The Economic Value of Rating in App Market

Transcription

1 The Econoic Value of ating in pp arket btract Thi paper invetigate the influence of rating on an eerging oftware application arket app arket Given the nature of oftware application a experience good and the general carcity of other quality ignal uch a advertiing or branding for ajority of app developer conuer' ex ante belief on app utility eentially relie on the app rating which itelf i derived fro the ex pot utility received by peer conuer We develop an analytical fraework which explicitly characterize thi bidirectional ratingutility converion proce alo naed a conuer rating behavior with a new concept "reervation rating" fter integrating conuer rating behavior into conuer' utility foration we derive the arket equilibriu and reveal how the change in conuer rating behavior affect developer and platfor owner' profit and how both developer and the platfor owner hould optially react to variou conuer rating behavior in ter of the choice of app price quality level and revenue haring percentage We alo reveal how change in conuer rating behavior would ipact the ocial welfare uggeting conuer' reponibility in ter of proper rating behavior to the overall goodne of app counity The rating-dependent utility function further enable u to derive a elf-election echani to achieve the eparating equilibriu in which high and low cot rate developer chooe differentiated revenue haring percentage Keyword: conuer rating obile app revenue haring elf-election

2 Introduction The traditional third-party application arket i now heading toward it next phae It ha been witneed that a novel third-party application arket obile app arket i currently experiencing it exploive growth depite the recent econoic downturn pple pp Store the world leading obile app arket launched in July 8 reached total nuber of billion download in January while it wa jut 3 billion in January (Wall Street Journal January Kaufan Brother LP etiated that over $ billion revenue wa generated fro ore than 35 application inide the pple pp Store in and Citibank expected thi revenue figure to be $ billion in Following pple ove Google icrooft eearch in otion (I and azon opened their own obile app tore Gartner Inc forecated that the total revenue of entire obile app arket would hit $5 billion in alot tripled it $5 billion in It will further increae to $35 billion in 4 according to International Data Corp (IDC projection eanwhile the treendou ucce in thi novel arket i initiating a new trend which ay change the whole cliate of future third-party application arket Enlightened by the ucce of pple pp Store pple extended the ae buine odel to dektop and laptop application On January 6 ac pp Store wa opened with ore than coputer app out of the gate In jut day Pixelator a all oftware copany achieved illion dollar ale on January 5 fro it one ingle iage proceing application old at unit price $999 Traditional giant oftware copanie uch a utodek alo joined the ac pp Store The arket i o enticing that even icrooft pple ajor copetitor i conidering bringing it icrooft Office ac verion onto ac pp Store It oething we are looking at aid anda Lefebvre icrooft enior arketing anager (PCWorld January Concerning thi eerging econoy the proble of advere election caued by inforation ayetry i a eriou iue which could potentially diantle the arket (kerlof 97 due to the following reaon Firt oftware product belong to experience good of which conuer can hardly oberve the true quality ex ante (Shapiro 985 Second even if the objective true quality i oberved it could iply different utilitie for conuer depending on their ubjective valuation of quality The dicounted utility i not necearily known to conuer ex ante (Chen and Xie 8 Third a characteritic of app arket that i the ixture of individual and organizational app developer generate greater belief diperion on quality than in the ituation where vendor are relatively ore hoogenou Thu without the ignal to ditinguih the quality of app conuer are alot cluele about their own ex pot utility and can hardly figure out their correponding willingne to pay To counter advere election rating a derived fro conuer ex pot experience i a good ource for conuer to forulate the correct ex ante belief on ex pot net utility and therefore deterine their willingne to pay (Li and Hitt Sun Though it i not the only ource it i uch ore

3 influential than other factor in app arket large aount of rating are aggregated and available at one ingle ite for intance itune for iphone app and hence eay to be found Conuer are allowed to rate at that ite only after they purchae an app Thi help to a large extent to avoid hilling behavior and hence aintain the credibility of rating ot iportantly other ignaling device uch a advertiing and branding are uually weak due to individual developer budget contraint or lack of arketing capabilitie Therefore rating i the ain criterion that conuer rely on in app arket Beide conuer developer and the platfor owner alo pay ignificant attention on rating The evidence fro real buine practice how that rating i one of the hottet topic and the bigget concern aong developer Ten of thouand of pot on iphonedevdkco one of the ot popular online iphone developer counitie are related to how to iprove rating and how rating affect app ale revenue Furtherore developer agree upon revenue haring contract with the platfor owner whoe revenue i alo connected with rating ll thee fact indicate that in app arket rating play a very ignificant role in deterining both the ucce of an app and the properity of the arket Given it great iportance thi tudy focue on the ipact of rating on app arket in ter of conuer choice of purchae developer choice of app price and quality level the platfor owner choice of revenue haring policy and the ocial welfare We firt characterize conuer rating behavior and incorporate it into conuer utility function We then derive developer optial choice of app price and quality level The platfor owner deciion on revenue haring policy will be aociated with the paraeter decribing conuer rating behavior We aue that conuer rating behavior conit of two procee One i to give rating alo referred to a ex pot rating baed on ex pot uer experience which can be quantified by conuer received net utility after purchae (Kukov and Xie The other i to accept ex pot rating and tranlate the into ex ante perceived net utility Thee two procee when cobined allow u to contruct a bidirectional rating-utility fraework in which we call the forer utility-to-rating proce and the latter rating-to-utility proce We account for an eential apect of rating behavior ubjectivity which i alo called yteatic rater error a one type of rating error dicued in the vat anageent literature regarding perforance rating (Kane 994 Kane et al 995 Yun et al 5 Boran 977 Saal et al 98 In the utility-torating proce it i a conuer ubjective opinion to rate for exaple 4 or 6 in a typical -point rating yte when her received net utility i zero Siilarly in the rating-to-utility proce exactly which rating that a conuer believe to correpond to her perceived ex ante zero net utility i alo ubjective Having rando rating error reoved thi ubjectivity in both procee ha been deontrated to be yteatic (Kane 994 if no effort i ade to control it yteatic ource Obviouly thi i the cae for app arket ince conuer are under no control for their characteritic uch a aturity concientioune and degree of ophitication in uing app which could erve a uch yteatic 3

4 reource To odel the ubjective rating behavior in the utility-to-rating proce we aue a poitive linear relationhip between ex pot rating and received net utility which we define a the rating function For the rating-to-utility proce we introduce a new concept: reervation rating eervation rating i defined a the ex pot rating which ignifie zero received net utility in conuer ex ante perception Baed on reervation rating a linear function between ex pot rating and ex ante perceived net utility i etablihed with potentially different lope and intercept than the rating function Thi work contribute to the exiting literature in the following two apect The firt i the bidirectional rating-utility fraework we contruct While we take app arket a our reearch context thi fraework can be applied in any arket where conuer rating play an iportant role in purchae deciion The concept of reervation rating introduced for rating-to-utility proce i an attept to yteatically odel how conuer interpret rating into net utility Second our finding provide the guidance for developer and the platfor owner on how to react to the change in conuer rating behavior by adjuting their choice of quality price and revenue haring percentage We identified different apect of rating behavior elicit different choice We dicover that rating leniency i detriental to app quality The analyi on ocial welfare deontrate the potential ialignent between the interet of platfor owner and the ocial welfare when conuer rating behavior change Conuer reponibility in ter of their proper rating behavior for the welfare of app ociety i alo revealed We alo deontrate that iniu app price a coon practice in real buine work a an intruent to drive out developer with poor atching perforance and high cot rate It i further hown that the platfor owner can dicriinate developer through a elf-election echani It achieve a eparating equilibriu in which high and low cot rate developer chooe different revenue haring percentage and the platfor owner profit i axiized The ret of the paper i organized a follow In Section we preent a review of the related literature In Section 3 we propoe the bae odel Section 4 extend the bae odel by ipoing ayetric rating-utility converion rate and analyze the ocial welfare under uch etting In Section 5 we add iniu app price retriction into the bae odel and exaine how it affect the optial choice In Section 6 we tudy the platfor owner optial revenue haring policy when developer cot rate are unobervable We derive a elf-election echani to achieve eparating equilibriu between developer with high and low cot rate In Section 7 a Win-Win effect i identified when conuer reervation rating are heterogeneou We conclude and offer the direction for future reearch in Section 8 Literature eview The literature on the effect of online word-of-outh (WO ha been proliferating rapidly during the lat ten year ot of the are epirical work in the context of ovie and book indutry focuing on 4

