Competition for Information under Privacy Concerns

Transcription

1 Competition for Information under Privacy Concern Ramnath K. Chellappa Goizueta Buine School Emory Univerity Atlanta, GA Raymond G. Sin School of Buine and Management Hong Kong Univerity of Science and Technology Clear Water Bay, Hong Kong Atract Due to inherent privacy concern, online peronalization ervice uch a thoe offered through toolar and dektop widget, are characterized y no-free-dipoal (NFD) property in that more ervice are not necearily etter for the conumer. There are two defining characteritic of thi market: Firt, thee ervice are free a firm value conumer preference information hared for peronalization; and econd, while ome firm provide toolar of a fixed-length a a take-it or leave-it offer, many other provide conumer with the option of chooing a uet of the portfolio of ervice offered. Our finding ugget that in a fixed-ervice duopoly where firm are endowed with ufficiently different marginal value for information (MVI), the high MVI firm cater to convenience eeker in the market while the low MVI firm erve a portion of largely privacy eeking conumer in equilirium. On the other hand, if the duopoly were characterized y ufficiently high MVI, the firm would minimize differentiation and offer the ame numer of ervice. However, when two high- MVI firm purue variale-ervice trategy, there i a unique ymmetric equilirium that maximize conumer urplu. Counter to intuition, ome very high-mvi firm may prefer the conumer-urplu maximizing trategy of offering the full et of variale ervice over the fixed-ervice trategy, thu maximizing oth conumer and ocial welfare. Our reult lead to important managerial and policy implication and intereting extenion to the exiting location model. Keyword: peronalization, privacy, patial competition, Nah-equilirium, welfare analyi Introduction A a recent Federal Trade Commiion (FTC) workhop ugget, a et of technologie that have egun to raie conumer concern of privacy are rower-emedded toolar, while ome group characterized thi a pyware, many other tout toolar-enaled peronalization a the future of online ervice (FTC). A toolar i a Brower Helper Oject (BHO), wherein once downloaded and emedded it ha the aility to monitor and report uage information (including We ite viited, information filled in online form, etc.) a well a to tailor future

2 online interaction. More recently, Google Dekar, Microoft Live (now undled with Vita) and Yahoo! Konfaulator technologie have egun to offer thee ervice right from the dektop and are expected to replace current We-aed tatic peronalization. Once emedded, firm can diallow conumer from turning off elect feature, thu conumer may need to remove the entire toolar (and hence forgo all peronalization) if their comfort level in haring information i elow that of the amount acquired y the toolar. A the FTC continue to ae it poition on thee technologie, thee technologie have ecome uiquitou with every online portal (Yahoo!, MSN, AOL, etc.) and many large online firm (ebay, Amazon, etc.) offering them, e.g. currently over 68 Million earche originate from conumer uing toolar. Thu, one important ojective of thi paper i to invetigate the regulatory implication regarding the allowance of uch peronalization technologie through a ocial welfare analyi. The operational ai for thee online firm that rely on conumer information i unique. Peronalization ervice are entirely free of charge to the conumer; portal-like firm rely on their aility to ell rowing profile to advertier and targeted marketer (Dewan et al., January 05-08) while e-tailer ue information acquired for peronalization to manage their own inventory, marketing goal, and to enhance cutomer atifaction and loyalty (Shankar et al.). Indeed, the FTC alo acknowledge the legitimate ue of conumer information y uinee provided that uch uage can alo e eneficial to conumer (See workhop report (FTC)). From the conumer ehavior perpective, online peronalization i an example of good with no free dipoal (NFD) property, an economic claification of good meaning that more of the good i not necearily etter. Recent marketing reearch on pricing acce ervice online (Eegaier et al., Spring), oerve, Unlike phyical good for which free dipoal i alway an option and more i, in general, alway etter, ervice delivery i intrinically participatory. Participation require time commitment and phyical effort on the part of conumer. Thu, there i no free dipoal for ervice, and time cot and phyical effort limit the effectivene of price incentive in altering conumer uage hait. An important cot intrinically related to the uage of peronalization ervice i the privacy cot that individual incur when haring their preference and uage information needed for tailoring ervice to their tate (Volokh, Augut). Therefore even if free of cot, not all conumer will prefer all ervice offered y the firm. Thi property poe many unique challenge to online firm and portal who incur cot of creating peronalized ervice o a to acquire conumer uage information.

3 Thu, our paper examine a competitive market for privacy where firm have to trategically chooe their level of peronalization ervice offering for acquiring conumer information. Further, we incorporate the poiility of online firm eing imilarly or differently endowed in their capacity to generate revenue or lower operating cot from mining and uing conumer information and thu they may vary in the value placed on conumer information. For example, many large firm uch a AOL and MSN do not imply reell their information, ut they operate their own advertiing network with their own profiling technologie a well. On the other hand, many maller firm and portal motly act a a carrier of other advertiing network uch a from DouleClick (DART network at thi time Google intend to purchae DouleClick) and Atla (Atla Suite). Offering peronalization i not cotle and thee technologie are uiquitou and availale to all, hence firm need to invetigate their optimal ervice offering when their competitor can alo potentially offer identical ervice. Firm trategie in thi regard have largely een unexplored in academic reearch, particularly given the NFD nature of conumer utility from peronalization amidt their privacy concern. In order to tudy the welfare implication of allowing toolar/dekar-like technologie, we examine the market equilirium when one or oth firm offer variale ervice wherein a conumer i allowed the option to chooe the full et of ervice in the toolar or diale ome ervice aed on their privacy concern. We contrat thi with equilirium finding when firm offer a fixed et of ervice wherein conumer are made a take-it or leave-it offer to emed a toolar of fixed-length or to not ue it all. The latter cenario i of particular relevance to privacy-group that are concerned aout the poiility of conumer haring more information than they would ideally want.. Review of relevant literature A recent work in Management Science call for the tudy of online peronalization particularly in the preence of privacy concern (Murthi and Sarkar, Octoer). Some have poited that a market for preference information will emerge where conumer will engage in tranaction that involve privacy concern (Rut et al.). In thi regard, ehavioral work ha uggeted that conumer are more likely to accept lo of privacy if it accompanie ome enefit (Laufer and Wolfe), and conumer deciion to hare information i aed on ome cot-enefit tradeoff, known a the privacy calculu (Culnan and Bie). Recent analytical work ha atracted thi privacy calculu in the context of peronalization through conumer peronalization for privacy (p4p) tradeoff (Chellappa and Shivendu, Chellappa and Shivendu). However, to the et of our knowledge, there ha 3

