《电子商务 E-business》阅读文献：The Impact of Recommender Systems on Sales Diversity

MANAGEMIENT SCIENCE ToPms vol.55No.5,May2009,pp.697-712 Do110.1287/mnsc.10800974 IssN0025-1909|EssN1526-55011091550510697 @2009 INFORMS Blockbuster Culture's next rise or fall The Impact of Recommender Systems on Sales diversity Daniel Fleder, Kartik Hosanagar and Informatio delphia, Pennsylvania 19104 Idfleder@wharton. upenn. edu, kartik@wharton. up his paper examines the effect of recommender systems on the diversity of sales. Two anecdotal views exist about such effects. Some believe recommenders help consumers discover new products and thus increase sales diversity. Others believe recommenders only reinforce the popularity of already-popular products. This paper seeks to reconcile these seemingly incompatible views. We explore the question in two ways. First, mod- eling recommender systems analytically allows us to explore their path-dependent effects. Second, turning to simulation, we increase the realism of our results by combining choice models with actual implementations of recommender systems. We arrive at three main results. First, some well-known recommenders can lead to a reduction in sales diversity. Because common recommenders(e.g, collaborative filters)recommend products based on sales and ratings, they cannot recommend products with limited historical data, even if they would be rated favorably. In turn, these recommenders can create a rich-get-richer effect for popular products and vice versa for unpopular ones. This bias toward popularity can prevent what may otherwise be better consumer- product matches. That diversity can decrease is surprising to consumers who express that recommendations ave helped them discover new products. In line with this, result two shows that it is possible for individual- level diversity to increase but aggregate diversity to decrease. Recommenders can push each person to new products, but they often push users toward the same products. Third, we show how basic design choices affect the outcome, and thus managers can choose recommender designs that are more consistent with their sales Key words: If policy and management; electronic commerce; application contexts/sectors; IT impacts on industry and market structure; marketing, advertising and media History: Received June 21, 2007; accepted November 18, 2008, by Barrie Nault, information systems. Published online in Articles in Advance March 6, 2009 1. Introduction filters, [which include online recommender systems media has historically been a"blockbuster"industry is to help people move from the world they know (Anderson 2006). Of the many products available, (hits) to the world they don' t (niches")"(Anderson sales have concentrated among a small number of 2006, p. 109) hits. In recent years, such concentration has begun Although recommenders have been assumed to to decrease. The last 10 years have seen an extraor- push consumers toward the niches, we present an linary increase in the number of products available argument why some popular systems might do the (Brynjolfsson et al. 2006, Clemons et al. 2006),and opposite. Anecdotes from users and researchers sug- consumers have taken to these expanded offerings. gest that recommenders help consumers discover ne Many believe this increased variety allows consumers products and thus increase diversity(Anderson 2006) to obtain more ideal products, and if it continues it Others believe several recommender designs might could amount to a cultural shift from hit to niche reinforce the position of already-popular products products. One difficulty that arises, however, is how and thus reduce diversity(Mooney and Roy 2000, consumers will find such niche products among seem- Fleder and Hosanagar 2007). This paper attempts to ingly endless alternatives Recommender systems are considered one solu ing supply-side offerings fixed, we ask whether rec tion to this problem. These systems use data on pur- ommenders make media consumption more diverse chases, product ratings, and user profiles to predict or more concentrated which products are best suited to a particular user. 1 with ate a univer These systems are commonplace at major online firms different recommenders employed cannot st al result for all. Instead, this paper picks sev- such as Amazon, Netflix, and Apple's iTunes Store. eral recommenders that we believe are commonly used in industry In author Chris Andersons view " The main effect of and focuses on them

MANAGEMENT SCIENCE Vol. 55, No. 5, May 2009, pp. 697–712 issn0025-1909 eissn1526-5501 09 5505 0697 informs ® doi 10.1287/mnsc.1080.0974 © 2009 INFORMS Blockbuster Culture’s Next Rise or Fall: The Impact of Recommender Systems on Sales Diversity Daniel Fleder, Kartik Hosanagar Department of Operations and Information Management, The Wharton School, University of Pennsylvania, Philadelphia, Pennsylvania 19104 {dfleder@wharton.upenn.edu, kartikh@wharton.upenn.edu} This paper examines the effect of recommender systems on the diversity of sales. Two anecdotal views exist about such effects. Some believe recommenders help consumers discover new products and thus increase sales diversity. Others believe recommenders only reinforce the popularity of already-popular products. This paper seeks to reconcile these seemingly incompatible views. We explore the question in two ways. First, mod￾eling recommender systems analytically allows us to explore their path-dependent effects. Second, turning to simulation, we increase the realism of our results by combining choice models with actual implementations of recommender