Marketing Letters 4:4, (1993): 285-295 © 1993 Kluwer Academic PuNishers. Manufactured in the Netherlands.

Offensive and Defensive Marketing: Closed-Loop Duopoly Strategies GARY M. ERICKSON

Departrnent of Marketing and International Business DJ-IO University of Washington Seattle WA 98195 [January 1993 Revised March 1993] Key words: Offensive and Defensive Marketing, Lanchester Mode~, Closed-Loop Strategies.

Offensive and Defensive Marketing: Closed-Loop Duopoly Strategies A modified Lanchester garne is used to develop closed-loop strategies for offensive and defensive marketing expenditures of duopolistic competitors in a market share rivalry. Analysis of the model reveals that • well-defined closed-loop strategies can be developed that show directly the inf!uence of market share on offensive and defensive marketing; • steady state is marked by balance between offensive and defensive marketing expenditures; • defensive marketing is more critical than offensive marketing due to greater risk of loss under deviation from closed-loop strategies. The last resuit would appear to have particularly important implications for both practice and research. M a r k e t i n g can be used both offensively, to attract c u s t o m e r s , and defensively, to hold on to the f i r m ' s present c u s t o m e r s . To the extent that this distinction has been recognized in the literature, research interest has been directed p r i m a r i l y t o w a r d the offensive use of marketing, e.g. to e n c o u r a g e brand switching or to e n c o u r a g e sales growth, although there have been a few research efforts ( H a u s e r and Shugan 1983, H a u s e r and G a s k i n 1984, Fornell and Wernerfelt 1987, 1988) showing a specific interest in defensive m a r k e t i n g strategy. Also, defensive marketing has been revealed as being of current interest to m a r k e t i n g p r a c t i t i o n e r s , as is e x h i b i t e d in recent articles in the p o p u l a r press (e.g., U.S. N e w s & World Report 1992, Business Week 1992). M a r k e t s are d y n a m i c a l l y m a r k e d by both o p p o r t u n i t i e s to a t t r a c t new cust o m e r s and the threats from c o m p e t i t i o n trying to lure the f i r m ' s c u s t o m e r s away. To deal with such o p p o r t u n i t i e s and threats, the firm needs to have the ability to engage in both offensive and defensive marketing, know which is more critical in a d y n a m i c sense, and be able to strike an a p p r o p r i a t e balance b e t w e e n offense and defense. The literature is e s p e c i a l l y lacking in insight in this area. To the a u t h o r ' s k n o w l e d g e , only Fornell and Wernerfelt (1987), with a model that inter-

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GARY M. ERICKSON

prets customer complaint management as defensive marketing and advertising as offensive marketing, deal in a substantive way with the issue of resource allocation between offense and defense, although Gensch (1984) reports an application in which an allocation decision was made after a firm identified customers as being "our loyal," "competitive," "switchable," or "competitor loyal." The present study explores the nature of the balance between offensive and defensive marketing in a dynamic setting of duopolistic competition for market share. Offensive and defensive marketing are viewed in general terms as expenditure items, and closed-loop equilibrium strategies, that depend on changing levels of market share, are developed from a duopolistic differential game model, which is based on an extension of the Lanchester model to include both offensive and defensive marketing expenditures. Well-defined closed-loop strategies for offensive and defensive marketing are developed, and dynamic and steady state implications for balance between offensive and defensive marketing are analyzed. In addition, the relative importance of offensive versus defensive marketing is investigated.

1. Model

The Lanchester model (Kimball 1957, Little 1979) has become a useful foundation for studying duopolistic marketing competition (Erickson 1991, 1992, Chintagunta and Vilcassim 1992). The model is, however, basically an offensive one, in which a competitor's marketing (advertising in applications to date) acts to take sales and market share from its rival (Little 1979). As such, the Lanchester model as developed to date deals with only one aspect of dynamic marketing strategy. The model can be modified, however, to allow defensive as well as offensive marketing. Define Fi = firm i's offensive marketing expenditure rate, i =- 1, 2 Ei = firm i's defensive marketing expenditure rate, i = 1, 2. An offensive marketing expenditure would be any such expenditure designed to attract a rival's customers, e.g., a campaign offering an incentive to the rival's customers to switch to the firm's brand. A defensive marketing expenditure would be that designed to help retain the firm's existing customers, e.g., providing incentives such as premiums to repeat customers. Also define M -- firm l's market share (firm 2's share being 1 - M) ~ and consider the following modification of the Lanchester model: M -

dM dr

I~'L - oL2~M - og~_2(l - M)

