary demand,1 or by increasingmarket share. When the relevant marketing instru-ment is advertising, we define advertising whoseeffect is to increase category sales as generic adver-tising, and advertising whose effect is to gain marketshare as brand advertising. Operationally, genericadvertising generates new sales by targeting beliefsabout the product category while downplaying oroftentimes not mentioning the sponsoring brand. Incontrast, brand advertising provides consumers withinformation about the brands value proposition that

1 The terms primary demand and category demand are usedinterchangeably.

differentiates it from its competitors, thereby encour-aging consumers to choose the advertised brand overcompeting brands (Krishnamurthy 2000, 2001).

Allocating funds to generic advertising has an inter-esting consequence for the firm. Because genericadvertising promotes the general qualities of theproduct category, it benefits all the firms in the cat-egory regardless of whether or not they paid for

the advertising. Competing firms can benefit fromthe firms contribution by free-riding, i.e., by notspending significant amounts of their own moneyon generic advertising (Krishnamurthy 2000). In thispaper, we determine how much different firms shouldcontribute towards generic advertising, and how firmand competitive factors affect their contributions.

Characterizing the optimal advertising policies inthe presence of competitive effects is of great inter-est to researchers. However, the extant researchon this topic is limited to either static models

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Bass et al.: Generic and Brand Advertising Strategies in a Dynamic DuopolyMarketing Science 24(4), pp. 556568, 2005 INFORMS 557

that incorporate generic and brand advertising (e.g.,Krishnamurthy 2000) or dynamic models that do notexplicitly consider generic advertising (e.g., Sorger1989, Chintagunta and Vilcassim 1992, Erickson 1992).Thus, an important contribution of this paper is toexamine dynamic competition in brand and generic

advertising. We will examine the relevant literature inthe next section.The current research answers the following ques-

tions: (1) What should a firms generic and brand-advertising budget be, and how should it bedynamically allocated? (2) How do the nature ofcompetition (symmetric or asymmetric) and otherfirm and market characteristics affect this alloca-tion? Answering these questions contributes to thesubstantive literature on optimal advertising strate-gies in the presence of competition. We model mar-ket expansion by specifying a modified form ofthe Lanchester model of combat (Little 1979). We

model the two types of sales growth in a dynamicduopolyvia market expansion (size of the pie)through generic advertising and market share allo-cation (slice of the pie) through brand advertising.Because both advertising and sales are time vary-ing, optimal control methods are used to analyzethe situation (Sethi and Thompson 2000). Specifically,the Hamilton-Jacobi or value function approachis used to obtain explicit closed-loop Nash equilib-rium solutions for the optimal advertising decisions(Villas-Boas 1999). We examine both symmetric andasymmetric competition.

The rest of the paper is organized as follows: In 2and 3, we review the existing literature. Section 4presents the model. Section 5 deals with the analysisand the results for symmetric firms. Section 6 presentsthe results for asymmetric firms. Section 7 examinesextensions of the basic model. Section 8 contains adiscussion of the results. Finally, 9 concludes with asummary and directions for future research.

2. Literature ReviewThe effect of advertising on sales is an oft-researchedtopic (e.g., Bass and Parsons 1969). The bulk of this

literature is devoted to brand advertising, justified by casual empirical evidence that suggests it to bethe more common form of advertising. Thus, we firstelaborate on the less known merits of generic adver-tising. We will then be in a better position to considerthe relevant managerial decisions of budgeting andallocation of brand versus generic advertising.

Generic advertising increases primary demand byattracting new consumers, increasing per capita con-sumption of the product, and lengthening the prod-uct life cycle (Friedman and Friedman 1976). Let us

consider these cases in more detail:Case (a). New product categories: Generic advertis-

ing is particularly effective in the introductory stageof the product life cycle. Consumers are unawareof the products uses and benefits and need to beinformed and educated. For example, when P&G

introduced Pampers diapers, it tried to enhance prod-uct acceptance by highlighting the advantages ofusing disposable diapers. Consider also advertise-ments by Sirius and XM, competitors in the nascentmarket for satellite radio. Douglas Wilsterman, Mar-keting VP of Sirius, says, Youve got to do a lit-tle bit of both [viz. brand and generic ads]. Youcant just talk about yourself without people know-ing what you represent in terms of a revolution-arily dynamic change (Beardi 2001). Along similarlines, Steve Cook, XMs VP of Sales and Marketing,adds, XMs ads will be about continuing to growthe whole category pie, rather than competing with

Sirius (Boston and Halliday 2003). Other examplesof generic advertising in new product categories, suchas high-definition TV and the recordable DVD for-mat, show advertisements promoting the advantagesof these new standards without touting brand-specificfeatures. Although the brand name may be men-tioned, advertisements ask customers to compare thenew technology with their existing technology with-out differentiating each firms brand from competitorsoffering the same technology.

Case (b). Increased penetration of mature products:Firms use generic advertising to market mature prod-ucts by promoting new uses. Examples include Arm

and Hammers informing the public of new waysto use baking soda, and Skippy showing consumersnontraditional ways to enjoy peanut butter. Otherattempts to increase the sales of established productscan be seen in De Beers advertisement urging cus-tomers to buy diamonds for all occasions (Bates 2001),Dannon promoting the benefits of yogurt consump-tion, Norelcos Gotcha! campaign about the advan-tages of electric shavers over razors, and the Trojancondoms advertising campaign in the 1970s stress-ing the importance of family planning (Friedman andFriedman 1976).

