Strategic segmentation of a market

Transcription

1 Internatonal Journal of Industral Organzaton 18 (000) locate/ econbase Strategc segmentaton of a maret Santanu Roy* Department of Economcs, Florda Internatonal Unversty, Unversty Par, Mam, FL 33199, USA Receved 1 January 1998; accepted 31 October 1998 Abstract When competng frms target nformaton towards specfc consumers through drect maretng actvtes, complete segmentaton of marets can result. We analyze a two-stage duopoly where, pror to prce competton, each frm targets nformaton to specfc consumers and only consumers nformed by a frm can buy from t. Ths has the effect of endogenously determnng maret segments n a model of sales. In equlbrum, pure local monopoly emerges; frms target and sell to mutually exclusve maret segments. When the cost of maretng approaches zero, maret shares reflect relatve producton effcency (equal shares when frms are symmetrc); ths may not be the case when maretng cost s hgh. 000 Elsever Scence B.V. All rghts reserved. Keywords: Segmentaton; Fragmentaton; Advertsng; Drect maretng; Olgopoly JEL classfcaton: L13; D43; O17; D63 1. Introducton The last two decades have been characterzed by a rapd ncrease n drect maretng actvtes of frms. These nclude a wde range of promotonal and sellng actvtes where frms dentfy, target and drectly contact potental * Tel.: ; fax: E-mal address: [email protected] (S. Roy) / 00/ $ see front matter 000 Elsever Scence B.V. All rghts reserved. PII: S (98)0005-6

2 180 S. Roy / Int. J. Ind. Organ. 18 (000) consumers through telephone, drect mal, sales representatves, personalzed newspaper nserts etc. The New Yor based Drect Maretng Assocaton estmates that n 1996, 58% of all maretng expendture n the U.S. was for some form of drect maretng (The Economst, 1997). Busnesses have developed extensve databases contanng vast amount of nformaton about actual and potental customers leadng to a rapd ncrease n the ablty of frms to target potental customers wth extreme precson. When competng frms decde whch specfc consumer lsts they wsh to target, mportant strategc consderatons arse. In partcular, the extent of overlap n the sectons of consumers targeted by frms wth smlar promotons and product nformaton determnes the extent of maret segmentaton and monopoly power. Ths paper examnes the extent and pattern of maret segmentaton that can result from strategc drect maretng and targeted promotonal actvtes by competng frms. We analyze a smple model of homogenous good duopoly where, ex ante, consumers are unaware of the exstence of dfferent frms operatng n the maret. Frms smultaneously ndulge n promotonal drect maretng whch s targeted towards specfc consumers nformng them about ther exstence. Only consumers who are targeted by the drect maretng strategy of a specfc frm become aware 1 of t and may choose to buy from ths frm. In the next stage, frms engage n prce competton. Frms may, f they so wsh, completely segment the maret by targetng dsjont sets of customers leadng to pure local monopoly. At the other extreme, target sets of frms may be dentcal n whch case we have the classcal Bertrand outcome. We analyze the sub-game perfect equlbra of ths two stage game. Begnnng wth the model of sales by Varan (1980), there has developed a sgnfcant lterature dealng wth competton n marets whch are exogenously segmented. Narasmhan (1988) and Denecere et al. (199) analyze the outcomes of prce competton n a homogenous good symmetrc duopoly where some consumers are loyal to a partcular frm; equlbrum n ths maret necessarly nvolves mxed strateges and the frm wth the larger captve segment s less aggressve n prce competton. In our paper, the sze of the captve segments of competng frms s endogenous. Followng the classc artcle by Butters (1977), there have been a number of studes whch analyze strategc advertsng n models where consumers can buy only from frms from whch they receve nformatve advertsement. One secton of ths lterature models advertsng as conveyng nformaton about the exstence 3 as well as the prce charged by a frm. Another secton of ths lterature (closer to 1 Our analyss also extends to stuatons n whch a consumer can choose to buy the product of a frm only f the latter provdes some consumer-specfc nfrastructural support (e.g. cable lne connecton). See also, Shlony (1977), Baye and de Vres (199) and Fshman (1994). 3 See, among others, Grossman and Shapro (1984), Stegeman (1991), Boyer and Moreaux (1993), Stahl (1994) and Bester and Petras (1995).

