Online Price Competition within and between Heterogeneous Retailer Groups


 Cleopatra Hancock
 3 years ago
 Views:
Transcription
1 Onlin Pric Comptition within and btwn Htrognous Rtailr Groups Cnk Kocas Dpartmnt of Markting and Supply Chain Managmnt, Michigan Stat Univrsity Abstract This study prsnts a modl of pric comptition in a markt for a homognous good with many asymmtrically positiond rtailrs, a typical xampl of which could b th onlin markts for books, music, movis or softwar. Ths markts ar highly comptitiv oligopolis srvd by hundrds of activ rtailrs and that hav bn affctd by Information Tchnologis such as pric comparison ngins and shopping bots. In ths markts, firms can only idntify broad group mmbrships to clustrs of firms, and compt within and across clustrs basd on this information, du to th incompltnss of information on th charactristics of firms. Th charactristics of th firms that shap thir comptitiv bhavior ar thir stablishd loyal sgmnt sizs and potntial comparison shoppr sgmnt sizs. To analyz such markts, w dvlop and solv a static gam of pric comptition in an asymmtric oligopoly with numrous clustrs of firms. In our analysis w s that th firms with th smallst loyal sgmnt sizs and th largst switchr sgmnt sizs ngag in a firc pric comptition whil th mmbrs of all othr groups prfr to pric at thir rsrvation pric points. W also tst and provid mpirical support for our modl prdictions using pricing data on thr catgoris. Our data st contains prics on 112 printrs from 20 rtailrs, 95 camras from 53 rtailrs and 1388 books from 15 rtailrs. Kywords: Pric Comparison Shopping; Pric Comptition; Oligopoly; Intrnt Economics. 1. Introduction Onlin markts ar incrasingly populatd with almost countlss numbrs of rtailrs that offr idntical products to thir customrs. Th onlin markts for softwar, music, movis, computrs, lctronics, appliancs, and books ar typical xampls. Th lack of ntry barrirs also contributs to th abundanc of rtailrs in onlin markts. Entry into any of ths markts is only as costly as stting up an commrc nabld sit, rsulting in many small playrs offring thir srvics to th onlin buyrs. Whn customrs compar prics of a givn idntical product across rtailrs, ths rtailrs ar in dirct comptition for th businss of that customr rgarding that particular product. Th prolifration of pric comparison ngins and shopping agnts contributs to th practic of pric comparison shopping and has potntial to incras comptition. Evidnc of such comptition is providd in rcnt rsarch on comptition btwn convntional rtailrs ([19]), convntional rtailrs and mail ordr stors, ([23]), convntional rtailrs and onlin stors ([5],[12]) as wll as onlin stors ([14],[7],[22]). Thrfor, thr is hightnd attntion to comptitiv stratgis that could mrg as information tchnologis chang th way popl shop. W mak a distinction btwn comparison shopprs who may us information sourcs such as pric comparison ngins and shopping agnts and loyal customrs who prfr a singl rtailr for thir shopping in a particular catgory. W rfr to th customrs, who can compar prics of som products across stors as informd customrs or switchrs as in [21], [24] and [18]. Smallr rtailrs, or nw ntrants, in th onlin markts, rly on th pric comparison shopprs as thir sol sgmnt of potntial customrs. W considr such firms to b mor intrstd in and dpndnt on switchrs rathr than stablishd loyal sgmnts. Slling to this sgmnt of informd customrs rquirs that th firms compt with all othr firms that ar similarly accssibl from th pric comparison ngin utilizd by th customrs. Thrfor, firms that plac a highr mphasis on pric comparing shopprs ar mor likly to oprat in mor comptitiv nvironmnts /04 $17.00 (C) 2004 IEEE 1
2 On th othr hand, th mor stablishd firms also compt in th sam markt. Howvr, having srvd th markt for a whil, th mor stablishd firms also njoy th loyalty of a largr sgmnt of its customr bas and can xtract monopoly profits from ths customrs who ar uninformd of, or prhaps simply unintrstd in th offrings of othr rtailrs. W rfr to ths customrs as th loyal customrs. Ths mor stablishd firms also wish to sll to th switchr sgmnts. Howvr, sinc th targtability, th ability to prdict if th customr is a loyal or a switchr as wll as th addrssability, th ability to contact customrs individually, is imprfct, rtailr hav no way of pric discriating ([8],[3]). Morovr, whras th mor stablishd firms njoy having considrabl loyal sgmnt sizs, th loyal customrs of a nw ntrant, or a small playr ar ngligibly small, which is a sourc of positional asymmtry that is typical of spcially onlin markts. Thrfor, on important charactristic of th onlin markts undr inspction so far is that thy ar markts with many asymmtrically positiond firms compting for th businss of th potntial customrs. An analysis of markts with many asymmtrically positiond firms thrfor bcoms a ncssary nxt stp givn prvious works that dalt with th many and asymmtrical componnts sparatly. [24] xas th many componnt analyzing a symmtric oligopoly and [18] xas th asymmtrical componnt analyzing an asymmtric duopoly. Howvr, nithr th [24] nor th [18] modls ar sufficint to analyz a markt with many asymmtrically positiond firms. Our work analyzs an asymmtric oligopoly by introducing groups of rtailrs with various lvls of loyal and pric comparing customrs. Although w work with similar modling assumptions, our modl of asymmtrical many firms is nithr a dirct intrpolation of ths prvious modls, nor a simpl xtnsion of ithr. Mor spcifically, our modl assums that thr ar many firms that may or may not hav similar sizs of loyal and switchr customr sgmnts. This is an oligopoly of many asymmtrical firms with incomplt information. Noticing th fact that nithr th loyal nor th switchr sgmnt sizs ar publicly availabl information across firms, our modl rcognizs that firms can group any othr firm as ithr a firm with possibly largr, th sam or smallr loyal/switchr sgmnt siz. W also assum that firms can corrctly classify thmslvs with at last som othr firms in th sam group and obsrv at last som firms within ach othr group. Hnc, w hav an oligopoly with firms that hav incomplt information on th sizs of loyal and switchr sgmnts of ach othr. In ordr to analyz th mrging pric comptition with many rtailrs, w dvlop a stylizd modl of pric comptition in this asymmtric oligopoly and solv it as a static, on shot modl with incomplt information. Whil coopration, larning, rputation and punishmnt may b issus that shap stratgis in gams playd rpatdly, w bliv th costs of including ths complicatd stratgis by adapting a rpatd gams framwork would outwigh th bnfits. As a rsult w rsort to a on shot static gam and dmonstrat how firms classify thmslvs as pric promotrs or rgular pric stors givn th abundanc of comptition. W assum that, although firm lvl loyal and switchr sgmnt sizs ar unknown, firms can idntify clustrs of firms with similar loyal and switchr sgmnt sizs. In this work w analyz a markt with basically four clustrs of firms, whras th rsults can asily b xtndd to markts with finr lvls of clustring. W catgoriz ach firm as having a small or larg numbr of switchr customrs and as having a small or larg numbr of loyal customrs. This catgorization rsults in four clustrs. W rfr to th clustrs as LL, LS, SL, SS clustrs, whr th first lttr rfrs to th numbr of loyal customrs (Larg vs. Small) and th scond lttr rfrs to th numbr of switchr customrs. Thrfor, LS clustr, for xampl, is th group of firms with a larg numbr of loyal customrs and a small numbr of switchr customrs, a typical firm in which can b a nich click and mortar firm that has an stablishd loyal sgmnt but rlativly ngligibl onlin prsnc. Typical xampls from th onlin book markt could b powlls.com and wordsworth.com. On th othr hand a typical firm blonging to th SL clustr would b a pur onlin playr with no stablishd loyal sgmnt but a motivation to attract switchr sgmnts by utilizing traffic gnration stratgis onlin. Typical xampls, again from th onlin book markt could b txtatcost.com and campus.com. Firms that blong to LL clustr can b stablishd onlin firms that hav alrady invstd into building loyalty whil simultanously compting for th businss of switchrs in a hop to rtain thm as loyal customrs in th futur. A typical xampl could b a firm lik Amazon.com. Biggr clickand mortar firms such as Barns and Nobl /04 $17.00 (C) 2004 IEEE 2