4 een no academic reearch that examine non-price competition in a market for good with NFD property, uch a in the market for peronalization ervice. Murthi and Sarkar (Octoer) point out the need to explore the egmentation apect to a peronalization market, and oerve that when competing firm provide free product, differentiation along the line of price competition ecome irrelevant. Thi paper addree thee apect in that we model a market where firm differentiate themelve on the level of peronalization ervice offered even when no price i eing charged. Further, we model a market that exhiit vertical egmentation characteritic in two way: Firt, producing higher level of ervice i increaingly cotly (convex cot of producing a good along the line of Mua and Roen, and many other). Second, we conider a ditriution of conumer effective marginal value for ervice (captured through their p4p tradeoff), imilar to cae where conumer marginal valuation for quality i ditriuted in a vertically egmented market. However, note that for mot good in a vertically egmented market more quality (or any valued attriute) i trictly preferred y all conumer, i.e. while the marginal value for quality may differ amongt conumer, more i alway etter. Therefore, conumer utilitie are typically trictly increaing in quality or monotonic (non-decreaing) concave. On the contrary, an important apect of the peronalization market i the NFD property of the ervice, where the general principle eing that more i not alway preferred to le. In uch a market, every conumer ha an ideal level of ervice he would like to ue, imilar to the ideal location point in a patial market. Thi ideal point i a reult of internalizing the tradeoff etween gain from peronalization and lo from privacy, which lead to a non-monotonic utility function that firt increae then fall in ervice conumed (purely quality model with monotonic utilitie are ometime called infinite ideal-point conumer homogeneouly prefer an infinite amount of the good model (Moorthy, Augut)). While omewhat le tudied than their free dipoal counterpart, we commonly come acro NFD good when uer have an intrinic diutility from conuming eyond their atiation level (Nahata et al.). Claic example include identifying the right package ize of traveler toiletrie (larger ize are not alway optimal), ideal level of weetne of a drink (over-weetne may not e preferred) and the optimal unit of power production for a townhip (production create pollution) (Rothwell and Rut). Hence our model of competition alo exhiit propertie of horizontally egmented market. 4

5 Finding in purely vertically egmented market are well known in economic, marketing and information ytem (which conider egmentation with zero marginal cot of erving additional conumer). Commonly, egmentation y producing oth high and low quality product i uperior to only producing one product type except under hutdown condition wherein a market comprie of largely high-type conumer. Given the nonprice nature of competition and NFD property of the good, thee finding need to e re-examined in the market for information. On the other hand, finding in horizontally egmented market, commonly decried through patial competition in Hotelling linear market or Salop circular market, are divere and highly dependent on pecific aumption on tranport cot and reervation price. We hall dicu extenion to the linear market a it i mot relevant to our model etup while recognizing that in all the model decried elow, firm do not incur any production cot or any other cot of locating themelve anywhere in the market. The many extenion to Hotelling model focu on the exitence (or lack thereof) of equilirium in a duopoly. For example, D Apremont et al. (Sept., 979) how that the original Hotelling model with linear tranport cot doe not reult in an equilirium olution of minimum differentiation; rather convex tranport cot lead to a price equilirium in any location pair and firm will attempt to maximize their differentiation y locating a far away from each other a poile. While our model doe have the equivalent of convex tranport cot, D Apremont aumption of infinite reervation price (reulting in a fully covered market) do not apply to our cae. In thi regard, Economide and Moorthy etup of a market with finite reervation price i cloer in principle to our. In particular, Economide oervation that the real ource of non-exitence of equilirium in uch market i the non-quaiconcavity (caued y infinite reervation price), not merely the dicontinuity of the payoff function, i mot relevant. A we hall dicu in our reult, ome degree of monopolitic competition oerved y hi work i poile under narrowly defined circumtance in our market a well. There are, however, alo a limited numer of paper that conider ome apect of oth vertical and location-aed competition. For example, Gazewicz and Thie (Mar., 986) conider a market where there are vertical and horizontal differentiation with quadratic tranport cot aleit with infinite reervation price for conumer. While they exogenouly conider an inide and outide-location (firm placed inide v. outide conumer ditriution on a treet) game, in our model firm endogenouly determine their location with repect to the conumer ditriution. However, one of their reult where an equilirium condition i alo ocially optimal ring true for a particular cae of competition in our model a well and i dicued at length in the 5