systems. We arrive at three main results. First, some well-known recommenders can lead to a reduction in sales diversity. Because common recommenders (e.g., collaborative filters) recommend products based on sales and ratings, they cannot recommend products with limited historical data, even if they would be rated favorably. In turn, these recommenders can create a rich-get-richer effect for popular products and vice versa for unpopular ones. This bias toward popularity can prevent what may otherwise be better consumer￾product matches. That diversity can decrease is surprising to consumers who express that recommendations have helped them discover new products. In line with this, result two shows that it is possible for individual￾level diversity to increase but aggregate diversity to decrease. Recommenders can push each person to new products, but they often push users toward the same products. Third, we show how basic design choices affect the outcome, and thus managers can choose recommender designs that are more consistent with their sales goals and consumers’ preferences. Key words: IT policy and management; electronic commerce; application contexts/sectors; IT impacts on industry and market structure; marketing; advertising and media History: Received June 21, 2007; accepted November 18, 2008, by Barrie Nault, information systems. Published online in Articles in Advance March 6, 2009. 1. Introduction Media has historically been a “blockbuster” industry (Anderson 2006). Of the many products available, sales have concentrated among a small number of hits. In recent years, such concentration has begun to decrease. The last 10 years have seen an extraor￾dinary increase in the number of products available (Brynjolfsson et al. 2006, Clemons et al. 2006), and consumers have taken to these expanded offerings. Many believe this increased variety allows consumers to obtain more ideal products, and if it continues it could amount to a cultural shift from hit to niche products. One difficulty that arises, however, is how consumers will find such niche products among seem￾ingly endless alternatives. Recommender systems are considered one solu￾tion to this problem. These systems use data on pur￾chases, product ratings, and user profiles to predict which products are best suited to a particular user. These systems are commonplace at major online firms such as Amazon, Netflix, and Apple’s iTunes Store. In author Chris Anderson’s view, “The main effect of filters, [which include online recommender systems], is to help people move from the world they know (‘hits’) to the world they don’t (‘niches’)” (Anderson 2006, p. 109). Although recommenders have been assumed to push consumers toward the niches, we present an argument why some popular systems might do the opposite.1 Anecdotes from users and researchers sug￾gest that recommenders help consumers discover new products and thus increase diversity (Anderson 2006). Others believe several recommender designs might reinforce the position of already-popular products and thus reduce diversity (Mooney and Roy 2000, Fleder and Hosanagar 2007). This paper attempts to reconcile these seemingly incompatible views. Hold￾ing supply-side offerings fixed, we ask whether rec￾ommenders make media consumption more diverse or more concentrated. 1 With so many different recommenders employed by firms, one cannot state a universal result for all. Instead, this paper picks sev￾eral recommenders that we believe are commonly used in industry and focuses on them. 697

Fleder and He 698 eli ve explore this question in two ways. First, mod- systems use product information(e.g. author, genre) g recommender systems analytically allows us to to recommend items similar to those a user rated explore their path-dependent effects. Second, using highly. Collaborative filters, in contrast, recommend simulation, we increase the realism of our results what similar customers bought or liked. Perhaps bycombiningchoicemodelswithactualimplemen-thebest-knowncollaborativefilterisAmazon.com tations of recommender systems. Our main result is with its tagline,"Customers who bought this also at some popular recommenders can lead to a reduc- bought tion in diversity. Because common recommenders The design of these systems is an active research (e.g, collaborative filters)recommend products based area. Reviews are provided in Breese et al.(1998) on sales or ratings, they cannot recommend products and Adomavicius and Tuzhilin(2005). For busir with limited historical data, even if they would be contexts, Ansari et al. (2000) describes how firms viewed favorably. These recommenders create a rich- can integrate other data sources(e. g, expert opin t-richer effect for popular products, and vice versa ions)into recommendations. Work by Bodapati(2008) or unpopular ones. Several popular recommenders places recommender systems into a profit-maximizing explicitly discount popular items, in an effort to pro- framework. For industry applications, implementa moteexplorationEvensoweshowthatthissteptionsatfirmssuchasAmazon.comandCdnow.com may not be enough to increase diversity are described by Schafer et al. (1999)and Linden et al That diversity can decrease is surprising to con-(2003). Although there is a large body of work on sumers who express that recommendations have building these systems, we know less about how they helped them discover new products. The model pro- affect consumer choice and behavior vides two insights here. First, we find it is possible for Studies have recently begun to examine individual- individual-level diversity to increase, but aggregate level behavioral effects. In marketing, Senecal and person to new products, but they often push similar tions do influence choice. They find that online recom- users toward the same products. Second, if recom- mendations can be more influential than human ones menders are simply replacing best-seller lists, diver- Cooke et al.