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 <10-4 probability Item 1 item j'with vi=vi+8. The functional form is anal- is purchased with probability 0.85. If the 75th per- gous to the modeling of store displays in market- centile item is recomme ded for 8=(1, 5, 10, 15)the ing(e.g, Guadagni and Little 1983), which might be item takes on purchase probability (<10-3,<0.01,0.15, considered an offline example of recommendations. and 0.48), respectively. Thus, 8=0-1 is low, for it has The resulting choice probability is P(ci buys P; at tl ci little effect on purchase probability. a value 8=15 is aware of P, at t)=eet(Ekti e ikt +een)- high, because it makes a close item(100th percentile) When 8=0, the recommender has only an aware- and far item(75th percentile)equal in probability ness effect. Recommended items enter the awareness set if not there already. When 8>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 requestFleder 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 pur￾chase. 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 out￾side good is closer than roughly 90% of the other goods. This means consumers have a fairly good out￾side option. If the outside good is farther, consumers substitute farther products for the outside good and diversity increases. The change in Gini under recom￾mendations, 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 anal￾ogous to the modeling of store displays in market￾ing (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 aware￾ness effect. Recommended items enter the awareness set if not there already. When  > 0, the recommender also has a salience effect, which increases the prob￾ability of buying the item (conditional on aware￾ness). 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 rec￾ommended 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 objec￾tive, 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 adver￾tisement. We assume that the combined effect is to increase the salience by . Experiments have begun to demonstrate that recommendations can have influ￾ential 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 rea￾son, 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 per￾centile 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 per￾centile 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 real￾world recommenders.12 We use 50 consumer points and 50 products sampled from a bivariate normal dis￾tribution 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, recommenda￾tions 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.