3 also blongs to this clustr bcaus of thir high traffic gnration and loyalty potntials Finally, a firm from th SS clustr would b a fring playr with nithr a significant numbr of loyal customrs nor an ffctiv attmpt to b found by switchr customrs. Thr ar possibly hundrds of pur onlin booksllrs that could b catgorizd in this clustr. Whras loyal customrs ar xclusiv to ach firm, switchr customrs ar not. Hnc, w also assum that all th switchrs that an LS and SS clustr firm can sll to ar as wll rachabl by any firm in th LL and SL clustr. To put it anothr way, th switchrs that th LL and SL clustrs can srv only partially know firms within th LS and SS clustrs (W mak this assumption to ascrtain that if firms within th SL clustr ar th only ons compting for switchrs offring low prics, as our analysis shows in th modl sction, thn all switchrs ar srvd by ths firms and no switchr rmains who dos not know any of th firms in th SL clustr.). Our objctiv in spcifying groups of rtailrs is rathr simpl. In our analysis that will follow w dmonstrat that, in a markt with many asymmtrically positiond firms, only thos firms that hav a highr intrst in th switchr sgmnt ngag in pric promotional bhavior by offring any pric discounts at all. Our analysis shows that, thr ar two divrs stratgis that mrg in this markt, on adaptd by th firms in th LL, SS and LS clustrs, and on adoptd by firms in th SL clustr. Th firms in th SL clustr compt for th switchrs and thir comptition rsults in randomizd prics ranging from th rsrvation pric to almost down to th marginal cost of th itm. Drivn away by this firc pric comptition, firms in th othr clustrs do not pric promot at all. Also notic that, our choic of S and L sizs ar somwhat random, but this choic is sufficint nough to dmonstrat th fact that only th firms with th highst proportion of switchr customrs, or with th lowst Switchr/Loyal ratio will b offring pric promotions. Our findings also provid an oprational xplanation to th obsrvd pric disprsion that has rcivd widsprad rsarch attntion. Rsarch strams in conomics and markting hav rportd and attmptd to xplain th sourcs of disprsd prics whr a onpric rul was xpctd to apply ([21], [6], [5], [9], [2], [15], [19] and [11]). Our modl shows that, asymmtrically positiond firms may ngag in comptitiv bhavior that rsults in a varity of promotional pattrns, which in turn displays pric disprsion for th homognous product xad. Litratur rviw Economics, markting and conomics of information systms litraturs hav rich rsarch strams on pricing in a comptitiv nvironmnt. Th rsarch strams in pricing in a comptitiv nvironmnt ar ithr gam thory basd modls that sk quilibria in stylizd modls of profit maximizing firms ([24], [18], [17], [16], [20] and [19]) or mpirical paprs ([4] and [13]). Som ky findings of th gam thortical modls is that (i) loyal and switchr sgmnts and thir sizs affct firms pricing stratgis ([24], [18]); (ii) brands strongr vs. wakr in trms of brand/stor loyalty and brand/stor positioning dvlop rlativly divrs optimal pricing stratgis. Howvr, conflicting rsults ar rportd for such promotional activity. Whras [20] conclud that th avrag discount offrd by th strongr brand is largr than th avrag discount offrd by th wakr brand, [19] conclud on th contrary. Similarly, thr ar inconsistncis in findings rlating to th frquncy of pric promotions. [18] and [20] conclud that th frquncy of promotions for th strongr brand is lss than th frquncy of promotions for th wakr brand. With thortical and mpirical vidnc, again [19] concluds on th contrary. Uniquly, [19] also conclud that traffic building and consumr rtntion ar important considrations in dtring th dpth and frquncy of pric promotions. Th rcnt works on pricing stratgis in onlin markts hav gnrally attmptd to xplain th rasons for disprsd prics and xplor th natur of pricing stratgis ([11], [2], [5], [14], [9], [15] and [10]). On important considration is on th xistnc of collusiv and comptitiv pricing stratgis that may coxist in onlin markts. [14] show that industry and firm spcific attributs may lad to ithr collusiv or comptitiv pricing in an onlin markt. Th rsults of this study paralll our findings whr firm stratgis ar ithr collusiv or comptitiv basd on th rlativ sgmnt sizs of th firms. Th rst of th papr is organizd as follows. In th nxt sction w prsnt our modl with th solution. Thn w provid mpirical validation for th basic prdictions of our modl. W furthr xplor som aspcts of our modl and its mpirical validation in th discussion sction. W wrap up with th conclusions sction /04 $17.00 (C) 2004 IEEE 3
4 MODEL Th assumptions and charactristics of our modl ar similar to thos in [24] and [18]. Howvr, as mntiond bfor, nithr th [24] modl nor th [18] modl suffic to analyz a markt with many rtailrs, som with symmtric som with asymmtric loyal sgmnt sizs. Thrfor our modl is nithr a dirct intrpolation of ths prvious modls, nor a simpl xtnsion of ithr. Introducing groups of rtailrs with various lvls of loyal customrs, our modl analyzs an asymmtric oligopoly. W assum a markt for a homognous good, such as a book, CD, DVD, a brand nam computr, lctronics or an applianc. On th dmand sid, thr ar two sgmnts of customrs, loyal customrs and comparison shopprs, and ach customr wishs to purchas a singl unit of th good. On th supply sid of our modl thr ar k 8 Firms; Firm 1 thru Firm k. Th loyal customrs ar loyal to only on firm, and w rprsnt th numbr of customrs who ar loyal to Firm i as n i. W assum that ni can tak ithr of th two valus, larg (L) and small (S). This is not a strict assumption and can b rstatd with a largr st of valus without any chang on th rsults. Th comparison shopprs, s, (switchrs) ar not loyal to any firm and buy from th lowst pricd firm. Th potntial numbr of comparison shopprs, or switchrs that considr a firm can as wll tak ithr of th two valus, larg (L) and small (S). Again, this assumption could as wll b rstatd with a largr st of valus without any chang on th rsults. Morovr, th valus larg (L) and small (S) nd not b idntical for loyal and switchr sgmnts, but w assum thm as idntical across sgmnts for simplicity. Conscutivly, ach firm blongs to any of th four clustrs, LL, LS, SL, SS clustrs, whr th first lttr rfrs to th numbr of loyal customrs (Larg vs. Small) and th scond lttr rfrs to th numbr of switchr customrs. W assum that thr ar at last two firms in ach clustr 1. 1 This assumption is also mad for simplicity purposs and is not crucial to th rsults. In fact, only for th SL clustr this assumption is somwhat mor crucial. Howvr, although w do not prsnt th dtails of such an analysis hr, vn if SL clustr had only on firm in it, th ovrall rsults would rmain th sam. Th only diffrnc in this cas would b that th firm in SL clustr along with th firm(s) in ithr SS and LL clustrs would pric promot whil firms in th LS clustr would pric at th rgular pric. For sak of simplicity w assum at last two firms in ach clustr. Howvr, also not Customrs buy from any firm only if th pric thy ar givn is lss than thir rsrvation pric, r. Whil th sizs of th sgmnts L and S and th rsrvation pric r ar common knowldg, firms cannot pric discriatly bcaus of imprfct addrssability and targtability. All firms fac cost functions with fixd and marginal costs that w assum to b zro without any loss of gnrality. Th profit functions of th firms ar givn by. pi ( ni + s) pi = Min[ p j ] π i = pi ( ni + s v) pi = pv = Min[ p j ] (1) pini pi > p j whr p i rprsnts th pric quotd by Firm i and p i rprsnts th vctor of prics quotd by all othr firms. As is vidnt from th profit function, w assum that in th vnt of a ti in prics, th firms in th markt srv switchrs qually. In th analysis that follows w first show that thr is no Nash quilibrium in pur stratgis in this gam. Howvr, thr xists a mixd stratgy Nash quilibrium and w sktch this mixd stratgy quilibrium latr in our analysis. Th Analysis As usual, w first dfin th uppr and lowr boundaris of firms supports. Th uppr bound of th fasibl pric st is th rsrvation pric. Prics highr than th rsrvation pric will rsult in no sals at all, whil positiv profits ar possibl whn th rsrvation pric is quotd. Thrfor, th highst pric that any firm can charg is th common rsrvation pric, r. Th lowst pric any firm will vr considr charging is givn by pi = nir /( ni + s). To s this, not that Firm i can hav a motivation to rduc its pric down to a lvl whr, if it succssfully capturs th switchrs, it maks at last th sam profit it would gt from slling to its loyal customrs at r. That is; ( ni + s) pi = nir. Sinc for all firms in a givn clustr th sgmnt sizs ar assumd to b idntical, th imum prics ar also idntical. Morovr, biggr loyal sgmnt siz will man highr potntial loss in profit du to pric rductions, and consquntly, th lowst pric at which th firm can still bnfit from srving th that this assumption has gratr fac validity in a typical onlin markt givn th larg numbr of rtailrs /04 $17.00 (C) 2004 IEEE 4
