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, modeling 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 consumerproduct 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 individuallevel 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 extraordinary 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 seemingly endless alternatives. Recommender systems are considered one solution to this problem. These systems use data on purchases, 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 suggest 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. Holding supply-side offerings fixed, we ask whether recommenders 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 several 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, modeling 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 implementations of recommender systems. Our main result is that some popular recommenders can lead to a reduction 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 richget-richer effect for popular products, and vice versa for unpopular ones. Several popular recommenders explicitly discount popular items, in an effort to promote exploration. Even so, we show that this step may not be enough to increase diversity. That diversity can decrease is surprising to consumers who express that recommendations have helped them discover new products. The model provides 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 recommenders are simply replacing best-seller lists, diversity can increase by cutting out what is an even more popularity-biased tool. The results have implications for firms and consumers. 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 promote diversity may be more desirable. The rest of this paper is organized as follows. Section 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 incorporate actual recommender designs, a complementary simulation is developed in §§5–7. The simulation combines consumer choice models with actual recommender algorithms. Section 8 discusses the implications for producer and consumer welfare. Section 9 concludes, reviewing the findings and offering directions 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 taxonomy divides recommenders into content-based versus 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 opinions) into recommendations. Work by Bodapati (2008) places recommender systems into a profit-maximizing framework. For industry applications, implementations 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 individuallevel behavioral effects. In marketing, Senecal and Nantel (2004) show experimentally that recommendations do influence choice. They find that online recommendations 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 diversity than its offline channel. They suggest demandside causes, such as active tools (search engines) and passive tools (recommender systems), but do not isolate the specific effect of recommenders. In contrast, Mooney and Roy (2000) suggest that collaborative filters 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 balkanization are also related. The information cascades literature has looked at aggregate effects of observational learning and resulting convergence in behavior, or “herding” (Bikhchandani et al. 1998). The Internet balkanization literature asks whether the Internet creates a global community freed of geographic constraints. 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 complementary in highlighting the social implications of technologies 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, recommender systems research in the data-mining literature has focused more on system design than understanding 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 common 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 question of whether positive feedback cycles could emerge and lower diversity. For ease of exposition, throughout 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 product diversity. Product diversity, or product variety, typically measures how many different products a firm offers. It is a supply-side measure of breadth. In contrast, we use sales diversity to describe the concentration 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 percentage 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 measures how much Lu deviates from the 45 line. A value G = 0 reflects diversity (all products have equal sales), whereas values near one represent concentration (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 products 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. Consider 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 generates 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 generated using a function gXt ∈ w b , where Xt is the segment 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 recommends the product with higher segment share. This choice of g has a parallel with collaborative filters, 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) where Xt ∈ 0 1. Figure 2 plots this. When Xt = 1 2 and the products have equal shares, the recommendation 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 constituting 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 industry, real-time updating of segments is often computationally 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 representing products w and b. A fraction p of the balls in urn 1 are white; this fraction is the consumer’s purchase probability for w in the absence of recommendations. 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 recommendation. 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 consumer 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 updating 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 process, 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→X10 and P(lim,→x2>2)>0 This is evident because I 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) Xp when p>2 and lim,oo X,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 “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 illustrate the results derived next. 4.2. Model Results 4.2.1. Theoretical Results. The following results are derived in a random walks framework by examining 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 values depend on the consumer’s initial p and recommender’s influence r and are given by Proposition 1. Support points. As t → , Xt converges to Support Support Case point 1 point 2 1. p ≤ 1 2 − r 1 − r l — 2. 1 2 − r 1 − r 0 and P limt→ Xt > 1 2 > 0. This is evident because l 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 recommendations. Increased concentration means limt→ Xt > p when p > 1 2 and limt→ Xt 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).