6 paper. A more recent paper y Deai in marketing ha alo conidered a market characterized y oth vertical and horizontal egmentation, where conumer are ditriuted along two attriute (marginal value for quality and tate preference) that are independent of each other. Thi i perhap the model etup cloet to our in pirit, ut note that our model characterization i not a reult of ditriuting two different conumer characteritic; rather, it i the ditriution of p4p ratio comined with the NFD property of the good that ring out the vertical and horizontal apect in our model. The aove difference comined with the non-price, zero marginal cot and zero verioning cot of ervice in our market reult in finding that are very diimilar to Deai model of price-competition for durale good. While the durale good model find that high valuation egment are more likely to get their preferred attriute level, our reult ugget the oppoite either the entire market i atified at it preferred level or under other circumtance the low type are more likely to e atified. Interetingly, Moorthy work on product and price competition ha intermediate tep that appear tructurally very imilar to our even if the motivation, model formulation and reult are very different. However, note that even if there are no patial characteritic to Moorthy market (no ideal location), there are tructural imilaritie in the payoff and et repone function etween hi model and one of the cae in our model. For reaon dicued later, oth model have two dicontinuitie in the payoff function that ditinctly depend on whether one firm quality (ervice in our model) i the ame, equal to or more than the other firm quality offering. Thi comined with the fact that the payoff are concave in one own quality (ervice) and linearly decreaing in the other quality (ervice) create the impreion of imilarity in the model. In ummary, our model i ditinct from the one dicued aove in that:. We model a good with NFD property that intrinically generate a conumer utility function that i nonmonotonic concave in ervice uage. Previou work generally model durale good with free dipoal or ome trictly preferred property.. We model a market with non-price competition, thu retricting the trategic intrument availale to the firm. While not identical, thi allow u to draw parallel with a purely location game or the location ugame within a price-location game. 3. In our model, firm incur a quadratic fixed cot of offering ervice, i.e., incur a cot of locating themelve. While purely patial model have no firm cot aociated with locating, vertically egmented market erve a a comparion point. 6

7 4. There are no marginal cot of erving additional conumer and there are no cot aociated with offering any ervice level that i a uet of the maximum ervice produced y the firm. Thi property i unique to online ervice and ring out the cotle verioning property explored elewhere (Varian). 5. No aumption i made a priori on whether a market i covered or not. Along the line of a couple of work dicued earlier, conumer have finite reervation. Similar to Moorthy, firm characteritic relative to ditriution of conumer parameter i derived to determine whether a market will e covered or not in equilirium. However, no aumption are made on relative firm characteritic while earlier work have generally modeled identical firm in the duopoly. In we preent the aic model etup when firm purue fixed v. variale ervice and riefly dicu the monopoly reult. In 3, we derive equilirium ervice offering for different duopolitic market where one or oth firm purue fixed (or variale) ervice trategy. We conclude thi ection with an invetigation of welfare implication for each type of the market etup dicued earlier. 4 examine the policy implication of our finding and conclude with a dicuion of theoretical and managerial implication of our analye. The model Our model develop the trategic interaction etween online firm and conumer of peronalization ervice. Conumer engage in a privacy calculu in their deciion to ue peronalization ervice a they incur privacy cot in haring information needed for thi activity (Culnan and Bie). Thi willingne to hare information i aed on the conumer perceived enefit of dicloure alanced with it rik (Derlega et al.). Conumer ehavior in thi context ha een modeled y prior reearch (Chellappa and Shivendu) a a function of conumer marginal value for peronalization p and their coefficient of information privacy concern r given y ui,, p, r p ri, where i the level of peronalization ervice conumed and i i the preference information that need to e hared y the conumer in order for ervice to e peronalized. The numer of peronalized ervice that can e created from a unit of information i commonly a function of the prevalent peronalization and data mining technologie (Raghu et al., Winer). One can view thi a a production function wherein ome technology determine how many ervice can e created from ome information i that i provided. While theoretically more than one ervice can e created for every unit of information hared, it i generally accepted that thi technology i till evolving depite ignificant advance in 7

8 information acquiition (Chen and Hitt, Septemer 00). Hence we aume that one unit of preference information hared provide one unit of correponding peronalized ervice i. Since the firm determine the numer of peronalization ervice to e offered in the market, and through the uage of ervice the conumer determine how much information they will hare, we can write a conumer c utility a a function of peronalization ervice conumed uc, p, r pc rc () It i important to note two alient apect of conumption here: Firt, ervice are provided for free. Conumer do not pay any price to the firm. Second, more ervice are not necearily etter. Each conumer ha an optimal ervice level c that he prefer over all other ervice level. The latter (and it quadratic form) i a characteritic of a cla of economic good with the no free dipoal property which implie that individual derive diutility from conuming additional quantitie eyond their atiation level (Nahata, Kokovin and Zheloodko). Thu the utility function i non-monotonic (an inverted-u function) in ervice conumed, and i characterized y the two level, the utility maximizing arg max u, p, r c 0 c c and reak-even 0 : u p, r, 0 ervice level repectively. For the utility function decried y equation (), we can c ee that 0 c p c and pc c. The ratio p r r r c c i known a the conumer peronalization for privacy (p4p) ratio and i a critical parameter for analyi of conumer ehavior a it determine oth their indifference and optimal ervice level. Empirical reearch find that conumer may vary in their value for peronalization and concern for privacy (Chellappa and Sin, April). Without lo of generality, we conider a market where p conumer are uniformly ditriuted in their p4p ratio given y U0, r. Thi alo allow u to repreent 0 the two conumer-ehavior characterizing level along the ame dimenion given y U 0, and c U 0,. We hall generally refer to conumer with low p4p ratio a privacy-eeker and thoe with high p4p value a convenience-eeker. A ummary explanation of major notation ued in thi paper i preented in Tale in the appendix. c 8

