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Production and Manipulation of Reviews Luciana Nicollier & Marco Ottaviani Manchester Business School & Università Bocconi December 19, 2014 Luciana Nicollier & Marco Ottaviani () Production and Manipulation of Reviews December 19, 2014 1 / 37 Outline Some evidence of impact of reviews on sales & manipulation Luciana Nicollier & Marco Ottaviani () Production and Manipulation of Reviews December 19, 2014 2 / 37 Outline Some evidence of impact of reviews on sales & manipulation manipulation depending on number of reviews Luciana Nicollier & Marco Ottaviani () Production and Manipulation of Reviews December 19, 2014 2 / 37 Outline Some evidence of impact of reviews on sales & manipulation manipulation depending on number of reviews Toy model of production of costly reviews by consumers; seller: Luciana Nicollier & Marco Ottaviani () Production and Manipulation of Reviews December 19, 2014 2 / 37 Outline Some evidence of impact of reviews on sales & manipulation manipulation depending on number of reviews Toy model of production of costly reviews by consumers; seller: 1 Sets …xed price & does not manipulate Luciana Nicollier & Marco Ottaviani () Production and Manipulation of Reviews December 19, 2014 2 / 37 Outline Some evidence of impact of reviews on sales & manipulation manipulation depending on number of reviews Toy model of production of costly reviews by consumers; seller: 1 Sets …xed price & does not manipulate 2 Sets …xed price & manipulates Luciana Nicollier & Marco Ottaviani () Production and Manipulation of Reviews December 19, 2014 2 / 37 Outline Some evidence of impact of reviews on sales & manipulation manipulation depending on number of reviews Toy model of production of costly reviews by consumers; seller: 1 Sets …xed price & does not manipulate 2 Sets …xed price & manipulates 3 Sets optimal price & does not manipulate Luciana Nicollier & Marco Ottaviani () Production and Manipulation of Reviews December 19, 2014 2 / 37 Outline Some evidence of impact of reviews on sales & manipulation manipulation depending on number of reviews Toy model of production of costly reviews by consumers; seller: 1 Sets …xed price & does not manipulate 2 Sets …xed price & manipulates 3 Sets optimal price & does not manipulate 4 Sets optimal price & manipulates Luciana Nicollier & Marco Ottaviani () Production and Manipulation of Reviews December 19, 2014 2 / 37 Evidence on Impact of Reviews on Sales & Manipulation Pilot data collected in 2013 about some 3,000 books on Amazon Luciana Nicollier & Marco Ottaviani () Production and Manipulation of Reviews December 19, 2014 3 / 37 Evidence on Impact of Reviews on Sales & Manipulation Pilot data collected in 2013 about some 3,000 books on Amazon More data is currently being collected Luciana Nicollier & Marco Ottaviani () Production and Manipulation of Reviews December 19, 2014 3 / 37 Evidence on Impact of Reviews on Sales & Manipulation Pilot data collected in 2013 about some 3,000 books on Amazon More data is currently being collected Evidence of impact of reviews on sales and manipulation Luciana Nicollier & Marco Ottaviani () Production and Manipulation of Reviews December 19, 2014 3 / 37 Evidence on Impact of Reviews on Sales & Manipulation Pilot data collected in 2013 about some 3,000 books on Amazon More data is currently being collected Evidence of impact of reviews on sales and manipulation adding to Luca & Chevalier and Mayzlin Luciana Nicollier & Marco Ottaviani () Production and Manipulation of Reviews December 19, 2014 3 / 37 Evidence on Impact of Reviews on Sales & Manipulation Pilot data collected in 2013 about some 3,000 books on Amazon More data is currently being collected Evidence of impact of reviews on sales and manipulation adding to Luca & Chevalier and Mayzlin Average