Fleder and He ar: The Impact of Recommender on Sales Diversity 12, @2009 INFORMS Figure 5 ing the p x r Space to Concentration Effects probability of arrivin This, in turn allow ers Refer to Cases in Proposition 2) us to calculate the expected effect on concentration. PROPOSITION 3. The distribution of lim ooX. P(lim oX,= P(lim a X, supp Case point 1 point 2 int 1) ≈0.5 2 h (1-m)·(1-l/(1-D) y m:(1-(1-h)/h)+(1-m):(1-1/(1-D∈(0,1 Case 2A occurs where the recommender's influence (r) is high relative to the initial probability (p). This his proposition will be applied subsequently two implications, one at the sample-path level 4. 2.2. Graph ical Example. A aphical example and one at the aggregate leveL. At the sample-path helps illustrate the results For the sake of illustration, level, either product can win the market, regardl take p=0.70 and r=0.50. Figure 6 plots 10 realiza of p. For example, p=0.55 and r=0.75 imply limit- tions of this process over time. The top part of the fig- In the first outcome w wins the market. In the sec- ond, b wins, even though p=0.55 initially favored w One sees that the limits are in accord with Propos (cf Corollary 1). This occurs because r is large rela- tion 1, which says the process converges to a random tive to p, and the recommender reinforces whichever Figure 6 The Two Limiting Outcomes for Our Example f(x) product does well early on without too much resis- tance from p. This leads to the finding that recom- menders can create hits. Some product will become a winner with a permanent, majority share, but we can- not say which beforehand. At the aggregate level,con centration always increases. We do not know which b will win but we know that one will, and whichever does will be an outcome with greater con centration. Although they start with different mode a similar phenomenon occurs in other contexts( e.g studies of firm location). Arthur(1994)provides an overview of applications, whereas earlier mathemati cal results are in Hill et al. (1980) Last, in Case 2B, neither the initial probability G Time nor the recommender's influence(r)is strong relative to one another. As a result, two outcomes are possible Frequency of outcome The tendency p can be reinforced by the recommender Increases concentration can give whichever product was not favored a small majority. This decreases concentration. For example, if P=0.60, which is mild, and r=0. 25, the limit points are 0.70 and 0.45. Often w has more early successes nd the recommender reinforces this, leading to less- diverse 0.70 outcome. In some cases, if b is chosen nough early on, the recommender reinforces b, lead- &ig to the 0.45 outcome, which entails less concentra- n than the initial share of 0.40 Although both outcomes are possible in Case 2B they are not equi likely. Next we determine the Limiting P(white)
Fleder and Hosanagar: The Impact of Recommender Systems on Sales Diversity 702 Management Science 55(5), pp. 697–712, © 2009 INFORMS Figure 5 Relating the p × r Space to Concentration Effects (Numbers Refer to Cases in Proposition 2) 0.0 0.5 1.0 0.0 0.5 1.0 r p 3 1 2B 2B 2A Case 2A occurs where the recommender’s influence (r) is high relative to the initial probability (p). This has two implications, one at the sample-path level and one at the aggregate level. At the sample-path level, either product can win the market, regardless of p. For example, p = 055 and r = 075 imply limiting market shares of w b ∈ 089 011 014 086 . In the first outcome, w wins the market. In the second, b wins, even though p = 055 initially favored w (cf. Corollary 1). This occurs because r is large relative to p, and the recommender reinforces whichever product does well early on without too much resistance from p. This leads to the finding that recommenders can create hits. Some product will become a winner with a permanent, majority share, but we cannot say which beforehand. At the aggregate level, concentration always increases. We do not know which of w or b will win, but we know that one will, and whichever does will be an outcome with greater concentration. Although they start with different models, a similar phenomenon occurs in other contexts (e.g., studies of firm location). Arthur (1994) provides an overview of applications, whereas earlier mathematical results are in Hill et al. (1980). Last, in Case 2B, neither the initial probability (p) nor the recommender’s influence (r) is strong relative to one another. As a result, two outcomes are possible. The tendency p can be reinforced by the recommender. This increases concentration. Or, the recommender can give whichever product was not favored a small majority. This decreases concentration. For example, if p = 060, which is mild, and r = 025, the limit points are 0.70 and 0.45. Often w has more early successes and the recommender reinforces this, leading to lessdiverse 0.70 outcome. In some cases, if b is chosen enough early on, the recommender reinforces b, leading to the 0.45 outcome, which entails less concentration than the initial share of 0.40. Although both outcomes are possible in Case 2B, they are not equally likely. Next we determine the probability of arriving at each. This, in turn, allows us to calculate the expected effect on concentration. Proposition 3. The distribution of limt→ Xt is P limt→ Xt = P limt→ Xt = Support Support support support Case point 1 point 2 point 1) point 2) 1 l 1 0 2 lh 1 − 3 h 1 0 where = 1 − m·1 − l/1 − l m ·1 − 1 − h/h + 1 − m·1 − l/1 − l ∈ 0 1 This proposition will be applied subsequently. 4.2.2. Graphical Example. A graphical example helps illustrate the results. For the sake of illustration, take p = 070 and r = 050. Figure 6 plots 10 realizations of this process over time. The top part of the figure shows these paths converging to two outcomes. One sees that the limits are in accord with Proposition 1, which says the process converges to a random Figure 6 The Two Limiting Outcomes for Our Example f x 1,000 1,500 0 0.35 0.85 1.00 P(white) 0 0.35 0.85 1.00 0 1 0.27 0.73 Frequency of outcome 10 sample paths Time Limiting P(white)
