Dynamic Targeted Promotions

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1 Dynamc argee Prmns A Cusmer Reenn an Acusn Perspecve Gla E. Frucher Bar-Ilan Unversy Z. Jhn Zhang Unversy f Pennsylvana hs research analyzes he sraegc use f argee prmns fr cusmer reenn an acusn n a ynamc an cmpeve envrnmen. he nrmave analyss shws ha a frm s pmal argeng sraeges, bh ffensve an efensve, epen n s acual mare share, he relevan reempn rae f s argee prmns, cusmer prfably, an he effecveness f s argee prmns. hese sraeges have he aracve feaure f beng an aapve cnrl rule. A frm can peranalze hese sraeges by ausng s planne prmnal ncenves n he bass f he bserve fferences beween acual an planne mare shares an beween acual an planne reempn raes. In he lng run, a fcus n cusmer reenn s n an pmal sraegy fr all frms. Keywrs: argee prmns; cmpeve sraegy; fferenal game Mareng nfrman echnlgy s raply ransfrmng he way n whch frms cnuc her mareng n servce nusres. Because f her unpreceene ably gaher, sre, an prcess cnsumer nfrman n a large scale a a lw cs, frms are banng ever sharper pcures f nvual cnsumers wh have been hhe largely annymus an, cnseuenly, gan much flebly n argeng esre cusmers wh alre prmnal ncenves acheve sraegc mareng becves. Fr nsance, a servce frm can ffer prmnal ncenves nly s curren cusmers n an eff efen s mare share frm cmpeve encrachmen r accuraely arge s rval s cusmers wh prmnal nucemens acure new cusmers. In hs acle, we suy he sraegc use f argee prmns an characerze he pmal argeng sraeges a frm can ap n a ynamc cne. he nense rvalry beween A& an MCI n he mare fr cnsumer lng-sance elephne servce prve a g eample f hw argee prmns ae by nfrman echnlgy cul help a frm realze s sraegc becves. Wh a mare share clse 3%, MCI launche s prmnal prgram Frens & Famly n he sprng f 99. he prgram was esgne arac A& s cusmers by fferng subsanal scuns fr famly-an-frens callng crcles. Ae by aabase mareng, MCI succeee n swchng a leas 5 mlln A& callers by he en f 993 an ncrease s mare share 9%. In respnse, A& nruce s wn versn f aabase mareng n 994, sgnng mre han 8 mlln callers s rue USA an rue Wrl savng prgrams shre up s cusmer base, an regane clse mlln subscrbers frm s cmpers. In he meanme, A& an MCI als engage n an epensve prmnal ug-f-war by argeng each her s cusmers. Fr eals n he prmnal rvalry beween A& an MCI snce 99, see Rapp (995) an Urry (995). Jurnal f Servce Research, Vlume 7, N., Augus DOI:.77/ Sage Publcans

2 4 JOURNAL OF SERVICE RESEARCH / Augus 4 wh wn-bac checs nuce swchng. In 994, fr nsance, he w frms nly spen an esmae $.3 blln n such checs, generang remenus cusmer churnng. I s esmae ha cnsumers swche 7 mlln mes n 994 alne, nwhsanng he fac ha bh frms als ffere freuency an lyaly prgrams. Accurae argeng f wn an rval s cusmers wh prmnal ncenves has clearly nae n he nusry a ynamc game f sraegc prmns fr cusmer reenn an acusn. Usng argee prmns rean curren cusmers an swch a cmper s cusmers s n lme he cnsumer lng-sance elephne servce nusry; nee, s lely becme a wesprea pracce n many her servce nusres such as banng an hspaly nusres, where cusmer cnac an recgnn are prereuse fr servce elvery. he aven f argee prmns hus rases many cmpeve an sraegc ssues fr servce managers ha have n been rase befre. Ms f hese ssues are cncerne n wh hw much spen bu wh where spen n prmns ( Brefngs 3). Specfcally, hw shul a frm use argee prmns? Hw shul a frm respn s rval s argee prmns? Wha are he pmal argeng sraeges fr a frm rean s wn cusmers an arac a rval s cusmers, gven ha he rval wll aus s argeng sraeges ver me? Hw cmpeng frms mare shares evlve ver me uner argee prmns? We ffer sme nrmave answers hese mpan manageral uesns by evelpng a fferenal game f argee prmns. Prevus Research Sues n argee prmns have n aresse hese uesns n a ynamc cne. Shaffer an Zhang (995), alng wh hers, use a sac game-herecal mel eplre cmpeve mplcans f argee prmns an pmal argeng sraeges. Alhugh her sac mel generaes many valuable nsghs abu hw argeng has change he naure f mare cmpen, cann aress ssues relae he ynamcs f cmpen, especally mare share mplcans f argee prmns. 3 Rss, McCullch, an Allenby (995) apprach argee prmns frm an emprcal angle by evelpng ecnmerc mehs fr a frm use n mplemenng argee prmns.. Fr mre eamples n servce nusres, see Fenberg, Krshna, an Zhang (). here are many smlar eamples n her nusres. Fr eamples n he cnsumer gs nusry, see Shaffer an Zhang (995). 3. here are many sac mels n argee prcng. See Shaffer an Zhang () fr a revew f hs leraure. Ms f hese mels cnclue ha eulbrum mare shares fr cmpeng frms are n affece by he nrucn f argee prmns. Sues n ynamc cmpen n mareng are numerus bu fcus msly n avesng base n he Lancheser mel. Early sues n hs ran nclue hse f Kmball (957), Vale an Wlfe (957), Isaacs (965), Hrsy (977), Lle (979), Case (979), Deal (979), an Deal, Seh, an hmpsn (979). hese sues eamne hw avesng epenure affecs sales n a ynamc seng. In recen years, much prgress has been mae n melng ynamc cmpen n avesng, espe he fac ha perssen echncal ffcules reman. Chnaguna an Vlcassm (99) an Ercsn (99) cnrbue valuable nsghs abu ynamc avesng cmpen by applyng a fferenal game slun he case f he cla war an fn ha he clse-lp slun prves a beer emprcal f han an pen-lp slun. Ercsn (993) fuher eens hs analyss allw bh ffensve an efensve avesng epenures. Because f nheren echncal ffcules n slvng a fferenal game, hese prevus sues have res resrcve assumpns n mel parameers an cann be use recly aress uesns f ynamc argee prmns when prmnal ncenves are specfc grups f recpens an cnngen n sales. A relae sream f leraure s n cusmer reenn as a prfable busness sraegy. 4 Ha, James, an Sasser (99) an Rechhel an Sasser (99), fr nsance, frcefully avcae a fcus n cusmer reenn hrugh nvesng n relanshp-base asses. Alhugh nfluenal, such a sraegc prescrpn bvusly cann be pmal fr all frms n a cmpeve cne because cusmer reenn s a meanngful sraegy nly f cusmer swchng by a cmper s a real hrea. Inee, McGahan an Ghemawa (994), usng a w-sage game mel, shw ha a larger frm can prfably fcus n cusmer reenn, whereas a smaller frm s beer ff fcusng n cusmer swchng. We een he analyss n hs mpan sraegy ssue he cne f argee prmns by usng a mre general ynamc mel, an we generae sme new nsghs abu frms sraegc renans n eulbrum. Suy Apprach an Man Resuls We evelp a fferenal game suable fr melng ynamc argee prmns an prve analycal sluns fr bh clse-lp an pen-lp sraeges by mfyng a echnue evelpe by Frucher an Kalsh (997) n he cne f avesng cmpen. We cnclue ha a frm s pmal argeng sraeges, bh ffensve an efensve, n a ynamc seng epen n s acual mare share, he relevan reempn rae f s ar- 4. See Dreze an Bnfrer (3) fr a recen survey f he leraure.