Amazon rating displayed is rounded to closest half star, e.g. Luciana Nicollier & Marco Ottaviani () Production and Manipulation of Reviews December 19, 2014 3 / 37 Evidence on Impact of Reviews on Sales & Manipulation Pilot data collected in 2013 about some 3,000 books on Amazon More data is currently being collected Evidence of impact of reviews on sales and manipulation adding to Luca & Chevalier and Mayzlin Average Amazon rating displayed is rounded to closest half star, e.g. average rating 4.74 -> 4.5 stars Luciana Nicollier & Marco Ottaviani () Production and Manipulation of Reviews December 19, 2014 3 / 37 Evidence on Impact of Reviews on Sales & Manipulation Pilot data collected in 2013 about some 3,000 books on Amazon More data is currently being collected Evidence of impact of reviews on sales and manipulation adding to Luca & Chevalier and Mayzlin Average Amazon rating displayed is rounded to closest half star, e.g. average rating 4.74 -> 4.5 stars average rating 4.76 -> 5 stars Luciana Nicollier & Marco Ottaviani () Production and Manipulation of Reviews December 19, 2014 3 / 37 Regression Discontinuity Design Dependent variable is log of sales rank Luciana Nicollier & Marco Ottaviani () Production and Manipulation of Reviews December 19, 2014 4 / 37 Regression Discontinuity Design Dependent variable is log of sales rank sales rank decreases in number of sold copies Luciana Nicollier & Marco Ottaviani () Production and Manipulation of Reviews December 19, 2014 4 / 37 Regression Discontinuity Design Dependent variable is log of sales rank sales rank decreases in number of sold copies Baseline model is ln(ranki ) = α0 + βc Di + γ(xi c ) + δDi (xi c ) + εi where: Luciana Nicollier & Marco Ottaviani () Production and Manipulation of Reviews December 19, 2014 4 / 37 Regression Discontinuity Design Dependent variable is log of sales rank sales rank decreases in number of sold copies Baseline model is ln(ranki ) = α0 + βc Di + γ(xi c ) + δDi (xi c ) + εi where: Main independent variable, xi , represents the average review rating Luciana Nicollier & Marco Ottaviani () Production and Manipulation of Reviews December 19, 2014 4 / 37 Regression Discontinuity Design Dependent variable is log of sales rank sales rank decreases in number of sold copies Baseline model is ln(ranki ) = α0 + βc Di + γ(xi c ) + δDi (xi c ) + εi where: Main independent variable, xi , represents the average review rating D = I (xi > c ) is dummy for being above threshold c 2 f1.25, 1.75, 2.25, 2.75, 3.25, 3.75, 4.25, 4.75g Luciana Nicollier & Marco Ottaviani () Production and Manipulation of Reviews December 19, 2014 4 / 37 Regression Discontinuity Design Dependent variable is log of sales rank sales rank decreases in number of sold copies Baseline model is ln(ranki ) = α0 + βc Di + γ(xi c ) + δDi (xi c ) + εi where: Main independent variable, xi , represents the average review rating D = I (xi > c ) is dummy for being above threshold c 2 f1.25, 1.75, 2.25, 2.75, 3.25, 3.75, 4.25, 4.75g Parameter of interest is coe¢ cient on dummy βc , the treatment e¤ect at discontinuity point Luciana Nicollier & Marco Ottaviani () Production and Manipulation of Reviews December 19, 2014 4 / 37 Regression Discontinuity Design Dependent variable is log of sales rank sales rank decreases in number of sold copies Baseline model is ln(ranki ) = α0 + βc Di + γ(xi c ) + δDi (xi c ) + εi where: Main independent variable, xi , represents the average review rating D = I (xi > c ) is dummy for being above threshold c 2 f1.25, 1.75, 2.25, 2.75, 3.25, 3.75, 4.25, 4.75g Parameter of interest is coe¢ cient on dummy βc , the treatment e¤ect at discontinuity point Other (endogenous?) covariates not included Luciana Nicollier & Marco Ottaviani () Production and Manipulation of Reviews December 19, 2014 4 / 37 Distribution of Ratings