5 switchrs will b highr for firms with largr loyal sgmnts. If w rfr to th common imum pric shard by th mmbr firms of th AA clustr as p AA, it is straightforward to notic that p SL = Sr /( L + S) will b lowr than p LL, p SS and p LS. Thrfor, firms in th SL clustr will hav th lowst imum pric. Sinc any firm assums that all firms thy ar in th sam clustr with shar th idntical sgmnt siz charactristics, thy will assign th idntical imum prics to thos othr firms. W first show th nonxistnc of a pur stratgy Nash quilibrium. Proposition 1: Thr is no Nash quilibrium in pur stratgis. Th tchnical proof is similar to thos in [18] and [24] and hnc omittd hr. Howvr, w provid an intuitiv xposition. Notic that, th motivation to undrcut th pric of othr lowr pricd firms in ordr to captur th switchrs rsult in a downward push in prics. This forc is spcially activ among all firms within th SL clustr, sinc thy ar th firms that can undrcut all othr firms. Simultanously, th motivation to incras th pric to th rsrvation pric, if th switchrs ar not srvd with a lowr pric, pushs prics up. Th rsult is a lack of pur stratgis. Bfor prsnting th xistnc of a mixd stratgy quilibrium by construction, w also nd to stablish th quilibrium profits of all th firms. Proposition 2: Th quilibrium profits of all firms in this gam will b qual to thir rsrvation utilitis which ar th lowst profits that a firms opponnts can hold it to by any choic of thir own prics. Proof: For this gam, th rsrvation utilitis, or max profits of all th firms ar givn by n i r. Thrfor, all firms in LL and LS clustrs hav rsrvation utilitiy Lr whil all firms in th SS and SL clustrs hav rsrvation utility Sr. Ths ar th lowst profits Firm i s opponnts can hold it to by any choic of p i providd that Firm i corrctly forss p i and plays a bst rspons to it. That is; mm π i = max π i ( pi, p i ) = nir i (2) p i pi Nxt w show that th quilibrium profits of ths firms will b qual to thir max profits. To s that this indd is th cas, not that all k firms hav a loyal sgmnt that will buy from thm irrspctiv of th pric, as long as th pric thy quot is lowr than or qual to th rsrvation pric. Hnc, all firms can guarant th profit n i r by choosing to pric at r. In trms of undrcutting all othr firms and srving th switchr sgmnt, only firms in th SL clustr hav an advantag. Howvr, sinc thr ar mor than two of ths firms with th small loyal sgmnt sizs, thy can also at most guarant a profit of n i r = Sr. That is, no singl firm has an absolut advantag to cut down prics to captur th switchr sgmnt for sur. Hnc, th highst attainabl profits for th firms in this gam ar thir max profits. Now that w hav stablishd th charactristics of th supports ovr th fasibl rang of prics, w can solv th quilibrium pricing stratgis of th firms. Any firm will srv its loyal sgmnts with th pric it chooss as long as th pric is blow th rsrvation pric, and any firm can captur th switchr sgmnt if th pric it quots is lowr than all th prics quotd by th compting firms. Thrfor, for any pric p, xcpt for any point whr firms may hav mass points, such as p = r, th quilibrium conditions for this pricing gam for k firms can b writtn as: E[π i ] = nir = ni p + (1 Fj ( p)) ps i (3) j i Nxt proposition discovrs and prsnts th uniqunss of som positions firms hold in this gam with many opponnts and nabl us to solv th st of quations w prsntd. Proposition 3: Only firms in th SL clustr will hav positiv support in th intrval [ p SL, r] or any othr intrval. Proof: W start our analysis in th intrval with th lowst prics. Sinc in [0, p SL ] no firm can raliz a profit highr than its max profit, it is th nxt intrval [ psl, p + ] that th firms in SL clustr can pric in. In this notation, w rfr to th imum of ( pss, p LL ) as p +. W dnot th numbr of firms in SL clustr as and also rfr to th firms in ithr SS or LL clustr with th nxt lowst imum pric as Firms +. Not that in th intrval [ p SL, p + ] all firms in SL clustr will hav lowr prics than th rst of th firms with probability 1, and hnc can captur th switchr sgmnt if thy can pric lowr than th /04 $17.00 (C) 2004 IEEE 5
6 othr firms in th SL clustr. Th comptition in this intrval can b thought to b vry similar to that in [24] with two xcptions. First th numbr of firms is dtrd xognously, and scond, thr ar in fact othr firms compting in th markt, but just not in this intrval. Thus, th firms in th SL clustr will randomiz thir prics in this intrval so that th xpctd profit will b qual to th rsrvation profits. W can writ th quilibrium conditions for this intrval as: mm π = Sr = Sp + [ 1 F ( p)] pl (4) whr rprsnts th numbr of firms in th SL clustr. Not that in this quation, th intractions with only th othr firms in th SL clustr ar includd in th formulation bcaus all othr firms hav imum fasibl prics abov th uppr limit of this intrval. Th solution to this quilibrium condition is: 1 r p S F ( ( ) p) 1 pl = (5) Not that with this solution F ( p SL ) = 0 as xpctd and th cumulativ probabilitis of firms in th SL clustr pricing blow p + is givn by: ( r F ( p) 1 = p p ) + s 1 S + (6) W will us this distribution function for our analysis in th nxt intrval. Not that, this cumulativ function rprsnts th mass of prics alrady lowr than th prics of th rmaining firms. Hnc, dpnding on th dtrimntal sizs ths functions rach for th intrvals in which + firms can vr pric, firms will dcid if thy pric at all. Aftr showing that th firms in th SL clustr pric in th intrval [ p SL, p + ], w procd to show that, it is not possibl for any othr firm to hav support in th intrval [ p SL, r]. Not that th lowst pric that Firms + will vr quot is p +, and at this pric th xpctd profit thy will raliz is givn by: π + ( p+ ) = n+ p+ + [1 F ( p+ )] p+ s (7) Yt, Firms + will nvr pric at p + if π + ( p+ ) is lss than thir max profit of r. Insrting valus from Equation (6) into n + Equation (7) w s that π + ( p+ ) < n + r always holds, which mans that Firms + will nvr pric at p + givn th SL firms ar alrady compting for th switchr sgmnt blow this pric. Also not that, sinc only th SL firms can compt at p+ and possibly abov as w hav just shown, th cumulativ distribution functions prsntd by Equation (5) will also rmain valid abov p +. In fact, w can solv for th lowst pric point abov p + that Firms + will vr rduc its pric to by solving th quation: n + r = n+ p + [ 1 F ( p)] ps (8) Th only solution of this quation that is abov p + is r. Hnc, givn th firms in th SL clustr ar alrady compting for th switchr sgmnt blow p +, Firms + will nvr pric in th intrval [ p +, r] but only at r. Morovr, sinc th firms in othr clustrs, including thos in LS ar no diffrnt than Firms + in rsponding to th pric comptition btwn th firms in SL clustr, thy will also not compt in any intrval but pric strictly at r. That is, all th firms in th group with rlativly largr loyal sgmnts will only pric at thir rsrvation prics. Hnc, in any givn intrval, only th firms in th SL clustr will hav support bcaus thy ar th only firms that can offr th dpst discounts to captur th switchr sgmnt. This is a critical rsult. Th frquncy and dpth of discounts th firms offr in ordr to stal th switchr sgmnt from on and othr ar so significant that, it dos not pay off for any othr firm to vn attmpt to srv th switchr sgmnt. That is, only th firms that hav th last to los offring th dpst discounts will offr discounts forcing th othr firms pric at th rsrvation pric. Hnc, most firms dlgat th pric comptition to th firms that can profitably compt with ach othr in this quilibrium. Solving Equation 3 accordingly, w driv th probability distribution functions rprsnting th quilibrium stratgis of th firms. 0 p < r f i ( p) = 1 p = r i LL, LS, SS (9) 0 p > r /04 $17.00 (C) 2004 IEEE 6
7 0 ( r p) S pl f = k ( p) rs 2 p L 1 i SL (10) ( 1 ) 1 p p < p SL p < r p r SL Equations (9) and (10) dmonstrat th two distinct promotional stratgis that firms adopt in a markt with many asymmtrically positiond rtailrs. Firms with larg loyal sgmnt sizs nvr promot in this markt. Figur 1 dpicts th cumulativ distribution functions that rprsnt th mixd stratgis firms adopt. F(p) P SL F SL (p) p + p LS r F LL (p) F LS (p) F SS (p) Figur 1: Th cumulativ pric distribution functions of th firms. Empirical Validation: In this sction, w us data from thr markts with many asymmtrically positiond rtailrs to tst our modl prdictions. W choos th onlin markts for books, printrs and camras for this purpos. Dscription of th Data St Our modl yilds prdictions on th promotional bhavior of th firms basd on th siz of thir rlativ loyal customr sgmnts, givn thr is also a switchr sgmnt that is awar of th prics quotd by at last som of ths rtailrs. Whil, on could list all th rtailrs that ar slling th homognous good to incorporat in such a study, it is also crucial that, th switchr sgmnt b awar of availabl prics from most of p ths rtailrs includd in th list. Othrwis, th comptitiv forcs that w modl in our rsarch would fail to b oprational. To find such a markt, in which not only th majority of th rtailrs slling th homognous good ar idntifiabl, but also all ar includd in th comparison shopping st of th switchr sgmnt, w turnd to th onlin markts for camras, printrs and books. Ths markts hav many favorabl proprtis. In addition to nabling th daily collction of pric information on many itms with th last rror, th onlin markt for camras, printrs and books ar also srvd by pric comparison ngins, which ar tools that th pric comparing customrs us in ordr to obsrv all th rtailrs and thir prics for a particular product. Whil hundrds of onlin rtailrs xist, w compild th list of rtailrs that w includd in this study for ach catgory as th list of all th rtailrs