Case (c). Commodities: The critical role of genericadvertising in the promotion of commodities can betraced to the 1950s, when producers of tea and but-ter used generic advertising to compete with mak-ers of coffee and margarine, respectively. Over theyears, dairy producers have invested hundreds ofmillions of dollars in promoting the consumptionof milk and other dairy products. These includethe well-known milk mustache campaign by theCalifornia Milk Advisory Board, advertisements foreggs by the American Egg Board, and the Pork: TheOther White Meat campaign. The advertisement for


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Bass et al.: Generic and Brand Advertising Strategies in a Dynamic Duopoly558 Marketing Science 24(4), pp. 556568, 2005 INFORMS

cotton, The Fabric of Our Lives, for plastics by theAmerican Plastics Council, and the California RaisinAdvisory Boards promotion of raisins as a whole-some natural snack for children also come to mindin this regard. Other associations have used genericadvertising to promote lamb, grapes, oranges, sav-

ings banks, life insurance, and the importance of hav-ing regular eye checkups (Friedman and Friedman1976). When firms form an association to managethe generic advertising campaign, the basic rule isone of co-opetition, i.e., cooperate first and then com-pete, which suggests that firms can gain advantage

by means of a judicious mixture of cooperation andcompetition (Brandenburger and Nalebuff 1997).

These examples show the range of uses of genericadvertising. However, from these examples, no intu-ition emerges about when to emphasize genericadvertising spending (initial or later stages of theproduct life cycle), under which circumstances to use

it (market characteristics, e.g., high-tech, commodity,or other markets), or what effect competitive struc-ture (symmetric or asymmetric competition) has onthe decision. Consequently, a modeling approach isrequired. In this paper, we will broadly cover theissues of whether, when, and how much generic ver-sus brand advertising should be undertaken.

We next examine the literature on generic and brand advertising.

3. Modeling BackgroundResearchers have studied competitive advertisingstrategies of firms using the theory of differential

games (e.g., Deal 1979; Deal et al. 1979; Erickson 1985,1992; Chintagunta and Vilcassim 1992; Chintagunta1993; Espinosa and Mariel 2001; Prasad and Sethi2004. Surveys of the literature are provided byErickson 2003, Feichtinger et al. 1994, Jorgensen 1982a,

Jorgensen and Zaccour 2004, and Sethi 1977). Anexample is the Lanchester model, given by

x1t = 1u1t1 x1t 2u2tx1t x10 = x10x2t = 2u2t1 x2t 1u1tx2t x20 = x20

(1)

where, for firm i, i=

1 2, at time t, xi

t is the mar-ket share, uit is the brand advertising, and i is theeffectiveness of advertising (Little 1979). Each firmuses brand advertising to capture market share fromits rival. The model is a competitive extension of theVidale-Wolfe (Vidale and Wolfe 1957) model of adver-tising studied in Sethi (1973), without the decay termin that model.

Sethi (1983) developed a variant of the Vidale-Wolfemodel and used it to derive optimal advertising poli-cies in a monopoly. Sorger (1989) extended the Sethi(1983) model to study brand-advertising competition.

The latter model is specified as

x1t =1u1t

1x1t2u2t

x1t x10=x10x2t =2u2t

1x2t1u1t

x2t x20=x20

(2)Sorger (1989) compares the model in (2) to other mod-

els of brand advertising, derives solutions for theoptimal advertising expenditures, and also discussesvarious desirable properties of the model, notablythe diminishing marginal returns to advertising andthe fact that the structure can be made to resem-

ble word-of-mouth and excess advertising models.Chintagunta and Jain (1995) find that this model fitsthe data from four product-markets (pharmaceutical,soft drink, beer, and detergent) well.

Krishnamurthy (2000, 2001) examines the relation-ship between generic and brand advertising, but ina nondynamic setting. The analysis suggests that ifthere is a dominant firm in the industry, the Nash

equilibrium is for that firm to contribute everythingand for the remaining firms to contribute nothing.Wrather and Yu (1979) also consider the static alloca-tion of generic and brand advertising when there is a

budget constraint.Espinosa and Mariel (2001), Fruchter (1999), and

Piga (1998) have proposed dynamic models of adver-tising competition with market expansion. However,in these models, both generic and brand advertis-ing are modeled using a single advertising variable,so their separate effects on sales are not distin-guished. Because sales respond differently to genericand brand advertising, their effects on sales should

ideally be modeled separately.A comparison of the various dynamic models of

advertising competition in the literature is presentedin Table 1.

From this table, we see that generic and brand-advertising decisions have not been simultaneouslyconsidered in a dynamic model. The present studyspecifically addresses this gap in the literature.

4. ModelConsider a dynamic duopoly with two firms labeled 1and 2. We use the index i = 1 2 to represent the twofirms. We begin by listing the main notation:

Sit Sales of firm i at time t.uit Brand advertising of firm i at time t.ait Generic advertising of firm i at time t.pit Price charged by firm i at time t.ci Advertising cost parameter for firm i.i Effectiveness of brand advertising of firm i.ki Effectiveness of generic advertising of firm i.i Allocation coefficient of firm i. We use 1 +

2 = 1.ri Discount rate for firm i.ViS1tS2t Value (or profit) function of firm i.


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Table 1 Comparison of Dynamic Competitive Models of Brand Advertising

Solution procedure

Market Generic Explicit solutions

Study expansion advertising Closed-loop for closed-loop Remarks

Chintagunta and Solutions are obtained only for the case of no discounting.

Vilcassim (1992)Chintagunta (1993) Explicit solutions are derived for a two-period model with

symmetric competitors.

Chintagunta and N/A The purpose of the study was econometric estimation toJain (1995) test the Sorger (1989) specification.

Deal (1979) Numerical techniques are used to obtain the optimal open-loopadvertising decisions.

Deal et al. (1979) Numerical techniques are used to obtain the optimal open-loopadvertising decisions.

Erickson (1985) Numerical techniques are used to obtain the optimal open-loopadvertising decisions.

Erickson (1992) Explicit solutions are obtained only for the case of no discounting.Erickson (1995) Numerical techniques are used to obtain the optimal closed-loop

advertising decisions.

Espinosa and Mariel (2001) Explicit solutions are presented only for symmetric firms. Even so,these solutions are obtained for pure informative and pure

predatory advertising, and when the sales level of one firm is

independent of the rivals advertising.

Fruchter and Kalish (1997) Explicit solutions are obtained assuming the two firms have thesame discount rate.