Luciana Nicollier & Marco Ottaviani () Production and Manipulation of Reviews December 19, 2014 5 / 37 Regression Discontinuity Estimates Regression implemented locally, considering average ratings within optimal bandwidth [Imbens and Kalyanaraman] of thresholds Luciana Nicollier & Marco Ottaviani () Production and Manipulation of Reviews December 19, 2014 6 / 37 Regression Discontinuity Estimates Regression implemented locally, considering average ratings within optimal bandwidth [Imbens and Kalyanaraman] of thresholds Example: Impact of crossing threshold 4.25 for book ranked 10,000? Luciana Nicollier & Marco Ottaviani () Production and Manipulation of Reviews December 19, 2014 6 / 37 Regression Discontinuity Estimates Regression implemented locally, considering average ratings within optimal bandwidth [Imbens and Kalyanaraman] of thresholds Example: Impact of crossing threshold 4.25 for book ranked 10,000? Rank: exp (9.21) = 10, 000 ! exp (9.21 Luciana Nicollier & Marco Ottaviani () 1.15 = 8.06) = 3, 165 Production and Manipulation of Reviews December 19, 2014 6 / 37 Regression Discontinuity Estimates Regression implemented locally, considering average ratings within optimal bandwidth [Imbens and Kalyanaraman] of thresholds Example: Impact of crossing threshold 4.25 for book ranked 10,000? Rank: exp (9.21) = 10, 000 ! exp (9.21 1.15 = 8.06) = 3, 165 Use ln (sales ) = 4 9.6 4 .78 ln(rank ) estimated by Shnapp and Allwine (2001) & others + sales growth Luciana Nicollier & Marco Ottaviani () Production and Manipulation of Reviews December 19, 2014 6 / 37 Regression Discontinuity Estimates Regression implemented locally, considering average ratings within optimal bandwidth [Imbens and Kalyanaraman] of thresholds Example: Impact of crossing threshold 4.25 for book ranked 10,000? Rank: exp (9.21) = 10, 000 ! exp (9.21 1.15 = 8.06) = 3, 165 Use ln (sales ) = 4 9.6 4 .78 ln(rank ) estimated by Shnapp and Allwine (2001) & others + sales growth Copies sold per week: sales (rank = 10, 000) = 45 ! sales (rank = 3, 165) = 111 Luciana Nicollier & Marco Ottaviani () Production and Manipulation of Reviews December 19, 2014 6 / 37 Validity Identi…cation relies on the following assumptions: 1 Discontinuities are only at thresholds Luciana Nicollier & Marco Ottaviani () Production and Manipulation of Reviews December 19, 2014 7 / 37 Validity Identi…cation relies on the following assumptions: 1 Discontinuities are only at thresholds Reasonable to assume that books with rating just below the threshold do not di¤er systematically from those with a rating just above it Luciana Nicollier & Marco Ottaviani () Production and Manipulation of Reviews December 19, 2014 7 / 37 Validity Identi…cation relies on the following assumptions: 1 Discontinuities are only at thresholds Reasonable to assume that books with rating just below the threshold do not di¤er systematically from those with a rating just above it 2 Density of forcing variable (average rating) is continuous at thresholds, i.e., there is no manipulation Luciana Nicollier & Marco Ottaviani () Production and Manipulation of Reviews December 19, 2014 7 / 37 Validity Identi…cation relies on the following assumptions: 1 Discontinuities are only at thresholds Reasonable to assume that books with rating just below the threshold do not di¤er systematically from those with a rating just above it 2 Density of forcing variable (average rating) is continuous at thresholds, i.e., there is no manipulation McCrary test of continuity of density on the full sample does not reject the null of no manipulation Luciana Nicollier & Marco Ottaviani () Production and Manipulation of Reviews December 19, 2014 7 / 37 Validity Identi…cation relies on the following assumptions: 1 Discontinuities are only at thresholds Reasonable to assume that books with rating just below