( 1)

OFFENSIVE

AND DEFENSIVE

287

MARKETING

where t indexes time. 2 The first term on the right hand side of (1) defines the effect of the competitors' marketing efforts acting on firm 2's market share. The offensive marketing expenditures of firm 1 act to attract a portion of 2's share, but these offensive expenditures are moderated by firm 2's defensive marketing expenditures; the riet effect on firm 2's share is the ratio of l's offensive expenditure to 2's defensive expenditure, multiplied by a constant el. Likewise, the second term on the right hand side of (1) defines the net effect of firm 2's offensive marketing, countered by firm l's defensive marketing, on firm l's market share? The model assumes (as does the basic Lanchester model) that all o f a firm's customers are vulnerable to the offensive marketing activities of the firm's rival - no hardcore loyal segment exists that stay with the firm no marter what the firm or its rival does - and the firm's entire customer base needs to be defended. Also, the model makes particular assumptions regarding functional relationships, especially regarding returns to scale. The primary value of the model is to allow offensive marketing activities to be tempered by defensive activities. As such, it can be useful for the purpose at hand, to study the allocation problem between offensive and defensive marketing in a competitive and dynamic struggle for market share. The offense-defense Lanchester model (1) becomes the foundation for a differential garne, in which the competitors have the following profit objectives: i max f o

e

where M 1 = M, share.

r'(g iMi -- Fi - E)dt M 2 =

(i = 1, 2)

(2)

1 - M, and the gi are gross profit rates in terms of market

2. Analysis Competitors' marketing strategies based on the differential garne in (1)-(2) are developed via closed-loop Nash equilibria a la Case (1979) and Kamien and Schwartz (1991). 4 Basically, closed-loop strategies allow marketing expenditures to change with changing market conditions; a firm can adjust its spending on, say, defensive marketing depending on the level of its market share. Such ongoing flexibility in marketing strategies would seem to be especially important in the present context; the allocation between offensive and defensive marketing at a point in time would surely be influenced by the firm's current market share and that of its rival. In addition, closed-loop strategies (as developed herein) are subgame perfect, in that they represent optimal strategies for the competitors for each level of the market share state variable to which the garne may evolve. Viewing the problem in a garne theoretic manner allows the development and analysis of optimal offensive and defensive marketing strategies, strategies that recognize the desire of a firm's rival also to maximize its profit. The competitive setting is a dynamic one, in which market share evolves according to the relation-

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GARY M. ERICKSON

ship in (1) (akin to a Markov process in which the transition probabilities depend on the offensive and defensive marketing expenditures o f the competitors). The competing firms take advantage of the dynamic demand relationship, it is assumed, to develop closed-loop Nash equilibrium strategies, strategies that are optimal given each other's strategies and that adjust to the changing value of market share. To derive the closed-loop offensive and defensive marketing strategies, first define the Hamiltonians:

Hi = g,M, -

Fs -

F, to2

E, + )t,(oq-~-[1 -

F2 M] - e~2-~-M). (i = 1,2) LI

(3)

Hamiltonians are objective functions that modify current profits by adding a term that accounts for the effect on future profits of change in market share due to current spending on offensive and defensive marketing. Next, determine Pi, l);i as functions of M and the Xi that form a Nash equilibrium for the auxiliary game i max Hi.