r and Hosanagar: The Impact of Recommender Systems on Sales Diversity gement Science 55(5), pp 12,⑥2009 INFORMS variable whose support is (0.35, 0.85]. The bottom part artifact of the initial conditions assumed for urn 2, of the figure shows the frequencies of arriving at the which places one w and one b in a high r recom- lower versus upper outcome approach 0.27 and 0.73, mender even when p a0 or a1.5 in accord with Proposition ummarizing, under recommendations the shares 4.2.3. Net effect on sales Concentration With converge to either one or two limiting outcomes the limiting distribution of (x, known, we complet depending on(p, r). When there is one outcome, the connection to sales concentration. For two prod- it always reflects increased concentration: the rec- ucts with shares p and 1-P, the Gini coefficient is ommender reinforces the popularity of the initially proportional to(Sen 1976): preferred product. In the two outcome cases, either G()=|-l both outcomes have greater concentration or one has greater concentration and the other has less. For the With recommendations, we define latter, a net effect must be calculated. This typically has greater concentration, although for extreme(p, Gp. -EG(lim x)p, rl as discussed, increased diversity may occur. Thus, the recommender seems to increase concentration among G(P(limx,=)+G(h)P(lim X, =h).(4) a set of similar users. The net effect on concentration is given by Gp, -Gp, 0, 5. Simulations which is >0(<0) when concentration increases (decreases). Substituting into(3)and(4)terms from 5.1. Rationale for Simulation the previous propositions gives Simulation offers three benefits for this problem. First, although actual recommender algorithms are difficult Case G G to represent analytically, they can be implemented in simulation. Second, heterogeneity in user preferences Ip-2 is easily accommodated. Third, more complex choice y+ h-2 5.2. Choice Model and Simulation Design p-i We now turn to a simulation that combines a choice model with actual recommender systems. Repeat pur- The above gives a closed-form expression for the chases are permitted in the simulation. Examples of change in Gini coefficient. Figure 7 shows this graph- contexts with repeat purchases could include music ically. For most of the p x r square, concentration and video streaming from a subscription service(e.g increases. This is true, of course, for areas under Rhapsody) Cases 1, 2A, and 3, where the only possibility was An overview of the process is as follows. There are increased concentration. It is also true for most areas I consumers and products positioned in an attribute where both outcomes were possible( Case 2B). In space. Consumers are not aware of all products. Each extreme cases, it is possible for a net decrease to occur, consumer knows most of the center products and a as shown by the shading. These areas are largely an small number of products in his own neighborhood Figure 7 Concentration Increases in White Areas and Decreases in Shaded ones the products or makes no purchase at all. To model this choice, a multinomial logit is used for J products plus an outside good. Just before choosing a product, a recommendation is generated. The recommender has two effects. First, the consumer becomes aware of the recommended product if he was not already This increase in awareness is permanent. Second, the .0.5 An example illustrates how this is related to initial conditions. uppose p=0.99, and r=0.99, which is in the shaded region Because X,=0.50, P(b on first purchase)N0.50. If b is chosen, the recommender next suggests b; because r=0.99 the next consumer is almost certain to pick b too, and so on for the con- sumers, even though p=0.99 favors w. If the initial conditions are determined by k Bernoulli(p) trials, diversity decreases even more: the shaded areas of Figure 7 begin to turn white even for small k. These additional experiments are available from the authors on
Fleder and Hosanagar: The Impact of Recommender Systems on Sales Diversity Management Science 55(5), pp. 697–712, © 2009 INFORMS 703 variable whose support is 035 085 . The bottom part of the figure shows the frequencies of arriving at the lower versus upper outcome approach 0.27 and 0.73, in accord with Proposition 3. 4.2.3. Net Effect on Sales Concentration. With the limiting distribution of Xt known, we complete the connection to sales concentration. For two products with shares p and 1 − p, the Gini coefficient is proportional to (Sen 1976): Gp = p − 1 2 (3) With recommendations, we define Gp r = E G limt→ Xt p r = GlP limt→ Xt = l + GhP limt→ Xt = h (4) The net effect on concentration is given by Gp r − Gp 0, which is >0 (<0) when concentration increases (decreases). Substituting into (3) and (4) terms from the previous propositions gives Case Gp r Gp 0 1 l − 1 2 p − 1 2 2 l − 1 2 + h − 1 2 1 − p − 1 2 3 h − 1 2 p − 1 2 The above gives a closed-form expression for the change in Gini coefficient. Figure 7 shows this graphically. For most of the p × r square, concentration increases. This is true, of course, for areas under Cases 1, 2A, and 3, where the only possibility was increased concentration. It is also true for most areas where both outcomes were possible (Case 2B). In extreme cases, it is possible for a net decrease to occur, as shown by the shading. These areas are largely an Figure 7 Concentration Increases in White Areas and Decreases in Shaded Ones 0.0 0.5 1.0 0.0 0.5 1.0 r p artifact of the initial conditions assumed for urn 2, which places one w and one b in a high r recommender even when p ≈ 0 or ≈1.5 Summarizing, under recommendations the shares converge to either one or two limiting outcomes depending on (p r). When there is one outcome, it always reflects increased concentration: the recommender reinforces the popularity of the initially preferred product. In the two outcome cases, either both outcomes have greater concentration or one has greater concentration and the other has less. For the latter, a net effect must be calculated. This typically has greater concentration, although for extreme (p r), as discussed, increased diversity may occur. Thus, the recommender seems to increase concentration among a set of similar users. 