3 Frucher, Zhang / DYNAMIC ARGEED PROMOIONS 5 gee prmns, cusmer prfably, an he effecveness f s argee prmns. In he lng run, a fcus n cusmer reenn cann be an pmal sraegy fr all frms. A frm wh a suffcenly large mare share shul sress cusmer reenn, whereas a frm wh a small mare share shul sress cusmer acusn. When mare shares are mre evenly ve n a mare, frms shul all fcus n cusmer acusn. We llusrae hrugh a numercal eample he raecres ver me f a frm s mare share, prmnal epenures, an prfs as cmpeng frms use argee prmns pmally. In wha fllws, we frs se up ur mel. Afer prvng analycal sluns he mel, we scuss he manageral mplcans f he sluns. We hen cnclue wh suggesns fr fuure research. MODEL Cnser an nusry where w cmpeng frms have he capably f usng argee prmns bh ffensvely fr cusmer acusn an efensvely fr cusmer reenn. We resrc ur analyss a mare f fe sze fcus n cmpen fr mare shares. herefre, cusmer acusn enals cusmer swchng n ur mel. Whu any lss f generaly, we nrmalze he number f cnsumers n he mare ne an hus ene a frm s eman by s mare share. nruce argee prmns, we assume ha a any pn n me, bh frms have aeuae nfrman enfy her wn an her cmper s cusmers an hence can mplemen a fferen prmnal prgram respecvely fr cusmer reenn an acusn. argee prmns, unle avesng, ffer fferen ncenves fferen ypes f cnsumers, epenng n a frm s mareng becves. rean her curren cusmers, bh A& an MCI, fr nsance, ffere savngs prgrams whereby a cusmer cul accumulae cre pns base n usage an reeem hem fr cash, free lngsance mnues, r freuen fler mles. hey als ffere wn-bac checs n he amun f $5 n average b fr her cmper s cusmers. herefre, capure he essence f argee prmns, we nruce heergeney n cusmer cmpsn an allw a frm alr s prmnal ncenves each enfable grup f cnsumers. Le () ene he mare share fr frm a me. he () cnsss f w ypes f purchases: hse frm repea cusmers, ene by (), an hse frm swchng cusmers, ene by (). herefre, a any me, we have () () + (). () mel a frm s pracce f usng fferen prmnal ncenves generae repea an swchng sales, le ()an ()ene frm s prmnal ncenves ffere, respecvely, repea an swchng purchases a me. hese ncenves can be cupns, premums, specal savngs, r hers. As hese prmnal ncenves are ypcally cnngen n cnsumer purchase, he frm s prmnal epenures wll epen n hw many peple acually reeem s prmnal ffers. herefre, frm s efensve an ffensve prmnal epenures are gven by () () an () (), 5 respecvely. We assume ha each frm maes nepenen prmnal ecsns a any me mamze s scune prf sream ver he plannng hrzn. When hs plannng hrzn s fne, frm s pmzan prblem s characerze by Ma Π ( ) e, r [ ] e + ( ( )) ( ) + ( ()) (). he cnsan represens he grss prf margn, 6 an he cnsan represens he value f frm s mare share a he ermnal me. Gven any prmnal ncenves, a frm s payffs a me epen n hw effecve s argee prmns are n generang sales. Le ( ( ) ( )) an ( ( ) ( )) be he respecve effecveness measures f frm s efensve an ffensve prmnal effs. Here he effecveness measure s aen as a suare funcn f a specfc prmnal epenure, as s cmmnly ne n he leraure fr racably, an mples a ecreasng reurn any prmnal epenure. he cnsans an are frm-specfc effecveness ceffcens ha capure he facrs ha affec he pency f a frm s argee prmns such as aabase ualy, he accuracy f aa analyss an argee elvery, cusmer lyaly, a frm s pruc characerscs, an s n. sm- plfy ur nan, le f ()( f ())ene he fference beween he effecveness f frm s (frm s) ffensve prmns an ha f frm s (frm s) efensve prmns a me. he varable f ()( f ())hus measures he cmpeve srengh f frm s (frm s) ffensve argee prmns n aracng he cusmers ha frm 5. Here we gnre any fe cs n cnucng argee prmns as ur fcus s n hw, raher han wheher, a frm shul cnuc argee prmns. 6. he mplcan s ha a frm s regular prce an margnal cs f prucn are cnsan ver me. ha assumpn s cmmnly mae n sues f ynamc prmnal ecsns manan racably. Hwever, n many maure nusres, such as he cnsumer gs nusry, such an assumpn s n unuly resrcve. ()