Fruchter (1999) Explicit solutions are obtained only for the case of no discounting.Horsky (1977) N/A The purpose of the study was econometric estimation of the sales

response function.

Horsky and Mate (1988) Numerical techniques are used to obtain the optimal closed-loopadvertising decisions.

Jorgensen (1982b) Explicit solutions are obtained assuming the two firms have thesame discount rate.

Piga (1998) Explicit solutions are obtained assuming the two firms aresymmetric.

Roberts and N/A The purpose of the study was econometric estimation of theSamuelson (1988) sales response function.

Sorger (1989) Explicit solutions are obtained assuming a mature market.Current study Explicit solutions are obtained for the general model.

The market is one where advertising is the dom-inant marketing-mix variable, and other marketing-mix decisions are less important or nonstrategic. Anexample of a market with such features is the colaindustry, dominated by Coke, Pepsi, and their ColaWars (Chintagunta and Vilcassim 1992, Erickson

1992). We start by modeling the effect of genericadvertising on category demand. The change in pri-mary demand, Qt, is given by

dQt

dt= Qt = S1t + S2t = k1a1t + k2a2t (3)

where Sit is the rate of change of firm is sales,ait is the generic advertising of firm i, and ki is theeffectiveness of firm is generic advertising for i = 1 2.(When no confusion arises, we will drop the phrasei = 1 2, as it applies whenever the index i is used.

When an equation for firm i requires use of the argu-ment relating to the other firm, we subscript this argu-ment as 3 i, because i = 1 implies 3 i = 2 and i = 2implies 3 i = 1.)

The increase in the category demand as a resultof generic advertising is shared unequally. Let i, the

allocation coefficient, denote the proportion of thesales increase that is transferred to firm i. The effect ofgeneric advertising on firm is sales, denoted Si gt,is then

Si gt = ik1a1t + k2a2t (4)To model the effect of brand advertising on sales,

we modify the Sorger (1989) model given by (2) intoa model of sales. The effect of brand advertising onfirm is sales, denoted Si bt, is

Si bt = iuit

Qt Sit 3iu3it

Sit (5)


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where uit is the brand-advertising decision of firm iand i is the effectiveness of that advertising. Hence,the brand-advertising model is based on Sethi (1983)and other papers, as discussed in the literature review.The total change in firm is sales is Sit = Si g t +Si bt. Adding Equations (4) and (5), the total effect of

generic and brand advertising on firm is sales rate is

Sit = iuit

Qt Sit 3iu3it

Sit

+ ik1a1t + k2a2t Si0 = Si0 (6)

where Si0 is the initial sales of firm i. Using S3it =Qt Sit yields

Sit = iuit

S3it 3iu3it

Sit

+ ik1a1t + k2a2t Si0 = Si0 (7)

Equations (7) is intuitive in that the change in salesis the sum of sales gain due to its brand advertising,iuit

S3it, minus the sales loss due to the rivals

brand advertising, 3iu3it

Sit, plus the salesgain due to market expansion, ik1a1t + k2a2t.

The control variables available to each firm are itsgeneric and brand-advertising decisions. Firm is dis-counted profit-maximization problem is

ViS1 S2 = maxuitaitpit

0

erit1 bipit + dip3it

pitSit Cuitaitdt (8)where ri is its discount rate, pit is the pricecharged, bi and di are demand parameters, andCuitait is the total advertising spending offirm i. The latter is specified as

Cu itait =ci2

ait2 + uit2 (9)

As in most of the literature, the cost of advertis-ing is assumed to be quadratic (e.g., Roberts andSamuelson 1988, Sorger 1989). Alternatively, one canuse linear advertising costs and have advertising

appear as a square root in the state equations.The term 1bipit+dip3it in the objective func-

tion multiplies the revenue pitSit and is interpretedas the reduction in the margin pit of firm i due toprice competition.2

2 The term 1 bipit + dip3it can be alternatively, and equiva-lently, interpreted as reduction in sales due to price competition. Inthat case, the term Sit may be referred to as a state variable (whichin equilibrium is sales of firm i times a constant). Note that constantmarginal costs can be included without affecting the results.

The discounted profit-maximization problems ofthe two firms can now be rewritten as the differentialgame

V1S1 S2 = maxu1ta1tp1t

0

er1t

1 b1p1t + d1p2t

p1tS1t c12 a1t2 + u1t2

dt

V2S1 S2 = maxu2ta2tp2t

0

er2t

1 b2p2t + d2p1t

p2tS2t c22

a2t2 + u2t2

dt

(10)such that

S1t = 1u1t

S2t 2u2t

S1t

+ 1k1a1t + k2a2t S10 = S10

S2t

=2u2tS1t 1u1tS2t+ 2k1a1t + k2a2t S20 = S20

(11)

where Vi is firm is profit function, also known as thevalue function.

5. AnalysisThe advertising differential game in (10)(11) can beanalyzed to yield either open-loop or closed-loopequilibria. Managers should find closed-loop strate-gies more useful because these strategies allow themto monitor the market and modify their advertising

trajectories to respond to sudden changes in the mar-ketplace (Erickson 1992). Chintagunta and Vilcassim(1992) and Erickson (1992) provide evidence that aclosed-loop solution fits empirical data better thanits open-loop counterpart. Therefore, we adopt theclosed-loop solution concept. The closed-loop equilib-rium is also the Markov perfect equilibrium.

The optimal advertising policies are given in Propo-sition 1 (proof in appendix):

Proposition 1. The differential game (10)(11) has aunique closed-loop Nash equilibrium solution for the two

firms. For firm i, i = 1 2, the optimal decisions are:(a) Brand advertising:

ui t =ici

i i

S3it (12)

(b) Generic advertising:

ai t =kici

ii + 3ii (13)

(c) Price:

pi t =di + 2b3i

4b1b2 d1d2 (14)


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(d) Value function:

ViS1 S2 = i + iSi + iS3i (15)

where 1, 2, 1, 2, 1, and 2 solve the six simultaneousequations

rii k2i

2ciii + 3ii2 k

23i

c3i11 + 21

22 + 12 = 0 i = 1 2 (16a)

rii mi +23ic3i

1 12 2=0 i=12 (16b)

rii 2i2ci

i i2 = 0 i = 1 2 (16c)

In view of (14), we replace the equilibrium mar-gin pi t1 bipi t + dip3it in the objective func-tion, which is a constant bidi +2b3i/4b1b2 d1d22,denoting it by mi henceforth.