5 the effect of online WO on predicting or influencing ale revenue (Dellaroca 4 Chevalier and ayzlin 6 Liu 6 Duan et al 8 Dellaroca (4 deontrate that online rating i a ueful proxy for WO in ovie indutry and it erve a one of the predictor for a ovie total revenue Dellaroca and Narayan (6 identify three etric of online word-of-outh: valence variance and volue in which valence i uually denoted by the average nueric average rating variance i uually eaured by it tatitical variance or entropy (Gode and ayzlin 4 and volue i counted a the nuber of rating Liu (6 how that online WO ha ignificant explanatory power for box office revenue while the volue i a tronger predictor than valence Duan et al (8 reveal that ovie online WO valence ignificantly affect the volue which in turn deterine the box office perforance For book arket Chen et al (4 find that the conuer rating i only a predictor for book ale However Chevalier and ayzlin (6 how that the iproveent of online WO valence will increae the book ale baed on the data fro azonco and BarneandNobleco Foran (8 deontrate that rater give ore poitive rating to the review with identity inforation and the dicloure of identity inforation increae the ale eearcher have alo invetigated the connection between conuer rating and ale in the context of other arket uch a beer DVD and video gae (Cleon 6 Hu et al 8 Zhu et al However little attention ha been paid to oftware arket One reaon ight be that online oftware elling ha not been widely etablihed until app arket appear Zhou and Duan ( find that fro CNET downloadco the increae in product variety trengthen the ipact of poitive conuer review but weaken that of negative one They alo how that poitive expert review lead to ore oftware download Given the above aociation between online WO and product ale it i the natural next tep for reearcher to conceive fir optial trategy to leverage uch aociation growing body of literature ha been devoted to thi topic Chen and Xie (5 how that a fir hould chooe advertiing intead of price to adapt conuer review when ufficient conuer value the product horizontal feature Dellaroca (6 deontrate how fir hilling behavior ie pot anonyou eage that exalt their product on the purpoe of changing the conuer perception will influence fir profit and conuer urplu Chen and Xie (8 reveal when and how eller hould adjut their arketing counication trategy by changing product attribute inforation they offer to adapt conuer review Kukov and Xie ( tudy the optial pricing and whether the fir hould give an unexpected frill to early cutoer to boot their product experience Li and Hitt ( how analytically and epirically that unidienional rating are ore correlated with the net value rather than quality of the product Fir need to account for price effect and can better erve the conuer by etting up review yte which explicitly eparate the perceived value and quality Jiang and Chen (7 exaine both conuer 5

6 review and conuer rating and find that fir ay have the incentive to under-charge in the early period They alo invetigate how it will affect the arket copetition ot of the fir adaption trategie entioned above are iplicitly baed on the underlying auption that rating can ignal the underlying true quality (or true value to novice conuer at leat in an expectation ene However thi conjecture doe not ee to be alway true The topic concerning how precie the rating reflect the underlying true quality an iue involved with conuer rating behavior becoe increaingly popular in the rating-related reearch area Hu et al (6 epirically how that in the preence of under-reporting ie only extreely atified or extreely unatified conuer would rate conuer ay not extract the true quality fro the rating if only valence (ean value i known Sun ( analytically deontrate that novice conuer can figure out product true quality fro the ditribution of the rating given by earlier conuer Li and Hitt (8 how that later conuer perception on the quality ay be inaccurate becaue of the biaed rating left by early buyer whoe preference on quality are different fro later one Hu (9 uarize two elfelection biae: purchaing bia partially entioned in Li and Hit (8 and under-reporting bia entioned in Hu (6 a two reaon which potentially lead to biaed perception on true quality under certain circutance oe and Truov ( and oe and Schweidel ( epirically how that conuer rating behavior i ignificantly affected by previouly poted rating Lee (9 deontrate that ocial iitation and learning affect can influence uer rating generation nother iportant apect of rating behavior which influence appraial accuracy i the yteatic rater error While having not been noticed in the context of online WO it ha been tudied in the anageent literature for decade Kane (994 uarize rating error into ultiple categorie and point out that leniency everity and non-differentiation are three iportant one which could be potentially yteatic Kane et al (995 deontrate that rating leniency i the ot troubleoe rating error and find it to be a relatively table repone tendency Spence and Keeping ( ugget that when anager give perforance rating to their eployee ore experienced anager are aociated with lower rating which indicate lower degree of leniency Berger et al ( epirically how that under the ituation where eployee bonu payent are aociated with rating a forced differentiated ditribution requireent on rating actually lead to higher productivity Thi i epecially intriguing ince by analogy conuer in our context are ore or le alike anager who rate developer app and conequently developer revenue i aociated with thee rating Thi work incorporate the effect of thi unique apect of rating behavior yteatic rater error on conuer perception on utility 3 The odel Suppoe that the platfor owner app developer and app conuer are the three player on an app arket three-tage dynaic gae theoretic odel i contructed to tudy the equilibriu of the arket 6

7 In the firt tage the platfor owner deterine and publicize developer revenue-haring percentage By oberving thi percentage at the beginning of the econd tage developer chooe either not to adopt and exit the arket or to adopt and then deterine the optial quality level and optial app price If developer chooe not to adopt the gae end Otherwie in the third tage conuer decide whether to purchae and if a purchae occur rate the app baed on the received net utility The third tage i repeated uch that after a ufficient tie period the rating becoe teady The goal of the platfor owner and developer are to axiize their own benefit in thi teady-tate repectively Developer would chooe to participate when the profit i greater than or equal to zero Likewie conuer would ake the purchae when the expected net utility i greater than or equal to zero In the following we tart with everal eential preliinarie which erve a the foundation of our odel ating Function We aue a linear relationhip between the received net utility and the ex pot rating Since the rating r i bounded between and the atheatical forula i given by: { { } r in ax ku+ r In the above expreion u i the received net utility r i the ex pot zero net utility rating which i an iportant concept in ter of eauring the degree of everity low r indicate that conuer are evere with repect to giving rating k i the rating-utility converion rate It repreent conuer enitivity of the ex pot rating on the difference in received net utility eceived Net Utility Following Chen and Xie (8 we partition conuer into two group One conit of all high valuation conuer who conider the app atch their tate o that they appreciate the quality The other conit of all low valuation conuer who find the app a iatch of their tate The received net utility which i aociated with the app objective true quality level q it price p and conuer valuation for quality i given by: u q p u p atched unatched We denote b a the fraction of conuer who belong to high valuation group It i worth noting that b i an indicator of developer atching perforance large b repreent a high level of atching perforance ince ot of conuer are atched We aue that b ( eervation ating Following the definition of reervation rating in the introduction ection we further explain how it fit into econoic utility theory eervation rating i intuitively a bar which an app need to pa to be conidered for purchae and it alo fundaentally affect conuer willingne to pay It work a a ruler origin to eaure the ex ante perceived net utility fro an app For intance with regard to a 5-tar rating yte when a conuer with reervation rating 35-tar oberve an app with current rating of 45-tar he would expect oe poitive net utility fro the app In other word 7