4 6 JOURNAL OF SERVICE RESEARCH / Augus 4 (frm ) res rean hrugh s efensve argee prmns. hen, we have f () ( () ()) ( () ()), (3) f () ( () ()) ( () ()). (4) A frm s mare share an s cmpsn change ver me because f cmpeve argee prmns, whch n urn affec s prmnal ecsns. capure hese ynamc lnages, we specfy a ynamc sysem as fllws: erm). hs specfcan f ynamcs s mre general han Ercsn s (993). 7 Fr he fferenal game asscae wh euans (), (5), an (6), we wan fn clse-lp Nash eulbrum sraeges (,,, ) ha sasfy Π(,,, ) Π(,,, ),,,,,. (8) In mahemacal erms, a clse-lp sraegy can be epresse as () f ()( () ()) f () (), (), (5) (,,,, ) an (,,,, ),., (9) () f ()( () ()) f () (), (), where an,. Euan (5) capures he effec f argee prmns n a frm s repea sales. Frm s repea sales wll ncrease f he frm can effecvely cnve swchng cusmers repea purchasers hrugh s ffensve argee prmns ha vercme he rval s efensve prmns (he frs erm). I als ncreases f he frm can effecvely fen ff he rval s ffensve argee prmns rean s repea purchasers (he secn erm). Euan (6) ncaes ha frm can acure mre new cusmers frm cmpen f can effecvely ap he rval s cusmers hrugh s ffensve argee prmns agans he rval s efensve prmns (he frs erm) an/r effecvely fen ff he rval s ffensve argee prmns ame a swchng cusmers (he secn erm). As () () + (), we have () f ()( ()) f () (), (). (6) (7) Euan (7) escrbes he mare share ynamcs, an s he well-nwn Lancheser ynamcs mfe ncrprae frms nwlege abu cnsumers an her ably ffer argee prmns. hs ynamc prcess mples ha a frm s verall mare share wll ncrease f can successfully acure he rval s cusmers hrugh s verpwerng ffensve argee prmns agans he rval s efensve prmns rean hem (he frs erm) an/r successfully fen ff he rval s ffensve argee prmns an rean s curren cusmers (he secn 7. Our specfcan, n cnras Ercsn s (993), allws mre freem n he chce f parameers an leas mre general cnclusns. he pacular case when he sraegy es n epen n he nal cnn s nwn n he leraure as feebac sraegy. Bh feebac an clse-lp sraeges are cnngen n he bserve sae f he sysem (mare shares n ur mel) an herefre bes capure he ynamc naure f cmpeve prmns. Hwever, s echncally very challengng erve an eulbrum f feebac r clse-lp sraeges. An pen-lp sraegy s nly me epenen. Such a sraegy prescrbes a he begnnng f he game hw a frm shul prme a each pn n me an s never revse ver he curse f he game. hs sraegy capures sme realsc aspecs f sraegc plannng n prmns; hwever, s we applcan s ue manly he relave ease wh whch ne can slve fferenal games by usng sanar pmal cnrl mehs. Inee, Chnaguna an Vlcassm (99) an Ercsn (99) prve emprcal evence ha feebac sluns f he acual aa beer han pen-lp sluns. Frucher an Kalsh (997) prve smlar evence fr clse-lp sraeges. As, we can als een he prevus fferenal game he case f nfne plannng hrzn as fllws: [( ()) () + ( ()) ()] e Ma Π, s... () f ()( () ()) f ( ) ( ), ( ) () f ()( () ()) f () (), ( ) () he cnrl funcns (), (),,, are amssble cnrls f hey are bune wh he values f f () an f ()beng psve. Fr such values, euans (5), (6), an (7) reveal an, an

5 Frucher, Zhang / DYNAMIC ARGEED PROMOIONS 7 he negrals asscae wh he abve fferenal games es. In seay sae, we have an ss f ss f + f f f ss ss [ f + f ] ss ss (), () wh,,. I s sraghfrwar shw ha fr f ()> an f ()>, he seay-sae sluns n euans () an () are asympcally sable. 8 OPIMAL (EQUILIBRIUM) ARGEING SRAEGIES As we shw n appen, we can erve eplcly Nash eulbrum sraeges, bh pen lp an clse lp, fr he w games specfe n he preceng secn. he clse-lp eulbrum-argee epenures, respecvely fr he fne- an nfne-me hrzn, are gven by 4 ( ) an 4 Φ () e an 4 Φ () e ( ) 4,,, (3),,. he pen-lp euvalen epenures are gven by () () () an 4 () ()( ()) () 4 (),,, (4) (5) 8. Fr nsance, n he case f euan (7), he frs ervave f he rgh-han se wh respec s negave. ABLE Varus Relanshps Beween Opmal Prmnal Sraeges ype f Cmparsn Relanshp Fne me Infne me argee prmnal ncenves al argee prmnal epenures () () () Φ e an 4 () () ( ()) () Φ e 4 ( ) ( ) ( ),, (6) he eulbrum sraeges cnane n euans (3) hrugh (6) can all be relevan pmal sraeges fr frms praccng argee prmns. If a frm has a sh plannng hrzn, sraeges n euans (3) an (5) are mre relevan. Hwever, f a frm has a lng plannng hrzn, sraeges n euans (4) an (6) are mre penen. In an, he laer case fen ffers a g apprman he frmer wh much reuce cmpley f cmpuan. Open-lp sraeges n euans (5) an (6) are beer sue capure he plannng sages f prmns, whereas clse-lp sraeges n euans (3) an (4) cnvey a beer sense f ynamc cmpen. Ineresngly, all hese fferen sraeges yel mre r less smlar manageral nsghs (varus relanshps beween pmal prmnal sraeges are lse n able ), whch we scuss ne. ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )

6 8 JOURNAL OF SERVICE RESEARCH / Augus 4 ANALYSIS OF RESULS AND MANAGERIAL INSIGHS In a ynamc seng where bh cmpeng frms can use argee prmns an can reac each her base n he hsry f her neracns, he allcan f a frm s prmnal epenures ver me, bh fr he efensve an ffensve purpses, s an mpan manageral ecsn ha can be ue nracable mae. Fr nsance, hw shul a frm aus s argee epenures ver me? Shul a frm wha s rval es n erms f s sraegc psure, fcusng n cusmer acusn r reenn whenever s rval es? Or shul a frm always fcus n cusmer reenn regarless f wha cmpen es, as sme epes apparenly avcae (Rechhel an Sasser 99)? he answers all hese uesns can be ue elusve whu any nrmave melng. Our analyss prves an answer each f hese uesns. Alhugh ur analyss f he fferenal game self s cmple an even smewha serenpus, ur answers all hese uesns urn u be surprsngly smple an nuve, whch shul enhance he praccal applcably f ur cnclusns. Deermnans f Opmal argeng Sraeges By analyzng he clse-lp sraeges n euans (3) an (4), we can characerze hw a frm can pmally engage s prmnal epenure fr cusmer reenn an acusn. Prpsn : A frm s pmal efensve (ffensve) prmnal ncenves ncrease (ecrease) wh s mare share, wh efensve (ffensve) argeng effecveness ( ), an wh he value f mare share ( ()r Φ( ) e n he nfne-me hrzn case), bu hey ecrease wh he acual reempn rae f efensve (ffensve) argee prmns θ / ( θ /( )). Prpsn s nuve bu mpan. I essenally cnfrms he pmaly f sme nsncve manageral pracces. When a frm has a larger (smaller) mare share, ceers parbus, s ffensve (efensve) prmns generae less (mre) a bang n sales, an hence he frm shul ranally prve mre ncenves fr cusmer reenn (cusmer swchng). hus, ne may bserve a any pn n me ha a frm engages mre resurces n cusmer reenn as s mare share ncreases. he fac ha any prmnal ncenves, efensve an ffensve ale, shul ncrease wh respecve argeng effecveness ( r ) perhaps eplans why he Inerne has spawne a rap grwh f crprae epenures n argee prmns (Ber an Krl ). As he value f mare share n ur mel s essenally cusmer prfably, ur analyss hus warns agans a wesprea pracce f mplemenng cusmer reenn r acusn prgrams wh lle regar cusmer prfably ( Brefngs 3). Fnally, any argee prmnal ncenves shul ecrease wh he acual reempn rae f specfc argee prmns, as a hgher reempn rae reuces he un prf margn a any gven level f sales. Open-lp sraeges n euans (5) an (6) sugges smlar manageral nsghs fr prmnal plannng. he ey fference beween hese w ypes f sraeges s ha a frm s planne prmnal ncenves are base n planne mare shares, (), an epece reempn raes, efne analgusly as θ () ()/ () an θ () ()/( ()). Inee, hese w ypes f sraeges are relae. In bh fne- an nfne-me cases, we have frm euans (3) an (4) r (5) an (6): θ an ( ) θ. θ ( ) θ hs analyss gves us he fllwng prpsn: Prpsn : A frm can mplemen s prmnal sraeges pmally by ausng s planne prmnal ncenves reflec he bserve fference beween acual an planne mare shares, as well as beween acual an planne reempn raes. If a frm s acual mare share s larger (smaller) han planne an f acual reempn raes are lwer han epece, he frm shul aus upwar s planne ncenves fr s efensve (ffensve) argee prmns. Prpsn ges ne sep fuher han prpsn n suggesng ha s an avsable pracce aus planne prmnal ncenves fr cusmer acusn an reenn n accrance wh hw he planne mare share an reempn rae are fulflle. hs w-sage ausmen prcess s mre acnable, emanng less nfrman mplemen. Sraegc Orenan We can als she lgh n he general renan f a frm s prmnal sraeges, as measure by he ra f he frm s al efensve an ffensve prmnal epenures. Frm euans (3) an (4), we have. ( )

7 hen, we have he fllwng prpsn: Prpsn 3: A frm shul be efense rene (ffense rene), spenng mre n cusmer reenn (swchng) f s verall mare share s larger han s rval s, weghe by s argeng effecveness n respecve mares. Fuhermre, a frm shul becme mre efense rene (ffense rene) as s mare share ncreases (ecreases). hus, a smaller (larger) share frm may pmally chse fcus n cusmer reenn (acusn), nsea f cusmer acusn (reenn). Inuvely, he sze f a frm s mare share, n us he effecveness f he frm s efensve r ffensve argeng he cmmnly recgnze facr shul be an mpan facr fr eermnng he frm s sraegc renan. As a frm s mare share ncreases, shul ncrease s epenure n efensve argeng bh because cusmer acusn s less effecve n generang sales an because cusmer reenn helps fen ff mre aggressve cusmer swchng frm he rval. In he case f a ecrease n mare share, a frm shul ncrease s epenure n ffensve argeng ae avanage f he rval s vulnerably an bul up s mare share, as s fen ne n pracce. hus, Prpsn 3 suggess ha he cmpeng frms are engagng n a ug-f-war n whch mre ffensve epenure by ne frm rggers mre efensve epenure by he her. Prpsn 3 als suggess ha a frm s sraegc renan shul nee epen crcally n he relave effecveness f argee prmns. Everyhng else beng eual, f a frm s mre effecve n usng ffensve (efensve) argee prmns ncrease s mare share, shul spen mre n cusmer swchng (reenn). hs means ha a frm shul spen relavely mre n he ype f prmn ha ncreases he frm s mare share he ms. Ineresngly, as a frm s sh-erm sraegc renan epens n s mare share as well as s relave argeng effecveness, he sweepng sraegc prescrpn ha all frms r all larger share frms shul fcus n cusmer reenn can be msleang. Prpsn 3 pns u ha a smaller (larger) mare share frm can pmally chse fcus n cusmer reenn (acusn) f argeng wn (rval s) cusmers s sgnfcanly mre effecve r less csly fr he frm. Smlarly, we can ae avanage f ur analycal sluns an eamne many her eulbrum relanshps. In general, he relave argee epenure fr a specfc grup f cnsumers epens nly n he relave argeng effecveness an n he relave value f mare share ncrease fr he cmpeng frms. If we cmpare frms argee epenures acrss cnsumer grups, he relave epenure als epens n he sze f each cnsumer grup. Lng-Run Mare Share an Sraegc Orenan We can carry u he analyss f he lng-run eulbrum by usng euans () an () (relanshps fr pmal prmnal sraeges n seay sae are lse n able ). Ne frs ha he asympc sably f he eulbrum reures > >. (7) Le y ene he relave un prf margn, an efne ξ () y y y. Frucher, Zhang / DYNAMIC ARGEED PROMOIONS 9 ABLE Relanshps Beween Opmal Prmnal Sraeges n Seay Sae ype f Cmparsn Relanshp Seay-Sae Value argee prmnal ncenves al prmnal epenures