(2002)examine how purchase decisions sity can increase by cutting out what is an even more under recommendations depend on the information provided, context, and familiarity. The results have implications for firms and con Whereas the above studies ask how recommenders sumers. For retailers, we show how design choices affect individuals, our interest is the aggregate effect affect sales and diversity. For consumers and niche they have on markets and society. In particular, we are content producers, we show how a recommender's interested in how recommenders affect sales diversity bias toward popular items can prevent what would In related work, Brynjolfsson et al.(2007)find that a otherwise be better consumer-product matches. We firms online sales channel has slightly higher diver find that recommender des that explicitly pro- sity than its offline channel. They suggest demand- mote diversity may be more desirable side causes, such as active tools(search engines) and The rest of this paper is organized as follows. Sec- passive tools(recommender systems), but do not iso- tion 2 reviews prior work. Section 3 gives a formal late the specific effect of recommenders. In contrast, problem statement. Section 4 presents the analytic Mooney and roy(2000)suggest that collaborative fil- model, which is stylized but still able to show how ters may perpetuate homogeneity in choice but do not sales information can bias recommenders. To increase study it formally the realism of our setting, and in particular incor Given our focus on aggregate effects, the streams porate actual recommender designs, a complemen- of work on information cascades and Internet balka- tary simulation is developed in SS5-7. The simulation nization are also related. The information cascades combines consumer choice models with actual recom- literature has looked at aggregate effects of observa mender algorithms. Section 8 discusses the implica- tional learning and resulting convergence in behavior tions for producer and consumer welfare. Section 9 or"herding"(Bikhchandani et al. 1998). The Inter- concludes, reviewing the findings and offering direc- net balkanization literature asks whether the Internet tions for future work creates a global community freed of geographic con- straints. Van Alstyne and Brynjolfsson(2005)find that 2. Prior work although increased integration can result, the Internet Recommender systems help consumers learn of new can also lead to greater balkanization, wherein groups roducts and select desirable products among myriad with similar interests find each other. Although our choices(Resnick and Varian 1997). A simplified tax- problem is different, we see these papers as comple- onomy divides recommenders into content-based ver- mentary in highlighting the social implications of tech sus collaborative filter-based systems. Content-based nologies that share information among users

Fleder and Hosanagar: The Impact of Recommender Systems on Sales Diversity 698 Management Science 55(5), pp. 697–712, © 2009 INFORMS We explore this question in two ways. First, mod￾eling recommender systems analytically allows us to explore their path-dependent effects. Second, using simulation, we increase the realism of our results by combining choice models with actual implemen￾tations of recommender systems. Our main result is that some popular recommenders can lead to a reduc￾tion in diversity. Because common recommenders (e.g., collaborative filters) recommend products based on sales or ratings, they cannot recommend products with limited historical data, even if they would be viewed favorably. These recommenders create a rich￾get-richer effect for popular products, and vice versa for unpopular ones. Several popular recommenders explicitly discount popular items, in an effort to pro￾mote exploration. Even so, we show that this step may not be enough to increase diversity. That diversity can decrease is surprising to con￾sumers who express that recommendations have helped them discover new products. The model pro￾vides two insights here. First, we find it is possible for individual-level diversity to increase, but aggregate diversity to decrease. Recommenders can push each person to new products, but they often push similar users toward the same products. Second, if recom￾menders are simply replacing best-seller lists, diver￾sity can increase by cutting out what is an even more popularity-biased tool. The results have implications for firms and con￾sumers. For retailers, we show how design choices affect sales and diversity. For consumers and niche content producers, we show how a recommender’s bias toward popular items can prevent what would otherwise be better consumer-product matches. We find that recommender designs that explicitly pro￾mote diversity may be more desirable. The rest of this paper is organized as follows. Sec￾tion 2 reviews prior work. Section 3 gives a formal problem statement. Section 4 presents the analytic model, which is stylized but still able to show how sales information can bias recommenders. To increase the realism of our setting, and in particular incor￾porate actual recommender designs, a complemen￾tary simulation is developed in §§5–7. The simulation combines consumer choice models