3 S. Roy / Int. J. Ind. Organ. 18 (000) our paper) deals wth non-prce promotonal actvtes of frms and analyzes outcomes of competton where frms decde on levels of consumer awareness pror to prce competton. Thus, n a two stage sequental move ncumbent-entrant game, Fudenberg and Trole (1984) show that entry deterrence may be assocated wth strategc under-nvestment n awareness creaton; a hgh level of awareness for the ncumbent s product mples a large captve maret for ts product whch reduces ts ncentve to respond aggressvely to ts compettor. Smlar strategc under-nvestment results are establshed by Ireland (1993) and Fershtman and Muller (1993) n a two stage (smultaneous move) olgopoly. The man dfference between our paper and ths class of mult-stage games s that we endow frms wth 4 the ablty to precsely target the dssemnated nformaton to specfc consumers. We show that, n equlbrum, the entre maret s dvded nto mutually exclusve captve segments where each frm acts as a pure local monopolst. Thus, n comparson wth models of non-targeted advertsng, the possblty of targeted maretng ncreases the extent of segmentaton and monopoly power. We characterze the allocatons of maret shares whch are sustanable n equlbrum. There s a contnuum of equlbrum allocatons. The set of such allocatons contracts when the margnal cost of nformng consumers s reduced; when ths cost approaches zero, the set of equlbrum allocatons contracts to a unque outcome, vz. one n whch each frm s a local monopolst over exactly half the maret. The ntuton s as follows: f nformng consumers s relatvely costless and a frm does not leave a reasonable share of the maret for ts rval, then the latter fnds t optmal to encroach on the frm s target group of consumers and compete aggressvely n prces thus reducng ts expected proft. On the other hand, f the cost of nformng addtonal consumers s large, the margnal cost of encroachng on the terrtory covered by a rval frm becomes hgh and therefore, a frm mght choose to accommodate an unequal dvson of the maret. The result can be generalzed to the case of asymmetrc duopoly. Secton sets up the model formally. Secton 3 outlnes the equlbrum proft from prce competton n the second stage. Secton 4 analyses the equlbra of the reduced form game n the frst stage and characterzes the set of subgame perfect outcomes. Secton 5 provdes an outlne of how the results generalze when we allow for frms wth asymmetrc producton costs.. The model Consder the maret for a homogenous good wth two frms we shall refer to them as frms 1 and, respectvely. We use the ndex for a typcal frm; whle ndces and j dstngush between rval frms. The frms produce ther output at 4 Basu and Bell (1991) analyze a two stage game where competng lenders, who are also landlords, frst hre worers for farm producton and these specfc worers become captve borrowers later.

4 18 S. Roy / Int. J. Ind. Organ. 18 (000) constant unt cost denoted by c. There s a contnuum of dentcal consumers whose total measure s normalzed to be 1. Consumers are located unformly on the unt nterval [0,1. Locaton s not a proxy for taste; t smply specfes the address of a consumer. Frms are fully nformed about the locaton of all consumers. Intally, consumers are unaware of the exstence of ether frm. Frms target ther drect maretng actvtes towards specfc consumers n ths case, nformng them about ther exstence. Consumers have unt demand.e. buy ether 0 or 1 unt of the commodty. The gross surplus from consumng a unt s u. 0. A consumer who becomes aware of the exstence of only one frm, buys from that frm f the prce charged does not exceed u. If a consumer becomes aware of both frms, she buys from the frm offerng the lower prce, provded t does not exceed u (f both prces are equal, she randomzes between the frms wth equal 5 probablty). Consumers not targeted by ether frm do not buy. If the cost of drect maretng s not consumer locaton specfc and all consumers are otherwse dentcal, a frm could target any subset of the unt nterval. For example, f both frms wsh to target non-overlappng halves of the maret, any two dsjont sets wth measure 1/ whose unon s the unt nterval, could be used as target sets. However, all such outcomes would be equvalent n terms of the maret prce, profts and welfare. In order to eep the analyss and notaton clean, we formally assume that frm 1 targets consumers located n the sub-nterval [0,a for some chosen a [ [0,1, whle frm targets consumers on [ a,1 for some chosen a [ [0,1. Thus, the maretng decson by each frm s smply to choose a number n the unt nterval. We shall refer to a, 5 1,, as the maret coverage of frm. The maretng cost for each frm s gven by the functon mf(a ), where m. 0 and f s a contnuously dfferentable convex functon on the unt nterval, f(0)5 0 and f 9(x). 0 on the unt nterval. We allow for the case where f s lnear whch represents a stuaton where the cost of nformng a consumer s constant (ndependent of how many other consumers are nformed or ther locaton). However, n much of the strategc advertsng lterature, t s assumed the margnal cost of nformng s ncreasng n the number of consumers nformed (ths would be consstent wth the stuaton descrbed n footnote 6). We also assume that: mf 9(1) 1 c,u Ths mples that the margnal cost of producng and sellng a unt to a consumer s 5 In the maretng lterature, t s farly well recognzed that consumers choce set (or evoed set ) depends on ther awareness and may not nclude all products and frms n the maret (see Kotler, 1997). 6 Ths s qute reasonable f frms dffer n ther cost of maretng to specfc consumers and for any frm, the cost of maretng dffers across consumers. For example, f frms dffer n ther geographcal locaton and send sales representatves to reach spatally dspersed consumers.