9 . Online firm trategie Firm vary in their aility to ue conumer information y virtue of the extent to which thi information can e exploited to their own purpoe, repreented y their marginal value for information (MVI). For example, portal uch a Yahoo! and AOL that run their own advertiing network do not imply reell uage/preference information; rather they have a portfolio of advertiing related product unlike portal uch DogPile and AkJeeve. Yahoo! Search Marketing diviion offer product uch a Search Optimizer and Marketing Conole that are geared toward mall to medium firm, and provide a fully cutomized advertiing program for firm that have a udget of over $0,000 per month. Similarly, retailer like Amazon.com that carry many product categorie and engage in cro-elling trategie have greater MVI than firm that ell one type of product or ue their ervice to hot advertiement. Offering peronalization ervice i not cotle; either firm incur their own cot of uilding a toolar, or they incur licening and technology cot from uying from firm uch a BetToolBar.net and eztoolar.com. In addition, firm offering peronalization alo incur cot of licening content, uilding trut through alliance with truted third-partie (e.g., TRUSTe, WeCPA, Veriign), and implementing ecurity mechanim to comply with FTC requirement (FTC 000) and pecial legilative requirement uch a Children' Online Privacy Protection Act (COPPA) and Health Inurance Portaility and Accountaility Act (HIPPA) a well (Anonymou, Jun 00, Bloom et al., Scott). Hence we contruct a firm profit a j ja () where j i the marginal value for information (MVI) of a firm j and A i the aggregate information acquired from the uage of peronalization ervice. In thi paper we aume that firm incur imilar cot in offering ervice ut are heterogeneou in their marginal value for information. The identical cot function not only rule out a trivial explanation that any difference in firm trategie i due to difference in cot, ut i alo conitent with the uiquitou availaility and open-tandard nature of peronalization technologie. The aility to ue information however i indeed a function of firm uine trategie and endowment and may affect their overall peronalization offering. The fixed and variale peronalization ervice offering of online firm can e operationalized in one of the following two way through their toolar (or dektop) technologie: 9

10 . A toolar of fixed length where the firm contract to peronalize a fixed numer of ervice and will monitor and acquire information correponding to the entire et of ervice. The conumer i faced with a take-it or leave-it offer where they will ue a long a the utility i non-negative for the ervice level, i.e., 0 0, c. A9.com (affiliated with Amazon.com) toolar i a claic example of thi approach where a conumer ha to agree to all the information eing monitored (which i fully dicloed in the firm privacy policy) or to not ue the toolar at all. Through out the paper we hall refer to thi a the fixed-ervice trategy.. Toolar of variale length where the firm offer a toolar with it full lit of ervice and allow conumer to chooe a uet. In thi cae when conumer vary in their p4p tradeoff, each conumer will ue a different ervice level according to her optimal level c if availale, ele the level provided y the firm (formally min c, ). Many toolar including Google and Yahoo! follow thi approach where conumer have the option to turn off peronalization aed on increaingly enitive information, e.g., the PageRank (called We Rank in Yahoo!) feature can e removed when uing Google toolar ervice. We hall refer to thi a the variale-ervice trategy. In a monopoly, it might appear that the firm would prefer a fixed-ervice approach to a variale one a the latter involve letting conumer chooe their preferred level while in the former the firm i aured that all conumer who participate will ue the level precried y the toolar. However, we have to note that in the fixed-ervice approach a portion of the market may not e erved if the ervice level i too high for ome conumer (more than their reak-even level), and the urplu extracted from the participating conumer i reduced if the ervice i too low. Thi tradeoff comined with the cot of offering ervice will clearly point toward an optimal ervice offering for thi trategy, given y maximizing F 0 0 m U c dc. However, the trategy to offer variale-ervice can e more complex due to oth the NFD nature of peronalization ervice contrated with the zero-marginal cot of oth erving additional conumer and verioning. While the NFD property implie that conumer may ue fewer ervice than thoe precried y the full toolar, the firm alo get a greater numer of people to participate in fact all conumer will participate under variale ervice. Thu the firm will evaluate the increaed market ize, differential urplu acquired from 0

11 each conumer, and the cot of offering the full et of ervice in determining it optimal ervice level, given y o V maximizing m c U c d c U c d c. Solving for optimal ervice y maximizing the repective profit function, we find the optimal ervice and profit to e the ame for the monopolit in oth cae V V F F m, m m, m, 4, although the ize of the market erved and conumer p welfare are different. While in the variale-ervice trategy the entire market 0, r i erved, under fixed offering only the market given p r, will e covered, i.e., a monopolit might e indifferent etween the two trategie a the marginal lo in urplu extracted from each conumer i compenated againt the gain in market ize when variale ervice approach i ued. However, firm trategie and equilirium outcome in a competitive market may e dratically different; not only will the portion of market erved y one firm depend on the relative level of ervice offered y oth, ut the equilirium will alo depend on whether one or oth firm engage in the ame or different trategie (fixed or variale). 3 Competition in a duopoly We conider a duopoly where the two firm have MVI given y and, no aumption i made on the relative value of the two MVI at thi juncture. We conider a game in which oth firm imultaneouly chooe their repective ervice level S and S. Note that the trategy pace are alo ounded y S, S 0, a no conumer would ue eyond thi level and hence no firm will ever conider a trategy of offering ervice eyond thi limit.