8 cobining reervation rating and current ex pot rating conuer will figure out their ex ante perceived net utility In the bae odel reervation rating r i aued to be hoogenou aong all conuer Suppoe r i the ex pot rating given by high valuation conuer The ex ante perceived net utility of high valuation conuer i given by: r r ue k In order to ditinguih the degree of critici between utility-to-rating and rating-to-utility procee we define that conuer with low r are evere and conuer with high r are critical The value of r and r are between and Since generally conuer are equally critical or ore critical in accepting rating than giving rating we aue that r r or r > r Now we derive conuer expected net utility EU ( We aue that both true quality level and type of valuation are unknown to conuer before they experience the app However by exaining the ditribution of app ex pot rating they would dicover that the probability of being in the high valuation group i b and that in the low valuation group i b Hence the expected net utility i given by: ( ( ( If EU ( conuer would ake the purchae where Developer profit i given by: EU b p+ bu e u p hq D h i the cot rate on quality and h > The quadratic for of cot repreent the diinihing return of invetent on quality (Choudhary 7 The condition for developer to participate i ud Developer eek to axiize their profit by chooing the optial p and q under contraint EU ( Table odel Paraeter and Deciion Variable Paraeter k ating-utility converion rate r r r b ex pot zero net utility rating eervation rating ex pot rating fro high valuation group conuer Fraction of conuer in the high valuation group h Developer cot rate on quality Deciion Variable q Quality level of the app p Price of the app Developer revenue haring percentage 8

9 The platfor owner revenue i given by: P ( u p where i bounded between and The platfor owner goal i to find the optial which axiize u P In our odel the platfor owner cot i neglected egarding the variable cot uch a app hoting cot we aue that they are already covered by a fixed annual fee paid by developer For exaple pple ios platfor charge $99 for annual eberhip to allow a developer upload her app on the pple pp Store We peculate that thi eberhip fee ay cover the cot but not be the ajor revenue ource The evidence i that nowaday roughly 35 app are available on the pple pp Store Even under the ot extree cae that they correpond to 35 developer the annual revenue fro eberhip i 35 illion at ot which account for le than 4% of the total platfor owner app ale revenue Once a developer decide to participate the eberhip fee i a unk cot which doe not affect her choice of app quality level and price Table uarize the notation of the odel Baed on the above auption we have the following propoition Propoition Given the revenue haring percentage developer optial choice of price quality level q are: i egion - (elf-driven: where b> b and < h h p ( q ( ( b r br r b r + ; k b k b ii egion - (platfor owner driven: where b> b and h < h h ( + b b r r b p + q ; h k h iii egion -3 (poor atching: where b b and < h h3 p ( q ( ( b r br r b r + k b k b 3 3 In all other region of ( bh developer cannot ake non-negative profit The above threhold are: r b h r r ( b bk br r b r + bk h 4 r r 9 and h kb( b( r ( br r b r + 3 p and Propoition how that developer optial choice of price and quality level i divided into three region depending upon their atching perforance b and cot rate h Generally peaking a higher Propoition can be hown by olving the correponding Lagrangian in different region defined by the odel paraeter The ketch of proof of other propoition and corollarie can be found in the appendix

10 quality level q will lead to higher ex pot rating fro high valuation conuer The overall ex pot rating get elevated; thi ubequently increae conuer ex ante perceived net utility a well a their willingne to pay Thu developer can gain by charging a higher app price p to exploit the additional willingne to pay For developer in egion - becaue of low cot rate ( < h h the arginal gain i alway greater than arginal cot of quality until the rating r reache it axiu Therefore the optial quality level that q i the one at which high valuation conuer will give the axiu rating (note r k( q p + r In egion - when atching perforance i good but the cot rate i high ( h h h > the arginal cot of quality increae fater than that in egion - and will urpa the arginal gain fro additional conuer willingne to pay before the axiu r i realized Thu the r in egion - will be between r and In egion -3 the optial price p 3 and quality level q 3 are of the ae analytical for a egion - Thi indicate when their atching perforance i poor but the cot rate i relatively low ( < h h3 developer optial choice i to produce at the quality level which yield r The intuition i that ince only a all portion of conuer belong to high valuation type who appreciate high quality and rate poitively after purchae developer need to provide ufficient atifaction to the in order to ake the rate a high a poible Otherwie the ubequent conuer ex ante perceived net utility a well a their willingne to pay would be too low becaue the overall rating i too low Figure depict developer are non-increaing function of developer cot rate h p q r u D in egion - and - ll of the Figure Developer optial choice given Figure Developer optial choice againt Corollary p / > and q / > Corollary how that for developer in egion - their optial choice of quality level i driven by the revenue percentage they obtain By increaing the platfor owner can provide ore incentive for developer to iprove the quality of the app We hence nae egion - a platfor owner-driven and refer the developer a platfor owner-driven developer In egion - the optial quality level

11 i not affected by and therefore the developer are elf-driven We further nae egion -3 a poor arketing region Since the optiality in poor arketing region hare any iilaritie with elfdriven region and it i unlikely to be the ain coponent of the arket we focu our attention on elfdriven and platfor owner-driven region Notice that the boundarie of the region ( h h are proportional to revenue haring percentage which i et by the platfor owner at the firt tage of the gae Thi indicate that given their cot rate h whether developer chooe to be in elf-driven or platfor owner region depend on not only on conuer rating behavior ( k r r but alo the platfor owner choice of Figure illutrate that a increae owner-driven developer are induced to increae their q and the axiu where they becoe elf-driven Corollary / q r < ; q / r In all region p / r < p until the rating r hit Corollary indicate that when conuer becoe ore critical in accepting rating (higher r developer in both platfor owner-driven region and elf-driven region need to charge lower app price In platfor owner driven-region charging a lower price according to our rating function will generate a higher r which i ued to atify higher r In elf-driven region ince r ha already reached it axiu to atify higher r o that enable EU ( the price need to be decreaed at an even fater rate (hown in Figure 3 egarding the quality level platfor owner-driven developer keep the ae quality level while elf-driven developer chooe to lower the quality Thi i becaue in elf-driven region a long a the axiu rating i retained further quality iproveent will not proote conuer perception on ex ante net utility Since the price drop at a fat rate the quality level required to achieve the axiu rating can be et lower Corollary 3 q / r < ; p / r p / r > ; q / r When conuer becoe ore lenient in giving rating (higher r elf-driven developer repond by etting a lower quality level but keep the price unchanged Thi i becaue when conuer becoe ore lenient in the elf-driven region even though the quality decreae a little the rating r will till be at the axiu Decreae in quality won t change the conuer willingne to pay o that the developer can charge the ae price while decreaing the quality definitely ave the cot For platfor ownerdriven developer the bet trategy i to increae the price when conuer becoe ore lenient In a uary the developer take advantage of conuer leniency by increaing the price when he i in platfor owner-driven region and by decreaing the quality when he i in the elf-driven region Notice that the boundarie of the region ( h h are affected by r and r Figure 3 how that when r increae platfor owner-driven region hrink but elf-driven region expand However a r