5. Simulations 5.1. Rationale for Simulation Simulation offers three benefits for this problem. First, although actual recommender algorithms are difficult to represent analytically, they can be implemented in simulation. Second, heterogeneity in user preferences is easily accommodated. Third, more complex choice processes can be represented. 5.2. Choice Model and Simulation Design We now turn to a simulation that combines a choice model with actual recommender systems. Repeat purchases are permitted in the simulation. Examples of contexts with repeat purchases could include music and video streaming from a subscription service (e.g., Rhapsody). An overview of the process is as follows. There are I consumers and J products positioned in an attribute space. Consumers are not aware of all products. Each consumer knows most of the center products and a small number of products in his own neighborhood. Every period, a consumer either purchases one of the products or makes no purchase at all. To model this choice, a multinomial logit is used for J products plus an outside good. Just before choosing a product, a recommendation is generated. The recommender has two effects. First, the consumer becomes aware of the recommended product if he was not already. This increase in awareness is permanent. Second, the salience of the recommended product is increased 5 An example illustrates how this is related to initial conditions. Suppose p = 099, and r = 099, which is in the shaded region. Because X1 = 050, P(b on first purchase) ≈ 050. If b is chosen, the recommender next suggests b; because r = 099 the next consumer is almost certain to pick b too, and so on for the remaining consumers, even though p = 099 favors w. If the initial conditions are determined by k Bernoulli(p) trials, diversity decreases even more: the shaded areas of Figure 7 begin to turn white even for small k. (These additional experiments are available from the authors on request.)
Fleder and He ar: The Impact of Recommender on Sales Diversity ORMS temporarily, raising the chance that the recommended The system then recommends product product is purchased in that purchase instance. The next consumer makes a purchase in a similar manner r1:j= arg max∑ nd the process repeats after all consumers have pur- chased. After a predetermined number of iterations, Recommender r, has one difference. When selecting the Gini is computed. The Gini is then compared to a the most popular product among similar users,can- benchmark Go, the Gini from an equivalent period in didate items are first discounted by their overall pop which recommendations were not offered ularity in the entire population: We now discuss each of the simulation components (i) the map of products and consumers,(i) the rec- ommender r, (iii) the awareness distribution, (iv) the 2:= arg max|∑ salesi I∑sles-(7) choice model, and (v) the salience factor 8 (i) Map of product and consumer points. The map The motivation for r2's popularity discounting is a of products and ideal points is the input for the belief that popular items are so obvious they should choice model. Plotting consumer points and product not be suggested. This was described to us in indus- locations goes back at least to Hotelling(1929)and is try interviews as common practice. For example, if commonly used in marketing(e.g, Elrod and Keane a consumer is expected to buy or be aware of a 1995). Our consumers and products are points in a product with high probability, the firm should rec- two-dimensional space. The use of two dimensions ommend something else. Note, r2 is not the same is for simplicity and visualization; for contexts with as applying"term-frequency inverse-document fre- more than two attributes, the maps can be consid- quency"weights(tf-idf) to algorithm ri. tf-idf would ered dimensionality-reduced versions, as is common insert discounting in the user similarity calculation in marketing research. We take both ideal points(Breese et al. 1998), whereas r2 inserts it in the final and products to be standard bivariate normal. The arg max of (7). In 57, we test other recommenders, normality assumption for consumers is common in including one with tf-idf weights, and show the factor-analytic market maps ( e. g, Elrod and Keane results are directionally the same 1995). Our base case uses 50 consumers and 50 prod (iii)Awareness. Recommenders are valuable to con- ucts,an example of which is in Figure 8 umers because they help overcome information (ii)The recommender system. An advantage of simu- asymmetry: the seller and other users may know of lation is the ability to test real recommender systems. a product, but the given consumer may not.Recom- Our base case examines sales diversity under two menders share this information across the population systems, termed here r, and t2. In the taxonomy of We assume that each consumer is aware of a subset Adomavicius and Tuzhilin(2005), both are memory of the j products, and only items in this awareness based,collaborative filters. Recommender r, is the set can be purchased. Once an item is recommended most basic collaborative filter: For a given user. it first to a consumer, he is always aware of it in future peri- ods. At the start consumers of the using cosine similarity to compare vectors of pur- central products on the map plus a few items in their chase counts. It then recommends the most popu- each consumer-product pair are sampled according to lar item among this group. Formally, let sales be an I users x] items matrix of purchase counts, with distance /8 salesi the(i, )element and sales: the row vector of ci (G aware of pi)=Ae purchase counts. For a given user ci let +(1-A)e-dm/(k where distance; and distance are, respectively, the Euclidean distances from the origin to product P; and st.