12 Conumer utility maximizing ervice level (ideal point) Portal ervice offering (vendor location) 0 c 0 c Ditriution of ideal point cmax p r Ditriution of p4p ratio Conumer reak-even ervice level (reervation value) 0 cmax p r Figure : Ditriution of conumer preference and firm location on a line Figure characterize our peronalization market a a linear one where each conumer location or ideal ervice level c i uniformly ditriuted from 0 to. If a firm offer a certain ervice level at ome ditance c c c x from the ideal point of a conumer, we can ee that the diutility given y u u will e rx. In other word, conumer uffer a convex tranportation cot along the line of D Apremont et al. (Sept., 979) for which equilirium in location exit under certain condition. While firm incur convex cot of locating themelve on the line (normally ignored in purely patial model), the zero-marginal cot and zero verioning cot of ervice (a lower ervice-level can e offered cotlely once a toolar of higher ervice i uilt) comined with the NFD property create unique competitive ituation non-exitent in phyical good market. While the fixed ervice approach appear to e tructurally imilar to phyical good model etup (i.e., once a firm ha located, all conumer have to uy from that point), the variale-ervice trategy create a unique poiility wherein if the firm offer a ervice level, he can cotlely erve all conumer with c at their ideal level. Again, we do not aume a priori a to whether the market i covered (motly the cae in patial model) or not, i.e., conumer do not have infinite reervation. In view of thee difference, it i not clear if any

13 equilirium poiilitie exit at all, hence thi i an intereting model to analyze from a location model perpective a well. 3. Market outcome when oth firm offer fixed ervice We firt conider the cae when oth firm offer a toolar of fixed length, i.e., a take-it or leave-it offer where conumer who pick up the contract agree to the acquiition of a fixed amount information on their uage. In thi cae, conumer will ue the level of ervice that i provided o long a their utilitie are non-negative. In the duopoly, a conumer will chooe Firm if her utility from uing i greater than that from uing. Firt conider the cae when Firm might offer fewer ervice than Firm (, cae uc uc a ). A conumer will derive a higher utility from uing ervice provided y Firm if: p p r p r (3) r p And ince, equation (3) implie r. Notice that conumer with c 0 would not ue any 0 ervice at all, therefore conumer whoe reak-even ervice level, would ue Firm ervice c 0 and the remaining conumer c, would ue Firm ervice. By ymmetry, we know that if Firm 0 offer more ervice than Firm (, cae c ), conumer with c, will ue Firm ervice. If oth firm offer the ame level of ervice level (, cae ), then given that conumer are indifferent etween the two firm, Firm will get half the market of all conumer uing the ervice, i.e. half of the 0 conumer whoe reak-even ervice level are c,. Therefore, the amount of information that a firm acquire depend upon oth hi level of ervice and it magnitude relative to that of the econd firm. We can formally write Firm profit function a F a c c 0 0 if U d F F U c d c F c U c d c 0 0 if 0 0 if Alphaet in the ucript of the profit function correpond to the repective cae regarding the relative ervice level of the firm a dicued aove. 3

14 By ymmetry, we can contruct Firm profit function and notice that the payoff function of oth firm are dicontinuou in the ervice pace. The dicontinuity could lead one to elieve that there may e no equilirium in pure trategie at all and that only mixed trategie equiliria exit. However, for our analye, we conider only pure trategy equiliria for two reaon: Firt, mixed trategie everely limit the explanatory power of the model; econd, work y Dagupta and Makin (Jan., 986) ugget that it i not the dicontinuity itelf, ut rather failure of the payoff function to e quai-concave that i the reaon for the non-exitence of equilirium in pure-trategie. They propoe that under certain condition (quai-concavity, upper emi-continuity and graph continuity of the payoff function), even a game with function that have limited continuity can poe a puretrategy Nah equilirium. Later work ha argued thee condition are far too retrictive and only certain condition on the aggregator function need to e atified for a pure trategy equilirium to exit (Baye et al.). In the appendix we how that our profit function atify thee condition. Thu, we go on to develop the trategic interaction etween the two firm o a to find pure-trategy equiliria. Firm trategy i a et repone to the trategy of Firm if it maximize F F F F max a,, c, in the trategy pace S for any given. In conidering the et repone of Firm, not only doe he need to decide on the ervice level ut he alo need to determine whether to offer a ervice level that i lower than, equal to or greater than the competing firm. By ymmetry, we can ee that Firm alo need to make a imilar deciion in reponding to ervice offered y Firm. Independently, profit in their defined region are all trictly concave, hence interior optima are candidate for equilirium outcome. However, note that for ome firm parameter the function do not attain their maximum within the defined region, e.g., when, F a i till increaing a approache, implying that thi firm type will attempt to undercut Firm y offering lightly more ervice. Hence when a firm MVI i greater than, offering ervice fewer than thoe offered y hi competitor can never e a profit-maximizing trategy in equilirium. Similarly, when a competitor offer a ervice level, irrepective of hi own MVI, it i not optimal 3 for Firm to offer more than Firm a F c i monotonically decreaing in ; hence region c cannot e an The ufficient condition are Diagonal Tranfer Continuity and Diagonal Tranfer Quaiconcavity. See Appendix for detail. 4