12 increae both region expand Platfor owner-driven developer ay witch to be elf-driven a r or r increae Figure 3 alo depict how developer choice of optial quality and price change acro different region Figure 3 egion ditribution and developer optial choice acro region Corollary 4 Change in rating behavior ( r r doen t change the developer quality incentive in platfor owner region Corollary 4 reult fro the cobination of Corollary 3 and Corollary 4 Fro Figure 3 we can ee that the developer in platfor owner region doen t need to adjut optial quality level when ( r r change Price i the only factor need to adjut to optially react to change in ( r r in platfor owner region Figure 3 alo reveal an intereting phenoenon Given developer cot rate h either increae in r or r could potentially incentivize the developer to witch fro the platfor owner-driven region to the elf-driven region where the developer ake the r However the underlying reaon are different Increae r ie the conuer becoe ore critical in accepting rating force the developer to render r to guarantee a enough pace between r and r to utain the price Increae in r ie conuer becoe ore lenient in giving rating pleae the developer to render r to elicit conuer axiu willingne-to-pay at a lower quality cot

13 Propoition The platfor owner optial choice of developer revenue haring percentage i: i egion - (queezing: when b> b and < h h α ( + bk ( b h br br r ii egion --α (encourageent: when b> b and h < h α h /3 ( r h r bk iii egion --β (retention: when b> b and h /3< h h iv egion -3: when b b and < h h3 The threhold: h 3 α α + ; ( r 4h r β ; bk ( + b( r k( b h br br r bk ( b + br br r r Propoition characterize the ubgae perfect Nah equilibriu (SPNE It how how the platfor owner in the firt tage hould offer different revenue haring percentage to different type of developer depending upon their cot rate h and atching perforance b The SPNE endogenize developer bet repone in the econd tage For exaple the platfor owner know that the developer in egion - would axiize their utility u P by chooing to be elf-driven in the econd tage and hence offer to incentivize the to do o ; Corollary / h> where or α β 3 Figure 4 depict the optial revenue haring percentage a a function of cot rate h Both egion --α and --β correpond to platfor owner-driven region in Propoition Figure how that when platfor owner-driven developer cot rate increae the optial quality level q decreae Corollary ugget that in thi ituation the platfor owner hould offer a higher revenue haring percentage to encourage developer to produce at a higher quality level The lo due to a lower haring percentage for the platfor owner will be ore than copenated by the additional revenue gained fro a higher quality level 3

14 Figure 4 Platfor owner optial choice of egion - correpond to elf-driven region in Propoition where the optial quality q i not a function of revenue haring percentage In thi region the platfor owner can queeze developer by giving a lower haring percentage Due to their low cot rate developer can till obtain non-negative utility by chooing the quality level q at which the rating r and charging the price p Squeezing developer ay be dangerou ince developer ay leave One reaon why low cot rate developer do not leave thi platfor even when receiving low revenue haring percentage lie in our auption that the platfor owner i a onopoly or ha the onopoly power on the arket uch a predoinance in conuer bae For exaple pple till grap roughly 7% of the entire obile app arket and thi nuber i 994% two year ago Developer are allured by the large nuber of potential cutoer nother reaon i that conuer uing different platfor are uually eparated for exaple chance are little that a conuer ue both iphone and ndriod phone Since cannibalization i a ild iue developer can releae their app on another platfor a long a profitable Baed on the above dicuion we give ore intuitive nae to the region in Propoition egion - i hereafter referred to a queezing region Developer in queezing region will be incentivized to chooe elf-driven region in the econd tage egion --α i naed a encourageent region egion --β i referred to a retention region where developer ake zero profit and are hence on the verge of exiting the arket It can be oberved in Figure 4 that developer whoe cot rate i at the interection of queezing and encourageent region can obtain the highet utility Lower cot rate developer utility will be queezed The extree cae i when the cot rate i cloe to zero the platfor owner can take alot all the revenue but leave very little hare to developer Developer participation can till be jutified becaue developing app cot nearly nothing for the Corollary > / where α or β Thi coincide with our obervation fro real buine practice for intance pple ios platfor offer a revenue haring percentage of 7% In app arket given the fact that a large portion of developer are individual or developent tea ade up of everal individual whoe cot rate i 4

15 relatively high the platfor owner ay conider the to be in encourageent or retention rather than queezing region Therefore it i the optial trategy for the platfor owner to offer a revenue haring percentage greater than one half Corollary 3 / r < / r > where α or β ccording to Propoition when conuer becoe ore critical in accepting rating developer in encourageent and retention region would decreae the price Such a price drop reduce the total revenue raie in haring percentage would encourage developer to chooe a higher quality level and increae the price The trategy in queezing region appear to be a little counterintuitive It tate that in queezing region when conuer reervation rating increae the platfor owner prefer queezing developer ore rather than incentivizing the by offering higher revenue haring The underlying logic i the following Notice that the threhold h α increae with r Developer in queezing region would till chooe elf-driven region at the econd tage when r increae higher would not proote the choice of quality level a in encourageent region but only ubidizing ore revenue haring to developer Intead if the platfor owner decreae and a long a the decreaed till aintain developer choice of price and quality level ie taying in elf-driven region the total app ale revenue doen t change due to the unchanged price By giving le to the developer platfor owner would benefit illutrated in Figure given developer cot rate h when the haring percentage decreae developer originally in elf-driven region ay witch to platfor owner-driven region (notice that h α decreae However it turn out that oving to platfor owner-region will incur greater lo than taying in elf-driven region even with le revenue percentage Chooing between the two evil developer will be better off to tay in elf-driven region Hence the platfor owner i able to queeze Corollary 4 / r < / r < where or α β When r increae ie conuer generally give higher rating developer in encourageent and retention region would charge a higher price but aintain the ae level of quality Higher price indicate higher revenue in thi cae and the platfor owner can extract part of the additional revenue by decreaing the haring percentage For developer in queezing region the optial price doe not change but the quality level decreae ince conuer are ore lenient in giving rating The arguent why decreae with r i iilar to the cae that r decreae in queezing region in Corollary 3 Corollary 5 For queezing encourageent and retention region in SPNE developer profit atifie u / r and u / r For the platfor owner revenue u / r > and u / r < D D P P 5

16 4 yetric ating-utility Converion ate In thi ection we extend the bae odel by etting different converion rate between rating-to-utility and utility-to-rating procee We denote the converion rate in the rating-to-utility proce a k and that in the utility-to-rating proce a k U Here we aue that k > k U Thi auption ugget that conuer are le enitive to the difference in received net utility when giving rating than the change in ex pot rating when tranlating to their perceived net utility a well a correponding willingne to pay 4 The Platfor Owner and Developer Optial Choice The proble can be olved iilar to the yetric (ae- k cae in the previou ection The olution i preented in Propoition in the appendix Siilarly we have identified three region for developer: elf-driven platfor owner-driven and poor arketing Their correponding optial price and quality are denoted a ( p q ( p q and ( p q repectively Propoition in the appendix 3 3 decribe the optial revenue haring percentage Siilar to thoe in Propoition we have repectively for queezing region α for encourageent region β for retention region and 3 The following corollarie characterize how converion rate k U and k affect the quality q price p and revenue haring in thee region Corollary 3 In all region Corollary 3 In elf-driven region region q / k U > and p / k U > q / k < and p / k < q / k U < and p / k U In platfor owner-driven When k decreae ie conuer are willing to pay ore for a higher rating developer in any region hould offer a higher quality level and charge a higher price Corollary 3 ugget that when k U increae ie conuer are ore enitive to the difference in received net utility and willing to give ore differentiated rating developer in platfor owner-driven region hould chooe a higher quality level a well a a higher price The reaon i that when conuer appreciate high quality app by giving ore differentiated rating the ex pot rating will be tranlated into willingne to pay in the rating-toutility proce hence the benefit of producing high quality i augented On the contrary if k U decreae ie conuer don t appreciate high utility app and give alike rating for good and bad app platfor owner-driven developer have le incentive to produce at a higher quality level Here a ubcript i added to denote the ayetric cae 6