that a sarch for most itms within that catgory rturnd at th most utilizd pric comparison ngin. Th pric comparison sit with th biggst markt shar that w usd for th compilation of th rtailr list was MySimon.com. During th cours of th data collction priod, MySimon was th lading pric comparison ngin with 80% of th markt shar in pric comparison sit visits with an stimatd 14 M uniqu visitors in a markt with a potntial siz of 35 M ([15]). [1] rsarch th rliability of data collctd through pric aggrgators such as MySimon and othr pric comparison sits, collcting data on 459 diffrnt books from ight pric aggrgators daily for four months. Thy conclud that MySimon covrs th markt bst in trms of crosssctional consistncy as wll as longitudinal consistncy and rport that if a singl pric aggrgator wr to b usd, that ought to b MySimon. Sinc our rsarch rquirs th covrag of a switchr sgmnt that is informd about th rtailr offrings homognously across th switchrs, w wr rquird to work with a singl pric aggrgator, and this study by [1] confirm our choic of MySimon among th st of availabl pric comparison sits. W collctd data on a randomly compild list of 1388 books from 15 rtailrs, 112 printrs from 20 rtailrs and 95 camras from 53 rtailrs. Th prics wr collctd ovr a cours of on month, Jun 2002, as a typical usr of th pric comparison sit would hav obsrvd thm. Ovrall, this attmpt rsults in mor than 800,000 data points in our data st /04 $17.00 (C) 2004 IEEE 7
8 Tsting th Modl Prdictions Our modl yilds th pricing bhavior of firms givn asymmtrical loyal sgmnt sizs. Th pricing stratgy of a rtailr is rprsntd by th probability masur of quotabl prics, and hnc w attmpt to obsrv if such data could follow from th prdictd bhavior of th firms in tsting our modl prdictions. According to our modl rsults, w can hypothsiz that thr will b two groups of rtailrs with significantly sparat pricing bhavior. Morovr, th rtailrs with smallr avrag prics will also hav highr promotional activity, whil th rtailrs with gratr avrag prics will hav lss promotional bhavior. W dfin promotional activity as pric cuts from th ongoing pric, or in mor gnral trms as frquncy and dpth of changs in th prics in th cours of th month as thy ar capturd by th standard dviation in pric. In th analysis that follows, w utiliz th avrag standard dviation across products as an indicator of promotional activity whil th avrag prics across tim and products srv as th avrag pric. To calculat th avrag standard dviation across products, w calculat th standard dviation of prics for vry product across tim and tak th avrag of thos across products within a catgory. To mpirically validat our modl prdictions w run Kmans clustr analysis for th book, camra and printr catgoris. Basd on th clustr mmbrships, w also run indpndnt sampls t tst to s if clustrs ar formd such that w hav lowr pricd highr promotional activity firms as wll as highr pricd lowr promotional activity firms. Th rsults of th Kmans clustr analysis and ttst rsults ar prsntd in Tabl 1. As Tabl 1 shows, w s significant clustrs for ach of th catgoris that w v considrd. W v namd th first clustr in any markt such that that clustr also has th highr avrag pric. As is vidnt from Tabl 1, Clustr 1 for ach catgory, on top of having th highr pric, also has th lowr lvl of promotional activity. Th pric diffrncs btwn clustrs within any catgory ar significant at th lvls. Although, significanc lvls vary, th lvl of promotional activity is also highr for th clustrs with lowr avrag prics for all catgoris. Ths rsults support th prdiction of our modl that th lowr pricd group of rtailrs compt with mor randomizd prics to captur th switchr sgmnts whil th highr pricd group of rtailrs prfr charging th highr rsrvation pric with lss randomization to maximiz thir profits from thir loyal sgmnts. W also prsnt th groups of rtailrs with thir avrag prics and avrag rtailrs in Figur 1. Camras N Avrag Pric Avrag Clustr Clustr ttst Significanc Books N Avrag Pric Avrag Clustr Clustr ttst Significanc Printrs N Avrag Pric Avrag Clustr Clustr ttst Significanc Tabl 1: Clustrs s. with Avrag Prics and In addition to th clustr analysis, w can also tst to s if a ngativ corrlation xists btwn pric and promotional bhavior, on a firmbyfirm basis. In a rgrssion analyss of all th rtailrs in ach catgory, using avrag pric as th dpndnt variabl and avrag standard dviation across products as th indpndnt variabl, th standardizd cofficint of th indpndnt variabl along with its significanc ar by dfinition idntical to th Parson corrlation cofficint and its significanc. W rport ths corrlations in Tabl 2. W obsrv from Tabl 2 that th avrag standard dviation across products as an indicator of promotional activity is a significant prdictor of th dgr of avrag pric lvls for th firms. Th ngativ and significant signs point to th fact that highr pricd firms ngag in lss promotional pric cuts, supporting our finding that th firms that go aftr pric comparison shopprs with pric cuts will hav lowr prics whil othrs will prfr to pric at th highr rsrvation prics with no discounts. Avrag pric for a firm in product catgory Camras Books Printrs ** * ** * p<.10, ** p<.05, *** p<.01 Tabl 2: Corrlations of al activity and Rtailr Prics /04 $17.00 (C) 2004 IEEE 8
9 Printr Rtailrs Avrag Pric Book Rtailrs Clustr 1 Clustr Clustr 2 Clustr Avrag Pric Camra Rtailrs Avrag Pric Clustr 2 Clustr 1 Figur 1: Scattr Graphs of rtailrs in th thr catgoris. Discussion: On thortical finding that w would lik to discuss furthr rlats to th dlgation of pric promotion by th firms with largr loyal sgmnts. As our modl dmonstrats, all but th firms in th SL clustr dlgat comptition to th firms with th last to los from th dpst pric promotions. Howvr, w can not tst this finding dirctly sinc th loyal sgmnt sizs of ach firm ar privat information that no firm would rval. Whras it may b possibl to idntify th firms with largr loyal sgmnt sizs from industry rsourcs, it is spcially unattainabl to hav information on th loyal sgmnt sizs of smallr firms. Furthrmor, givn that th numbr of firms compting in any onlin markts is possibly in th hundrds, thr will b many smallr firms on which accurat information is unattainabl. For xampl, vn in our sampl of 20 printr rtailrs, thr xist many small playrs on which vn othr firms do not hav dtaild information 2. Thrfor, whras it is mpirically not possibl to idntify th firms in th SL clustr, sinc thy ar just som small firms along with othr firms in th SS and SL clustrs, thir ability to catgoriz thmslvs as SL mmbrs is sufficint for thm to dvlop th stratgic ractions that thy dvlop. Thrfor, th capability to gnrally classify itslf and th othr firms with rspct to thir loyal sgmnt sizs is nough for any firm to bhav stratgically in this comptitiv nvironmnt. Morovr, this typ of a classification not only hlps th firms to dcid how to pric comptitivly, but ssntially catgorizs ach firm in ithr of two groups; thos that compt for pric comparison shopprs and thos for which loyal customrs ar mor profitabl to srv with highr prics. Hnc, whil w rcogniz that not having a masur of loyal sgmnt sizs is a limitation of our mpirical work, w also acknowldg that this information in dtail is nithr availabl nor ncssary for firms to form thir stratgic ractions. Th information to classify firms in broad clustr mmbrships is all that is rquird for firms to choos thir pric promotion bhavior. Conclusion: Our objctiv in building and tsting a modl of pric comptition in an oligopolistic markt with asymmtrically positiond firms was to provid thortical and mpirical insight to markts in which pric comparison shopping was possibl. From a thortical point of viw, our modl dmonstrats th xistnc of at last two distinct pricing stratgis, indicating th trad offs diffrnt firms mak in ordr to balanc th dsir to srv th pric comparing switchr sgmnt and th dsir to maximiz th profit from thir loyal sgmnts. Morovr, th two distinct stratgis also provid a thortical xplanation to th obsrvd pric disprsions in th homognous goods markts. 2 Th 20 printr rtailrs in our sampl ar pcmall.com, computrs4sur.com, solutions4sur.com, cost.com, provantag.com, 2buystor.com, programmrsparadis.com, microwarhous.com, csourc.com, buy.com, bstprics.com, valumdia.com, thnrds.nt, pcnation.com, titanlogic.com, compuamrica.com, globalcomputr.com, mwav.com, insight.com and southastrncomp.com /04 $17.00 (C) 2004 IEEE 9