8 JOURNAL OF SERVICE RESEARCH / Augus 4 FIGURE Lng-Run Relanshp Beween Mare Share an Sraegc Orenan Frm Defensve Bh Frm Offensve Frm Offensve Offensve Frm Defensve ( ) 4 3 ( ) Cnn (7) mples ξ (y) >. In seay sae, a frm s ξ() y mare share s gven by () y. We can verfy + ξ() y ha lm ( y), ( ), an () y > fr y (, ). y hs means a frm s lng-run mare share ncreases wh s relave un prf margn. he reasn s ha a hgher un prf margn ue eher cs avanage (r perhaps cnsumer lyaly) wll mvae a frm spen mre n argee prmns an hus gan a hgher mare share n he lng run. I s als sraghfrwar shw, by ang ervaves f a frm s seay-sae mare share wh respec a specfc effecveness measure, ha a frm s lng-run mare share ncreases wh s argeng effecveness, bh efensve an ffensve. hus, ur mel suggess ha gan he lng-run mare share avanage when argee prmns are feasble, a frm shul srve bs s un prf margn eher by lwerng cs r bulng cnsumer lyaly an mprve s argeng effecveness. Ms mpan, we can she sme lgh n he relanshp beween a frm s lng-run mare share an s sraegc renan n argee prmns, as measure by he frm s relave epenure n efensve an ffensve argeng. In seay sae, we have. Le us efne w mre srucural varables, 3 + an 4 +, where > 3 > 4 > by cnn (7). Frm wll be efense rene (spenng mre n efensve argeng) ha s, >,f > 3 whereas frm wll be e- fense rene f < 4. hus, he sraegc renans fr he w frms n he lng-run eulbrum are as llusrae n Fgure. he fllwng prpsn cmes recly frm Fgure. Prpsn 4: A fcus n cusmer reenn s n an pmal lng-run sraegy fr all frms n a cmpeve cne. A frm wh a suffcenly large mare share shul fcus n cusmer reenn, whereas a frm wh a suffcenly small mare share shul sress cusmer acusn. hs s he case regarless f wheher r n he frm s mre effecve n argeng s curren cusmers. 9 When mare shares are mre evenly ve, he pmal sraegy fr a frm s fcus mre n cusmer acusn. hus, cusmer acusn can be a lng-erm wnnng sraegy fr all frms n an nusry. Inuvely, a fcus n efensve argeng s a sensble cmpeve sraegy fr a frm nly f faces a rval s nense ffensve argeng, whch s he case when he mare shares are unevenly srbue. When he mare shares are mre r less evenly srbue, he rval ees lle ffensve pressure, an a frm s beer ff reucng s efensve argeng. Cnseuenly, he eulbrum cann be susane when bh frms fcus n cusmer reenn hrugh efensve argeng. hese cnclusns een he man resul n McGahan an Ghemawa (994) ha nly ne frm (.e., he smaller mare share frm) can prfably fcus n cusmer acusn, an hey cnras wh Ercsn s (993) cnclusn ha efensve an ffensve prmns shul be balance n seay sae. In ur mel, hese w ypes f prmns are balance fr a frm nly f s mare share aes n a specfc value. he een ha ffensve argeng s he cause fr cusmer churnng, Prpsn 4 hus precs ha amng nusres where argee prmns are feasble, 9. If frm, fr nsance, s mre effecve n efensve argee prmns( > ), cnn (4) mples >. here ess n sa- ble lng-run eulbrum n whch bh frms are mre effecve n efensve argeng.

9 Frucher, Zhang / DYNAMIC ARGEED PROMOIONS Defensve an Offensve Epenures f Frms an FIGURE Dynamcs f Prmnal Epenure me Defensve- Offensve- Defensve- Offensve- Prfs FIGURE 4 Dynamcs f Prfably 3 me Frm Frm Mare Shares f Frms an me cusmer churnng wll be mre severe n he nusres n whch cmpeng frms are mre eually mache, all else beng eual. Numercal Eample FIGURE 3 Dynamcs f Mare Shares he raecres f a frm s prmnal sraegy, mare share, an prfs ver me can be llusrae hrugh a numercal eample. Fr hs purpse, we se. 9,. 9, 5, ().4, ()., ()., an ().3. he resuls f ur smulan are shwn n Fgures, 3, an 4. Frm, wh a smaller nal mare share, aggressvely pursues new cusmers hrugh ffensve argee prmns a he sa f he game. Over me, Frm ecreases s ffensve epenure an ncreases s efensve epenure as. We chse.9, as n he Ercsn (99) an Frucher an Kalsh (997) sues, an chse sasfy he sably cnn (4). s verall mare share ncrease s ue msly he ncrease n repea purchases, whch are belw he seaysae level a he use. Frm, n cnras, nally spens mre n efensve argeng han n ffensve argeng n an eff manan s large mare share bu becmes ncreasngly ffense rene as s mare share (msly repea purchasers) s chppe away by he rval. In he lng run, bh frms spen mre n cusmer swchng an share he mare eually n he ynamc lng-run eulbrum. In hs ynamc prcess f gravang war he lng-run mare shares, Frm s prfs ecrease whle Frm s ncrease, as shwn n Fgure 4. CONCLUSIONS argee prmns are ganng ppulary as a sraegc mareng l. Many frms acrss fferen servce nusres are embracng new nfrman echnlges an gearng up bul her wn sphscae cnsumer aabases mprve her argeng accuracy. Our analyss hus aresses a mely manageral uesn f hw a frm shul use argee prmns acheve he sraegc becves f cusmer reenn an acusn. Our nrmave analyss enables us enfy he eermnans f pmal argeng sraeges an characerze he pmal verall sraegc psure fr a frm s argeng prgrams: A frm s prmnal ncenves fr cusmer reenn (acusn) shul be relae psvely s wn (s rval s) mare share, s argeng effecve-. hs s because we have < < n hs eample he fac ha he mare s eually ve n seay sae an each frm has ne uaer f repea an swchng sales s ue he symmery n hs eample.