|N|=n,i≠j (5)from consumer ci to product p The higher is A, the (left term), and the higher is 1-A, the more users are We have tested sensitivity to different numbers of consumers and aware of products in their neighborhood. 8 and KA products, higher dimensions, and other distributions(e.g, uniform, determine how fast awareness decays with distance. normal, and Pareto for each combination of rs and prod- 3). The specific Gini values vary, but the conclusions are qualit Note that users are not aware of the same products ively similar. The main sensitivity results are in Online Appendix II hey are likely to overlap in their of th (provided in the e-companion) central products, but less so in the local products An alternative is to use correlation (ie, cosine on mean-centered The awareness model for one consumer is shown data). This does not tively affect the resul in Figure 9 for A=0. 75, .35,andK=1/3.W
Fleder and Hosanagar: The Impact of Recommender Systems on Sales Diversity 704 Management Science 55(5), pp. 697–712, © 2009 INFORMS temporarily, raising the chance that the recommended product is purchased in that purchase instance. The next consumer makes a purchase in a similar manner, and the process repeats after all consumers have purchased. After a predetermined number of iterations, the Gini is computed. The Gini is then compared to a benchmark G0, the Gini from an equivalent period in which recommendations were not offered. We now discuss each of the simulation components: (i) the map of products and consumers, (ii) the recommender r, (iii) the awareness distribution, (iv) the choice model, and (v) the salience factor . (i) Map of product and consumer points. The map of products and ideal points is the input for the choice model. Plotting consumer points and product locations goes back at least to Hotelling (1929) and is commonly used in marketing (e.g., Elrod and Keane 1995). Our consumers and products are points in a two-dimensional space. The use of two dimensions is for simplicity and visualization; for contexts with more than two attributes, the maps can be considered dimensionality-reduced versions, as is common in marketing research. We take both ideal points and products to be standard bivariate normal. The normality assumption for consumers is common in factor-analytic market maps (e.g., Elrod and Keane 1995). Our base case uses 50 consumers and 50 products, an example of which is in Figure 8.6 (ii) The recommender system. An advantage of simulation is the ability to test real recommender systems. Our base case examines sales diversity under two systems, termed here r1 and r2. In the taxonomy of Adomavicius and Tuzhilin (2005), both are memorybased, collaborative filters. Recommender r1 is the most basic collaborative filter: For a given user, it first finds the set N∗ of the n most similar customers by using cosine similarity to compare vectors of purchase counts. It then recommends the most popular item among this group.7 Formally, let sales be an I users × J items matrix of purchase counts, with salesij the (i j) element and salesi the row vector of ci’s purchase counts. For a given user ci, let N∗ = arg max N cj∈N cossalesi salesj s.t. N = n i = j (5) 6 We have tested sensitivity to different numbers of consumers and products, higher dimensions, and other distributions (e.g., uniform, normal, and Pareto for each combination of consumers and products). The specific Gini values vary, but the conclusions are qualitatively similar. The main sensitivity results are in Online Appendix II (provided in the e-companion). 7 An alternative is to use correlation (i.e., cosine on mean-centered data). This does not qualitatively affect the results. The system then recommends product r1 j∗ = arg max j ci∈N∗ salesij (6) Recommender r2 has one difference. When selecting the most popular product among similar users, candidate items are first discounted by their overall popularity in the entire population: r2 j∗ = arg max j I i=1 salesij−1 ci∈N∗ salesij (7) The motivation for r2’s popularity discounting is a belief that popular items are so obvious they should not be suggested. This was described to us in industry interviews as common practice. For example, if a consumer is expected to buy or be aware of a product with high probability, the firm should recommend something else. Note, r2 is not the same as applying “term-frequency inverse-document frequency” weights (tf-idf) to algorithm r1. tf-idf would insert discounting in the user similarity calculation (Breese et al. 1998), whereas r2 inserts it in the final arg max of (7). In §7, we test other recommenders, including one with tf-idf weights, and show the results are directionally the same. (iii) Awareness. Recommenders are valuable to consumers because they help overcome information asymmetry: the seller and other users may know of a product, but the given consumer may not. Recommenders share this information across the population. We assume that each consumer is aware of a subset of the J products, and only items in this awareness set can be purchased. Once an item is recommended to a consumer, he is always aware of it in future periods. At the start, consumers are aware of many of the central products on the map plus a few items in their own neighborhood. These initial awareness states for each consumer-product pair are sampled according to P ci aware of pj = e−distance2 0j / + 1 − e−distance2 ij / (8) where distance0j and distanceij are, respectively, the Euclidean distances from the origin to product pj and from consumer ci to product pj . The higher is , the more users are aware of central, mainstream products (left term), and the higher is 1− , the more users are aware of products in their neighborhood. and determine how fast awareness decays with distance. Note that users are not aware of the same products: they are likely to overlap in their awareness of the central products, but less so in the local products. The awareness model for one consumer is shown in Figure 9 for = 075, = 035, and = 1/3. We