10 Our cntral modl finding dmonstrats that only th firms that hav th last to los offring th dpst discounts will offr discounts forcing th othr firms pric at th rsrvation pric. W mpirically validat our modl prdictions using data from th onlin book, camra and printr markts. Th data gnrally supports our modl prdictions and provid xplanation to th divrs pricing stratgis as wll as th obsrvd prics and pric disprsions that w obsrv in many markts today. Our thortical and mpirical findings dmonstrat th waknss of firms that rly on traffic gnration thru pric comparison shopping whil simultanously signifying th accuracy of stablishd loyalty as an indicator of sustainabl profitability. A natural nxt stp for futur rsarch would b introducing htrognity to th positioning of firms. This htrognity could captur th quality tirs that firms blong to, and could rval itslf in th form of htrognous rsrvation prics compard to th homognous rsrvation prics that w assum in this study. Rfrncs: [1] Alln G., and Wu J., (2002), Data Collction From Intllignt Agnts: Whn Is Enough, Enough? Frman School of Businss, Tulan Univrsity, Working papr [2] Bay M. R. and Morgan, J. (2001), Information Gatkprs on th Intrnt and th Comptitivnss of Homognous Product Markts. Amrican Economic Rviw, Vol. 91, No. 3 pp [3] Blattbrg, R. and Dighton, J. (1991) "Intractiv Markting: Exploiting th Ag of Addrssability," Sloan Managmnt Rviw, (33)1, pp [4] Blattbrg, R. and Wisniwski, K. (1989) Pric Inducd Pattrns of Comptition, Markting Scinc, Vol. 8, No. 4. (Autumn), pp [5] Brynjolfsson E., and Smith, M. D. (2000) Frictionlss Commrc? A Comparison of Intrnt and Convntional Rtailrs, Managmnt Scinc, 46, 4 (April), [6] Burdtt, K., and Judd, K. L. (1983) Equilibrium Pric Disprsion, Economtrica 51, 4 (July), [7] Carlton D.W.; Chvalir J.A. (2001) Fr Riding and Sals Stratgis for th Intrnt, Journal of Industrial Economics, Dcmbr, vol. 49, no. 4, pp (21) [8] Chn, Y., Narasimhan, C., and Zhang, Z. J., (2001) "Individual Markting with Imprfct Targtability," Markting Scinc, 20(1), pp [9] Clay K.; Krishnan R.; Wolff E. (2001) Prics and Pric Disprsion on th Wb: Evidnc from th Onlin Book Industry Journal of Industrial Economics, Dcmbr, vol. 49, no. 4, pp (19). [10] Clay K.; Krishnan R.; Wolff E.; Frnands D. (2002), Rtail Stratgis on th Wb: Pric and Non pric Comptition in th Onlin Book Industry Journal of Industrial Economics, Sptmbr, vol. 50, no. 3, pp (17). [11] Clmons, E.K., Hann, I., Hitt., L. M., (2002) Pric Disprsion and Diffrntiation in Onlin Travl: An Empirical Invstigation, Managmnt Scinc vol. 48, No. 4. [12] Goolsb A. (2001), Comptition in th Computr Industry: Onlin Vrsus Rtail Journal of Industrial Economics, Dcmbr, vol. 49, no. 4, pp (13). [13] Kadiyali, V., Vilcassim, N. J., and Chintagunta P.K., (1996), Empirical Analysis of Comptitiv Product Lin Pricing Dcisions: Lad, Follow, or Mov Togthr? Journal of Businss, vol. 69, issu 4, pags [14] Kauffman, R.J., and Wood, C. A., (2000), Analyzaing Comptition and Collusion Stratgis in Elctronic Marktplacs with Information Asymmtry, Working Papr, Univrsity of Minnsota. [15] Kocas C., (2003) Evolution of Prics in Elctronic Markts Undr Diffusion of PricComparison Shopping. Journal of Managmnt Information Systms / Wintr , Vol. 19, No. 3, pp [16] Lal, R. (1990), "Pric s: Limiting Comptitiv Encroachmnt," Markting Scinc, 9, [17] Moorthy, K. S. (1988), "Product and Pric Comptition in a Duopoly," Markting Scinc, 7, [18] Narasimhan, C. (1988), Comptitiv al Stratgis Journal of Businss. 61, [19] Rajiv S., Dutta S. and Dhar K. (2002), Asymmtric Stor Positioning and al Advrtising Stratgis: Thory and Evidnc, with, Markting Scinc, Vol.21, no.1, pp [20] Raju, J. S., Srinivasan V., and Lal R., (1990), "Th Effcts of Brand Loyalty on Comptitiv Pric al Stratgis,'' Managmnt Scinc, 36, March, [21] Salop, S. and Stiglitz, J. (1977), Bargains and ripoffs: a modl of monopolistically comptitiv pric disprsion, Rviw of Economic Studis, 44 (Octobr), [22] Smith M. D. and Brynjolfsson E.( 2001), Consumr Dcisionmaking at an Intrnt Shopbot: Brand Still Mattrs, Journal of Industrial Economics, Dcmbr, vol. 49, no. 4, pp (18). [23] Sridhar Balasubramanian (1998) Mail vs. Mall: A Stratgic Analysis of Comptition btwn Dirct Marktrs and Convntional Rtailrs," Markting Scinc, Vol 17, No.3. [24] Varian. (1980), "A Modl of Sals," Amrican Economic Rviw, 70, [25] Washington Post (2000) On th Wb, Pric Tags Blur : What You Pay Could Dpnd on Who You Ar by David Stritfld Wdnsday, Sptmbr 27,; Pag A /04 $17.00 (C) 2004 IEEE 10
Adverse Selection and Moral Hazard in a Model With 2 States of the World
Advrs Slction and Moral Hazard in a Modl With 2 Stats of th World A modl of a risky situation with two discrt stats of th world has th advantag that it can b natly rprsntd using indiffrnc curv diagrams,
More informationQUANTITATIVE METHODS CLASSES WEEK SEVEN
QUANTITATIVE METHODS CLASSES WEEK SEVEN Th rgrssion modls studid in prvious classs assum that th rspons variabl is quantitativ. Oftn, howvr, w wish to study social procsss that lad to two diffrnt outcoms.
More informationby John Donald, Lecturer, School of Accounting, Economics and Finance, Deakin University, Australia
Studnt Nots Cost Volum Profit Analysis by John Donald, Lcturr, School of Accounting, Economics and Financ, Dakin Univrsity, Australia As mntiond in th last st of Studnt Nots, th ability to catgoris costs
More informationElectronic Commerce. and. Competitive FirstDegree Price Discrimination
Elctronic Commrc and Comptitiv FirstDgr Pric Discrimination David Ulph* and Nir Vulkan ** Fbruary 000 * ESRC Cntr for Economic arning and Social Evolution (ESE), Dpartmnt of Economics, Univrsity Collg
More informationThe example is taken from Sect. 1.2 of Vol. 1 of the CPN book.
Rsourc Allocation Abstract This is a small toy xampl which is wllsuitd as a first introduction to Cnts. Th CN modl is dscribd in grat dtail, xplaining th basic concpts of Cnts. Hnc, it can b rad by popl
More informationNonHomogeneous Systems, Euler s Method, and Exponential Matrix
NonHomognous Systms, Eulr s Mthod, and Exponntial Matrix W carry on nonhomognous firstordr linar systm of diffrntial quations. W will show how Eulr s mthod gnralizs to systms, giving us a numrical approach
More informationFACULTY SALARIES FALL 2004. NKU CUPA Data Compared To Published National Data
FACULTY SALARIES FALL 2004 NKU CUPA Data Compard To Publishd National Data May 2005 Fall 2004 NKU Faculty Salaris Compard To Fall 2004 Publishd CUPA Data In th fall 2004 Northrn Kntucky Univrsity was among
More informationLecture 3: Diffusion: Fick s first law
Lctur 3: Diffusion: Fick s first law Today s topics What is diffusion? What drivs diffusion to occur? Undrstand why diffusion can surprisingly occur against th concntration gradint? Larn how to dduc th
More informationKeywords Cloud Computing, Service level agreement, cloud provider, business level policies, performance objectives.
Volum 3, Issu 6, Jun 2013 ISSN: 2277 128X Intrnational Journal of Advancd Rsarch in Computr Scinc and Softwar Enginring Rsarch Papr Availabl onlin at: wwwijarcsscom Dynamic Ranking and Slction of Cloud
More informationRural and Remote Broadband Access: Issues and Solutions in Australia
Rural and Rmot Broadband Accss: Issus and Solutions in Australia Dr Tony Warrn Group Managr Rgulatory Stratgy Tlstra Corp Pag 1 Tlstra in confidnc Ovrviw Australia s gographical siz and population dnsity
More informationTheoretical aspects of investment demand for gold
Victor Sazonov (Russia), Dmitry Nikolav (Russia) Thortical aspcts of invstmnt dmand for gold Abstract Th main objctiv of this articl is construction of a thortical modl of invstmnt in gold. Our modl is
More informationEcon 371: Answer Key for Problem Set 1 (Chapter 1213)
con 37: Answr Ky for Problm St (Chaptr 23) Instructor: Kanda Naknoi Sptmbr 4, 2005. (2 points) Is it possibl for a country to hav a currnt account dficit at th sam tim and has a surplus in its balanc
More informationPrinciples of Humidity Dalton s law
Principls of Humidity Dalton s law Air is a mixtur of diffrnt gass. Th main gas componnts ar: Gas componnt volum [%] wight [%] Nitrogn N 2 78,03 75,47 Oxygn O 2 20,99 23,20 Argon Ar 0,93 1,28 Carbon dioxid
More informationAnalyzing the Economic Efficiency of ebaylike Online Reputation Reporting Mechanisms
A rsarch and ducation initiativ at th MIT Sloan School of Managmnt Analyzing th Economic Efficincy of Baylik Onlin Rputation Rporting Mchanisms Papr Chrysanthos Dllarocas July For mor information, plas
More informationExpertMediated Search
ExprtMdiatd Sarch Mnal Chhabra Rnsslar Polytchnic Inst. Dpt. of Computr Scinc Troy, NY, USA chhabm@cs.rpi.du Sanmay Das Rnsslar Polytchnic Inst. Dpt. of Computr Scinc Troy, NY, USA sanmay@cs.rpi.du David
More informationFree ACA SOLUTION (IRS 1094&1095 Reporting)
Fr ACA SOLUTION (IRS 1094&1095 Rporting) Th Insuranc Exchang (301) 2791062 ACA Srvics Transmit IRS Form 1094 C for mployrs Print & mail IRS Form 1095C to mploys HR Assist 360 will gnrat th 1095 s for
More informationPerformance Evaluation
Prformanc Evaluation ( ) Contnts lists availabl at ScincDirct Prformanc Evaluation journal hompag: www.lsvir.com/locat/pva Modling Baylik rputation systms: Analysis, charactrization and insuranc mchanism
More informationGenetic Drift and Gene Flow Illustration
Gntic Drift and Gn Flow Illustration This is a mor dtaild dscription of Activity Ida 4, Chaptr 3, If Not Rac, How do W Explain Biological Diffrncs? in: How Ral is Rac? A Sourcbook on Rac, Cultur, and Biology.