From Proposition 1(a), each firms brand advertis-ing is increasing in its competitors sales. This fol-lows from the specification of the brand-advertisingdynamics in (11) and is consistent with Sorger (1989).Proposition 1(b) and 1(c) suggest that the solutionsfor the optimal generic advertising and prices are sta-tionary. This finding of stationary solutions is consis-tent with the analysis of an infinite-horizon setting(Horsky and Mate 1988, Villas-Boas 1999).

We first consider the analysis for symmetric firms.In this case, i = , i = , i = , ki = k, i = ,mi = m, ci = c, ri = r, and i = 12 for i = 1 2. Corollary 1presents the solutions for symmetric firms (proof inappendix).

Corollary 1 (Symmetric Firms). For the solutionto the differential game (10)(11) obtained in Proposition 1,the explicit solutions for the parameters , , and are

given by

= 1108cr34

k2c2r4 3cmr22 + 18m24+ 6m2 cr2

cr2cr2 + 6m2 (17a)

= 3m2 2cr2 + 2

cr2cr2 + 6m2

9r2 (17b)

= 3m2 + cr2

cr2cr2 + 6m2

9r2 (17c)

The comparative statics for the variables on themodel parameters are presented in Table 2 (proof inthe technical appendix at http://mktsci.pubs.informs.org). A discussion of the comparative statics is in thenext section.

In the next section, we examine the solution givenin Proposition 1 to the differential game (10)(11) forasymmetric firms.

Table 2 Comparative Statics Results for the

Symmetric Case

Variables c m k r

? =

= ui = a

i Vi ? ? xi =

, increase; , decrease; =, unchanged; ?, ambiguous.

6. Asymmetric FirmsFor asymmetric firms, explicit solutions for the set ofsimultaneous equations in (16a)(16c) are presented inthe appendix. The comparative statics for the param-eters on the variables of interest are presented inTable 3 (proof in the technical appendix at http://

mktsci.pubs.informs.org). Note that i, i, and i arefunctions of the model parameters only, and not oftime.

One can see a few ambiguous effects. However, formost cases, the results are clear. The optimal genericadvertising of a firm increases with an increase in theeffectiveness of its generic advertising and the propor-tion of increase in its sales as a result of generic adver-tising. For the competitive effects, an increase in therivals advertising cost parameter and increase in theeffectiveness of the rivals generic advertising increasethe firms profit. An increase in one firms brandadvertising due to an increase in its effectivenessresults in a decrease in the rivals brand advertising.The increase of one firms profit with the effectivenessof the rivals generic advertising can be seen asevidence of the free-riding of generic-advertisingexpendituresthe greater the effort exerted by therival in developing better generic-advertising copy,the better off the other firm is likely to be. The param-eter for effectiveness of generic advertising and theproportion of sales increase due to generic adver-tising do not have an effect on the optimal brand-advertising policies.

Table 3 Comparative Statics Results for the Asymmetric Case

Variables ci c3i mi m3i ki k3i i 3i ri r3i i

i ? ? ? ? ? ? ? ? ?i ? = = ? =i = = =ui = = =ai = ? Vi ? ? ? ? ? ? ? ? ?xi = = =

, increase; , decrease; =, unchanged; ?, ambiguous.


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From the optimal advertising decisions, we cancompute the long-run equilibrium market shares ofthe two firms. These are listed in the following propo-sition (proof in the appendix):

Proposition 2. For the differential game given byEquations (10)(11), the long-run market shares of the two

firms arex1 =

21/c11 121/c11 1 + 22/c22 2

x2 =22/c22 2

21/c11 1 + 22/c22 2

(18)

where 1, 2, 1, and 2, are obtained from Proposition 1.

Although the long-run equilibrium market sharein (18) is constant through time, its level is deter-mined by the dynamic effects in the analysis. Theform of the long-run equilibrium market shares in

Equation (18) resembles the us/(us + them) marketattraction models in the marketing literature. Themarket share attraction model given by (18) takesinto account the effectiveness of brand advertising,the advertising cost parameter, and the other modelparameters as measures of a firms attractiveness. Theequilibrium market share of the firm increases withthat firms brand-advertising effectiveness and therivals advertising cost parameter, and decreases withits advertising cost parameter and the effectivenessof the rivals brand advertising. Therefore, improv-ing the effectiveness of brand advertising by develop-

ing better advertising copy not only has a short-termeffect on the firms sales, but also a long-run impacton the market share of the firm.

Note that the long-run market shares are unaf-fected by the parameter i, i = 1 2, which capturesthe proportion of the marginal increase in marketsize obtained by firm i. This is because the mar-ket share calculation is driven primarily by the shareof the existing market size and not by the share ofthe marginal increase (except during the introductoryphase when the established market is quite small).The latter is determined by the brand characteristicsand brand advertising.

In the next section, we turn our attention to thefree-riding of generic advertising.

6.1. Free-RidingWe consider the case of a pure monopoly to compareagainst generic-advertising investment under compe-tition. The results are summarized in Proposition 3(proof in the appendix):

Proposition 3. For the differential game given by(10)(11), if both brands are owned by the same firm,then: (a) Total generic advertising is higher than in the

competitive case, and (b) the optimal brand advertising iszero for one of the two brands, namely, the less profitablebrand.

A firms coordinated decision making with regardto the two types of advertising is an example of cat-egory management for different brands in the firms

product line (Zenor 1994). The increase in genericadvertising relative to the competitive case followsfrom the fact that there is no free-riding. Therefore,all the gains from generic advertising accrue to themonopolist.