r and Hosanagar: The Impact of Recommender Systems on Sales Diversity 12,⑥2009 INFORMS Figure 8 Map of Product and Consumer Points Figure9 High-Density Awareness Regions Shaded for One Customer ● Consumers x Products Attribute 1 Attribute 1 use these values for our base case. Setting A=0.75 Vijt Eit, where Dt is a deterministic component and creates a market with consumers more aware of main- Eit is an independent and identically distributed ran- stream goods than niche ones. This assumption is con- dom variable with extreme value distribution. Under sistent with a market in which mass advertising makes these assumptions, consumers aware of the center, mainstream products Under the opposite(A <0.5), the base case is already a market of niches, and it only strengthens later results P(c, buys p; at t Ic, aware of P; at t) that diversity can decrease. 8 determines how many central products users know. Setting 0=0.35 cre- The unconditional probability is defined P(c; buys pi ates an easy-to-understand"radius 1"rule: e-/0.3s= at #)=P(c; buys p; at t I c; aware of p, at t)P(; aware 0.057 x0. In other words, outside a radius of 1, the of p; at t). If a consumer is unaware of a product, the consumer is unlikely to be aware of the product In our rightmost term is zero, and he cannot buy it. maps, about 40% of the products are within one unit The deterministic component vit is often modeled from the origin; it is on this 40% of products that con- as a linear combination of a brand intercept, prod- sumers are likely to overlap most in their awareness. uct attributes, and covariates(e.g, price, promotion) The value K determines awareness in the consumer's In our context, because all relevant variables up to own neighborhood. The value K=1/3 creates roughly white noise are encompassed in the map we define a 0.5 radius rule. Outside the 0.5 radius, the consumer the logit's deterministic portion as is unlikely to know about products, unless they are the central ones. The approach in selecting these parame- similarity ==k log distance (10) ters was to create an interpretable base case. In sensi- tivity analysis, we find the Gini can change for other where distance is the Euclidean distance between parameter values but the results are directionally the consumer c; and product p; Our choice of a log trans- formation from distance to similarity is consistent (iv)Choice model. At each step of the simulation, with prior research(e.g, Schweidel et al. 2007) a consumer either purchases an item in his awareness The parameter k determines the consumers sen- set or makes no purchase at all. We model this using sitivity to distance on the map. The higher k is, the the multinomial logit. The logit is well established in more the consumer prefers the closest products. For economics and marketing and has an axiomatic ori- our base case as ranges fr om 1 to 40. the gini in in random utility theory(for a marketing appli- cation, see Guadagni and Little 1983). Consumer cis utility for product P; at time t is defined as u, 9 Other transformations have been used, and the literature does no have a single standard: for example, -k distance in Elrod (1988): (distance ) in Desarbo and Wu(2001); and -k log(distance )in 8If consumers know only the central products(A=1), the results Scheidel et al.(2007) with k a scaling parameter. While our base are directionally the same. If consumers are aware of all products case uses the log transformation Scheidel et al. 2007 and (e-o), the results are the same direction as well. The same holds other references contained therein), we have tested sensitivity to the if awareness is Pareto distributed instead of normal other specifications, and the results are not substantively different
Fleder and Hosanagar: The Impact of Recommender Systems on Sales Diversity Management Science 55(5), pp. 697–712, © 2009 INFORMS 705 Figure 8 Map of Product and Consumer Points –2 –1 0 1 2 –2 –1 0 1 2 Attribute 1 Attribute 2 Consumers Products use these values for our base case. Setting = 075 creates a market with consumers more aware of mainstream goods than niche ones. This assumption is consistent with a market in which mass advertising makes consumers aware of the center, mainstream products. Under the opposite ( < 05), the base case is already a market of niches, and it only strengthens later results that diversity can decrease. determines how many central products users know. Setting = 035 creates an easy-to-understand “radius 1” rule: e−1/035 = 0057 ≈ 0. In other words, outside a radius of 1, the consumer is unlikely to be aware of the product. In our maps, about 40% of the products are within one unit from the origin; it is on this 40% of products that consumers are likely to overlap most in their awareness. The value determines awareness in the consumer’s own neighborhood. The value = 1/3 creates roughly a 0.5 radius rule. Outside the 0.5 radius, the consumer is unlikely to know about products, unless they are the central ones. The approach in selecting these parameters was to create an interpretable base case. In sensitivity analysis, we find the Gini can change for other parameter values but the results are directionally