(i = I, 2)

(4)

Closed-loop strategies are derived through the Hamilton-Jacobi-Bellman equations?

g,M - P, - ~, + V, ( ~ @ 1

- M] - ~ 2 ~ M ) = rV,

,

F,

(5)

P,

g2(l - M) - /%2 - /~2 + V2 ((~,~[1 - M] - ~ 2 ~ M ) = rV2

with the substitution Vi' = ki, i = 1, 2. The Vi = Vi(t) are called value functions. Well-defined offensive and defensive marketing strategies can be derived if it assumed that the discount rate r = 0. 6 Further, first-order conditions for the auxiliary game (4), 7 OH i OF,

OH i -

OE,

-

0

(i

=

1,2)

(6)

lead to the following conditions:

Vl' --

oq(l

(7) -

E~ V1 r

--

oL2F2M

M)

OFFENSIVE AND DEFENSIVE MARKETING

289

E1

V2 t m

%M E~ v~, =

~1F1(1 - M)

Substitution into (5), with r = 0, yields a system of equations which involves only the F» E» and M, and does not involve the value functions. Sotving the system for the F~ and E~ as functions of M yields the following closed-loop strategies for offensive and defensive marketing for the two competitors i = 1, 2 O~

Fi_

2

3 ig3

i(1_

Mi)

(8)

2%gi Ei-

giMi 2

recalling that M~ = M and M2 = 1 - M. The closed-loop strategies (8) explicitly and appropriately characterize how the use of offensive and defensive marketing is coordinated with market share levels.

A competitor's offensive marketing expenditure decreases monotonically with its market share, and its defensive marketing increases monotonically with market share. That is, if market share is low, the competitor uses offensive marketing to increase its market share, and less offensive marketing is used as share becomes larger. As share increases, more defensive marketing is used to defend that share. H o w the closed-loop strategies proceed dynamically is indicated by the numeri c a l e x a m p l e s h o w n i n F i g u r e s 1 and 2, f o r w h i c h Πi = .1 a n d g i = 1, i = 1,2. Figure 1 shows offensive and defensive marketing expenditures for a competitor starting with a low market share and building share through offensive marketing, while defending what share it has with defensive marketing, s Figure 2 shows the progression of market share under equilibrium strategies. Note that when the steady state market share is achieved, the competitor's offensive and defensive marketing expenditures equal each other. Equality of offensive and defensive marketing expenditures in steady state is not limited to the example. To see this, first derive market share at steady state. From (1) and (8), M = 0--->

M 1 - 34

-

~IFjEI

-

~2F2E2

~2g~ «lg~

(9)

and therefore that M

-

~2g~

«lg~ + ~2g~"

(10)

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GARY M. ERICKSON

0.5

""

0.4

X

0

Offensive

= "4

--

=

-=.g.T.T.:

0.1 00 0

10

I

I

20

30

Period Figure I. Offensive and defensive marketing (example). 1.0 0.9 0.8 t,ù

0.7

rJ3

0.6 0.5

¢3

0.4 0.3 0.2 0.1 0.0 0

10

20

30

Period Figure 2. Market share (example). S u b s t i t u t i n g i n t o (8) y i e l d s

«3 ig~-igi

Fi = Ei = 2(eqg~ + o~2g~)"

(i = 1, 2)

(l l)

T h a t is, in t h e g e n e r a l c a s e , steady state is marked by a firm's offensive and defensive marketing being in balance. It is a l s o t h e c a s e t h a t this b a l a n c e b e t w e e n

OFFENSIVE AND DEFENSIVE MARKETING

291

offensive and defensive marketing does not depend on market share. A firm with a higher market share will spend more on both offense and defense. Also, expenditures are not equal across competing firms. Rather, FI + /7-]1

«292

F2 + Es

«lgl

(12)

in steady state.

3. Relative importance of offensive and defensive marketing We examine how critical is each of the two elements of marketing strategy by observing the long-run profit consequences of not spending at optimal levels. For comparative purposes, it can be shown that steady stare profit is zero if the firm follows the closed-loop equilibrium strategy. Is the firm hurt by over- or underspending on either offensive or defensive marketing? Say firm I consistently spends at a rate o f p F f on offensive marketing, where p can be either greater than or less than one, while spending at the equilibrium level E~ on defense. Also assume that firm 2 spends at its equilibrium level on both offensive and defensive marketing. Market share at steady state is then different from that in (I0) and is derived by substituting pF~ for F~ in (9): M = caIFIEE _ P~2g~ 1 - M %F2E 2 «,g~

(]3)

from which M =

po~2g~oqg~ + p%g~"

(14)

If firm 1 underspends, its steady state market share is smaller than that under equilibrium conditions; if firm 1 overspends, steady state market share is lärger. Steady state profit, whether firm 1 is overspending or underspending, is