10 JOURNAL OF SERVICE RESEARCH / Augus 4 ness, an cusmer prfably bu negavely he reempn rae f s prmns. A frm can prme pmally by ausng s planne prmnal ncenves reflec he bserve fference beween acual an planne mare shares, as well as beween acual an planne reempn raes. A frm shul spen mre n cusmer reenn f s mare share s ncreasng bu spen mre n cusmer acusn f s mare share s ecreasng. A fcus n eher cusmer reenn r acusn can be an pmal lng-run sraegy fr a frm. A frm wh a large mare share shul fcus mre n cusmer reenn. Oherwse, shul fcus n cusmer acusn. Inee, a fcus n cusmer acusn can be a wnnng busness sraegy fr all cmpeng frms f her mare shares are smlar, whereas a fcus n cusmer reenn s n. bul a lng-run mare share avanage n he age f nfrman-nensve mareng, a frm shul srve mprve s argeng effecveness an ncrease s un prf margn hrugh, fr nsance, bulng cusmer lyaly r mprvng pruc ualy. Fuure research can een ur analyss n w mar recns. Frs, he resuls frm any fferenal game always hnge n he specfcan f he ynamcs fr sae varables. Fuure research can eplre he rbusness f ur cnclusns by usng fferen bu eually plausble ynamcs fr sae varables. he rbusness can als be chece by eenng ur mel nclue mre frms an allw fr a varable mare sze. Such eensn s especally mpan fr aressng argeng ssues relae grwh nusres. Secn, ur sluns are analycal, an hey are well sue emprcal esman f prper aa are avalable. Such an emprcal eercse can help pn wn he parameers n he mel an prve mre specfc manageral guance fr pracners n fferen nusres. APPENDIX In hs appen, we erve clse-lp Nash eulbrum sraeges fr bh games specfe n he secn secn. Fr hese games, we prcee frs cnsruc clse-lp sraeges frm he frs-rer necessary cnns fr he pen-lp Nash eulbrum. hen we prve ha he clse-lp sraeges we have prpse sasfy he Nash eulbrum cnns cnane n euan (8). hs apprach avs echncal ffcules asscae wh he sanar mehs f ervng sae-epenen Nash eulbrum sraeges. he use f sanar mehs fr he prblems s nracable an a rcy as nee. he prceure fr eermnng he pen- an clse-lp sluns fr bh fne- an nfne-me prblems s escrbe afer we sae ur sluns frmally n he fllwng w herems. herem (clse-lp sraeges fr he fne-me prblem): Cnser he fferenal game asscae wh euans (), (5), an (6), where () s as n euan (7). Le 4 ( ) an,,, 4 (8) where sasfes he fllwng w-pn bunary value prblem (PBVP): () r () () [ ( ) ( ( ))] (), ( ), ο () [( κ () ()) ( ()) ( () ()) ()], () (9) wh,,,an. hen(,,, ) frms a glbal Nash eulbrum clse-lp sraegy f he abve fferenal game, ha s, sasfes cnn (8). Prf. See Appen C belw. he pen-lp sraeges are gven by (see Appen A belw) () () () an () 4 () where{, } are as n euan (9), an s gven by ()( ()) 4 (),,,

11 Frucher, Zhang / DYNAMIC ARGEED PROMOIONS 3 ( ) ( ( ) ( ))( ())( () ()) ( () ()) () ( )], (). () hen, s eermne hrugh. We can nw een herem he case f an nfne-me hrzn. herem (clse-lp sraeges fr he nfne-me prblem): Cnser he fferenal game asscae wh euan (). Le Ψ( ) sasfy he fllwng fferenal euan: Ψ ( ) Ψ( )[( ) () + ( )( ()) ] + Ψ ( ) [ ( ) ( ( ))] rψ( ), lm Ψ( ( )) e, () where f f. () Le Φ () e 4 Φ () e ( ) an 4,,, (3) where Φ() sasfes he fllwng nal value prblem Φ () e Φ () e [ ( )], Φ( ) Ψ ( ( )), (4) ( ) [( )( ()) ( ) ()] (), Φ e () wh,,,, an Φ s as n euan (). hen(,,, ) frms a glbal Nash eulbrum clse-lp sraegy f he fferenal game (); ha s, sasfes he cnn (8) fr he nfne-me prblem. Prf. See Appen D belw. he crrespnng pen-lp sraeges are gven by he fllwng (see Appen B belw): where{ Φ, } are as n (4), s gven by () () () Φ e an () 4 () () ( Φ e ()) 4,,, (5) ( ) [( )( ( ))( () ( )) ( ) () ()] () e, Φ (), (6) an s eermne hrugh. We frs escrbe he prceure fr cnsrucng he pen- an clse-lp sraeges fr he fferenal games sae n herems an. hen we prve ha he clse-lp sraeges we have cnsruce are Nash eulbrum sluns as sae n herems an.