More information5 2 index. e e. Prime numbers. Prime factors and factor trees. Powers. worked example 10. base. power
Prim numbrs W giv spcial nams to numbrs dpnding on how many factors thy hav. A prim numbr has xactly two factors: itslf and 1. A composit numbr has mor than two factors. 1 is a spcial numbr nithr prim
More informationQuestion 3: How do you find the relative extrema of a function?
ustion 3: How do you find th rlativ trma of a function? Th stratgy for tracking th sign of th drivativ is usful for mor than dtrmining whr a function is incrasing or dcrasing. It is also usful for locating
More informationEFFECT OF GEOMETRICAL PARAMETERS ON HEAT TRANSFER PERFORMACE OF RECTANGULAR CIRCUMFERENTIAL FINS
25 Vol. 3 () JanuaryMarch, pp.375/tripathi EFFECT OF GEOMETRICAL PARAMETERS ON HEAT TRANSFER PERFORMACE OF RECTANGULAR CIRCUMFERENTIAL FINS *Shilpa Tripathi Dpartmnt of Chmical Enginring, Indor Institut
More informationHave Debit Cards Changed Thai Consumer Shopping Behavior?
Intrnational Journal of Markting Studis Novmbr, 2009 Hav Dbit Cards Changd Thai Consumr Shopping Bhavior? Chtsada Noknoi Economics and Businss Administration Faculty, Thaksin Univrsity 140 Moo 4, Kanajanavanit
More information14.3 Area Between Curves
14. Ara Btwn Curvs Qustion 1: How is th ara btwn two functions calculatd? Qustion : What ar consumrs and producrs surplus? Earlir in this chaptr, w usd dfinit intgrals to find th ara undr a function and
More informationIMES DISCUSSION PAPER SERIES
IMES DISCUSSIN PAPER SERIES Th Choic of Invoic Currncy in Intrnational Trad: Implications for th Intrnationalization of th Yn Hiroyuki I, Akira TANI, and Toyoichirou SHIRTA Discussion Papr No. 003E13
More informationRealTime Evaluation of Email Campaign Performance
Singapor Managmnt Univrsity Institutional Knowldg at Singapor Managmnt Univrsity Rsarch Collction L Kong Chian School Of Businss L Kong Chian School of Businss 102008 RalTim Evaluation of Email Campaign
More informationSUBATOMIC PARTICLES AND ANTIPARTICLES AS DIFFERENT STATES OF THE SAME MICROCOSM OBJECT. Eduard N. Klenov* RostovonDon. Russia
SUBATOMIC PARTICLES AND ANTIPARTICLES AS DIFFERENT STATES OF THE SAME MICROCOSM OBJECT Eduard N. Klnov* RostovonDon. Russia Th distribution law for th valus of pairs of th consrvd additiv quantum numbrs
More informationTraffic Flow Analysis (2)
Traffic Flow Analysis () Statistical Proprtis. Flow rat distributions. Hadway distributions. Spd distributions by Dr. GangLn Chang, Profssor Dirctor of Traffic safty and Oprations Lab. Univrsity of Maryland,
More informationForeign Exchange Markets and Exchange Rates
Microconomics Topic 1: Explain why xchang rats indicat th pric of intrnational currncis and how xchang rats ar dtrmind by supply and dmand for currncis in intrnational markts. Rfrnc: Grgory Mankiw s Principls
More informationB285141. April 21, 2000. The Honorable Charles B. Rangel Ranking Minority Member Committee on Ways and Means House of Representatives
Unit Stats Gnral Accounting Offic Washington, DC 20548 Halth, Eucation, an Human Srvics Division B285141 April 21, 2000 Th Honorabl Charls B. Rangl Ranking Minority Mmbr Committ on Ways an Mans Hous of
More informationGold versus stock investment: An econometric analysis
Intrnational Journal of Dvlopmnt and Sustainability Onlin ISSN: 2688662 www.isdsnt.com/ijds Volum Numbr, Jun 202, Pag 7 ISDS Articl ID: IJDS20300 Gold vrsus stock invstmnt: An conomtric analysis Martin
More informationA Note on Approximating. the Normal Distribution Function
Applid Mathmatical Scincs, Vol, 00, no 9, 4549 A Not on Approimating th Normal Distribution Function K M Aludaat and M T Alodat Dpartmnt of Statistics Yarmouk Univrsity, Jordan Aludaatkm@hotmailcom and
More informationthe socalled KOBOS system. 1 with the exception of a very small group of the most active stocks which also trade continuously through
Liquidity and InformationBasd Trading on th Ordr Drivn Capital Markt: Th Cas of th Pragu tock Exchang Libor 1ÀPH³HN Cntr for Economic Rsarch and Graduat Education, Charls Univrsity and Th Economic Institut
More information(Analytic Formula for the European Normal Black Scholes Formula)
(Analytic Formula for th Europan Normal Black Schols Formula) by Kazuhiro Iwasawa Dcmbr 2, 2001 In this short summary papr, a brif summary of Black Schols typ formula for Normal modl will b givn. Usually
More informationIntermediate Macroeconomic Theory / Macroeconomic Analysis (ECON 3560/5040) Final Exam (Answers)
Intrmdiat Macroconomic Thory / Macroconomic Analysis (ECON 3560/5040) Final Exam (Answrs) Part A (5 points) Stat whthr you think ach of th following qustions is tru (T), fals (F), or uncrtain (U) and brifly
More informationThe Matrix Exponential
Th Matrix Exponntial (with xrciss) 92.222  Linar Algbra II  Spring 2006 by D. Klain prliminary vrsion Corrctions and commnts ar wlcom! Th Matrix Exponntial For ach n n complx matrix A, dfin th xponntial
More informationLecture notes: 160B revised 9/28/06 Lecture 1: Exchange Rates and the Foreign Exchange Market FT chapter 13
Lctur nots: 160B rvisd 9/28/06 Lctur 1: xchang Rats and th Forign xchang Markt FT chaptr 13 Topics: xchang Rats Forign xchang markt Asst approach to xchang rats Intrst Rat Parity Conditions 1) Dfinitions
More informationCategory 11: Use of Sold Products
11 Catgory 11: Us of Sold Products Catgory dscription T his catgory includs missions from th us of goods and srvics sold by th rporting company in th rporting yar. A rporting company s scop 3 missions
More informationEssays on Adverse Selection and Moral Hazard in Insurance Market
Gorgia Stat Univrsity ScholarWorks @ Gorgia Stat Univrsity Risk Managmnt and Insuranc Dissrtations Dpartmnt of Risk Managmnt and Insuranc 800 Essays on Advrs Slction and Moral Hazard in Insuranc Markt
More informationME 612 Metal Forming and Theory of Plasticity. 6. Strain
Mtal Forming and Thory of Plasticity mail: azsnalp@gyt.du.tr Makin Mühndisliği Bölümü Gbz Yüksk Tknoloji Enstitüsü 6.1. Uniaxial Strain Figur 6.1 Dfinition of th uniaxial strain (a) Tnsil and (b) Comprssiv.
More informationSIMULATION OF THE PERFECT COMPETITION AND MONOPOLY MARKET STRUCTURE IN THE COMPANY THEORY
1 SIMULATION OF THE PERFECT COMPETITION AND MONOPOLY MARKET STRUCTURE IN THE COMPANY THEORY ALEXA Vasil ABSTRACT Th prsnt papr has as targt to crat a programm in th Matlab ara, in ordr to solv, didactically
More informationAP Calculus AB 2008 Scoring Guidelines
AP Calculus AB 8 Scoring Guidlins Th Collg Board: Conncting Studnts to Collg Succss Th Collg Board is a notforprofit mmbrship association whos mission is to connct studnts to collg succss and opportunity.