the same.8 (iv) Choice model. At each step of the simulation, a consumer either purchases an item in his awareness set or makes no purchase at all. We model this using the multinomial logit. The logit is well established in economics and marketing and has an axiomatic origin in random utility theory (for a marketing application, see Guadagni and Little 1983). Consumer ci’s utility for product pj at time t is defined as uijt = 8 If consumers know only the central products ( = 1), the results are directionally the same. If consumers are aware of all products ( → ), the results are the same direction as well. The same holds if awareness is Pareto distributed instead of normal. Figure 9 High-Density Awareness Regions Shaded for One Customer –2 –1 0 1 2 –2 –1 0 1 2 Attribute 1 Attribute 2 Consumers Products vijt + ijt, where vijt is a deterministic component and ijt is an independent and identically distributed random variable with extreme value distribution. Under these assumptions, P ci buys pj at t ci aware of pj at t = evijt J k=1 evikt (9) The unconditional probability is defined P ci buys pj at t = P ci buys pj at t ci aware of pj at tP ci aware of pj at t. If a consumer is unaware of a product, the rightmost term is zero, and he cannot buy it. The deterministic component vijt is often modeled as a linear combination of a brand intercept, product attributes, and covariates (e.g., price, promotion). In our context, because all relevant variables up to white noise are encompassed in the map, we define the logit’s deterministic portion as vijt = similarityij = −k log distanceij (10) where distanceij is the Euclidean distance between consumer ci and product pj . Our choice of a log transformation from distance to similarity is consistent with prior research (e.g., Schweidel et al. 2007).9 The parameter k determines the consumer’s sensitivity to distance on the map. The higher k is, the more the consumer prefers the closest products. For our base case, as k ranges from 1 to 40, the Gini 9 Other transformations have been used, and the literature does not have a single standard: for example, −k · distanceij in Elrod (1988); (distanceij −k in DeSarbo and Wu (2001); and −k · logdistanceij in Schweidel et al. (2007) with k a scaling parameter. While our base case uses the log transformation (e.g., Schweidel et al. 2007 and other references contained therein), we have tested sensitivity to the other specifications, and the results are not substantively different.
Fleder and He ar: The Impact of Recommender Systems on Sales Diversity Management Science 55(5), PP. 697-712, @2009 INFORMS increases from 0.68 to 0. 75. This range is consistent Figure 10 One Sample Path Before and After Recommendations with several prior estimates of market concentration (r1,8=5) in media and e-commerce settings. An estimate for a major online clothing retailer is 0.70(Brynjolfsson et al. 2007), an estimate for the music sales of debut albums is 0. 724(Hendricks and Sorensen 2007), 0and an estimate for the online book market is also near G1=0.82 0.75( Chevalier and Goolsbee 2003). To fix a base g0.5 case, we use k=10 because the 0.72 Gini it produces matches the average of the estimates above. This k forms our base case. For other values the results change in magnitude but not direction. Last, as noted, consumers may choose not to pur- chase. This is modeled by an outside good with equal Cumulative fraction items distance to all users. This approach is one common sive effects. Recommendations often show an items specification for modeling a no-purchase option(eg-, packaging and artwork, akin to a persuasive adver- Chintagunta 2002). Our base case uses a distance tisement. We assume that the combined effect is to of 0.75 for this option, which implies that the outside increase the salience by 8. Experiments have begun good's proximity is about the 90th percentile (0.87) to demonstrate that recommendations can have influ for each consumer. That is, for each person, the out- ential effects beyond awareness(Senecal and Nantel de good is closer than roughly 90% of the other 2004). This simultaneity of both effects, awareness and goods. This means consumers have a fairly good out- salience, has parallels with advertising,s informative side option. If the outside good is farther, consumers and persuasive effects(e.g, Narayanan et al. 2005) substitute farther products for the outside good and The salience term 8 is a key parameter because it diversity increases. The change in Gini under recom- controls the strength of the recommender. For this rea- mendations, however, is in the same direction. son, the paper's main results are shown for a range (v) Salience 8. The term 8 is the amount by which of 8 and not a single point. To give some intuition a recommended product's salience is temporarily for 8, consider the purchase probability of the 75th per- increased in the consumer's choice set. The impact of centile closest item on the map(with 50 products, this the salience boost is that the purchase probability for is the 13th closest item). In our normal maps, if 8 the recommended item j is the same as that for an the user chooses item 13 with 0, the recommender 6. Results also has a salience effect, which increases the prob- We now present simulation results for the two real- bility of buying the item(conditional on aware- world recommenders. 12 We use 50 consumer poin ness).The salience effect exists for several reasons. and 50 products sampled from a bivariate normal dis- of ficulty comparing all of them; recommended items tribution N2(0, I)with k=10 become more salient in this comparison. Second, the 6.1. Example of a Single Sample Path salience boost may reflect the ease of clicking a rec- Before presenting overall results, we illustrate the ommended item versus continuing to search through process with one sample run. At first, recommenda 200 periods. Then n is enabled and customers make 10 The 0.724 could underestimate con on because the authors purchases for an additional 200 periods. For the sake data excludes less successful artists. This may not affect their objec- of illustration, 8=5, but more general results follow tive, which differs from that in this paper. The Lorenz curves and Ginis from both periods are n The Zipf formulation can be equated to a power law, and from shown in Figure 10. The example shows GI-Go ower law a closed-forn on for the gini can A rank-on-sales coefficient of 1.17 in a power law implies a Gini of (2×1.17-1)-1=0.75 The simulation code is available from the authors on request