Next, we use numerical analysis to determine theimpact of free-riding on the profitability of the twofirms. Let us define the stronger firm as the onewith more favorable model parameters, i.e., highereffectiveness of generic and brand advertising, highergross margin, etc., than the weaker firm.

Observations. (a) The stronger firm should tol-

erate free-riding of generic advertising more thanthe weaker firm. (b) Free-riding impacts the strongerfirms profitability only in the short run. The strongerfirm may obtain less profit in the initial periods thanthe weaker firm. However, in a de facto monopoly,the stronger firm is always more profitable. (c) As thedegree of asymmetry increases, the suboptimality ofindustry generic advertising decreases.

For a wide range of parameter values, the weakerfirm initially has higher profit than the stronger firm.This is because the weaker firm benefits from thestronger firms generic-advertising spending, while ittakes some time for the stronger firm to recoup its

investment. However, in the long run, the strongerfirm still wins out, implying that free-riding does notoffer a long-term market share and profit advantageto the weaker firm. This is referred to as the bigpig, little pig game in game theory, wherein the lit-tle pig (weaker firm) profits from the efforts of thebig pig (stronger firm). Commercials by IBM andDe Beers, as well as Campbells Soup advertisementsabout the benefits of soup consumption and that soupcan be used in casseroles and other dinner dishes,illustrate this phenomenon.

When the asymmetry between the firms increases,there is a greater difference between their generic-

advertising contributions. Interestingly, the weakerfirms investment in generic advertising never goes tozero. Therefore, to use Krishnamurthys (2000) termi-nology, there is cheap-riding, but no free-riding.In Krishnamurthys model, free-riding can occur, pos-sibly because future benefits are not considered.

As the degree of asymmetry grows, the subopti-mality of total industry generic advertising decreases.In other words, the free-riding problem is most seri-ous when the firms are identical. In contrast, whenone firm is a de facto monopolist, it spends on


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generic advertising near the optimal industry level.This explains the large generic-advertising expendi-tures of firms such as Campbells Soup and De Beers.

7. ExtensionsWe consider some extensions of the basic model to

determine the robustness of the results. First, weincorporate the idea of a market potential to providean upper bound for the market demand. In anotherextension, we relax the assumption that brand adver-tising is done solely for offensive reasons. We alsoexamine an endogenous specification of i, the alloca-tion coefficient.

7.1. Market PotentialThe sales model in (11) is modified by introducing amarket potential Q as follows:

Sit

=iuitS3it

3iu3itSit+ ik1a1t + k2a2t

Q S1t S2t

Si0 = Si0 (19)

The square root formulation from the original model

is retained, with

Q S1t S2t reflecting the factthat generic advertising informs the fraction of themarket that is uninformed.

The profit-maximization problems of the two firmsare given, as before, by Equation (10), subject to thestate equations in (19). The analysis is in the techni-cal appendix at http://mktsci.pubs.informs.org. The

optimal advertising decisions are given by

ui t =ici

i i

S3it i = 1 2 (20)

ai t =kici

ii + 3ii

Q S1t S2t

i = 1 2 (21)

where the unknowns 1, 2, 1, and 2, are the solu-tions of the simultaneous equations:

rii = mi k2i2ci

ii + 3ii2 23ic3

i

1 12 2

k23i

c3i11 + 2122 + 12 (22a)

rii = k2i2ci

ii + 3ii2 +2i2ci

i i2

k23i

c3i11 + 2122 + 12 (22b)

From the optimal generic advertising decisionin (21), one can see that the generic advertising is sig-nificantly greater when only a small fraction of the

market potential has been realized than when mostof the potential has been realized. This is because,if most of the market is untapped, the two firmshave greater incentive to expand the market, andthese investments decrease over time as the market

becomes saturated. As more of the market poten-

tial is tapped, the two firms decrease their genericadvertising, corresponding to an increase in brandadvertising. In the extreme case, when the market iscompletely saturated, generic advertising is zero, andall resources are invested in brand advertising.

7.2. Other ExtensionsTo model the fact that brand advertising can be usedto retain market share (defensive advertising), assumethat a proportion i of firm is brand advertising isspent purely for offensive reasons and 1 i is spentfor defensive reasons. Moreover, let i, the allocationcoefficient, be endogenized in terms of the sales levelsof the two firms as i

=S

i

/S1 +

S2

, with < 1 cap-turing diminishing returns. In other words, the firmwith greater sales obtains a greater fraction of the gainfrom market expansion.

The profit-maximization problems of the two firmsare given, as before, by Equation (10), subject to

Sit = iuit

i

S3it+1i

Sit3iu3it

3iSit + 1 3iS3it+ Sit

S1t + S2tk1a1t + k2a2t

Si0 = Si0 i = 1 2 (23)The analysis is presented in the technical appendix

at http://mktsci.pubs.informs.org, and only theresults from the simulation are discussed here. First,consider the effect of endogenizing i in terms of thesales of the two firms. From the numerical results, wefind that as increases from 0 to 1 in the symmet-ric case, i.e., when i changes from 0.5 to the mar-ket shares of the two firms, the stronger firm allo-cates a greater chunk of its advertising budget towardgeneric advertising. This is because it gains propor-tionately more from generic advertising because thevalue of i for the stronger firm is always greaterthan 0.5. Consequently, the brand advertising of thestronger firm decreases as increases. The weakerfirms strategies, on the other hand, are not greatlyaffected by this change in because the value of i forthat firm is relatively low, so a greater fraction of itssales comes as a result of its high brand-advertisingoutlay.

Moving to the effect of defensive advertising on theoptimal advertising decisions, the simulation revealsthat as decreases from 1 to 0, i.e., when more ofthe firms brand-advertising budget is expended fordefensive reasons (retaining its customers), both firms


9/13


increase their brand advertising significantly, with thestronger firm investing more because it has a greatershare to defend. Corresponding to this increase inthe brand advertising, the two firms decrease theirgeneric-advertising outlays. In the absence of defen-sive advertising, as in 4, the weaker firm would

invest more in brand advertising because it has moreto gain from its rival.