More informationImproving Managerial Accounting and Calculation of Labor Costs in the Context of Using Standard Cost
Economy Transdisciplinarity Cognition www.ugb.ro/tc Vol. 16, Issu 1/2013 5054 Improving Managrial Accounting and Calculation of Labor Costs in th Contxt of Using Standard Cost Lucian OCNEANU, Constantin
More informationExponential Growth and Decay; Modeling Data
Exponntial Growth and Dcay; Modling Data In this sction, w will study som of th applications of xponntial and logarithmic functions. Logarithms wr invntd by John Napir. Originally, thy wr usd to liminat
More informationCisco Data Virtualization
Cisco Data Virtualization Big Data Ecosystm Discussion with Bloor Group Bob Ev, David Bsmr July 2014 Cisco Data Virtualization Backgroundr Cisco Data Virtualization is agil data intgration softwar that
More informationNoble gas configuration. Atoms of other elements seek to attain a noble gas electron configuration. Electron configuration of ions
Valnc lctron configuration dtrmins th charactristics of lmnts in a group Nobl gas configuration Th nobl gass (last column in th priodic tabl) ar charactrizd by compltly filld s and p orbitals this is a
More informationC H A P T E R 1 Writing Reports with SAS
C H A P T E R 1 Writing Rports with SAS Prsnting information in a way that s undrstood by th audinc is fundamntally important to anyon s job. Onc you collct your data and undrstand its structur, you nd
More informationCategory 1: Purchased Goods and Services
1 Catgory 1: Purchasd Goods and Srvics Catgory dscription T his catgory includs all upstram (i.., cradltogat) missions from th production of products purchasd or acquird by th rporting company in th
More informationArchitecture of the proposed standard
Architctur of th proposd standard Introduction Th goal of th nw standardisation projct is th dvlopmnt of a standard dscribing building srvics (.g.hvac) product catalogus basd on th xprincs mad with th
More informationGlobal Sourcing: lessons from lean companies to improve supply chain performances
3 rd Intrnational Confrnc on Industrial Enginring and Industrial Managmnt XIII Congrso d Ingniría d Organización BarclonaTrrassa, Sptmbr 2nd4th 2009 Global Sourcing: lssons from lan companis to improv
More informationhttp://www.wwnorton.com/chemistry/tutorials/ch14.htm Repulsive Force
ctivation nrgis http://www.wwnorton.com/chmistry/tutorials/ch14.htm (back to collision thory...) Potntial and Kintic nrgy during a collision + + ngativly chargd lctron cloud Rpulsiv Forc ngativly chargd
More informationDeer: Predation or Starvation
: Prdation or Starvation National Scinc Contnt Standards: Lif Scinc: s and cosystms Rgulation and Bhavior Scinc in Prsonal and Social Prspctiv s, rsourcs and nvironmnts Unifying Concpts and Procsss Systms,
More informationAsset set Liability Management for
KSD larning and rfrnc products for th global financ profssional Highlights Library of 29 Courss Availabl Products Upcoming Products Rply Form Asst st Liability Managmnt for Insuranc Companis A comprhnsiv
More informationunion scholars program APPLICATION DEADLINE: FEBRUARY 28 YOU CAN CHANGE THE WORLD... AND EARN MONEY FOR COLLEGE AT THE SAME TIME!
union scholars YOU CAN CHANGE THE WORLD... program AND EARN MONEY FOR COLLEGE AT THE SAME TIME! AFSCME Unitd Ngro Collg Fund Harvard Univrsity Labor and Worklif Program APPLICATION DEADLINE: FEBRUARY 28
More informationCategory 7: Employee Commuting
7 Catgory 7: Employ Commuting Catgory dscription This catgory includs missions from th transportation of mploys 4 btwn thir homs and thir worksits. Emissions from mploy commuting may aris from: Automobil
More informationFraud, Investments and Liability Regimes in Payment. Platforms
Fraud, Invstmnts and Liability Rgims in Paymnt Platforms Anna Crti and Mariann Vrdir y ptmbr 25, 2011 Abstract In this papr, w discuss how fraud liability rgims impact th pric structur that is chosn by
More informationMathematics. Mathematics 3. hsn.uk.net. Higher HSN23000
hsn uknt Highr Mathmatics UNIT Mathmatics HSN000 This documnt was producd spcially for th HSNuknt wbsit, and w rquir that any copis or drivativ works attribut th work to Highr Still Nots For mor dtails
More informationSolutions to Homework 8 chem 344 Sp 2014
1. Solutions to Homwork 8 chm 44 Sp 14 .. 4. All diffrnt orbitals mans thy could all b paralll spins 5. Sinc lctrons ar in diffrnt orbitals any combination is possibl paird or unpaird spins 6. Equivalnt
More informationLong run: Law of one price Purchasing Power Parity. Short run: Market for foreign exchange Factors affecting the market for foreign exchange
Lctur 6: Th Forign xchang Markt xchang Rats in th long run CON 34 Mony and Banking Profssor Yamin Ahmad xchang Rats in th Short Run Intrst Parity Big Concpts Long run: Law of on pric Purchasing Powr Parity
More informationRemember you can apply online. It s quick and easy. Go to www.gov.uk/advancedlearningloans. Title. Forename(s) Surname. Sex. Male Date of birth D
24+ Advancd Larning Loan Application form Rmmbr you can apply onlin. It s quick and asy. Go to www.gov.uk/advancdlarningloans About this form Complt this form if: you r studying an ligibl cours at an approvd
More informationDehumidifiers: A Major Consumer of Residential Electricity
Dhumidifirs: A Major Consumr of Rsidntial Elctricity Laurn Mattison and Dav Korn, Th Cadmus Group, Inc. ABSTRACT An stimatd 19% of U.S. homs hav dhumidifirs, and thy can account for a substantial portion
More informationUserPerceived Quality of Service in Hybrid Broadcast and Telecommunication Networks
UsrPrcivd Quality of Srvic in Hybrid Broadcast and Tlcommunication Ntworks Michal Galtzka Fraunhofr Institut for Intgratd Circuits Branch Lab Dsign Automation, Drsdn, Grmany Michal.Galtzka@as.iis.fhg.d
More informationAn Broad outline of Redundant Array of Inexpensive Disks Shaifali Shrivastava 1 Department of Computer Science and Engineering AITR, Indore
Intrnational Journal of mrging Tchnology and dvancd nginring Wbsit: www.ijta.com (ISSN 22502459, Volum 2, Issu 4, pril 2012) n road outlin of Rdundant rray of Inxpnsiv isks Shaifali Shrivastava 1 partmnt
More informationBudget Optimization in SearchBased Advertising Auctions
Budgt Optimization in SarchBasd Advrtising Auctions ABSTRACT Jon Fldman Googl, Inc. Nw York, NY jonfld@googl.com Martin Pál Googl, Inc. Nw York, NY mpal@googl.com Intrnt sarch companis sll advrtismnt
More informationA Theoretical Model of Public Response to the Homeland Security Advisory System
A Thortical Modl of Public Rspons to th Homland Scurity Advisory Systm Amy (Wnxuan) Ding Dpartmnt of Information and Dcision Scincs Univrsity of Illinois Chicago, IL 60607 wxding@uicdu Using a diffrntial
More informationA Project Management framework for Software Implementation Planning and Management
PPM02 A Projct Managmnt framwork for Softwar Implmntation Planning and Managmnt Kith Lancastr Lancastr Stratgis Kith.Lancastr@LancastrStratgis.com Th goal of introducing nw tchnologis into your company
More informationTIME MANAGEMENT. 1 The Process for Effective Time Management 2 Barriers to Time Management 3 SMART Goals 4 The POWER Model e. Section 1.
Prsonal Dvlopmnt Track Sction 1 TIME MANAGEMENT Ky Points 1 Th Procss for Effctiv Tim Managmnt 2 Barrirs to Tim Managmnt 3 SMART Goals 4 Th POWER Modl In th Army, w spak of rsourcs in trms of th thr M
More informationStatistical Machine Translation
Statistical Machin Translation Sophi Arnoult, Gidon Mailltt d Buy Wnnigr and Andra Schuch Dcmbr 7, 2010 1 Introduction All th IBM modls, and Statistical Machin Translation (SMT) in gnral, modl th problm
More informationCostVolumeProfit Analysis
ch03.qxd 9/7/04 4:06 PM Pag 86 CHAPTER CostVolumProfit Analysis In Brif Managrs nd to stimat futur rvnus, costs, and profits to hlp thm plan and monitor oprations. Thy us costvolumprofit (CVP) analysis
More informationIncomplete 2Port Vector Network Analyzer Calibration Methods
Incomplt Port Vctor Ntwork nalyzr Calibration Mthods. Hnz, N. Tmpon, G. Monastrios, H. ilva 4 RF Mtrology Laboratory Instituto Nacional d Tcnología Industrial (INTI) Bunos irs, rgntina ahnz@inti.gov.ar
More informationSci.Int.(Lahore),26(1),131138,2014 ISSN 10135316; CODEN: SINTE 8 131
Sci.Int.(Lahor),26(1),131138,214 ISSN 1135316; CODEN: SINTE 8 131 REQUIREMENT CHANGE MANAGEMENT IN AGILE OFFSHORE DEVELOPMENT (RCMAOD) 1 Suhail Kazi, 2 Muhammad Salman Bashir, 3 Muhammad Munwar Iqbal,
More informationAre Health Insurance Markets Competitive? By Leemore Dafny*
Ar Halth Insuranc Markts Comptitiv? By Lmor Dafny* To gaug th comptitivnss of th group halth insuranc industry, I invstigat whthr halth insurrs charg highr prmiums, ctris paribus, to mor profitabl firms.