the threshold do not di¤er systematically from those with a rating just above it 2 Density of forcing variable (average rating) is continuous at thresholds, i.e., there is no manipulation McCrary test of continuity of density on the full sample does not reject the null of no manipulation What if we split the sample between books with few reviews and books with many? Luciana Nicollier & Marco Ottaviani () Production and Manipulation of Reviews December 19, 2014 7 / 37 Number of Reviews > 20 The test does not reject the null of no manipulation Luciana Nicollier & Marco Ottaviani () Production and Manipulation of Reviews December 19, 2014 8 / 37 Discontinuity of Density when #Reviews < 50 The test strongly rejects the null of no manipulation Luciana Nicollier & Marco Ottaviani () Production and Manipulation of Reviews December 19, 2014 9 / 37 Number of Reviews < 50 However, when number of reviews is low, we expect the ratings corresponding to the averages that are possible with n reviews to be over-represented These peaks may be mistaken as evidence of manipulation Luciana Nicollier & Marco Ottaviani () Production and Manipulation of Reviews December 19, 2014 10 / 37 Number of Reviews <50 By a Montecarlo experiment we tabulate the non-standard distribution of the McCrary test for books with few reviews Clear evidence of manipulation Luciana Nicollier & Marco Ottaviani () Production and Manipulation of Reviews December 19, 2014 11 / 37 1. Toy Model of Costly Reviews One FIRM selling product at …xed price p produced at zero cost Luciana Nicollier & Marco Ottaviani () Production and Manipulation of Reviews December 19, 2014 12 / 37 1. Toy Model of Costly Reviews One FIRM selling product at …xed price p produced at zero cost Product has unknown quality L, H Luciana Nicollier & Marco Ottaviani () Production and Manipulation of Reviews December 19, 2014 12 / 37 1. Toy Model of Costly Reviews One FIRM selling product at …xed price p produced at zero cost Product has unknown quality L, H H quality gives consumer utility 1, L quality gives 0 Luciana Nicollier & Marco Ottaviani () Production and Manipulation of Reviews December 19, 2014 12 / 37 1. Toy Model of Costly Reviews One FIRM selling product at …xed price p produced at zero cost Product has unknown quality L, H H quality gives consumer utility 1, L quality gives 0 λ = Pr (H ) is common prior that quality is H Luciana Nicollier & Marco Ottaviani () Production and Manipulation of Reviews December 19, 2014 12 / 37 1. Toy Model of Costly Reviews One FIRM selling product at …xed price p produced at zero cost Product has unknown quality L, H H quality gives consumer utility 1, L quality gives 0 λ = Pr (H ) is common prior that quality is H Timing, two periods each with a di¤erent buyer: Luciana Nicollier & Marco Ottaviani () Production and Manipulation of Reviews December 19, 2014 12 / 37 1. Toy Model of Costly Reviews One FIRM selling product at …xed price p produced at zero cost Product has unknown quality L, H H quality gives consumer utility 1, L quality gives 0 λ = Pr (H ) is common prior that quality is H Timing, two periods each with a di¤erent buyer: Luciana Nicollier & Marco Ottaviani () Production and Manipulation of Reviews December 19, 2014 12 / 37 1. Toy Model of Costly Reviews One FIRM selling product at …xed price p produced at zero cost Product has unknown quality L, H H quality gives consumer utility 1, L quality gives 0 λ = Pr (H ) is common prior that quality is H Timing, two periods each with a di¤erent buyer: 1. Buyer 1 = SENDER a. decides whether to buy Luciana Nicollier & Marco Ottaviani () Production and Manipulation of Reviews December 19, 2014 12 / 37 1. Toy Model of Costly Reviews One FIRM selling product at …xed price p produced at zero cost Product has unknown quality L, H H quality gives consumer utility 1, L