15 F F equilirium candidate for thi particular firm pair. Therefore, if the Nah equilirium pair i given y,, then from Firm perpective and for any Firm there might e. An aymmetric equilirium where Firm offer fewer ervice than Firm, given y F, F F F F, F and Firm MVI i.. An aymmetric equilirium where he offer more ervice than Firm, given y F F F F F F,, and Firm MVI F F A ymmetric equilirium where he offer the ame ervice a Firm, given y F F F F, F F, for any MVI of Firm. F In order for the ervice-pair F, to e an equilirium candidate, we need F F F a and max F,. F F c in cae, max F., F c F max., F F F a in cae, or max F., F F and max F,. F F max,. and in cae 3. Comining and and y ymmetry, we find that an aymmetric equilirium can exit etween two firm (uppoe that Firm offer the lower ervice level) only if and F F 3. From Figure, we can ee that for uch intance the payoff of oth firm are well ehaved in that they are continuou ut for upward jump a defined y Milgrom and Roert ; once again pointing toward the exitence of pure-trategy Nah equiliria. In order to identify thee MVI comination for which there exit an equilirium, we find ound on the firm parameter (MVI and ) that atify the aove requirement, i.e. for which two type of firm will the market reult in an equilirium outcome. While algeraically tediou (hence the proof i relegated to the appendix), our approach provide lucid olution to firm and regulator prolem, and allow u to derive managerially relevant inight on firm competition under privacy. Lemma : When oth firm offer only a fixed-ervice toolar, there exit an aymmetric equilirium given y F, F, 4 4 when the competition i characterized y one firm with low MVI and other with a relatively higher MVI

16 Lemma tell u that if firm are ufficiently differentiated y their marginal value for information and if one firm ha a low MVI, then the two firm will hare the marketplace in uch a way that the low MVI firm cater to conumer with low p4p ratio and the high MVI firm cater to thoe with high p4p ratio. Note that when oth firm offer fixed ervice, the NFD nature of the good doe not come into play, i.e., it doe not matter what the ideal point are, conumer will elect a ervice-level a along a their individual rationality (IR) contraint are atified, and their choice of firm will depend on the individual incentive compatiility (IC) contraint. We alo know that for a given ervice level, conumer utilitie are increaing in the p4p ratio, i.e., p p if u u r. Hence along the line of trictly vertically egmented market, we have an r equilirium where one firm erve the low type and the other erve the high type. (Moorthy). The condition on the eparation of MVI eentially enure that the firm with low MVI will not attempt to undercut the higher MVI competitor due to the trade off etween hi cot and marginal value for information., with 8 4, with Figure : Profit under aymmetric equilirium when oth firm offer fixed ervice Interetingly, note that while the ervice offered y oth firm are increaing in of the high MVI firm, the ervice offered y high MVI firm i decreaing in while the low MVI ervice continue to increae in hi own MVI. The intuition ehind thi i that if the MVI are ufficiently far apart, the firm will make themelve attractive to very ditinct egment and a the lower MVI approache, thi firm will egin to offer ervice that are now attractive to ome conumer (who were uing more than their optimal level) of the high MVI firm. Hence for the large MVI firm, the cot of offering high numer of ervice i not offet y the S 6

17 demand captured and will therefore lower hi ervice level. Further, we know that the numer of conumer who are not erved 0 c F increae in MVI, while on the other hand ome conumer (with high p4p ratio) might receive ervice cloer to their optima. Thi portend intereting conumer (and hence ocial) welfare implication that we hall explore later. In fact, ince lim F F, we not only know that the threhold i important in maintaining the aymmetric equilirium ut alo that there i potentially a ymmetric equilirium if the MVI of oth firm are ufficiently high. Lemma : When oth firm offer only a fixed-ervice toolar, then there exit a ymmetric equilirium given y F F,, F when competition i characterized y oth firm having high MVI,. 3 3 For all other firm characterization (e.g., oth firm with low MVI,, there exit no ymmetric equilirium even for identical MVI., with, with Figure 3: Profit of firm under ymmetric equilirium when oth firm offer fixed ervice Lemma ugget that when oth firm have high MVI and oth offer a fixed-ervice take-it or leave-it offer, the only feaile equilirium i characterized y firm offering the ame level of ervice and haring the market equally (ee Figure 3 for a graphical repreentation of profit of the high MVI firm with repect to ervice offered). Note that not only i the equilirium ervice level purely a function of conumer p4p ditriution, ut alo firm need not have identical MVI for ymmetric equilirium to exit; it i only required that oth firm have MVI weakly higher than a threhold. Thi ugget that even if two firm had the aility to offer a greater numer of ervice, doing o would make a firm attractive to conumer to the right 7 S