Firm 1 does not lose, at least in terms of long-run profit, by varying from its equilibrium offensive strategy. 9 On the other hand, if firm I deviates from its equilibrium defensive strategy, by consistently spending at a rate of pE~ while following its equilibrium offen-

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GARY M. ERICKSON

sive strategy F~, steady state market share is the same as in (14), hut steady stare profit is

Ill

eqg~ + po~2g~ P

oL2g~gl

(16)

2 (p-

1) 2

2(c~,g~ + po~2g~) The firm stands to suffer long run losses if it varies from its closed-loop equilibrium strategy for defensive marketing. The implication is that it is more critical for the firm to make sure its defensive marketing strategy is correct than to worry about its offensive marketing strategy. The explanation for this is as follows. If the firm underspends on either offense or defense, its steady stare market share is smaller than under the equilibrium strategy. Furthermore, at small market shares, the firm would under the equilibrium strategy spend more on offense than on defense. So, underspending on defense lowers marketing expenditures less than underspending on offense in the same proportion, although steady state market share is the same in each circumstance. Conversely, overspending by the same proportion on either offense or defense leads to the same steady state market share, higher than that under equilibrium spending. Also, at high market share, equilibrium spending on defense would be greater than that on offense, meaning that overspending on defense means a larger increase in marketing expensive than overspending on offense. In both directions, then, the profit consequence is more severe for deviations in defensive strategy.

4. Discussion

The above analysis indicates that a firm stands to incur long-run losses if it deviates from its closed-loop equilibrium strategy for defensive marketing, although not for offensive marketing. It is more dangerous to be wrong about defensive strategy, and, as a consequence, defensive marketing could be viewed as being more critical than offensive marketing. The specific form of the model analyzëd no doubt has an effect on the derived resülts. The conclusion regarding the relative criticality of defensive marketing versus offensive marketing appears to have some robustness, however. For example, numerical investigation of an alternative, square-root, form of the model

M = C~l

(1 - M) - a2

M

(17)

O F F E N S I V E AND D E F E N S I V E MARKETING

293

and investigating a broad set of closed-loop strategies that can yield non-zero steady state profits, consistently shows greater sensitivity of steady state profit to deviations from equilibrium defensive strategies than to deviation from equilibrium offensive strategies. For instance, with symmetric competitors and equilibrium strategies that yield a steady stare profit for each firm of. l, a firm spending at I/2 the equilibrium offensive marketing rate achieves a steady stare profit of .0886, versus a steady state profit of .0690 when spending at 1/2 the equilibrium defense rate. (Note that in general steady state profit is not completely insensitive to variation in the offensive spending rate from the equilibrium strategy. However, steady state profit is less sensitive to offensive deviations from equilibrium than to deviations in defensive spending.) Also, regarding the nature of the equilibrium strategies under the alternative model (17), equality of offensive and defensive expenditures at steady stare holds. However, equilibrium strategies do not in general exhibit monotonicity in market share. We should not interpret the relative sensitivity of profit to defensive marketing as implying that we should focus entirely on defensive marketing and ignore offensive marketing. Both defense and offense are important; each has a definite role to play in marketing strategy. Offensive marketing is needed to expand market share, and defensive marketing is needed to maintain market share. Indeed, as the analysis above shows, a firm should aim for a steady-state balance between the two.

5. Conclusions The present paper offers an analysis of dynamic market share rivalry that includes both offensive and defensive marketing strategies. The modeling and analysis involve restrictions and limitations, to be sure: a specific, albeit expanded, form of the Lanchester model, a zero discount rate, and a simple characterization of offensive and defensive marketing as overall expenditure levels. Such simplifications, however, allow the following revealing conclusions: • well-specified closed-loop strategies are defined that show directly how offensive and defensive marketing expenditures vary with market share levels • marketing expenditures at steady state show an equal balance between offensive and defensive marketing • defensive marketing deviations from equilibrium strategies have a greater bottom-line impact than offensive marketing deviations The last conclusion, in particular, regarding the critical nature of defensive marketing, would appear to have especially important implications for marketing practice as weil as research. Both offensive and defensive marketing are irnportant in the broad sense of

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GARY M. ERICKSON

marketing strategy. Future efforts in research and practice would benefit from this realization. Much work has been done on offensive aspects of marketing, and study of the defensive side has begun. The marketing field would benefit from increased efforts to unify the two.