8. DiscussionWe now discuss some salient features of the modeland analysis, such as the need for integrated decisionmaking with respect to generic and brand advertising,the trade-off between generic and brand advertising,and the impact of free-riding.

Integrated Advertising Decisions. Coordinateddecision making with regard to generic and brandadvertising and price is an example of integrated mar-

keting communications (Naik and Raman 2003). Inparticular, the analysis in the paper suggests that thegeneric-advertising strategy of a firm must be deter-mined together with its brand-advertising strategy toprevent suboptimal advertising.

This conclusion is important given the literaturereview in Table 1, which shows that differential gamemodels of advertising competition have not modeledgeneric advertising as a decision, but have recognizedthe need to model market expansion due to advertis-ing. The assumption has been that there is some sortof leakage category-expansion effect of brand adver-tising. However, it is impossible to say from thesemodels how much a firm should invest in expand-ing the market, versus winning market share due tothe single control. As Krishnamurthy (2000) and oth-ers have discussed, it is an institutional feature ofindustries that firms decide how much to invest inmarket expansion programs. They do not rely on aleakage of their brand-advertising efforts. It is also aninstitutional feature that advertising is done with spe-cific objectives in mind. One can design advertisingcampaigns for whether one wants category expan-sion or market share. Advertising done with the pur-pose of expanding the category is termed generic

advertising. We provide several examples of genericadvertising in 2 of the paper. Having separate deci-sion variables for brand and generic advertising is animportant innovation in this paper. Although thereare static game theory models that have examined thedecisions separately, this paper provides a differentialgame that includes generic advertising as a theoreticalcontribution for the first time.

Budgeting and Allocation of Advertising. Propo-sitions 1 and 2 completely describe the budget andallocation of advertising for the two firms in terms of

the nature of competition and firm and market char-acteristics, thereby answering the research questionsposed in the introduction.

One can get some insights into the allocation ofthe budget (into generic and brand advertising) bysolving different problems that have the same opti-

mal budget and different parameters, without impos-ing a budget constraint. In this approach, we notethe ith firms net present value of the total adver-

tising budget,T

0eritci/2a

2i + u2i dt for a given set

of parameter values. We then change the parametervalues by trial and error in such a manner that theoptimal budget remains unchanged. For example, wecan change 1, the first firms brand-advertising effec-tiveness, and find out the value of another parameter(e.g., k1, the first firms generic advertising effective-ness) that will result in the same NPV of the totaladvertising budget. Although the advertising budgetremains the same, the allocation will be different from

that obtained earlier.Figure 1 illustrates this trade-off between generic

and brand advertising for the two cases (1 = 06,k1 = 06 and 1 = 05, k1 = 093).

As can be seen from the plot, the optimal adver-tising trajectories for the two cases are different. Asthe parameter values change from 1 = 06, k1 = 06 to1 = 05, k1 = 093, i.e., as the firms brand-advertisingeffectiveness decreases and the generic-advertisingeffectiveness increases, the optimal brand advertis-ing of the firm decreases, corresponding to an increasein its generic advertising. Given the same advertising

budget, the decrease of one type of advertising corre-

sponding to an increase in the other type is a measureof the trade-off between the two types of advertising.

Expressing the generic and brand-advertisingexpenditures as the share of an advertising dol-lar offers another measure of trade-off between theinvestments in the two types of advertising. Thepercentage of generic advertising over time can beplotted for different values of the effectiveness of

Figure 1 Optimal Generic and Brand Advertising for the Same

Advertising Budget

15

16

17

18

19

20

21

0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0

Time (years)Optimalgenericandbrandadvert

ising

u1 (1=0.6, k1=0.6)

a1 (1=0.6, k1=0.6)u1 (1=0.5, k1=0.93)

a1 (1=0.5, k1=0.93)


10/13


Figure 2 Proportion of Optimal Generic and Brand Advertising

0.30

0.35

0.40

0.45

0.50

0.4 1.4 1.9 2.4 2.9 3.9 4.4

Time (years)

Costofgenericadvert

ising(%o

ftotal)

k>

k=

0.9 3.4 4.9

the two types of advertising (Figure 2). We use thesame parameter values from the earlier analysis, i.e.,1

=06, k1

=06 and 1

=05, k1

=093. Figure 2 rep-

resents the split of a marginal dollar between genericand brand advertising at any time.

If the effectiveness of generic advertising is greaterthan that of brand advertising k > , the proportionof the budget invested in generic advertising is ini-tially high, but decreases over time. If, on the otherhand, both types of advertising have the same effec-tiveness k = , then we find that the proportion ofthe advertising budget invested in generic advertisingis lower than in the previous case, but it increases ini-tially before decreasing in later periods. Qualitatively,in all cases, generic advertising should be given rel-atively more importance in the initial periods (com-pared to later periods), and brand advertising should

be given relatively more importance in the later peri-ods (compared to initial periods).

Effect of Free-Riding. Analysis shows that totalgeneric advertising is higher if both brands are owned

by the same firm than in the case of competition. Theintuition behind this result is the commonly seen free-riding effect in public goods activities. Each firm mustdivide its gains with competitors; hence, the marginal

benefit from investing in generic advertising is dimin-ished. As a result, industry growth is less than itscooperative-optimal. The implication for the industry

is that it would be better to coordinate the activitiesof the firms. This explains why industry associationsundertake the task of doing collective advertising forthe industry. Examples such as the milk and plasticsindustry were discussed in 2 of the paper.

Under joint ownership, one would expect that therewould be no brand advertising when the brands are

jointly owned and that advertising under competitioncan be considered as a prisoners dilemma. However,we find that in the case of joint ownership, optimal

brand advertising is not zero for both brands, but

only for one brand. The intuition is that one brandis more profitable to the firm than the other, so thefirm would like to drive demand towards that brandthrough brand advertising.