12 4 JOURNAL OF SERVICE RESEARCH / Augus 4 A. HE FINIE-IME CASE Sep : Dervan f Open-Lp Sraeges Defne he cnrl varables u an u,,, as u an u,,. (A) In erms f u an u, he fferenal game asscae wh euans (), (5), an (6) becmes Ma Π ( ) e + ( ( ) u ( ) u ( ) ) e u, u () ( u () u ())( ()) ( u () u ()) (), ( ). (A) he curren-value Hamlnan fr player fr game (A) s gven by H H (, u, u, u, u, ) u u +, (A3) where s he curren-value mulpler asscae wh he sae euan. he necessary pmaly cnns fr player s pen-lp sraeges are gven by he mamzan cnn (cf. Kamen an Schwaz 99), H / u u + an H / u u + ( ), (A4) an he an euans wh he ermnal cnns H r r ( u u ), ( ). (A5) Frm (A4), we have u an u ( ),,. (A6) Pluggng (A6) n (A5) an he sae euan, we ban he fllwng w-pn bunary value prblem (PBVP): () r () () [ ( ) ( ( ))] (), ( ), () [( () () )( ()) ( () ()) ()], () (A7) where,,. Pluggng (A6) n he sae euan (5), we ban ο () [( () ())( ( ))( κ () ()) ( () ()) () ()], ( ). (A8) Cnserng (A7), we fn he pen-lp sluns be u () () () an u () ( ()) (),,. (A9)

13 Frucher, Zhang / DYNAMIC ARGEED PROMOIONS 5 We have n erms f he rgnal varables () () () an () 4 () ()( ()) 4 (),,, (A) where (), () are as n (A7); () s as n (A8), an. (A) Frm (A7), we ban <,,, (A) whch, geher wh he ermnal cnn n (A7), mples ()> (A3) fr all [, ]. Sep : Cnsrucng he Clse-Lp Sraeges Cnserng (A) an subsung he values f,, we ban by he acual saes (mare shares) as gven n euans (), (5), an (6), () () () an () 4 () ()( ()) 4 (),., (A4) In Appen C, we prve ha he clse-lp sraeges efne n (A4) are Nash eulbrum sraeges; ha s, hey sasfy cnn (8). B. HE INFINIE-IME CASE Le () () e Φ. (B) hen, as, he w euans n (A7) fr can be ransfrme n nly ne euan, () Φ e Φ () e [ () ( ( ))], Φ(. ) (B) Euan (B) fllws mmeaely by subsung (B) an s ervave wh respec n he euans fr n (A7). Frm (B), as befre, we ban Φ() > fr all [, ), whch s a smple cnseuence f he ermnal cnn n (B) an he prpey erve frm (B). In cnclusn, he PBVP (A7) s nw reuce Φ () Φ e < (B3)

14 6 JOURNAL OF SERVICE RESEARCH / Augus 4 () () Φ e Φ e [ () ( ( ))], Φ ( ), ( ) [( )( ()) ( ) ()] (), Φ e () (B4) where,,. Ne ha reucng a PBVP frm w en pns ne en pn reuces sgnfcanly he cmpley f cmpuan. Nw we wan ae anher sep n reucng he cmpley f cmpuan. Le f f (B5) an suppse Φ() e Ψ( ). (B6) hen Ψ( ) sasfes he fllwng fferenal euan: Ψ ( ) Ψ( )[( ) () + ( )( ()) ] + Ψ ( ) [ () ( ( ))] rψ( ), lm Ψ( ( )) e. (B7) Euan (B7) fllws frm (B) an he relanshp () Φe + rψ ( ). (B8) Mang use f (B7) an (B6), we can ransfrm he PBVP (B4) n he fllwng nal value prblem: () () Φ e Φ e [ ( ) ( ( ))], Φ() Ψ( )( )), ( ) [( )( ()) ( ) ()] Φ() e, () (B9) where,,, an Ψ( ( )) s bane by slvng he bacwar euan (B7). Pluggng (B) n (A8), we als have ( ) [( )( ( ))( () ( )) ( ) () ()] (), e () Φ. (B) Cnserng (B) an (A), we have he pen-lp sraeges fr hs case as () () () Φ e an () 4 () () ( Φ e ()) 4 (),,, (B) where Φ(), () are as n (B9); () s as n (B); an s as n (A). Cnserng (B) an subsung he values f,, by he acual saes (mare shares) as gven n euan (), we cnsruc he clse-lp sraeges fr hs case as

15 Frucher, Zhang / DYNAMIC ARGEED PROMOIONS 7 () Φ () e () an () 4 () Φ () e ( ()) 4 (),,. (B) In Appen D, we prve ha he clse-lp sraeges efne n (B) are Nash eulbrum sraeges fr he nfne-me hrzn prblem; ha s, hey sasfy cnn (8). C. PROOF OF HEOREM Cnser he zer-sum e + ( ), e (C) where s as n euan (9) r (A7), an s as n euan (7). Cnserng (C), we ban r + e ( ) ( ) + [ + ( r ) ] e. (C) Cnserng euan (7), we ban r e + [( ( ) + ( ) )( ) ( ) ( ) ( ( ) e ) ) ] + ( r ). (C3) Nw, subsung n frm euan (9), we ban [( ( ) ( ) )( ) ( ( ) r e + ( ) ( ) + ( e ) ) ] + ( () [ () ( ())] ()). (C4) Usng he nan n (A9), n erms û an û, we rewre euan (C4) as [( ( ) ( ) )( ) ( ( ) r e + ( ) ( ) + ( ) ) ] + [ ( u u )] e. (C5) Cnserng (8) r (A4), afer rearrangemen f euan (C5), we have r e ( ) + ( ) + + [ ( ) ( ) + ( ) ( ) ( ) u ( ) u ( u u + ) e + ( )[( ) ( ( ) u ) ( ) ( u ( ) )] +. (C6)

16 8 JOURNAL OF SERVICE RESEARCH / Augus 4 Ang he zer-sum (C6) Π Π(,,, ) as n euan () an rearrangng, we ban Π (,,, ) ( ) + [ + ( ) ( ) + ( ) ( ) ( ) ( ) u ( ) u + u u + ( )[( ) ( u ( ) ) ( + ) ( u ( e ) )]. (C7) Or, Π (,,, ) ( ) + [( ) ( ) ] [( ) ( ) ] + + ( ) ( ) ( u u + u u ) + ( )[( ) ( ( ) ) ( u + ) ( u ( ) )] e. (C8) In pacular, Π (,,, ) ( ) + [ + ( ) u ( ) u + ( u u ) + ( )[( ) ( u ( ) ) + ( ) ( u ( ) )] e (C9). Cnserng (C8) an (C9), we have Π (,,, ) ( ) + [( ) ( ) ] [( ) ( ) ] + + ( ) ( ) + ( u u u u ) + ( )[( ) ( u ( ) ) + ( u ) ( ( ) )] e (C). herefre, [ ] ( ) ( ) Π(,,, ) Π(,,, ) e Π (,,, ), + [( ) ( ) ] (C) fr every,. hs cmplees he prf f ur herem. D. PROOF OF HEOREM prve hs herem, we prcee eacly as n herem, wh he ecepn ha, nsea f he zer-sum (C), we cnser he zersum Φ() + ( Φ() ), (D) where Φ() s as n euan (4) r (B9), an s as n euans (7) an ().