with actual recom￾mender algorithms. Section 8 discusses the implica￾tions for producer and consumer welfare. Section 9 concludes, reviewing the findings and offering direc￾tions for future work. 2. Prior Work Recommender systems help consumers learn of new products and select desirable products among myriad choices (Resnick and Varian 1997). A simplified tax￾onomy divides recommenders into content-based ver￾sus collaborative filter-based systems. Content-based systems use product information (e.g., author, genre) to recommend items similar to those a user rated highly. Collaborative filters, in contrast, recommend what similar customers bought or liked. Perhaps the best-known collaborative filter is Amazon.com’s, with its tagline, “Customers who bought this also bought” The design of these systems is an active research area. Reviews are provided in Breese et al. (1998) and Adomavicius and Tuzhilin (2005). For business contexts, Ansari et al. (2000) describes how firms can integrate other data sources (e.g., expert opin￾ions) into recommendations. Work by Bodapati (2008) places recommender systems into a profit-maximizing framework. For industry applications, implementa￾tions at firms such as Amazon.com and CDNOW.com are described by Schafer et al. (1999) and Linden et al. (2003). Although there is a large body of work on building these systems, we know less about how they affect consumer choice and behavior. Studies have recently begun to examine individual￾level behavioral effects. In marketing, Senecal and Nantel (2004) show experimentally that recommenda￾tions do influence choice. They find that online recom￾mendations can be more influential than human ones. Cooke et al. (2002) examine how purchase decisions under recommendations depend on the information provided, context, and familiarity. Whereas the above studies ask how recommenders affect individuals, our interest is the aggregate effect they have on markets and society. In particular, we are interested in how recommenders affect sales diversity. In related work, Brynjolfsson et al. (2007) find that a firm’s online sales channel has slightly higher diver￾sity than its offline channel. They suggest demand￾side causes, such as active tools (search engines) and passive tools (recommender systems), but do not iso￾late the specific effect of recommenders. In contrast, Mooney and Roy (2000) suggest that collaborative fil￾ters may perpetuate homogeneity in choice but do not study it formally. Given our focus on aggregate effects, the streams of work on information cascades and Internet balka￾nization are also related. The information cascades literature has looked at aggregate effects of observa￾tional learning and resulting convergence in behavior, or “herding” (Bikhchandani et al. 1998). The Inter￾net balkanization literature asks whether the Internet creates a global community freed of geographic con￾straints. Van Alstyne and Brynjolfsson (2005) find that although increased integration can result, the Internet can also lead to greater balkanization, wherein groups with similar interests find each other. Although our problem is different, we see these papers as comple￾mentary in highlighting the social implications of tech￾nologies that share information among users.

Fleder and Hosanagar: The Impact of Recommender Systems on Sales Diversity 12,⑥2009 INFORMS This prior work reveals four themes. First, recom- Figure 1 Lorenz Curve mender systems research in the data-mining literature has focused more on system design than understand ing behavioral effects. Second, the marketing literature is just beginning to examine such behavioral effects Third, of the existing behavioral work, the focus has been more on individual outcomes than aggregate effects. Fourth, regarding aggregate effects, there are 5安 opposing conjectures as to the effect of recommenders on sales diversity 3. Problem definition 3.1. Focus on Collaborative filters The current work focuses on collaborative filtering Fraction of products(u) recommender systems, which appear to be more com- mon than content-based ones. The diversity debate 3.3. Problem Statement focuses specifically on collaborative filters because Consider a firm with I customers Cr/...,CI and j prod recommendations. Content-based systems do not use function r that maps a customer c, and database onto mmended product Pj. Typically, the database historical data, and so do not naturally raise the ques- a rec a t a set of different recommenders r1,.,Tk tion of whether positive feedback cycles could emerge reco consumer purchases and/or ratings. Con- and lower diversity. For ease of exposition, through- sider ne ut the paper recommender system is synonymous Each r; reflects certain design choices. For example, with collaborative fil ri might be thestandard" user-to-user collaborative filter, whereas r; might be a variant that explicitly 3.2. Measure of Sales Diversity gives low weight to popular items. Denote by Go the Our context is a market with a single firm selling one Gini coefficient of the firm's sales during a fixed time class of good(e. g, music versus movies) period in which a recommender system was not used Before examining recommender systems' effects, it In contrast, let G; be the Gini coefficient of the firms Is necessary to distinguish between sales and prod- sales in which ri was employed with all else equa ically measures how many different products a firm is said to have a concentration bias, diversity a uct diversity Product diversity, or product variety, typ- DEFINITION(RECOMMENDER BIAS). Recommende offers.It is a supply-side