5 S. Roy / Int. J. Ind. Organ. 18 (000) always less than her wllngness to pay for t. The game proceeds n two stages. In the frst stage, frms 1 and smultaneously choose ther maret coverage a1 and a. In the next stage, they smultaneously set prces p1 and p, p >c. The payoff to each frm s ts expected proft, net of maretng cost. The soluton concept used s subgame perfecton. 3. Prce competton In ths secton, we outlne the Nash equlbra of the subgames n the second stage where frms set prces, gven ther decsons about maret coverage. Consder any (a,a ), where a 1a.0. Let n 5mn(a,1a ), j±, denote the sze of the j captve segment of frm, 51,. Further, let m5max(a 1a 1,0) denote the sze of the contested segment of consumers. Fg. 1 depcts the contested and captve segments n a stuaton where a11a.1, 0,a,1. Let p,51,, denote the expected proft of frm n the product maret, gross of maretng cost. Gven n and m, let p denote the crtcal prce level such that f frm charges a prce below ths crtcal level, ts proft, even when t sells to all the consumers covered by t, s less than what t can earn by sellng only to ts captve maret segment at monopoly prce.e. (p c)(n 1 m) 5 (u c)n (1) so that p5 c 1 [(n /(n1 m))(u c), 5 1, () A frm wll never charge a prce below p wth postve probablty. Note that p >c. If frm has no captve segment (n 50), then p5c. On the other hand, f there s no contested segment of consumers (m50), then p s equal to u, the monopoly prce. If p,p, then frm s wllng to undercut j ts rval at prces lower than what the latter s wllng to charge; frm s the more aggressve prce compettor. Further, p,p j f and only f n,n j. The frm wth a larger captve maret s less aggressve n prce competton. Fg. 1. Captve and contested segments of consumers when a 1a.1. n : sze of the captve segment for frm ; m: sze of the contested segment.