17 Developer in elf-driven region however act differently when k U increae They will keep the price unchanged but chooe a lower quality level Thi i becaue whenever the rating r reache it axiu any further iproveent on quality will no longer be reflected by the rating Conuer won t recognize uch effort in the rating-to-utility proce Therefore elf-driven developer cannot take advantage of increaed k U in the ae way a platfor owner-driven developer Nonethele they can benefit fro higher k U through the reduction of the cot on quality ince it would be le cotly for the to achieve the quality level which realize the axiu rating It hould be noted that when r increae elf-driven developer quality level q decreae but for platfor owner-driven developer q reain unchanged However q increae with k Thi U obervation upport the finding in anageent literature that -leniency i a ignificant proble Berger et al ( dicover epirically in corporate environent a forced ditribution on perforance rating will lead to higher productivity We how that when r decreae (le lenient and ditributed the productivity indicator q increae Corollary 33 Change in rating behavior ( U k U increae (ore k k change the developer quality incentive in all region Thi corollary i a counterpart to Corollary 4 Corollary 4 tate that the change in rating behavior with repect to ( r r doen t change the developer quality incentive in platfor ownerdriven region Here we reveal that change in ( k k on the contrary change the developer quality U incentive in all ituation Corollary 33 highlight the fact that different apect of rating behavior are attached to different apect of developer incentive The tateent that conuer becoe ore lenient in giving rating could be interpreted by either higher r or higher k U However the incentive conequence are quite dicrepancy depending on which type of rating leniency i Corollary 34 In encourageent or retention region / k > and or α β / k U < where When conuer are unwilling to pay differentiated price for high rating app (ie decreaing k or conuer are unwilling to give differentiated rating to high utility app (ie increaing k U according to Corollarie 3 and 3 developer in encourageent or retention region chooe a lower quality level Therefore the platfor owner hould offer higher revenue haring to developer o a to aintain the quality level and hence the price for the platfor owner revenue Corollary 35 In queezing region / k U < With repect to k 7

18 ˆ 3 + /4 i Cae : if r r ( r / k < ; ii Cae : if r < rˆ and k > kˆ r bk r U ( b / k > ; iii Cae 3: if r ˆ < r and ˆ ku < k k / k < dicued earlier when the developer would keep chooing elf-driven region at the econd tage ie the final choice of price and the total app revenue are not influenced by the firt tage at firt tage the platfor owner can decreae the to ake itelf better off Cae and Cae 3 deontrate thi principle However Cae ee to violate it The underlying reaon i that when r ˆ < r high k could lead the developer into the platfor owner region Figure 5 and 6 clearly illutrate thi dynaic Figure 5 preent the ituation for Cae It how that when r rˆ ie the conuer are ufficiently critical in r dienion developer in elf-driven region would alway be in that region a k increae However when the conuer are not ufficiently critical in r dienion ( r < rˆ which i illutrated by Figure 6 for Cae and 3 developer in elf-driven region will tay there when k i low but chooe witching to platfor owner region when k i high It i not the bet interet for the platfor owner that developer witche to the platfor owner-driven region Therefore a illutrated by Figure the platfor owner chooe to increae to ake the developer tay in the elf-driven region The underlying reaon for the non-onotonic property hown in Figure 6 i the following The k and r repreent two type of criticalne in accepting rating For r it i the bar that r ha to pa for aking purchae happen the bar becoe higher ( r increae the elf-driven developer ut adjut the price and quality to pa that bar otherwie no purchae will occur However for k it i not the bar which ha to be paed When k i on the low ide eaning that conuer would interpret little extra rating above reervation rating to a great value the developer doen t have to hit the axiu rating Hence he would chooe the platfor owner-driven region When k turn to be on the high ide eaning that conuer trut very little value within rating it becoe not worthy for developer to pend extra quality cot to obtain high rating long a r i paed purchae will occur Corollary 36 For queezing encourageent and retention region in SPNE the platfor owner revenue u / k > P U u / k < P u / r > and u / r < P P 8

19 Figure 5 egion ditribution a 4 nalyi of Social Welfare k ( r rˆ Figure 6 egion ditribution a k ( r < rˆ In thi ubection we analyze the ipact of conuer rating behavior on ocial welfare of app arket The ocial welfare i defined a: W bq hq Corollary 4 In encourageent or retention region W / r > and W / r < In encourageent or retention region if r increae or r decreae the ocial welfare increae In thee region there exit unrealized urplu becaue conuer are lenient toward developer When conuer becoe ore critical in accepting rating or ore evere in giving rating uch urplu will be tiulated out Corollary 4 W / k < in encourageent region and W / k in retention region W / k U > if h h α and W / k U < if h > h α where: h kbk U ( b ( bk k b + k ( r r α U In encourageent region the ocial welfare increae a k becoe all Thi indicate that conuer need to appreciate rating that i to accept the ignal of utility and be willing to pay higher price for higher rating for the ake of welfare of the arket If developer cot rate i relatively lower ( h h α the ocial welfare increae when conuer give ore differentiated rating for good and bad app (higher k U On the other hand if there are high cot developer ( h > h α on the arket ore differentiated rating behavior i detriental to the ocial welfare Corollary 43 In queezing region W / x< where x r r k ku In queezing region developer cot rate i very low being evere in giving rating i beneficial for the ocial welfare The intuition coe fro the fact that developer have a great potential to produce high quality app Conuer everity in giving rating help to realize uch potential and iprove the 9

20 overall ocial welfare However paradoxically being ore critical in accepting rating will actually leen the ocial welfare Thi i becaue it fail to force developer to proote the quality ince they are elf-driven Such overly critical behavior would actually reduce developer incentive ince they cannot charge the price a high a before and conequently jutify their invetent on quality Table copare the direction of change for platfor owner u P and the ocial welfare W in repone to the rating paraeter r r k and U k in different region Poitive ign + repreent increae while negative ign repreent decreae N ean No effect We highlight the ituation where the interet of platfor owner and the ocial welfare are alway ialigned We can oberve that the adjutent of k i alway aligned but that of r i alway ialigned Thi how that leniency i alway detriental to the ocial welfare but alway favored by the platfor owner Table Platfor owner (PO interet VS Social welfare (SW r r k U k Squeezing egion Encourageent egion etention egion PO + + SW PO + + SW + + PO + + SW + N 5 iniu pp Price In thi ection we ipoe the iniu price retriction to the bae odel to tudy it ipact on developer optial choice of quality level and price and the platfor owner optial revenue haring percentage We denote the iniu app price a Lea 5 If ( p p pˆ r r / k developer optial choice of price and quality level in elf-driven and platfor owner-driven region reain unchanged p affect only poor arketing region ˆ Lea 5 If p p poor arketing region becoe unavailable It i not very difficult to how p > p > p So when p tart to increae fro zero to p < pˆ it 3 will affect poor arketing region When p reache p ˆ developer in that poor arketing region cannot earn any non-negative net utility and are driven out the arket

21 price Propoition 3 If p ˆ > p given the revenue haring percentage developer optial choice of p and quality level q are: i egion 3-: when b> b and h h p p q q ; ii egion 3--α: when b < b b and h < h hα or b> b and h < h h p p q q ; α α iii egion 3--β: when b < b b and hα < h h pk rb + rb pβ p qβ bk In all other region of ( bh developer cannot ake non-negative profit The above threhold are: b pk r + p k b pk r r bk h α br r b + p k and h ( br r b + p k pbk Figure 7 plot the region defined in the above propoition egion 3- i derived fro elf-driven region but cut aller by p Siilarly egion 3--α and 3--β reult fro platfor owner-driven region but are odified by p Propoition 3 reveal that developer with arket perforance b< b will be driven out of the arket regardle of their cot rate Thi i becaue when b< b even if developer have the lowet cot rate to receive the axiu rating fro high valuation conuer at no cot there will be ufficient low valuation conuer to give the lowet rating Thi would reult in the overall ex ante perceived net utility not high enough for developer to charge of iniu app price p In thi ene one effect p i to drive low atching perforance developer out of the arket Figure 7 egion defined in Propoition 3 Figure 8 egion defined in Propoition 4