quality gives 0 λ = Pr (H ) is common prior that quality is H Timing, two periods each with a di¤erent buyer: 1. Buyer 1 = SENDER a. decides whether to buy b. after buying, observes noisy signal of quality q Luciana Nicollier & Marco Ottaviani () Production and Manipulation of Reviews FL , FH December 19, 2014 12 / 37 1. Toy Model of Costly Reviews One FIRM selling product at …xed price p produced at zero cost Product has unknown quality L, H H quality gives consumer utility 1, L quality gives 0 λ = Pr (H ) is common prior that quality is H Timing, two periods each with a di¤erent buyer: 1. Buyer 1 = SENDER a. decides whether to buy b. after buying, observes noisy signal of quality q c. releases review at cost c Luciana Nicollier & Marco Ottaviani () Production and Manipulation of Reviews FL , FH December 19, 2014 12 / 37 1. Toy Model of Costly Reviews One FIRM selling product at …xed price p produced at zero cost Product has unknown quality L, H H quality gives consumer utility 1, L quality gives 0 λ = Pr (H ) is common prior that quality is H Timing, two periods each with a di¤erent buyer: 1. Buyer 1 = SENDER a. decides whether to buy b. after buying, observes noisy signal of quality q c. releases review at cost c FL , FH 2. Buyer 2 = RECEIVER observes review & decides whether to buy For now, FIXED price & NO manipulation Luciana Nicollier & Marco Ottaviani () Production and Manipulation of Reviews December 19, 2014 12 / 37 1. Model: Preferences, Information, and Reviews PREFERENCES: Sender altruistically cares about surplus of receiver Luciana Nicollier & Marco Ottaviani () Production and Manipulation of Reviews December 19, 2014 13 / 37 1. Model: Preferences, Information, and Reviews PREFERENCES: Sender altruistically cares about surplus of receiver INFORMATION: After buying, sender observes signal q 2 [0, 1] Luciana Nicollier & Marco Ottaviani () Production and Manipulation of Reviews December 19, 2014 13 / 37 1. Model: Preferences, Information, and Reviews PREFERENCES: Sender altruistically cares about surplus of receiver INFORMATION: After buying, sender observes signal q 2 [0, 1] densities fH (q ) = fL (1 Luciana Nicollier & Marco Ottaviani () q ), fH (0) = 0, fH0 (q ) > 0 so MLRP Production and Manipulation of Reviews December 19, 2014 13 / 37 1. Model: Preferences, Information, and Reviews PREFERENCES: Sender altruistically cares about surplus of receiver INFORMATION: After buying, sender observes signal q 2 [0, 1] densities fH (q ) = fL (1 q ), fH (0) = 0, fH0 (q ) > 0 so MLRP example: fH (q ) = 2q and fL (q ) = 2 (1 q ) Luciana Nicollier & Marco Ottaviani () Production and Manipulation of Reviews December 19, 2014 13 / 37 1. Model: Preferences, Information, and Reviews PREFERENCES: Sender altruistically cares about surplus of receiver INFORMATION: After buying, sender observes signal q 2 [0, 1] densities fH (q ) = fL (1 q ), fH (0) = 0, fH0 (q ) > 0 so MLRP example: fH (q ) = 2q and fL (q ) = 2 (1 q ) REVIEWS: Sending any review r costs c > 0, no review ? costs 0 Luciana Nicollier & Marco Ottaviani () Production and Manipulation of Reviews December 19, 2014 13 / 37 1. Model: Preferences, Information, and Reviews PREFERENCES: Sender altruistically cares about surplus of receiver INFORMATION: After buying, sender observes signal q 2 [0, 1] densities fH (q ) = fL (1 q ), fH (0) = 0, fH0 (q ) > 0 so MLRP example: fH (q ) = 2q and fL (q ) = 2 (1 q ) REVIEWS: Sending any review r costs c > 0, no review ? costs 0 Information contained in a review is not veri…able Luciana Nicollier & Marco Ottaviani () Production and Manipulation of Reviews December 19, 2014 13 / 37 1. Model: Preferences, Information, and Reviews PREFERENCES: Sender altruistically cares about surplus of receiver INFORMATION: After buying, sender observes signal q 2 [0, 1] densities fH (q ) = fL (1 q ), fH (0) = 0, fH0 (q ) > 0 so MLRP example: fH (q ) = 2q and fL (q ) = 2 (1 q ) REVIEWS: Sending any review r costs c > 0, no review ? costs 0 Information contained in a review is not veri…able so review’s meaning depends on signals for which it is sent Luciana Nicollier & Marco Ottaviani () Production and Manipulation of Reviews December 19, 2014 13 / 37 1. Model: Preferences, Information, and Reviews PREFERENCES: Sender altruistically cares about surplus of receiver INFORMATION: After buying, sender observes signal q 2 [0, 1] densities fH (q ) = fL (1 q ), fH (0) = 0, fH0 (q ) > 0 so MLRP example: fH (q ) = 2q and fL (q ) = 2 (1 q ) REVIEWS: Sending any review r costs c > 0, no review ? costs 0 Information contained in a review is not veri…able so review’s meaning depends on signals for which it is sent Example: review (“praise”) sent for signals q 2 [q̄, 1] = P, resulting in posterior = Receiver’s expected valuation λP = Luciana Nicollier & Marco Ottaviani () (1 (1 FH (q̄ )) λ FH (q̄ )) λ + (1 FL (q̄ )) (1 Production and Manipulation of Reviews λ) >λ December 19, 2014 13 / 37 1. Equilibria Clearly, there is always a no-review equilibrium (NE): ? always Luciana Nicollier & Marco Ottaviani () Production and Manipulation of Reviews December 19, 2014 14 / 37 1. Equilibria Clearly, there is always a no-review equilibrium (NE): ? always Key to equilibrium with reviews is value of information Luciana Nicollier & Marco Ottaviani () Production and Manipulation of Reviews December 19, 2014 14 / 37 1. Equilibria Clearly, there is always a no-review equilibrium (NE): ? always Key to equilibrium with reviews is value of information receiver must make di¤erent decision with review than without (?) Luciana Nicollier & Marco Ottaviani () Production and Manipulation of Reviews December 19, 2014 14 / 37 1. Equilibria Clearly, there is always a no-review equilibrium (NE): ? always Key to equilibrium with reviews is value of information receiver must make di¤erent decision with review than without (?) Given that receiver’s decision is binary (buy or not buy) and that Sender pays cost c when sending a review, in equilibrium review is sent either when q Q or when q < Q with cuto¤ Q Luciana Nicollier & Marco Ottaviani () Production and Manipulation of Reviews December 19, 2014 14 / 37 1. Equilibria Clearly, there is always a no-review equilibrium (NE): ? always Key to equilibrium with reviews is value of information receiver must make di¤erent decision with review than without (?) Given that receiver’s decision is binary (buy or not buy) and that Sender pays cost c when sending a review, in equilibrium review is sent either when q Q or when q < Q with cuto¤ Q Praise Equilibrium (PE): send (good) review for q otherwise Luciana Nicollier & Marco Ottaviani () Production and Manipulation of Reviews q̄, no review ? December 19, 2014 14 / 37 1. Equilibria Clearly, there is always a no-review equilibrium (NE): ? always Key to equilibrium with reviews is value of information receiver must make di¤erent decision with review than without (?) Given that receiver’s decision is binary (buy or not buy) and that Sender pays cost c when sending a review, in equilibrium review is sent either when q Q or when q < Q with cuto¤ Q Praise Equilibrium (PE): send (good) review for q q̄, no review ? otherwise Complaint Equilibrium (CE): send (bad) review for q < q, no review ? otherwise Luciana Nicollier & Marco Ottaviani () Production and Manipulation of Reviews December 19, 2014 14 / 37 1. Equilibria Clearly, there is always a no-review equilibrium (NE): ? always Key to equilibrium with reviews is value of information receiver must make di¤erent decision with review than without (?) Given that receiver’s decision is binary (buy or not buy) and that Sender pays cost c when sending a review, in equilibrium review is sent either