6 184 S. Roy / Int. J. Ind. Organ. 18 (000) If m50, then the unque equlbrum outcome s that of local monopoly wth prces p15p5u and profts p5(u c)n, 51,. If m51, then n15n50, the maret coverages of both frms are dentcal and we have a case of classcal Bertrand competton wth profts p 5p 50. If 0,m,1, then there s no equlbrum n pure strateges as frm undercuts frm j f pj s hgh but prefers to charge the monopoly prce and just serve the captve maret f p,p. There exsts j a mxed strategy equlbrum. Narasmhan (1988) has rgorously characterzed the unque mxed strategy equlbrum when 0,m,1 (see also Denecere et al., 199). If p <p j (.e. n <n j), then the support of the equlbrum strateges for both frms can be shown to be equal to the nterval [p j,u. Furthermore, t can be shown that f p,p, then frm j charges the monopoly j prce u wth strctly postve probablty; except for ths, nether frm s equlbrum prce dstrbuton has any other mass pont. Thus frm j, whch s less aggressve n prce competton s undercut wth probablty one when t charges prce u and therefore, ts expected equlbrum proft s just what t would earn f t sold only to ts captve segment at monopoly prce,.e. n (u c). Frm, whch s the more aggressve prce j compettor, earns expected proft equal to what t gets f t sells to all the (n 1m) consumers covered by t at prce p, the lower bound of the prce support. To j summarze: Proposton 3.1: Let m, n, 51, be as defned above. Further, suppose that n <n j. The support of equlbrum prce strateges for both frms s dentcal and equal to [p,u. The (unque) Nash equlbrum expected profts (gross of j advertsement cost) for the two frms are: p 5 n [(n 1 m)/(n 1 m)(u c) and p 5 n (u c) j j j j 4. Strategc maret coverage: reduced form game In ths secton, we consder the reduced form game n the frst stage where both frms smultaneously choose ther maret coverage,.e. (a 1,a ), and ther payoff s the Nash equlbrum proft from the resultng prce subgame (as descrbed n Proposton 3.1), net of maretng cost. Let R denote the net payoff to frm. Then R (a,a ) 5 p (a,a ) mf(a ) (3) j j Suppose that frm chooses some a [[0,1. If frm j chooses a [(1a ), then the j maret s perfectly segmented n the next stage resultng n pure local monopoly and frm j earns monopoly proft on ts captve maret of sze (1a ). On the other hand, f a j.(1a ) then t covers a larger maret but faces non-trval prce competton n stage. If the chosen value of a s greater than both a and (1a ) j then we have a stuaton where there s prce competton for a segment of

7 S. Roy / Int. J. Ind. Organ. 18 (000) consumers whch are nformed by both frms, the captve segment of frm j s larger than that of frm so that frm j s the less aggressve prce-compettor and ts expected (gross) proft s exactly what t would get by sellng only to ts captve terrtory (1a ) at monopoly prce (see Proposton 3.1). Tang nto account the addtonal maretng cost nvolved n reachng consumers n excess of (1a ), frm j would then earn strctly lower net proft compared to what t could get by settng a equal to (1a ). Therefore, gven a, frm j never chooses values of a j j greater than maxh(1a ),aj. An mmedate mplcaton of ths s that f frm follows a tmd maretng strategy whch covers less than half the maret,.e. a <1/, then any choce of a.(1a )byfrmj mples that a.a and so the unque best response of frm j j j s to choose aj5(1a ),.e. accommodate and cover the part of the maret not covered by frm. Thus, the allocaton a 5a 51/ where each frm acts as a local monopolst over exactly half the maret s an equlbrum outcome for all values of m. We wll see that ths s also the lmtng pont of the set of equlbra as m 0. Let the crtcal value g be mplctly defned by: g 5 [(u c)/h(u c) mf 9( g )j (4) It s easy to chec that, 0,g,1 and that: 1 g. and g 1/ as m 0 We clam that: a frm fnds t optmal to ntrude nto the terrtory clamed by ts rval f and only f the latter ams for a maret coverage exceedng g. Proposton 4.1: In the reduced form frst stage game, the best response functon for frm j, j51,, ±j, s gven by a j(a )51a, f 0<a <g, whle for g,a <1, a j(a ).1a and satsfes: 0 5 (u c)(a (a ) 1) 1 mf 9(a (a ))a (5) j j (where g s as defned by Eq. (4)). Proof. We have seen that f frm j chooses a j.(1a ), then t must choose aj lyng n the segment ((1a ),a ) and f t does so, n j<n and frm j s expected net proft wll be gven by: R (a ) 5 [a h(( a )/a )(u c)j mf(a ) j j j j j Tang the dervatve of R (a ) and evaluatng t at the pont a 5(1a ) yelds: j j j R 9j( a ) 5 (u c)[ (1/a ) mf 9( a ) 9 whch mples that R <0 ata 51a f and only f a <g. Ifa.g then the j j