9. Conclusions

To increase the sales of its brand, a firm can usegeneric advertising to expand the entire market or

brand advertising to win market share. The benefits ofgeneric advertising are conferred to all firms regard-less of who contributed. As a result, the generic-advertising strategy of a firm must be integrated withits brand-advertising strategy, necessitating a thor-ough understanding of the relationship between thetwo. However, the market expansion role of advertis-ing has been understudied relative to its share expan-sion role.

This paper explicitly considers market expansionand market share effects. We derive the closed-loop

Nash equilibrium strategies for a dynamic duopolywhere firms make decisions on generic and brandadvertising. Explicit solutions are obtained for sym-metric and asymmetric competitors. The effects of themodel parameters on the optimal advertising poli-cies and profits are found. A general conclusion isthat generic and brand advertising must be properlycoordinated, and neglecting one of the two will leadto suboptimal allocation of the advertising budget.We also examined free-riding in generic advertisingand its effect on the long-run profitability of the twofirms, and find that although there is free-riding, thestronger firm is better off tolerating this free-riding

because this does not affect its long-term profitabilitygreatly.

Three extensions to the basic model were exam-ined. The first deals with the inclusion of a marketpotential, the second with generalizing the allocationof gains from generic advertising, and the third with

brand advertising being used for defensive reasons.Analyses of these extensions provide evidence of therobustness of the basic model.

Some limitations of the current study should also beacknowledged. First, we do not micromodel the con-sumer purchase decision or disaggregate customersinto separate segments, such as a loyal segment,or consider how brand preferences may be perma-nently altered through trial due to learning (Villas-Boas 2004), creating hysteresis effects. Second, unlikein Liu et al. (2004), product quality is exogenous and isnot affected by competition. Finally, threshold effectsin advertising response have been posited on and off(e.g., Vakratsas et al. 2004), but are not considered inthe present model, which assumes a concave response.

Future research should consider including theseeffects and other alternative or more general speci-fications, including models with interaction between


11/13


generic and brand advertising, and the use of con-tracts to achieve the cooperative-optimal genericadvertising. One may also extend the model to studyadvertising competition in an oligopoly (Erickson1995, Teng and Thompson 1984, Villas-Boas 1993).Finally, the comparative statics results can be tested

empirically.AcknowledgmentsThis paper is based on Chapter 2 of Anand Krishnamoor-thys unpublished 2004 Ph.D. dissertation at The Universityof Texas at Dallas. Authors are listed alphabetically. Theauthors thank Ram Rao; B. P. S. Murthi; Ernan Haruvy;Ronald Michaels; Ramarao Desiraju; Rong Zhang; seminarparticipants at the University of Texas at Dallas, the Univer-sity of California, Berkeley; and the University of California,Riverside; the editor; the area editor; and three anonymousreviewers for their valuable suggestions. Any remainingerrors are our own.

AppendixProof of Proposition 1. The Hamilton-Jacobi-Bellman

(HJB) equation for firm i, i = 1 2 is given by

riVi = maxui ai pi

pi1 bipi + dip3iSi ci2

a2i + u2i

+ ViSi

iui

S3i 3iu3i

Si

+ ik1a1 + k2a2

+ ViS3i

3iu3i

Si iui

S3i

+ 3ik1a1 + k2a2

(A1)

From this, the first-order conditions for ui and ai yield,respectively,

ui=

i

ci Vi

Si

Vi

S3iS3i

ai =kici

i

ViSi

+ 3iVi

S3i

(A2)

The first-order conditions for p1 and p2 yield

1 2b1p1 + d1p2 = 0 1 + d2p1 2b2p2 = 0 (A3)Solving the two simultaneous equations in (A3), we obtainthe optimal price of firm i to be

pi =di + 2b3i

4b1b2 d1d2 (A4)

We can, therefore, simplify the price terms in (A1) so that

pi 1

bipi

+dip

3

i=

bi di + 2b3i4b1b2 d1d2

2

mi (A5)

Henceforth, we will use m1 b1d1 + 2b2/4b1b2 d1d22and m2 b2d2 + 2b1/4b1b2 d1d22 to denote the equilib-rium margins of the two firms.

Substituting (A2) and (A5) into (A1) yields

riVi = miSi +k2i2ci

i

ViSi

+3iVi

S3i

2+

2i

2ci

ViSi

ViS3i

2S3i

23i

c3i

V1S1

V1S2

V2S2

V2S1

Si

+ k23i

c3i

1

V1S1

+ 2V1S2

1

V2S1

+ 2V2S2

(A6)

The linear value function Vi = i +iSi +iS3i satisfies (A6).The optimal brand and generic-advertising decisions in (A2)may now be rewritten as

ui =ici

i i

S3i ai =

kici

ii + 3ii (A7)

Substituting Vi = i +iSi +iS3i into (A6) and simplifying,we have

rii +riiSi +riiS3i=miSi +

k2i2ci

ii +3ii22i2ci

i i2S3i

23i

c3i1 12 2Si

+k23i

c3i11 +2122 +12 (A8)

Equating the coefficients of Si, S3i, and the constant inEquation (A8) results in the following simultaneous equa-tions to solve for 1, 2, 1, 2, 1, and 2:

rii =k2i

2ci ii + 3ii2

+k23

i

c3i 11 + 2122 + 12i = 1 2 (A9)

rii = mi 23ic3i

1 12 2 i = 1 2 (A10)

rii =2i2ci

i i2 i = 1 2 (A11)

Let y = 1 1 and z = 2 2. Solving for y using Math-ematica v4.0 yields

y = 241

+ 12

1 +5 +6

+21 5 6 +7

4

1+

5+

6 (A12)where 1 = 3c241, 2 = 4c1c221r1 + r2, 3 = 4c1c1c22r1r2 r21 + 2c1m222 c2m121, 4 = 8c21 c2m1r1 r2, 5 = 4c21 c2m21,1 = 22/421 23/31 2 = 23 324 1215 3 =233 9234 + 27124 27522 + 72135 4 = 3 +

23 4321/3, 5 = 21/32/314 6 = 4/321/31, and7 = 423/21 32/31 84/1.