Notes I. Total market sales are assumed fixed. A firm achieves growth by taking market share fiom its rival. 2. It should be noted that the model (1) may not be defined ifE~ or E2 has a zero value. This is not a problem if the competitors follow the closed-loop Nash equilibrium strategies derived in the F~ F, following section, however. Under those strategies, it can be shown that the ratios Ë2' Ë~' are /

always weil defined. Other model forms could potentially be analyzed, such as a Luce-type model M

3. 4.

5.

6.

7. 8.

9.

F~ (1 - M) «z ~ F~ M. Such a model, however, presents mathemati°qFi + E~-'~ cal difficulties. Note that «~ and «2 allow for brand specific effects. Case (1979) refers to the equilibrium strategies as petfect equilibria, and Kamien and Schwartz (1991) use the more widely accepted term feedba«k for the strategies they discuss, which, for infinite horizon autonomous problems like the one in the present study, essentially coincide with those of Case (1979). The more generic term closed-loop is adopted here (although perhaps a more correct term would be autonomousfeedback). A wider set of strategies can be obtained by adding an arbitrary constant to the right-hand side of each equation in (5) (Case 1979). Resulting strategies from doing so in the present situation, however, exhibit undesirable properties, calling for negative expenditure values for certain regions of M. As such, such strategies are not further considered. Such strategies can be viewed as good approximations for small values of r (Case 1979). Note that with a small value of r, long-term profit maximization in a dynamic setting becomes especially important, since with a small discount rate future profits are not discounted to the extent they would be with a large value of r. Second-order conditions assure a maximum. The expenditure leve[s are derived without consideration of a budget limit. The impact of such a budget limit would have the effect, if any, of slowing the progress of market share toward its steady state value. Also, the initial level of market share, more specifically the distance between the initial share and the steady stare level, affects market share progress. That the profit loss is exactly zero in this situation is due to the specific form of the model (1), and is related to conditions needed to obtain interior solutions.

References Business Week. (1992). "Forget the Green Stamps - Give Me a Ticket to Miami." February 24, 70-71. Case, James H. (1979). E«onomi«s and the Competitive Pro«ess. New York:New York University Press. Chintagunta, Pradeep, and Naufel Vilcassim. (1992). "An Empirical lnvestigation of Advertising Strategies in a Dynamic Duopoly," Manaßernent Science 38, 1230-1244.

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Erickson, Gary M. (1991). Dynamic Models of AdvertisinL, Competition. Boston: K[uwer Academic Publishers. Erickson, Gary M. (1992). "Empirical AnaIysis of Closed-Loop Duopoly Advertising Strategies,'" Manaßeme,Tt S«ience 38, 1732-1749. Forne[l, Claes, and Birger Wernerfelt. (1987). "Defensive Marketing Strategy by Customer Complaint Management: A Theoretical Analysis," Journal of Marketing Resear«h 24,337-346. Fornell, Claes, and Birger Wernerfelt. (1988). "A Model for Customer Complaint Management," Marketing S«ien«e 7, 287-298. Gensch, Dennis H. (1984). "Targeting the Switchable lndustrial Customer2' Marketing S«ien«e 3, 41-54. Hauser, John R., and Steven P. Gaskin. (1984). "Application of The Defender Consumer Mode1," Marketinü Scien«e 3,327-351. Hauser, John R., and Steven M. Shugan. (1983). "Defensive Marketing Strategies," Marketin~ Science 2, 319-360. Kamien, Morton I., and Nancy L. Schwartz. (1991). Dynamit Optimization: The Cal«uius oj' Variations and Optimal Control in Economics and Manaj~emeßt (Second EditionL Amsterdam: North-Holland. Kimball, George E. (1957). "Some lndustrial Applications of Military Operations Research Methods," Operations Research 5,201-204. Little, John D. C. (1979). "Aggregate Advertising Models: The State of the Art," Operations Resear«h 27, 629-667. U.S. News & W«»'ld Report. (1992). "Buying Shopper Loyalty," April 27, 77.