18 conumer with c, while thoe on the left with c, 3 might egin to prefer the competitor. Eentially, aove the equilirium ervice level, gain from high p4p conumer uage of ervice doe not outweigh lo from offering ervice aove thi level. Thi implie that with a fixed-ervice approach, a portion of the market will alway e left un-covered. In particular, a third of the market will not e erved a conumer with reak-even ervice elow the equilirium ervice level 0 c 3 will not ue any peronalization ervice. The implication of thi reult i that even if the marginal cot of erving an additional conumer i zero, the competitive dynamic of a fixed-ervice approach will lead firm to maximize profit y not erving the egment of conumer with minimal value for peronalization and/or high privacy concern. At the ame time ome conumer c 3 are left wanting for more ervice a the equilirium ervice level will not fully atify thi egment. An important reaon a to why firm need to poe ufficiently high MVI for the ymmetric equilirium to exit i that when one firm i elow the threhold, there i alway tendency for the firm to erve different portion of the market a in Lemma. On the other hand, when oth are elow the threhold, ymmetric equilirium i not feaile either ecaue haring the market i never an optimal trategy. The imple intuition i that ince conumer are indifferent etween the ervice offered y the two firm a long a they offer the ame level of ervice, oth firm incur the full infratructure cot while only getting half the market and firm could alway increae thi market ize y offering lightly more or fewer numer of ervice. Another important implication i one that hint at reducing conumer privacy concern. We can ee that profit of oth firm are increaing in conumer p4p ratio and prior reearch (Chellappa and Sin, April) ugget that engendering trut in a peronalization context may reduce privacy concern. While it i eyond the cope of thi paper, one could oerve that even if ervice offering are inditinguihale, firm may etter their profit y differentiating themelve on the ai of conumer trut. 3. Market outcome when oth firm offer variale ervice We now conider the more common cenario where firm offer a toolar of certain length, ut allow conumer to ue only a uet of ervice y turning off information acquiition for ome ervice thu forgoing peronalization enefit from thee ervice a well. The NFD property of the good play an important role here in that with the option of chooing their own ervice level, conumer will chooe only their optimal ervice level 8

19 c if availale. Since conumer will e indifferent etween the ervice offered y the two firm, oth firm will hare the conumer egment with min,. The remaining conumer min, will ue c ervice from the firm offering a higher ervice level ecaue they can no longer e atified y the other firm. However, note that thi egment of conumer can only ue their ideal level of ervice up to the level offered y the firm with more ervice; eyond which they can only ue the exact amount that i offered. Thu, we can formally write Firm profit function a V a c U c d c 0 V V c U c d c U c d c 0 if if V c c U c d c cu c d c U c d c if 0 c We can oerve that for ome firm parameter, offering a ervice level lower than that of the competitor i a trictly dominated trategy; when, V a i negative regardle of the ervice level offered y Firm. The intuitive reaon i that when oth firm offer variale ervice, the firm offering lower ervice level incur the full cot of offering the ervice while eing aured of only half the market correponding to that ervice level. On the other hand, if, V a i till increaing a approache, implying that thi firm will prefer to offer the ame or higher numer of ervice a hi competitor. Extending thi logic to Firm and y ymmetry we can eaily preclude the poiility of an aymmetric equilirium when variale ervice define the market. V V Therefore if the Nah equilirium pair i given y,, then from Firm perpective and for any Firm there might e. A ymmetric equilirium where he offer the ame ervice a Firm, given y V V V V, V V, for any MVI of Firm. No aymmetric equilirium. 9

20 V In order for the ervice-pair V, to e an equilirium candidate, we need to have V V V and max V,. V V max.,. Similar to the previou cae, we derive oundarie on the firm parameter o a to explore for the poiility for any equilirium trategy., Lemma 3: When oth firm allow conumer to elf-elect their repective ervice level, only a ymmetric equilirium i poile; which exit only when the competition i characterized y two high MVI firm. The equilirium numer of ervice offered y each firm will e the full et, given y, V V,, V. For all other firm type there i no market equilirium even if their MVI are identical. Thi ituation i unique to our model that i characterized y NFD property of the ervice, and the zero marginal and verioning cot of offering variale ervice. The intuition ehind Lemma 3 i a follow: ince conumer are indifferent etween the two firm and are free to chooe their individual deired level of peronalized ervice, if two firm offer different ervice level, then the firm offering the higher ervice level would get half of market of it competitor and will further capture the entire egment of conumer whoe peronalization need are higher than the competitor offering i.e. conumer with min,, max,. While offering more ervice than the competitor c appear preferale, ecaue no conumer ha c greater than, no firm would offer ervice higher than thi level. Hence, if the MVI are high enough for firm to offet the cot of offering uch a high level of peronalization, oth firm would offer the maximum level of ervice deired y the conumer in equilirium. Thu the equilirium ervice level i independent of the firm own MVI (a long a they are aove the threhold) and all conumer enjoy their ideal level of peronalization ervice. It i alient to note the difference etween the full length of the toolar (the maximum numer of peronalization ervice offered) in the two ymmetric equiliria decried in Lemma and 3, given y 3 and repectively. While the market i not covered under the fixed-ervice cae, not only are all conumer eing erved ut conumer welfare i alo maximized in the latter cae. While a monopolit would e indifferent etween offering a fixed toolar trategy or one that allow conumer to chooe their preferred level, in a 0

21 competitive model it i not clear yet whether firm with high MVI will necearily prefer one over the other. Intuitively, it might appear that firm would prefer to et the ervice level and conumer ue the precried level, conitent with price etting ehavior in mot market. However, in our context of zero marginal and verioning cot, the reult might yet e urpriing a even if variale ervice i conumer-welfare maximizing, the market i fully covered thu holding out the ditinct poiility of eing etter for the firm than the fixedervice trategy when a third of the market i alway left un-erved. Before we dicu the ocial welfare implication of fixed and variale trategie, we hall firt conider a hyrid cae where one firm chooe to offer a variale-ervice contract while the other opt for a fixed-ervice one. 3.3 Market outcome when one firm purue fixed while the other purue variale Without lo of generality, aume Firm to e the one that offer a toolar of fixed length, while Firm allow conumer to chooe ervice in a variale fahion. Firt conider the cae when oth firm offer different level of ervice. If Firm offer fewer numer of ervice than, then all conumer with urplu maximizing numer of ervice lower than that offered y Firm c would chooe Firm ecaue they can freely chooe their ideal level to conume. The remaining conumer would chooe Firm if their utility from uing i greater than that from, i.e. u u c c. We can ee that conumer whoe p4p ratio p r, will till ue Firm ervice. However, if Firm offer more ervice than, all conumer will chooe Firm and ue their individual utility-maximizing numer of ervice. If oth firm offer the ame level of ervice, Firm would capture all conumer whoe c and half the market of all remaining conumer. Thu the profit function of the firm offering variale ervice can e written a V 0 0 a c U c d c U c d c if 0 V V c U c d c U c d c if 0 V c c U c d c U c d c if 0 And the profit function of the firm offering fixed ervice can e written a