More informationThe Constrained SkiRental Problem and its Application to Online Cloud Cost Optimization
3 Procdings IEEE INFOCOM Th Constraind SkiRntal Problm and its Application to Onlin Cloud Cost Optimization Ali Khanafr, Murali Kodialam, and Krishna P. N. Puttaswam Coordinatd Scinc Laborator, Univrsit
More informationUse a highlevel conceptual data model (ER Model). Identify objects of interest (entities) and relationships between these objects
Chaptr 3: Entity Rlationship Modl Databas Dsign Procss Us a highlvl concptual data modl (ER Modl). Idntify objcts of intrst (ntitis) and rlationships btwn ths objcts Idntify constraints (conditions) End
More informationAbstract. Introduction. Statistical Approach for Analyzing Cell Phone Handoff Behavior. Volume 3, Issue 1, 2009
Volum 3, Issu 1, 29 Statistical Approach for Analyzing Cll Phon Handoff Bhavior Shalini Saxna, Florida Atlantic Univrsity, Boca Raton, FL, shalinisaxna1@gmail.com Sad A. Rajput, Farquhar Collg of Arts
More information7 Timetable test 1 The Combing Chart
7 Timtabl tst 1 Th Combing Chart 7.1 Introduction 7.2 Tachr tams two workd xampls 7.3 Th Principl of Compatibility 7.4 Choosing tachr tams workd xampl 7.5 Ruls for drawing a Combing Chart 7.6 Th Combing
More informationUpper Bounding the Price of Anarchy in Atomic Splittable Selfish Routing
Uppr Bounding th Pric of Anarchy in Atomic Splittabl Slfish Routing Kamyar Khodamoradi 1, Mhrdad Mahdavi, and Mohammad Ghodsi 3 1 Sharif Univrsity of Tchnology, Thran, Iran, khodamoradi@c.sharif.du Sharif
More informationSharp bounds for Sándor mean in terms of arithmetic, geometric and harmonic means
Qian t al. Journal of Inqualitis and Applications (015) 015:1 DOI 10.1186/s166001507411 R E S E A R C H Opn Accss Sharp bounds for Sándor man in trms of arithmtic, gomtric and harmonic mans WiMao Qian
More informationPlanning and Managing Copper Cable Maintenance through Cost Benefit Modeling
Planning and Managing Coppr Cabl Maintnanc through Cost Bnfit Modling Jason W. Rup U S WEST Advancd Tchnologis Bouldr Ky Words: Maintnanc, Managmnt Stratgy, Rhabilitation, Costbnfit Analysis, Rliability
More informationSimulated Radioactive Decay Using Dice Nuclei
Purpos: In a radioactiv sourc containing a vry larg numbr of radioactiv nucli, it is not possibl to prdict whn any on of th nucli will dcay. Although th dcay tim for any on particular nuclus cannot b prdictd,
More informationEntityRelationship Model
EntityRlationship Modl Kuanghua Chn Dpartmnt of Library and Information Scinc National Taiwan Univrsity A Company Databas Kps track of a company s mploys, dpartmnts and projcts Aftr th rquirmnts collction
More informationAnalysis of Trade Before and After the WTO: A Case Study of India
Global Journal of Financ and Managmnt. ISSN 09756477 Volum 6, Numbr 8 (2014), pp. 801808 Rsarch India Publications http://www.ripublication.com Analysis of Trad Bfor and Aftr th WTO: A Cas Study of India
More informationSOFTWARE ENGINEERING AND APPLIED CRYPTOGRAPHY IN CLOUD COMPUTING AND BIG DATA
Intrnational Journal on Tchnical and Physical Problms of Enginring (IJTPE) Publishd by Intrnational Organization of IOTPE ISSN 077358 IJTPE Journal www.iotp.com ijtp@iotp.com Sptmbr 015 Issu 4 Volum 7
More informationCPS 220 Theory of Computation REGULAR LANGUAGES. Regular expressions
CPS 22 Thory of Computation REGULAR LANGUAGES Rgular xprssions Lik mathmatical xprssion (5+3) * 4. Rgular xprssion ar built using rgular oprations. (By th way, rgular xprssions show up in various languags:
More informationDefining Retirement Success for Defined Contribution Plan Sponsors: Begin with the End in Mind
Dfining Rtirmnt Succss for Dfind Contribution Plan Sponsors: Bgin with th End in Mind David Blanchtt, CFA, CFP, AIFA Had of Rtirmnt Rsarch Morningstar Invstmnt Managmnt david.blanchtt@morningstar.com Nathan
More informationThe Australian Rules Football Fixed Odds and Line Betting Markets: Econometric Tests for Efficiency and Simulated Betting Systems
Th Australian Ruls Football Fixd Odds and Lin Btting Markts: Economtric Tsts for Efficincy and Simulatd Btting Systms by Adi Schnytzr and Guy Winbrg a Papr to b prsntd at: Th 4 th Binnial Equin Industry
More informationMaintain Your F5 Solution with Fast, Reliable Support
F5 SERVICES TECHNICAL SUPPORT SERVICES DATASHEET Maintain Your F5 Solution with Fast, Rliabl Support In a world whr chang is th only constant, you rly on your F5 tchnology to dlivr no mattr what turns
More information14.02 Principles of Macroeconomics Problem Set 4 Solutions Fall 2004
art I. Tru/Fals/Uncrtain Justify your answr with a short argumnt. 4.02 rincipls of Macroconomics roblm St 4 Solutions Fall 2004. High unmploymnt implis that th labor markt is sclrotic. Uncrtain. Th unmploymnt
More informationConsumer Preference and Spending Pattern in Indian Fast Food industry
Intrnational Journal of Scintific and Rsarch Publications, Volum 4, Issu 2, Fbruary 2014 1 Consumr Prfrnc and Spnding Pattrn in Indian Fast industry Y Prabhavathi, N T Krishna Kishor, M. Ramsh Kumar Abstract
More informationRelationship between Cost of Equity Capital And Voluntary Corporate Disclosures
Rlationship btwn Cost of Equity Capital And Voluntary Corporat Disclosurs Elna Ptrova Eli Lilly & Co, Sofia, Bulgaria Email: ptrova.lnaa@gmail.com Gorgios Gorgakopoulos (Corrsponding author) Amstrdam
More informationMONEY ILLUSION IN THE STOCK MARKET: THE MODIGLIANICOHN HYPOTHESIS*
MONEY ILLUSION IN THE STOCK MARKET: THE MODIGLIANICOHN HYPOTHESIS* RANDOLPH B. COHEN CHRISTOPHER POLK TUOMO VUOLTEENAHO Modigliani and Cohn hypothsiz that th stock markt suffrs from mony illusion, discounting
More informationNorthern Ireland Petrol and Diesel prices data analysis
Rsarch and Information Srvic Papr 163/12 04 Octobr 2012 NIAR 72012 Aidan Stnntt and Barbara Lov Northrn Irland Ptrol and Disl prics data analysis 1 Background On th 5 Sptmbr 2012, th Offic of Fair Trading
More informationDevelopment of Financial Management Reporting in MPLS
1 Dvlopmnt of Financial Managmnt Rporting in MPLS 1. Aim Our currnt financial rports ar structurd to dlivr an ovrall financial pictur of th dpartmnt in it s ntirty, and thr is no attmpt to provid ithr
More informationVersion Issue Date Reason / Description of Change Author Draft February, N/A 2009
Appndix A: CNS Managmnt Procss: OTRS POC Documnt Control Titl : CNS Managmnt Procss Documnt : (Location of Documnt and Documnt numbr) Author : Ettin Vrmuln (EV) Ownr : ICT Stratgic Srvics Vrsion : Draft
More informationA Derivation of Bill James Pythagorean WonLoss Formula
A Drivation of Bill Jams Pythagoran WonLoss Formula Ths nots wr compild by John Paul Cook from a papr by Dr. Stphn J. Millr, an Assistant Profssor of Mathmatics at Williams Collg, for a talk givn to th
More informationJune 2012. Enprise Rent. Enprise 1.1.6. Author: Document Version: Product: Product Version: SAP Version: 8.81.100 8.8
Jun 22 Enpris Rnt Author: Documnt Vrsion: Product: Product Vrsion: SAP Vrsion: Enpris Enpris Rnt 88 88 Enpris Rnt 22 Enpris Solutions All rights rsrvd No parts of this work may b rproducd in any form or
More informationCloud and Big Data Summer School, Stockholm, Aug., 2015 Jeffrey D. Ullman
Cloud and Big Data Summr Scool, Stockolm, Aug., 2015 Jffry D. Ullman Givn a st of points, wit a notion of distanc btwn points, group t points into som numbr of clustrs, so tat mmbrs of a clustr ar clos
More informationUsing the Aggregate DemandAggregate Supply Model to Identify Structural. DemandSide and SupplySide Shocks: Results Using a Bivariate VAR
Fbruary, 4 Using th Aggrgat DmandAggrgat Supply Modl to Idntify Structural DmandSid and SupplySid Shocks: Rsults Using a Bivariat VAR Jams Pry Covr Univrsity of Alabama Waltr Endrs Univrsity of Alabama
More informationFactorials! Stirling s formula
Author s not: This articl may us idas you havn t larnd yt, and might sm ovrly complicatd. It is not. Undrstanding Stirling s formula is not for th faint of hart, and rquirs concntrating on a sustaind mathmatical
More informationIn the first years of the millennium, Americans flocked to Paris to enjoy French
14 chaptr Exchang Rats and th Forign Exchang Markt: An Asst Approach 320 In th first yars of th millnnium, Amricans flockd to Paris to njoy Frnch cuisin whil shopping for dsignr clothing and othr spcialtis.
More informationOverinvestment of free cash flow
Rv Acc Stud (2006) 11:159 189 DOI 10.1007/s1114200690121 Ovrinvstmnt of fr cash flow Scott Richardson Publishd onlin: 23 Jun 2006 Ó Springr Scinc+Businss Mdia, LLC 2006 Abstract This papr xamins th
More information