Fleder and Hosanagar: The Impact of Recommender Systems on Sales Diversity 706 Management Science 55(5), pp. 697–712, © 2009 INFORMS increases from 0.68 to 0.75. This range is consistent with several prior estimates of market concentration in media and e-commerce settings. An estimate for a major online clothing retailer is 0.70 (Brynjolfsson et al. 2007), an estimate for the music sales of debut albums is 0.724 (Hendricks and Sorensen 2007),10 and an estimate for the online book market is also near 0.75 (Chevalier and Goolsbee 2003).11 To fix a base case, we use k = 10 because the 0.72 Gini it produces matches the average of the estimates above. This k forms our base case. For other values, the results change in magnitude but not direction. Last, as noted, consumers may choose not to purchase. This is modeled by an outside good with equal distance to all users. This approach is one common specification for modeling a no-purchase option (e.g., Chintagunta 2002). Our base case uses a distance of 0.75 for this option, which implies that the outside good’s proximity is about the 90th percentile (0.87) for each consumer. That is, for each person, the outside good is closer than roughly 90% of the other goods. This means consumers have a fairly good outside option. If the outside good is farther, consumers substitute farther products for the outside good and diversity increases. The change in Gini under recommendations, however, is in the same direction. (v) Salience . The term is the amount by which a recommended product’s salience is temporarily increased in the consumer’s choice set. The impact of the salience boost is that the purchase probability for the recommended item j is the same as that for an item j with vij = vij + . The functional form is analogous to the modeling of store displays in marketing (e.g., Guadagni and Little 1983), which might be considered an offline example of recommendations. The resulting choice probability is P ci buys pj at t ci aware of pj at t = e evijt k =j evikt + e evijt −1. When = 0, the recommender has only an awareness effect. Recommended items enter the awareness set if not there already. When > 0, the recommender also has a salience effect, which increases the probability of buying the item (conditional on awareness). The salience effect exists for several reasons. First, consumers aware of many goods may have dif- ficulty comparing all of them; recommended items become more salient in this comparison. Second, the salience boost may reflect the ease of clicking a recommended item versus continuing to search through a firm’s website. Last, salience may capture persua- 10 The 0.724 could underestimate concentration because the authors’ data excludes less successful artists. This may not affect their objective, which differs from that in this paper. 11 The Zipf formulation can be equated to a power law, and from the power law a closed-form expression for the Gini can be derived. A rank-on-sales coefficient of 1.17 in a power law implies a Gini of (2 × 117 − 1 −1 = 075. Figure 10 One Sample Path Before and After Recommendations r1 = 5 0 0.5 1.0 0 0.5 1.0 Cumulative fraction purchases G0 = 0.72 G1 = 0.82 Cumulative fraction items sive effects. Recommendations often show an item’s packaging and artwork, akin to a persuasive advertisement. We assume that the combined effect is to increase the salience by . Experiments have begun to demonstrate that recommendations can have influential effects beyond awareness (Senecal and Nantel 2004). This simultaneity of both effects, awareness and salience, has parallels with advertising’s informative and persuasive effects (e.g., Narayanan et al. 2005). The salience term is a key parameter because it controls the strength of the recommender. For this reason, the paper’s main results are shown for a range of and not a single point. To give some intuition for , consider the purchase probability of the 75th percentile closest item on the map (with 50 products, this is the 13th closest item). In our normal maps, if = 0, the user chooses item 13 with <10−4 probability. Item 1 is purchased with probability 0.85. If the 75th percentile item is recommended, for = 1 5 10 15 the item takes on purchase probability (<10−3, <0.01, 0.15, and 0.48), respectively. Thus, = 0–1 is low, for it has little effect on purchase probability. A value = 15 is high, because it makes a close item (100th percentile) and far item (75th percentile) equal in probability. 6. Results We now present simulation results for the two realworld recommenders.12 We use 50 consumer points and 50 products sampled from a bivariate normal distribution N20 I with k = 10. 6.1. Example of a Single Sample Path Before presenting overall results, we illustrate the process with one sample run. At first, recommendations are disabled and customers make purchases for 200 periods. Then r1 is enabled and customers make purchases for an additional 200 periods. For the sake of illustration, = 5, but more general results follow. The Lorenz curves and Ginis from both periods are shown in Figure 10. The example shows G1 − G0 = 12 The simulation code is available from the authors on request.