17 Frucher, Zhang / DYNAMIC ARGEED PROMOIONS 9 REFERENCES Ber, E. an C. Krl (), Drec Quesns, Drec Answers, B B, 87 (),,. Brefngs (3), arge Mareng, 6 (), Case, J. H. (979), Ecnmcs an he Cmpeve Prcess. New Yr: New Yr Unversy Press. Chnaguna, P. K. an N. J. Vlcassm (99), An Emprcal Invesgan f Avesng Sraeges n a Dynamc Duply, Managemen Scence, 38, Deal, K. (979), Opmzng Avesng Epenures n a Dynamc Duply, Operans Research, 7 (4), 68-9., S. P. Seh, an G. L. hmpsn (979), A Blnear-Quarac Dfferenal Game n Avesng, n Cnrl hery n Mahemacal Ecnmcs, P.. Lu an J. G. Sanen, es. New Yr: Marcel Deer, 9-9. Dreze, X. an A. Bnfrer (3), A Renewable-Resurce Apprach Daa Valuan, manuscrp. Ercsn, G. M. (99), Emprcal Analyss f Clse-Lp Duply Avesng Sraeges, Managemen Scence, 38, (993), Offensve an Defensve Mareng: Clse-Lp Duply Sraeges, Mareng Leers, 4 (4), Fenberg, F., A. Krshna, an Z. Jhn Zhang (), D We Care Wha Ohers Ge? A Behavrs Apprach argee Prmns, Jurnal f Mareng Research, 39, Frucher, E. G. an S. Kalsh (997), Clse-Lp Avesng Sraeges n a Duply, Managemen Scence, 43 (), Ha, C., L. H. James, an W. E. Sasser Jr. (99), he Prfable A f Servce Recvery, Harvar Busness Revew, 68 (4), Hrsy, D. (977), An Emprcal Analyss f he Opmal Avesng Plcy, Managemen Scence, 3, Isaacs, R. (965), Dfferenal Games. New Yr: Jhn Wley. Kamen, M. I. an N. L. Schwaz (99), Dynamc Opmzan: he Calculus f Varans an Opmal Cnrl n Ecnmcs an Managemen. Amseram: Nh-Hllan. Kmball, G. E. (957), Sme Inusral Applcans f Mlary Operans Research Mehs, Operans Research, 5, -4. Lle, J. D. C. (979), Aggregae Avesng Mels: he Sae f he A, Operans Research, 7, McGahan, A. M. an P. Ghemawa (994), Cmpen Rean Cusmers, Mareng Scence, 3 (), Rapp, S. (995), he Bale f he Daabases: w Cmbave elephne ans Clash n he Recen Run f ay s Relanshp Mareng Wars, Drec, 7 (), 8. Rechhel, F. F. an W. E. Sasser Jr. (99), Zer Defecns: Qualy Cmes Servces, Harvar Busness Revew, 68 (5), 5-. Rss, P. E., R. E. McCullch, an G. M. Allenby (995), he Value f Purchase Hsry Daa n arge Mareng, manuscrp. Shaffer, G. an Z. Jhn Zhang (995), Cmpeve Cupn argeng, Mareng Scence, 4 (4), an (), Cmpeve One One Prmns, Managemen Scence, 48 (9), Urry, M. (995), elephne Lnes ha ry Bn: A L a he Effecs f he Mareng War Beween Lng-Dsance US Cmmuncan Cmpanes, Fnancal mes, July 6,. Vale, M. L. an Wlfe, H. B. (957), An Operans Research Suy f Sales Respnse Avesng, Operans Research, 5, Gla E. Frucher s a senr lecurer f mareng a he Schl f Busness Amnsran a Bar-Ilan Unversy, Israel. She earne all her egrees n mahemacs frm he echnn, Israel Insue f echnlgy. She hel vsng psns n mareng a Washngn Unversy n S. Lus; MI Slan Schl f Managemen; Unversy f Calfrna, Bereley; an Hng Kng Unversy f Scence an echnlgy. Her curren research fcuses n ynamc cmpeve mareng sraegy, servce mareng, an relanshp mareng. Her recen papers have appeare n Managemen Scence, Mareng Scence, Jurnal f Servce Research, Jurnal f Opmzan hery an Applcan, Jurnal f Ecnmcs, Dynamcs an Cnrl, Eurpean Jurnal f Operanal Research, Opmal Cnrl Applcans an Mehs, an Inernanal Game hery Revew. She s a member f he eral bar f he Revew f Mareng Scence, an she serves as a referee fr leang mareng acaemc urnals, amng hem Mareng Scence an Managemen Scence. Z. Jhn Zhang s an asscae prfessr f mareng a he Whan Schl f he Unversy f Pennsylvana. He earne a bachelr s egree n engneerng auman an phlsphy f scence frm Huazhng Unversy f Scence an echnlgy (Chna), a Ph.D. n hsry an sclgy f scence frm Unversy f Pennsylvana, an als a Ph.D. n ecnmcs frm he Unversy f Mchgan. Hs research fcuses n cmpeve prcng sraeges an he esgn f prcng srucures. He has publshe numerus acles n p mareng an managemen urnals n varus prcng ssues such as measurng cnsumer reservan prces, prce-machng guaranees, argee prcng, access servce prcng, he chce f prce prmn vehcles, an channel prcng. He als serves as asscae er fr he Jurnal f Quanave Mareng an area er f Mareng Scence. Hs acle, Invual Mareng Wh Imperfec argeably, cauhre wh Yun Chen an Cha Narasmhan, wn he Jhn Lle Awar an he Fran Bass Awar n.