Knowing y, we can compute the following:

1 =21

2c1r1y2 1 = y +

212c1r1

y2

z = c222y

m1

212c1

y2 r1y

2 =22

2c2r2z2 (A13)

2 =2

22c2r2

z2 + zOne can see from (A13) that i > 0, i > 0, and i > i,

resulting in positive values for the controls. Proof of Corollary 1. Solving the following simulta-

neous equations for symmetric firms:

r = 3k2

8c + 2 (B1)

r = m 2

c 2 (B2)

r = 2

2c 2 (B3)


12/13


yields the following solution for :

= 3m2 + cr2

cr2cr2 + 6m2

9r2 (B4)

To find out which of the two roots to choose, we usethe test that = 0 when m = 0. This is because the valuefunction should be identically equal to zero when the gross

margin is zero because the firm makes zero profit in thiscase. Checking with (B4), it is easy to see that

= 3m2 + cr2

cr2cr2 + 6m2

9r2(B5)

is the only root that satisfies this condition.Knowing , we can compute and using = m/r2

and (B1), respectively, to be

= 3m2 2cr2 + 2

cr2cr2 + 6m2

9r2 (B6)

= k2c2r4 3cmr22 +18m24 +6m2 cr2

cr2cr2 +6m2

108cr34

(B7)

An examination of Equations (B6)(B7) reveals that > 0, > 0, > 0, and > , so the controls and the value func-tions are positive.

Proof of Proposition 2. To derive the optimal salespaths, we substitute the results from Proposition 1 into thetwo state equations to obtain the following system of dif-ferential equations:

S1 =21c1

1 1S2 22c2

2 2S1

+ 1

k21c1

11 + 21 +k22c2

12 + 22

S10 = S10

S2 =22c2

2 2S1 21c1

1 1S2

+ 2

k21c1

11 + 21 + k22c212 + 22

S20 = S20

(C1)For expositional ease, denote

1 =21c1

1 1 2 =22c2

2 2

3 =k21c1

11 + 21 +k22c2

12 + 22(C2)

The differential equations can now be rewritten as

S1 = 1S2 2S1 + 13 S10 = S10S2 = 2S1 1S2 + 23 S20 = S20

(C3)

Note from (C3) that there is no long-run equilibrium in

sales; i.e., S1 and S2 need not go to zero. The long-run equi-librium market shares resulting from the equations in (C3)are given by

x1 = limt

S1t

S1t + S2t x2 = lim

tS2t

S1t + S2t

(C4)

Simplifying, we havex1 =

21/c11 121/c11 1 + 22/c22 2

x2 =22/c22 2

21/c11 1 + 22/c22 2

(C5)

Proof of Proposition 3. If the firm owns both brands,its decision problem is

maxu1ta1tp1tu2ta2tp2t

V

=

0ert

p1tS1t1b1p1t +d1p2t

+p

2tS

2t1

+d

2p

1t

b

2p

2t

c12

a1t2 +u1t2

c22

a2t2 +u2t2

dt (D1)

s.t. S1t = 1u1t

S2t 2u2t

S1t

+1k1a1t +k2a2t S10=S10(D2)

S2t = 2u2t

S1t 1u1t

S2t

+2k1a1t +k2a2t S20=S20where the notation is as described earlier.

The HJB equation is

rV= maxu1a 1p 1u 2a 2p 2

p1S11b1p1 +d1p2+p2S21+d2p1 b2p2 c1

2u21 +a21

c22

u22 +a22

+ VS1

1u1

S2 2u2

S1

+1k1a1 +k2a2+ V

S22u2

S1 1u1

S2

+2k1a1 +k2a2(D3)

The first-order conditions for the optimal advertisingdecisions yield

u1 =1c1

V

S1 V

S2

S2 a

1 =

k1c1

1

V

S1+2

V

S2

(D4)

u2 =2c

2

V

S2

VS

1S1 a2 =

k2c

21

V

S1

+2V

S2 (D5)

As before, substituting the solutions from (D4)(D5) into(D3) suggests that a linear value function V = m + mS1 +mS2 will solve the resulting partial differential equation.The optimal advertising decisions can now be rewritten as

u1 = max

01c1

mm

S2

a1 =

k1c1

1m +2m (D6)

u2 = max

02c2

mm

S1

a2 =

k2c2

1m +2m (D7)

Note from (D6)(D7) that either u1 or u2 is always posi-

tive. If m > m, u1 > 0 and u

2 = 0 because Brand 1 is more

profitable. If m < m, the opposite is true. Therefore, in

a monopoly, total brand-advertising need not necessarilybe zero.The monopolist can choose the optimal advertising deci-

sions to ensure that the value function in the monopolycase is never less than that in the competitive one. In otherwords, V V1 + V2, where V1 and V2 are the profits in thecompetitive case. We therefore have

m + mS1 + mS2 1 + 1S1 + 1S2 + 2 + 2S1 + 2S2(D8)

m 1 + 2 + m 1 + 2S1 + m 2 + 1S2 0(D9)


13/13


Because Equation (D9) holds S1 0, S2 0, it must be thecase that

m 1 +2 m 1 +2 m 2 +1 (D10)where each of the above coefficients is nonnegative.

From Equation (A7), the total generic advertising in thecompetitive case is

k1c1

11 + 21 + k2c212 + 22 (D11)

while that in the monopoly case is, from Equations(D6)(D7),

k1c1

1m + 2m +k2c2

1m + 2m (D12)

Subtracting Equation (D11) from (D12), the differencebetween the total generic advertising in the monopoly caseand that in the competitive case is

k1c1

1m 1+2m 1+k2c2

1m 2+2m 2(D13)

which, from Equation (D13), is greater than zero. Therefore,

the monopolists total generic advertising is greater thanthat under competition.

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