22 F 0 0 a U c d c if F F U c d c if F c if Let the Nah equilirium pair e given y V F,. We can immediately oerve that when the firm offering higher numer of ervice allow conumer to chooe their preferred level, it i never optimal for the firm offering a maller length toolar to purue a fixed-ervice trategy. The intuitive reaon i that conumer would undoutedly ue their ideal ervice level if given the choice, i.e., F V i never an equilirium poiility. Notice that imilar to ection 3., for ome firm parameter the profit function do not attain their maximum within the defined region: when, V a of the firm offering variale ervice i till increaing a approache, implying that when a firm MVI i greater than, offering ervice fewer than that offered y hi competitor i an unlikely equilirium trategy. Since any aymmetric equilirium implie F V, from Firm perpective and for any Firm there might e. An aymmetric equilirium where Firm offer fewer ervice than Firm, given y V, F V F F, F and Firm MVI i.. A ymmetric equilirium where he offer the ame ervice a Firm, given y V F V F V F,, for any MVI of Firm. In order for the ervice pair V F, to e an equilirium candidate, we need max., V V a V and F F c F max,. in cae, or max., V V V and F F F max,. in cae. Since it i never optimal for the firm puruing fixed-ervice to offer fewer ervice than the firm puruing variale-ervice trategy, the only poile aymmetric equilirium will e characterized y V F when. Lemma 4: In a duopoly where one firm purue a fixed-ervice trategy while the other doe not, there i no ymmetric equilirium. An aymmetric equilirium exit if the MVI of the firm allowing variale ervice i low

23 and that of the one puruing fixed-ervice trategy i ufficiently higher The equilirium pair i given y. V, F, 4 4 It i quite apparent that it cannot e optimal for a firm to engage in a fixed-ervice trategy and offer the ame or fewer numer of ervice than it competitor who allow conumer to chooe their preferred level. Alo note that the ervice offering are the ame a in Lemma (aymmetric equilirium when oth firm offer fixed ervice), although the difference of MVI etween the two firm need to e larger. Thi differentiation i driven y oth ound, i.e., the mall MVI firm i maller than hi counterpart in Lemma and the large MVI firm ha to e larger at the ame time. Intuitively, we can ee that the mall MVI firm, y offering variale ervice, i eentially erving thoe conumer who would have een left un-erved when oth firm offered fixed ervice (Lemma ), i.e., thoe with very low p4p ratio 0 c 4. Further, unlike in Lemma, the market will e fully covered in thi ituation a the wort any conumer in thi market can do i to ue V. An important finding of our analye i that in equilirium, whenever at leat one firm offer variale ervice, the market will alway e fully covered and the conumer urplu will alway e higher. The imple intuition ehind thi i that whenever one firm allow conumer to chooe their deired ervice level, every conumer can find a ervice level that correpond to a non-zero utility; while low type will pick up ome ervice level lower than that offered y the variale-ervice firm, the high type will chooe etween thi firm and the competitor who offer a higher ervice level. Thu from a conumer urplu point of view a well even if one firm offer variale-ervice, conumer are alway etter off. Further, note that when the MVI of the fixedervice firm increae, oth firm would find it optimal to increae their ervice level. While the increae in the fixed-ervice level may or may not lead to increaed conumer urplu, the increae in the maller MVI firm offering will reult in a greater portion of conumer in the market eing atified at their preferred level. The equilirium numer of ervice a well a profit for the firm and the equilirium region are ummarized in Tale (in the appendix) and Figure 4, repectively. 3

24 Symmetric Equiliria Both vendor adopt the ame (fixed or variale) ervice trategy Aymmetric Equilirium Both vendor offer fixed-ervice Aymmetric Equilirium High MVI vendor offer fixed-ervice; Low MVI vendor offer variale-ervice Figure 4: Equilirium region in the duopoly 3.4 Welfare analye Having derived the equilirium olution under different comination of ervice-trategy, we hall now analyze their implication to conumer and ocial welfare. From our earlier dicuion, it i quite evident that when one (oth) firm purue a variale ervice trategy, ome (all) conumer enjoy their urplu maximizing level of ervice. Lemma 5: In the duopoly where there i at leat one low MVI firm and the higher MVI firm offer fixedervice, the market i fully covered and conumer-welfare i higher when the low MVI firm offer variale ervice than when oth offer fixed-ervice. In the market characterized y two firm with ufficiently high MVI,, we oerve the following: i. Conumer urplu i alway maximized when oth firm adopt a variale-ervice trategy in equilirium. ii. Firm equilirium profit from adopting variale-ervice trategy i higher than their correponding profit from engaging in fixed-ervice, when their repective MVI are very high, 0 and the ocial-welfare i the highet in thi cae. iii. Even if firm MVI are lower than the threhold in (ii), equilirium ocial welfare in variale-ervice trategy i higher than that under fixed-ervice trategy under a lowered limit 0 6 4