22 Corollary 5 When p p ( r r > ˆ / k iniu app price hrink platfor owner-driven region to allow developer with lower cot rate Notice that pˆ ˆ > p and when p ˆ > p we have b > Therefore the ub region ( b> b and h < h h in egion 3--α becoe unavailable and platfor owner-driven region i defined by ( b b > and h < h hα It can be eaily hown that b > b and h < α h Thi indicate another effect of iniu app price higher p can not only control for the entry of poor atching perforance developer but alo expel developer with high cot rate fro the arket Lea 53 When p ˆ > p and b> b the SPNE reain the ae a that in Propoition except that egion -3 i unavailable and b> b i required a the lower bound of b Propoition 4 When p ˆ > p and b < b b the SPNE i: i egion 4-: when b < b b α and < h h α or when b < b α b and < h h α ; (4 ii egion 4-c: when b < b b α and h < h α h or when b < b α b and h < h β h c ( + hbr rb pk iii egion 4--α: when b < b α b and h α < h hβ where b α ; (4 pbk α α (43 b b i a root of f ( b ( b b (( b ( b + ( b ( b ( + b b ; and h 3 b ( r k( b pb k ( b ( r ( + br br r b ( br br + p k ( b α h ( ( pk + r r b pk r r b kb β 6( r r b + 8pk( r r b+ 4pk Figure 8 plot the region defined in Propoition 4 The introduction of iniu app price a a tool for the platfor owner can lead to coniderable change in the trategy of chooing optial haring percentage One key iplication hidden in the Propoition 4 can be eparated out in the following corollary Corollary 5 For developer in egion 4-c the optial haring percentage c atifie: / p > c / r > and / r < c c

23 Corollary 5 reveal an iportant dynaic between iniu app price p and the optial revenue haring percentage It epecially coplie with our obervation in real buine practice Copared to pple ios platfor ha iniu app price p $99 and a revenue haring percentage of 7% I et iniu app price p $99 for Blackberry app and offer a revenue haring percentage 8% higher than pple Notice that egion 4-c actually could repreent a large portion of developer epecially individual developer in app arket if the gap between r and r i not very large 6 Unoberved Cot ate ccording to Propoition in the bae odel the platfor owner optial choice of revenue haring percentage i a function of developer cot rate h However h ay be unobervable by the platfor owner In thi ection we preent the optial choice of haring percentage when h i unoberved We alo deontrate that the platfor owner can offer developer a enu with cobination of ex pot rating and revenue haring percentage to engage the into a elf-election proce 6 Unobervable h Suppoe that the platfor owner ha no inforation about h One approach to odel the uncertainty with no prior inforation i to aue unifor ditribution ue that h i uniforly ditributed in [ ] U h where hu > h3 Thi repreent the ituation where developer cot rate pace i not fully covered It i reaonable ince there are alway developer whoe cot rate i o high and who cannot earn nonnegative net urplu even when all the revenue goe into the Propoition 5 When h i uniforly ditributed the expected optial developer revenue haring percentage N / Fro the bae odel we can ee the optial haring percentage i a linear function of h Intuitively peaking when h i on the lower ide of the ditribution the optial haring percentage i le than one half; wherea when h i on the higher ide of the ditribution the optial haring percentage i greater than one half Propoition 5 tell the expectation i exact one half In real buine practice thi percentage i actually adopted by China obile the China larget wirele carrier for China app arket any coentator quetion whether thi i a right deciion to ake epecially after coparing to the ucceful buine odel uch a pple ios and Google ndroid in US app arket Our odel provide an explanation that on expectation one half i the optial under unifor ditribution of developer cot rate However if the platfor owner believe the ditribution i kew toward higher value the one half will be no longer optial and in uch cae the optial haring percentage i greater than one half 3

24 6 Self-election In thi ubection we how that the platfor owner can deign a enu of ( r to engage developer to a elf-election proce Note that developer with different cot rate have different objective for the rating Figure how that elf-driven developer ai at r while platfor owner-driven developer goal i between r and Therefore although cot rate h i not obervable the rating r i an obervable factor ignaling developer cot rate h Hence if the platfor owner can offer different revenue haring percentage bundled with different realization of r developer will elf-elect the cobination which i ot profitable to the Thi turn the inforation tructure of our three-party gae into a creening gae in conjunction with a ignaling gae The creening gae i between the platfor owner and developer where the platfor owner i the uninfored party The ignaling gae i between developer and conuer where developer are uninfored In both gae developer are the infored party who would like to ignal their app quality to conuer (ignaling gae and alo engage into a elfelection generated by the platfor owner (creening gae Figure 9 how the role of rating in a twoided arket Figure 9 The role of rating in two-ided arket We conider a eparating equilibriu between elf-driven and platfor owner-driven developer Therefore uppoe that there exit a repreentative elf-driven developer with cot rate h L in queezing region and a repreentative platfor owner-driven developer with cot rate h H in priary encourageent region (egion - We have the following reult Propoition 6 There exit a eparating equilibriu in which the repreentative developer hl and h H would elf-elect to L and H repectively if the following enu i offered: where rˆ ( r r ( + b bk( b r 4 hh N if ˆ H r r; if ˆ L r > r L ( + bk ( b hl br br r and ( h r r H H + bk 4

25 Propoition 6 characterize a eparating equilibriu for the creening gae By offering thi election to developer without inforation on developer cot rate h the platfor owner can incentivize hh -type developer to elf-elect the correponding haring percentage H and developer to L both of which are tated in Propoition 5 hl -type Corollary 6 rˆ / r > and rˆ / r < Corollary 6 indicate that when conuer becoe ore evere in giving rating the equilibriu threhold rating ˆr hould decreae However if conuer becoe ore critical in accepting rating ˆr hould alo decreae 7 Heterogeneou eervation ating In the bae odel we aue that conuer have hoogenou reervation rating In thi ection thi auption i relaxed to allow a dicrete ditribution of heterogeneou reervation rating Suppoe that conuer have either one of the two reervation rating r L and r H The correponding fraction of conuer population are nl and nh nl For iplicity we aue that rl r and rh > r Thi tructure of heterogeneou reervation rating offer developer two choice targeting on low reervation rating only to attract conuer in uch group or on high reervation rating to draw conuer fro both group In the baed odel developer ut raie r at leat to r in order to have the deand Here developer only need to reach r L which i potentially le than r and enjoy n L hare of the arket Developer would ake the deciion on electing between thee two alternative depending upon their ( bh We ake the auption that n ( r /( r < In app etting the ditribution of L reervation rating i kew toward higher value ince ot of the people are ore evere in giving rating than accepting rating The reult of developer choice of quality and price are preented in Propoition 3 in the appendix The SPNE reeble the tructure tated in Propoition Here we preent a pecial phenoenon when reervation rating are heterogeneou Propoition 7 If b> b H and h H WW both H ( E E h rh r or + bk E E E are Nah equilibriu (NE while i the SPNE yield a greater profit than for both platfor owner and developer Here b H ( nl ( rh ( + nl ( rh r and H WW ( L ( L H ( H ( L kb n kb n 8 r r r r 3 + n