measure of breadth In con- or no bias depending on the following condition g trast, we use sales diversity to describe the concentra- tion of market shares conditional on firms assortment I Concentration bias G:>Go decisions. To measure sales diversity, we adopt the Diversity bias Gini coefficient. The gini is a common measure of No bias G:=G distributional inequality. It has been applied to many problems, the most common perhaps being wealth For various recommenders, we examine whether a quality(e.g, Sen 1976) bias exists and its direc tion Let L(u) be the Lorenz curve denoting the percent age of the firm s sales generated by the lowest 100u% 4. Analytical Model ods sold during a fixed time period. The Gini cient is defined 4.1. Assumptions and Model Collaborative filters can operate on purchase or rating data. To fix a context, our model considers purchases A+B We consider a set of customers making purchases sequentially. A=/(u-L(u)du, B Ass 1. each 1e Figure 1 illustrates this. Thus, G E[0, 1, and it mea time step. sures how much L(u) deviates from the 45 line The customer's decision is which product to buy, A value G=0 reflects diversity (all products have not whether to buy. For example, at a subscription qual sales), whereas values near one represent con- media service, this could reflect customers who centration(a small number of products account for decide to consume an item( e.g. a movie or song)but most of the sales) have not vet chosen which

Fleder and Hosanagar: The Impact of Recommender Systems on Sales Diversity Management Science 55(5), pp. 697–712, © 2009 INFORMS 699 This prior work reveals four themes. First, recom￾mender systems research in the data-mining literature has focused more on system design than understand￾ing behavioral effects. Second, the marketing literature is just beginning to examine such behavioral effects. Third, of the existing behavioral work, the focus has been more on individual outcomes than aggregate effects. Fourth, regarding aggregate effects, there are opposing conjectures as to the effect of recommenders on sales diversity. 3. Problem Definition 3.1. Focus on Collaborative Filters The current work focuses on collaborative filtering recommender systems, which appear to be more com￾mon than content-based ones. The diversity debate focuses specifically on collaborative filters because these systems use historical sales data to generate recommendations. Content-based systems do not use historical data, and so do not naturally raise the ques￾tion of whether positive feedback cycles could emerge and lower diversity. For ease of exposition, through￾out the paper recommender system is synonymous with collaborative filter. 3.2. Measure of Sales Diversity Our context is a market with a single firm selling one class of good (e.g., music versus movies). Before examining recommender systems’ effects, it is necessary to distinguish between sales and prod￾uct diversity. Product diversity, or product variety, typ￾ically measures how many different products a firm offers. It is a supply-side measure of breadth. In con￾trast, we use sales diversity to describe the concentra￾tion of market shares conditional on firms’ assortment decisions. To measure sales diversity, we adopt the Gini coefficient. The Gini is a common measure of distributional inequality. It has been applied to many problems, the most common perhaps being wealth inequality (e.g., Sen 1976). Let Lu be the Lorenz curve denoting the percent￾age of the firm’s sales generated by the lowest 100u% of goods sold during a fixed time period. The Gini coefficient is defined G = A A + B  A = 1 0 u − Lu du B = 1 2 − A Figure 1 illustrates this. Thus, G ∈ 0 1, and it mea￾sures how much Lu deviates from the 45 line. A value G = 0 reflects diversity (all products have equal sales), whereas values near one represent con￾centration (a small number of products account for most of the sales). Figure 1 Lorenz Curve 0 1.0 0 0.2 0.2 0.4 0.4 0.6 0.6 0.8 0.8 1.0 A B Fraction of products (u) Fraction of sales L(u) f(u) = u 3.3. Problem Statement Consider a firm with I customers c1cI and J prod￾ucts p1pJ . Define a recommender system as a function r that maps a customer ci and database onto a recommended product pj . Typically, the database records consumer purchases and/or ratings. Con￾sider next a set of different recommenders r1rk. Each ri reflects certain design choices. For example, ri might be the “standard” user-to-user collaborative filter, whereas rj might be a variant that explicitly gives low weight to popular items. Denote by G0 the Gini coefficient of the firm’s sales during a fixed time period in which a recommender system was not used. In contrast, let Gi be the Gini coefficient of the firm’s sales in which ri was employed with all else equal. Definition (Recommender Bias). Recommender ri is said to have a concentration bias, diversity bias, or no bias depending on the following conditions: ⎧ ⎪⎨ ⎪⎩ Concentration bias Gi > G0 Diversity bias Gi < G0 No bias Gi = G0 For various recommenders, we examine whether a bias exists and its direction. 4. Analytical Model 4.1. Assumptions and Model Collaborative filters can operate on purchase or ratings data. To fix a context, our model considers purchases. We consider a set of customers making purchases sequentially. Assumption 1. Each consumer buys one product per time step. The customer’s decision is which product to buy, not whether to buy. For example, at a subscription media service, this could reflect customers who decide to consume an item (e.g., a movie or song) but have not yet chosen which.