8 186 S. Roy / Int. J. Ind. Organ. 18 (000) optmal acton a j(a ).(1a ) s obtaned by settng R j9 (a j)50 whch yelds Eq. (5). j From the expresson for the best response functon, one can chec that the best response functon a j(a ) s strctly deceasng n a on [0,1. A representatve set of best response functons on the (a,a )-space are depcted n Fg.. The lne AB s the set of pure monopoly allocatons of the maret,.e. the set of (a,a ) where a 1a 51. The best response functon of frm 1 s gven by BET and that for frm s gven by AE9S. As can be readly observed, the set of equlbrum allocatons (the ntersecton of the best response functons) s gven by the segment EE9. Thus, all equlbrum outcomes nvolve the emergence of pure local monopoly. The pont E corresponds to the equlbrum allocaton (g,1g ) whch s most favourable to Fg.. Best response functons and equlbra n the (a,a ) space for the (reduced form) frst stage game where frms decde on ther maret coverage. BET, best response of frm 1; AE9S, best response of frm ; EE9, set of equlbra.

9 S. Roy / Int. J. Ind. Organ. 18 (000) frm 1 and least favourable to frm ; the reverse s true for the pont E9 representng allocaton (1g,g ). The pont b s at the mdpont of EE9 represent- 1 1 ng allocaton (,). Proposton 4. [Man Result. The set of pure-strategy equlbra n the (reduced form) frst stage game s exactly equal to h(a 1,a ): a11a51,a 1[[1g,g, a [[1g,gj whch always ncludes the partcular allocaton (1/,1/). Ths set contracts as m decreases and converges, as m 0, to the unque pont (1/,1/). Proof. From Proposton 4.1, f a <g choosng aj51a s the unque best response of frm j. So any maret allocaton (a 1,a ) where a11a51, a 1[[1 g,g, a [[1g,g s an equlbrum and n fact, these are the only equlbrum outcomes wth a <g for some. Next, consder (a,a ) where a 5a.g for some. The best response for frm j s then a j(a )5a* (say). Observe that a*.1a. As the best response of frm a (.) s strctly decreasng, a (a*),a (1a). However, 1 1 a.g. mples 1a,, so that a (1a)5a. Thus, a (a*),a whch mples that there s no equlbrum allocaton (a,a ) where a.g for some. The set of equlbra are Pareto-effcent and every equlbrum nvolve complete segmentaton of the maret; n stage, frms smply choose monopoly prce over ther terrtory. For frm 1, the equlbrum outcome yeldng the hghest payoff s (a 5g, a 51g ) and the lowest payoff s yelded by the outcome (a 51g, 1 a 5g ); the reverse s true for frm. Interpret m as a parameter that affects the margnal cost of advertsement. As m ncreases, g ncreases whch mples that the set of equlbrum allocatons expands. In terms of Fg., the nterval EE9 becomes larger as E moves up and E9 moves down on the lne AB. On the other hand, as m s reduced, the set of equlbra contracts and, n the lmt as m 0, the set of equlbra s reduced to a unque allocaton (1/,1/) ndcated by pont b n Fg Note that the allocaton (1/,1/) s an equlbrum outcome for all m.0. For m.0, there always exst equlbra where one frm has a greater maret share even though both frms are equally effcent. As m ncreases, the largest maret share that each frm can attan n equlbrum ncreases; n terms of Fg., EE9 expands wth m to eventually cover the entre lne AB. Lastly, observe that every equlbrum s socally effcent; frms approprate the entre socal surplus and by j 7 If m s exactly equal to 0, then there are equlbra other than (1/,1/) where frms target overlappng sets and play mxed strategy n the prce subgame. Such equlbra are not robust to perturbatons n m (see Roy and Schreurs, 1994).