26 Propoition 7 ugget that there exit a pecial ituation in which the platfor owner can chooe between two increaing fro E for developer with their h locating in H WW Each alternative i a NE However by to E E although the platfor owner hare decreae it incentivize developer to ake a bigger pie o both the platfor owner and developer profit are augented We call thi a Win-Win effect and the interval of cot rate H WW i the Win-Win region It i worth noting that when n L increae thi Win-Win region diinihe Thi Win-Win region confir that our reult under the etting of hoogenou reervation rating are coniderably robut when the heterogeneity on reervation rating i not evere ( n ( r /( r L When n L i not large the reult are alike H between hoogenou and heterogeneou cae Hence the platfor owner can ake the deciion by largely ignoring the preence of heterogeneou reervation rating 8 Dicuion and Future eearch In thi paper we paraeterize conuer rating behavior into four paraeter ( k k r r and contruct U a bidirectional rating-utility fraework which incorporate thee paraeter into conuer utility function In the equilibriu analyi we identify three type of developer: elf-driven platfor ownerdriven and poor arketing and reveal how the change in conuer rating behavior ( k k r r affect U their optial choice of quality level and app price a well a the platfor owner optial choice of revenue haring policy and the ocial welfare We dicover the ( r r apect of rating behavior have different quality iplication than the ( k k apect The leniency iue a well-known proble which U ha been epirically dicovered in any behavioral anageent tudie i analytically oberved in our rating-utility econoic odel Our analyi on ocial welfare reveal that oe conuer rating behavior though increaing the ocial welfare ay not be aligned with the platfor owner interet We find that iniu app price can work a an intruent to rule out developer with low atching perforance The reult that the optial developer revenue haring percentage increae with iniu app price appear to explain what we oberve in real buine practice When developer cot rate i unobervable the platfor owner can deign a creening gae which yield a elf-election proce leading to a eparating equilibriu for high and low cot rate developer It hould be noted that the dynaic between platfor owner optial revenue haring percentage and ( k k r r are different in queezing and encourageent region Thi dicrepancy provide the U platfor owner the incentive to eparate thee two region into ultiple torefront Organizational developer uch a oftware copanie have relatively low cot rate and are ore likely to reide in queezing region The platfor owner ay et up an additional torefront for exaple copany app 6

27 tore copleentary to peronal app tore where individual developer are hoted The platfor owner ay deign different rating yte and adopt different revenue haring percentage for thee two tore We believe a the rapid expanion of app arket continue the increaed heterogeneity on app upply ide would call for thi approach While thi paper take a firt tep to incorporate ubjective rating behavior into traditional utilitybaed analyi one direction of future reearch ay be attributed to tudying the ipact of rating behavior on other apect of traditional indutrial organization (IO proble uch a copetition and product differentiation eearch quetion uch a how developer would copete on app rating and how conuer rating behavior affect the platfor copetition would be intereting The ipact of rating behavior on developer product differentiation trategy uch a how developer anipulate rating to for conuer ex ante perception on product differentiation would alo be a potential topic to explore nother direction for future reearch i fro the behavioral angle Extant behavioral reearch ugget that the dicrepancy of caling in rating yte for exaple 5-tar and -point cale rating would introduce bia in rating behavior Thu an intereting quetion i how the platfor owner deign an appropriate rating cale to hape conuer rating behavior to the deirable ( k k r r deontrated in U thi paper Finally our paper peculate the exitence of reervation rating r The epirical reearch ight be able to detect it by analyzing online WO data EFEENCE kerlof G 97 The arket for Leon : Quality Uncertainty and the arket echani The Quarterly Journal of Econoic Vol 84 No 3 pp Berger J Harbring C Sliwka D Perforance ppraial and the Ipact of Forced Ditribution: n Experiental Invetigation Working Paper Boran WC 977 Conitency of rating accuracy and rating error in the judgent of huan perforance Organizational Behavior and Huan Perforance Volue Iue Page 38-5 Chen Y Xie J 5 Third-Party Product eview and Fir arketing Strategy arketing Sci Vol 4 No pp 8 4 Chen Y Xie J 8 Online Conuer eview: Word-of-outh a a New Eleent of arketing Counication ix anageent Science Vol 54 No 3 arch 8 pp Chevalier J ayzlin D 6 The Effect of Word of outh on Sale: Online Book eview Journal of arketing eearch Vol XLIII

28 Choudhary V 7 Coparion of Software Quality Under Perpetual Licening and Software a a Service Journal of anageent Inforation Syte Vol 4 No pp 4 65 Foran C 8 Exaining the elationhip Between eview and Sale: The ole of eviewer Identity Dicloure in Electronic arket Inforation Syte eearch Vol 9 No 3 pp 9 33 Cleon EK Gao G Hitt L 6 When Online eview eet Hyperdifferentiation: Study of the Craft Beer Indutry Journal of anageent Inforation Syte Vol 3 No pp 49 7 Dellaroca C Farag N Zhang X 4 Uing Online eview a a Proxy of Word-of-outh for otion Picture evenue Forecating Working Paper Dellaroca C 6 Strategic anipulation of Internet Opinion Foru: Iplication for Conuer and Fir anageent Science Vol 5 No pp Gode D ayzlin D 4 Uing Online Converation to Study Word-of-outh Counication arketing Science Vol 3 No 4 pp Hu N Pavlou P Zhang J 6 Can online review reveal a product' true quality?: epirical finding and analytical odeling of Online word-of-outh counication Proceeding of the 7th C conference on Electronic coerce C New York NY US Hu N Liu L Zhang J 8 Do online review affect product ale? The role of reviewer characteritic and teporal effect Inf Technol anage 9: 4 Hu N Zhang J Pavlou P 9 Overcoing the J-haped Ditribution of Product eview Counication of the C Vol 5 No pp Jiang B Chen P 7 n Econoic nalyi of Online Product eview and ating Working Paper Kane JS 994 odel of Volitional ating Behavior Huan eource anageent eview Vol 4 No 3 pp 83-3 Kane JS Bernardin HJ Villanova P Peyrefitte J 995 Stability of ater Leniency: Three Studie The cadey of anageent Journal Vol 38 No 4 pp 36-5 Kukov D Xie Y Pricing Frill and Cutoer ating arketing Sci Vol 9 No 5 pp Lee YJ Tan Y Hoanager K 9 Do I Follow y Friend or the Crowd? Exaining Inforational Cacade in Online ovie eview Proceeding of WITS 9 Li X Hitt L 8 Self-Selection and Inforation ole of Online Product eview Inforation Syte eearch Vol 9 No 4 pp Li X Hitt L Price Effect in Online Product eview: n nalytical odel and Epirical nalyi IS Quarterly (34: 4 pp

29 Liu Y 6 Word of outh for ovie: It Dynaic and Ipact on Box Office evenue Journal of arketing Vol oe W Schweidel D Online Product Opinion: Incidence Evaluation and Evolution Working Paper oe W Truov eauring the Value of Social Dynaic in Online Product ating Foru Journal of arketing eearch forthcoing Saal F Downey G Lahey 98 ating the rating: eing the pychoetric quality of rating data Pychological Bulletin Vol 88 Iue pp Shapiro C 985 Optial pricing of experience good The Bell Journal of Econoic Vol 4 No pp Sun How Doe Variance of Product ating atter? Working Paper Yun GJ Donahue L Dudley N cfarland L 5 ater Peronality ating Forat and Social Context: Iplication for Perforance ppraial ating International Journal of Selection and eent Vol 3 No pp 97-7 Zhou W Duan W Online Uer eview and Profeional eview: Bayeian pproach to odel ediation and oderation Effect ICIS Proceeding Paper 56 Zhu F Zhang X Ipact of Online Conuer eview on Sale:The oderating ole of Product and Conuer Characteritic Journal of arketing Vol ppendix dditional Propoition Propoition Given the revenue haring percentage developer optial choice of price p and quality level q are: i egion -: (elf-driven when b> b and < h h p ( ( ( ( ( ( b r r b k + bk r q U k b kku b ii egion -: (platfor owner driven when b> b and h < h h p ( r bk r b bk ; bk k bk bk k bk h U U q hbk ( U U + k bk + U + iii egion -3: (poor arketing when b b and < h h3 p ( ( ; ( ( ( ( ( b r r b k + bk r q U 3 3 k b kku b 9