Fleder and He he Impact of Recommender Systems on Sales ORMS ASSUMPTION 2. We assume there are only two products, Figure 3 A Two-Urn Model for Recommender Systems w and b(white and black This assumption is for tractability, but it still allows us to illustrate how the use of sales information affects AsSUMPTION 3. Consumers have purchase probabilities (P, 1-p) for(w, b) in the absence of recommendations We do not model the decision process that gener- ates these purchase probabilities ASSUMPTION 4. At each occasion, the firm recommends a product, which is accepted with probability r AssUMPTION 5. The firm's recommendation is gener ated using a function 8(X,Elw, b, where X, is the seg ment share of w just before purchase t This segment of similar consumers is identified based on past behavior, possibly from purchases of The recommender's inputs are segment shares products in other categories. The assumption that (market shares within a segment of similar users), the group does not evolve is for tractability, but it nd its output is a product. The system modeled rec- does have a parallel with business practice. In indus- ommends the product with higher segment share. try, real-time updating of segments is often computa This choice of g has a parallel with collaborative fil- tionally prohibitive, so many firms update segments ers, which identify similar customer segments and periodically recommend the most popular item within them The process defined by these assumptions can be (e. g , "people who bought X also bought Y"). This illustrated by an urn model. Consider the two-urn recommender can be represented by the step function system of Figure 3. Urn 1 contains balls represent- ing products w and b. A fraction p of the balls in urn 1 are white; this fraction is the consumer's pur- chase probability for w in the absence of recommen 8( ) =P(w recommended (x)=1 X,=2 dations. Urn 2 is the recommender: its contents reflect the sales history within the segment, and it produces 1X2>2 recommendations according to 8(X,), where X, is the fraction of w in urn 2 just before t. To start,urn where X, E [0, 1]. Figure 2 plots this. When X,=5 2 contains one wo and one b. At time t=l, a ball and the products have equal shares, the recommen- is drawn with replacement from urn 1 representing dation is determined by a Bernoulli()trial. To start, the consumer's choice before seeing the recommenda the recommender does not favor either product, and tion. Next, a ball is drawn with replacement from urn we assume X1=2- 2 according to 8(X,), representing the recommended product. With probability r, the consumer accepts the ASsUMPTION 6. The segment of consumers constitut- recommendation, and with probability(1-r)the con- ing X is preselected and does not change over time sumer retains the original choice. The ball chosen represents the actual product purchased; a copy of Figure 2 Recommender g(X,) it is added to urn 2, which is equivalent to updat ing the recommender's sales history(e.g, the firms database). Consumer 2 then arrives, and the process repeats(p and r are the same, but X2 is used instead of X,, and so on for other customers From these assumptions, the probability that w is purchased at time t is f(X,): P(w chosen on occasion tIX, =p(1-r)+g(X)r Section 5 presents an alternate approach where we relax assumptions. Specifically, we model the consumer's decision cess, consider multiple products with a no-purchase option, allow segments to evolve over time

Fleder and Hosanagar: The Impact of Recommender Systems on Sales Diversity 700 Management Science 55(5), pp. 697–712, © 2009 INFORMS Assumption 2. We assume there are only two products, w and b (white and black). This assumption is for tractability, but it still allows us to illustrate how the use of sales information affects diversity. Assumption 3. Consumers have purchase probabilities (p 1 − p) for (wb) in the absence of recommendations. We do not model the decision process that gener￾ates these purchase probabilities. Assumption 4. At each occasion, the firm recommends a product, which is accepted with probability r. Assumption 5. The firm’s recommendation is gener￾ated using a function gXt ∈ w b , where Xt is the seg￾ment share of w just before purchase t. The recommender’s inputs are segment shares (market shares within a segment of similar users), and its output is a product. The system modeled rec￾ommends the product with higher segment share. This choice of g has a parallel with collaborative fil￾ters, which identify similar customer segments and recommend the most popular item within them (e.g., “people who bought X also bought Y ”). This recommender can be represented by the step function gXt=P w recommendedXt= ⎧ ⎪⎪⎪⎪⎨ ⎪⎪⎪⎪⎩ 0 Xt < 1 2  1 2 Xt = 1 2  1 Xt > 1 2  (1) where Xt ∈ 0 1. Figure 2 plots this. When Xt = 1 2 and the products have equal shares, the recommen￾dation is determined by a Bernoulli( 1 2 ) trial. To start, the recommender does not favor either product, and we assume X1 = 1 2 . Assumption 6. The segment of consumers constitut￾ing Xt is preselected and does not change over time. Figure 2 Recommender gXt 0 0.5 1.0 0 0.5 1.0 Xt g(Xt ) Figure 3 A Two-Urn Model for Recommender Systems p (1–r) r g(Xt ) Urn 1 Urn 2 This segment of similar consumers is identified based on past behavior, possibly from purchases of products in other categories. The assumption that the group does not evolve is for tractability, but it does have a parallel with business practice. In indus￾try, real-time updating of segments is often computa￾tionally prohibitive, so many firms update segments periodically.2 The process defined by these assumptions can be illustrated by an urn model. Consider the two-urn system of Figure 3. Urn 1 contains balls represent￾ing products w and b. A fraction p of the balls in urn 1 are white; this fraction is the consumer’s pur￾chase probability for w in the absence of recommen￾dations. Urn 2 is the recommender: its contents reflect the sales history within the segment, and it produces recommendations according to gXt, where Xt is the fraction of w in urn 2 just before t. To start, urn 2 contains one w and one b. At time t = 1, a ball is drawn with replacement from urn 1 representing the consumer’s choice before seeing the recommenda￾tion. Next, a ball is drawn with replacement from urn 2 according to gXt, representing the recommended product. With probability r, the consumer accepts the recommendation, and with probability (1−r) the con￾sumer retains the original choice. The ball chosen represents the actual product purchased; a copy of it is added to urn 2, which is equivalent to updat￾ing the recommender’s sales history (e.g., the firm’s database). Consumer 2 then arrives, and the process repeats (p and r are the same, but X2 is used instead of X1), and so on for other customers. From these assumptions, the probability that w is purchased at time t is f Xt = P w chosen on occasion tXt = p1−r +gXtr 2 Section 5 presents an alternate approach where we relax these assumptions. Specifically, we model the consumer’s decision pro￾cess, consider multiple products with a no-purchase option, and allow segments to evolve over time.

Fleder and Hosanagar: The Impact of Recommender Systems on Sales Diversity Management Science 55(5), pp. 12,⑥2009 INFORMS Figure 4 f(X, )and 45 line (p=0.7, /=0.5) The cases in Proposition 1 have an attractive geo- metric interpretation: The support points are simply the intersections of f(X,) with the 45 line in Figure 4 That is, the support points are Ir: f(x)=x- Visu ally, p and r shift and stretch the step function; as result, it has either one intersection occurring below f(,)=0.5(Case 1), one intersection occurring above f(X)=0.5(Case 3), or both( Case 2) CoROLLARY 1. Chance and winning the market. In Case2,P(im→X1<)>0 and P(lim,→x2>2)>0 This is evident because I <0.5 and h>0.5 are both support points. This shows an interesting aspect of Case 2: regardless of the initial p, either product can obtain and maintain the majority share P(1-r) X<l“” With the limiting value(s) of X,I known, we ask whether they reflect higher or lower concentration. Let p(1-r)]+p(1-n)+r] X1=im,(2) are less equal than they would be without recommen- dations. Increased concentration means lim oX>p when p>2 and lim,oo X,<p when p< 3. The effect igure 4 plots an example of f. The labels in(2)"I, on concentration is given by the following proposition m,""h"are shorthand; they visually refer to the PROPOSITION 2. Relation of limit points to concentra low((),middle(m), and high(h) portion of fs shape tion For any(p, r), the effect on concentration is in Figure 4. The geometry of this figure helps illus trate the results derived next Support 4.2. Model results Case points Effect on concentration relative to p 4.2.1. Theoretical Results. The following results 1 1 Increased concentration are derived in a random walks framework by exam- ing the difference w-b over time. All proofs are in 2 Case2A:p∈ Online Appendix I (provided in the e-companion concentration for both support points Without recommendations, shares converge to (P,1-p). The first proposition asks how this is affected Case 2B:PA/l-r Increased P of a recommender. as t converges to one of two values. These limiting val concentration for one support point; ues depend on the consumer's initial p and recom decreased for the other mender's influence r and are given by 1 Increased concentration PROPOSITION1. Support points.Ast→∞, X con These cases are shown in Figure 5. For Cases 1 and 3, there is a single outcome, and that outcome always has increased concentration. These are Support Support of the P x I space tror ise point 1 point 2 initial probability(p) relative to the recommender's strength(r); as a result, the recommender's effect is 1.P≤(-r)/(1-n) to reinforce this tendency even more. For example, 2.