10 188 S. Roy / Int. J. Ind. Organ. 18 (000) elmnatng any overlap n ther maret converge, frms avod what would be a 8 duplcaton n the socal cost of sendng product nformaton to consumers. 5. Extenson to asymmetrc duopoly The above mentoned results easly carry over to a stuaton where frms have asymmetrc producton costs. Let c1 and c denote the unt producton costs of the two frms. Assume that c,c and that mf 9(1)1c,u. Frst, consder the stage of prce competton where each frm has a captve segment n, 51, and there s a compettve segment m. Then, p (the crtcal prce level below whch frm never undercuts) s gven by: (p c )(n1 m) 5 (u c )n As before, f p,p j, frm s the more aggressve prce compettor. Wth equal producton costs, the frm wth a larger captve maret s less aggressve n prce competton. However, wth unequal costs, even f the low cost frm has a larger captve maret, t may be more aggressve. The explct dervaton of mxed strategy equlbra for ths case s contaned n Baye and de Vres (199) (see also Denecere and Kovenoc, 199, 1996). If p <p j, then the support of the equlbrum strateges for both frms can be shown to be equal to the nterval [p j,u. Further, frm j, whch s less aggressve n prce competton s undercut wth probablty one when t charges prce u and therefore, ts expected equlbrum proft s just what t would earn f t sold only to ts captve segment at monopoly prce,.e. n j(u c j). Frm, whch s more the aggressve prce compettor, earns expected proft equal to what t gets f t sells to all the (n 1m) consumers covered by t at prce p j, the lower bound of the prce support. Consder the reduced form stage 1 game where frms choose (a,a ) and defne a crtcal allocaton (b,b ): b 5 [(u c )/(u c ) 1 (u c ), 5 1, 1 Observe that, 0,b,1, 51,, and that b11b51. Further, note that b15b5 f c15c. In fact the allocaton (b 1,b ) represents the focal splt of the maret n the asymmetrc case just as the splt (1/,1/) does n the symmetrc case. It can be shown that the best response of frm j to any choce of a n [0,b stoset 8 Suppose frms could perfectly prce dscrmnate (by locaton) and, n the second stage, charge dfferent prces n the contested and captve segments. Ths would lead to the classcal Bertrand outcome n the contested segment and monopoly outcome n the captve segments. Once agan, n the frst stage, frms avod any overlap n ther terrtory,.e. complete maret segmentaton occurs. The only dfference s that every dvson of the maret can be sustaned as an equlbrum outcome.

11 S. Roy / Int. J. Ind. Organ. 18 (000) aj51a,.e. accommodate and cover the part of the maret not covered by frm no matter how small the cost of nformng addtonal consumers. Fnally, there exsts some crtcal value g hgher than b such that f a s below ths crtcal value, the net proft (net of maretng cost) of frm j from not ntrudng nto the maret covered by frm s greater than that obtaned by ntruson. These crtcal values g 1,g are defned by: g 5 [(u c )/h(u c ) 1 (u c ) mf 9( g )j j It can be easly verfed that for 51,, 0,g,1, g.b and that g b as m 0. Further, g11g.1. Also, g15g5g, f c15c5c and g 1.g, f c 1,c. The equlbrum set s as follows: Proposton 5.1: The set of pure-strategy equlbra n the (reduced form) game s exactly equal to h(a 1,a ): a1a51,a 1[[1g,g 1, a [[1g 1,g j whch always ncludes the partcular allocaton (b 1,b ). Ths set contracts as m decreases and converges, as m 0, to (b 1,b ). Once agan, every equlbrum nvolves complete maret segmentaton and the emergence of pure local monopoly. All the equlbra are Pareto-effcent. g1 and g are the largest maret shares frms 1 and can obtan n any equlbrum. As m ncreases, both g1 and g ncrease whch mples that the set of equlbrum allocatons expands. On the other hand, as m s reduced, the set of equlbra contracts and, n the lmt as m 0, t s reduced to the unque focal allocaton 1 (b 1,b ). In ths allocaton (b 1,b ) frm 1 gets a larger maret share (b 1..b ) and the dfference between the maret share of the two frms s strctly ncreasng n the dfference between the producton cost of the two frms. Interestngly enough, for m large enough there may be an equlbrum where the relatvely neffcent frm commands a larger maret share. Lastly, equlbrum s socal neffcent to the extent that the hgher cost frm serves part of the maret. Acnowledgements I than Sanjeev Goyal, Maarten Janssen and Dan Kovenoc for useful comments and suggestons. Observatons made by partcpants at the 1996 Internatonal Conference on Game Theory and Applcatons (Bangalore), the 1997 Royal Economc Socety Conference (Stoe-on-Trent) and the 1997 European Meetngs of the Econometrc Socety (Toulouse) have been helpful. The current verson has beneftted from comments made by the managng edtor and an anonymous referee of ths journal.

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