30 In all other region of ( bh developer cannot ake non-negative profit The above threhold are: i: b ( r r k ( r r k + k ( r h U 4 bk U h ( r r ( bk + k bk U bkuk ( b ( bk + k bk ( r ( b k + bk ( r and h ( U U kbk U ( r( b ( b( r k + bk ( r 3 ( U Propoition The platfor owner optial choice of developer revenue haring percentage i egion -: (queezing when b> b and < h h α ( ( U + ( ( + U ( bk k ( b hbk k bk r bk bk r U ii egion --α: (encourageent when b> b and h < h α h /3 ( ( + h r r bk k bk + ; U α bku iii egion --β: (retention when b> b and h /3< h h iv egion -3: when b b and < h h3 The threhold: h α ( ( + 4h r r bku k bk β bku ; (( ( + U ( kbk ( r( b h b r k bk r 3 U kbk U ( b ( bk + k bk ( r r ( b k + bk ( r ( U U Propoition 3 Given the revenue haring percentage and conuer are heterogeneou in reervation rating the developer optial choice of price i egion 3-: when b> b H and h h H p ( H H qh ( ( H ii egion 3-: when b> b H and hh < h hh p p and quality level b r br r b r + ; k b k b ( r b br b + ; h k h H H qh ; q are: 3

31 iii egion 3-3: when b b H > and hh p < h iv egion 3-4: when b b H and h h H 3 v egion 3-5: when b b H and h> h H 3 p bn n b L h h ; L L ql ( H H qh ( ( b r br r b r + ; k b k b H p bn n b L h h L L ql In all other region of ( bh developer cannot ake non-negative profit The above threhold are: b H ( nl ( rh ( + nl ( rh r h h H bk( b ( br r b r + H h H ( ( ( r b r + br H H L H H 3 H 4 bk ( nl ( r r r + r n r b r + br bk( b H and B Sketch of Proof We provide here the ketch of proof Proof of Propoition The goal i to axiize u p( P on We plug each region optial price and contraint in Propoition into it and derive each region optial u P uing Lagrange ethod We have explicitly ( r ( ( b b a x up t h h k ( r ( ( 3 b b a x up t h h k ax P b h optial choice of haring percentage a preented in Propoition Proof of Corollarie 3 and 3 The reult regarding p and linear function of h f / h ( + b r r u + ( t h h h > k and Coparing u P in different region we obtain the platfor owner p 3 are traightforward to prove We find that f h ( p / k U > and ( i a f > So p / k U > eanwhile we conider p / k a 3

32 a function of h and then p / k < i guaranteed by h < bk U ( r r ( k bk + bk U It i atified when h< h Proof of Corollary 35 One can find that f( b b ( / k U i a linear function of b f ( < and ( / k U < Under our auption that r r k k U concave quadratic function of b We find that f 3 ( > and ( r rˆ ( r 3 /4 + 3( inequalitie of k yield thi corollary Proof of Corollary 36 f < So > > f ( ( ( 3 b bh k Uk b / k + i a f 3 < It can be hown that when f b It root propertie in different cae which when turned into In queezing region f4 ( k k ( up / ku ( f k > So 4 k ku ( f h α < So 5 i a linear function of k f / 4 k > and u / k > We find f ( h u k P U i a linear function of h ( 5 P / f < and 5 up / k < We find f ( ( ( 6 h k b ku up / r i linear function of h and u / r < can be hown by 6 ( P f > and ( reult in other region can be hown iilarly Proof of Corollarie 4 and 4 In encourageent region ( ( f < and ( 7 / k 7 k ku f h α > u / r > i traightforward to prove The 6 ( ( P f7 k b k + bku W / r i a linear function of k f k < can be guaranteed when h bk / ( r r h< h /3 So W / r > We find that b( b f7 ( k ( W < 3 k 8 hbk + k bk U < which i atified when U f7 ( k ( W < r 4 k bk + bk k U U Define that h ( W k f ( k f ( h where ( / U and f h i a linear function of h with a negative lope and root at h α It i not difficult to how that h α < hα h /3 The reult in retention region are traightforward to prove 3

33 Proof of Corollary 43 In queezing region W / x where x r r k k can be written in the forat of ( U a poitive ter without h and f9 ( h i a linear function of h ( can be written a a function of k and ( Proof of Lea 5 and Propoition 3 We have up{ } ( h h Therefore ( r ( b b p p p k 9 p > p > p3 p becoe a contraint upon p Cx f9 h where C x i f < i not hard to how 9 f9 ( h α f h α < under our auption that k > ku So W / x< r r k up{ p } ( 3 p3 inf { p} p b b ( b b h h p and p When p ˆ p p only affect p 3 but if p ˆ > p it will affect both p and p dding p p a a new contraint to olve the proble in Propoition uing Lagrange ethod we have Propoition 3 Proof of Propoition 4 Thi propoition can be hown by the ae approach a in the proof of Propoition but changing the econd tage reult to thoe of Propoition 3 The correponding optiization proble are ( r ( ( b b a x up t h h k ( t α ax u p h < h h P Proof of Propoition 5 ax u b h ( + b r r 3 P + k ( t h α h> h h The platfor owner revenue i u ( b ( u + u + bu where ( P P P P3 P and u p dh h h 3 ( and P ( h 3 3 u p dh P Proof of Propoition 6 u p dh Solving u / we obtain P / are optial in it correponding region o that individual rationality contraint are atified To L H check incentive copatibility we define f ( r L ( ( ( ( b r r hl r + br br r k b k b that fl / r > Then the incentive copatibility contraint i fl( L fl( rˆ H alo atified we define F( h 6 ( ( ( ( ˆ H hl hhk b fl L fl r H It can be hown To how that it i in which 33

34 rˆ ( r r ( + b bk( b r We have F / h L 4 hh i not difficult to verify o we have ( > and F / h H > The econd order condition { F hh hl } F( h α It can be hown that ( inf F h α > Proof of Propoition 3 When two group of reervation rating r and r H exit developer have two cenario Scenario i to only atify the r conuer and obtain n L fraction of deand Scenario i to atify the r H conuer to obtain all the deand We follow the iilar procedure a Propoition uing Lagrange ethod Coparing and finding the overall optial olution for both cenario yield thi propoition Proof of Propoition 7 To attain the equilibriu in egion 3- which i ( /( 4 4 h k n b r r WW H L H which require h h ( E h r r kb H + the cot rate h ut atify To attain the equilibriu in egion 3-3 which i E we need to have h k ( n b/ ( 4r 4r > L L H which require h h WW > We can WW WW WW WW WW further how that h h > therefore H h h exit In ( i quadratic function of h ( f h u u PH PL f h > when h< h WW H ( nl r H we find that r kb It i not WW difficult to how h h > when n L r H r So we have u > u The reult that PH PL u > u can be hown with the ae procedure Thu the Win-Win effect i identified DH DL 34