(-r)/(1-n)<pP≤/(1-r) if consumers have a fairly strong tendency to buy w with p=0.90 and the recommender is fairly influen- 3.p≥/(1-n) tial with r=0. 25, the recommender creates a positive feedback loop, reinforcing the popularity of w and where the shorthand I and h are from Equation(4), giving it a limit share of 0.93>0.90. Product w was ∈0,1l,andr∈(0,1)(r=0or1 is trivial) initially bought more, which made it recommended more, which made it bought more, and so on 3 An electronic companion to this paper is available as part of the onlineversionthatcanbefoundathttp://mansci,journal.informs.*thevisualinterpretationappliesonlytowheref'slinesegments intersect the 45. line(not the sing

Fleder and Hosanagar: The Impact of Recommender Systems on Sales Diversity Management Science 55(5), pp. 697–712, © 2009 INFORMS 701 Figure 4 f Xt and 45 line (p = 07 r = 05) 0 0.5 1.0 0 0.5 1.0 f(Xt ) Xt = ⎧ ⎪⎪⎪⎨ ⎪⎪⎪⎩ p1−r Xt < 1 2 “l” p1−r +p1−r +r  2 Xt = 1 2 “m” p1−r +r Xt > 1 2 “h” (2) Figure 4 plots an example of f . The labels in (2) “l,” “m,” “h” are shorthand; they visually refer to the low (l), middle (m), and high (h) portion of f ’s shape in Figure 4. The geometry of this figure helps illus￾trate the results derived next. 4.2. Model Results 4.2.1. Theoretical Results. The following results are derived in a random walks framework by exam￾ining the difference w − b over time. All proofs are in Online Appendix I (provided in the e-companion).3 Without recommendations, shares converge to (p 1−p). The first proposition asks how this is affected by the presence of a recommender. As t → , {Xt} converges to one of two values. These limiting val￾ues depend on the consumer’s initial p and recom￾mender’s influence r and are given by Proposition 1. Support points. As t → , Xt con￾verges to Support Support Case point 1 point 2 1. p ≤  1 2 − r  1 − r l — 2.  1 2 − r  1 − r<p< 1 2 1 − r l h 3. p ≥ 1 2 1 − r h — where the shorthand l and h are from Equation (4), p ∈ 0 1, and r ∈ 0 1 (r = 0 or 1 is trivial). 3 An electronic companion to this paper is available as part of the online version that can be found at http://mansci.journal.informs. org/. The cases in Proposition 1 have an attractive geo￾metric interpretation: The support points are simply the intersections of f Xt with the 45 line in Figure 4. That is, the support points are {x f x = x}.4 Visu￾ally, p and r shift and stretch the step function; as a result, it has either one intersection occurring below f Xt = 05 (Case 1), one intersection occurring above f Xt = 05 (Case 3), or both (Case 2). Corollary 1. Chance and winning the market. In Case 2, P limt→ Xt < 1 2  > 0 and P limt→ Xt > 1 2  > 0. This is evident because l < 05 and h > 05 are both support points. This shows an interesting aspect of Case 2: regardless of the initial p, either product can obtain and maintain the majority share. With the limiting value(s) of {Xt} known, we ask whether they reflect higher or lower concentration. Let the term “increased concentration” define shares that are less equal than they would be without recommen￾dations. Increased concentration means limt→ Xt > p when p > 1 2 and limt→ Xt < p when p < 1 2 . The effect on concentration is given by the following proposition. Proposition 2. Relation of limit points to concentra￾tion. For any (p r), the effect on concentration is Support Case points Effect on concentration relative to p 1 1 Increased concentration 2 2 Case 2A p ∈ 1 − r 2 − r  1 2 − r  . Increased concentration for both support points Case 2B p 1 − r 2 − r  1 2 − r  . Increased concentration for one support point; decreased for the other 3 1 Increased concentration These cases are shown in Figure 5. For Cases 1 and 3, there is a single outcome, and that outcome always has increased concentration. These are areas of the p × r space where consumers have strong initial probability (p) relative to the recommender’s strength (r); as a result, the recommender’s effect is to reinforce this tendency even more. For example, if consumers have a fairly strong tendency to buy w with p = 090 and the recommender is fairly influen￾tial with r = 025, the recommender creates a positive feedback loop, reinforcing the popularity of w and giving it a limit share of 093 > 090. Product w was initially bought more, which made it recommended more, which made it bought more, and so on. 4 The visual interpretation applies only to where f ’s line segments intersect the 45 line (not the single point at Xt = 05).