when q Q or when q < Q with cuto¤ Q Praise Equilibrium (PE): send (good) review for q q̄, no review ? otherwise Complaint Equilibrium (CE): send (bad) review for q < q, no review ? otherwise Typically, there are multiple equilibria given that sender’s reviewing strategy is unobservable Luciana Nicollier & Marco Ottaviani () Production and Manipulation of Reviews December 19, 2014 14 / 37 1. Equilibria Clearly, there is always a no-review equilibrium (NE): ? always Key to equilibrium with reviews is value of information receiver must make di¤erent decision with review than without (?) Given that receiver’s decision is binary (buy or not buy) and that Sender pays cost c when sending a review, in equilibrium review is sent either when q Q or when q < Q with cuto¤ Q Praise Equilibrium (PE): send (good) review for q q̄, no review ? otherwise Complaint Equilibrium (CE): send (bad) review for q < q, no review ? otherwise Typically, there are multiple equilibria given that sender’s reviewing strategy is unobservable NE + interior PE & interior CE, if review cost c is not too high Luciana Nicollier & Marco Ottaviani () Production and Manipulation of Reviews December 19, 2014 14 / 37 1. Construction of Praise Equilibrium Suppose Receiver’s strategy is to buy only following a review (P) Luciana Nicollier & Marco Ottaviani () Production and Manipulation of Reviews December 19, 2014 15 / 37 1. Construction of Praise Equilibrium Suppose Receiver’s strategy is to buy only following a review (P) De…ning F = λFH + (1 λ) FL , Sender then 2 3 max q̄ λ p | {z } 1’s purchase utility with FOC Luciana Nicollier & Marco Ottaviani () +1 | 6 F (q̄ ) 4Pr (H jq 2 [q̄, 1]) {z } | {z Prob. praise 2’s purchase utility p+c fH (q̄ ) λ = fL (q̄ ) 1 λ 1 (p + c ) Production and Manipulation of Reviews p } 7 c 5 |{z} review cost (1) December 19, 2014 15 / 37 1. Construction of Praise Equilibrium Suppose Receiver’s strategy is to buy only following a review (P) De…ning F = λFH + (1 λ) FL , Sender then 2 3 max q̄ λ p | {z } 1’s purchase utility with FOC +1 | 6 F (q̄ ) 4Pr (H jq 2 [q̄, 1]) {z } | {z Prob. praise 2’s purchase utility p+c fH (q̄ ) λ = fL (q̄ ) 1 λ 1 (p + c ) p } 7 c 5 |{z} review cost (1) For Sender to be indi¤erent between sending a review () Receiver buys) and no review () Receiver does not buy), Receiver’s expected surplus when buying at marginal signal q = q̄ fH (q̄ ) λ (1 f (q̄ ) p) + 1 fL (q̄ ) λ f (q̄ ) (0 p) is equal to Sender’s cost of sending review: FOC (1) Luciana Nicollier & Marco Ottaviani () Production and Manipulation of Reviews December 19, 2014 15 / 37 1. Receiver Surplus Depending on Cuto¤ Q: Niche Market To understand better, plot receiver surplus depending on cuto¤ Q Luciana Nicollier & Marco Ottaviani () Production and Manipulation of Reviews December 19, 2014 16 / 37 1. Receiver Surplus Depending on Cuto¤ Q: Niche Market To understand better, plot receiver surplus depending on cuto¤ Q which is maximized at Q = q̄ 0 for c = 0 Luciana Nicollier & Marco Ottaviani () Production and Manipulation of Reviews December 19, 2014 16 / 37 1. Receiver Surplus Depending on Cuto¤ Q: Niche Market To understand better, plot receiver surplus depending on cuto¤ Q which is maximized at Q = q̄ 0 for c = 0 Fix [GREEN] p > λ [RED] Luciana Nicollier & Marco Ottaviani () Production and Manipulation of Reviews December 19, 2014 16 / 37 1. Receiver Surplus Depending on Cuto¤ Q: Niche Market To understand better, plot receiver surplus depending on cuto¤ Q which is maximized at Q = q̄ 0 for c = 0 Fix [GREEN] p > λ [RED] then [BLACK DASHED] q̄ 0 > q̃ neutral signal [YELLOW] 2's surplus 0.08 0.06 0.04 0.02 0.00 0.0 Luciana Nicollier & Marco Ottaviani () 0.5 Production and Manipulation of Reviews 1.0 Q December 19, 2014 16 / 37 1. Receiver Surplus Depending on Cuto¤ Q: Niche Market To understand better, plot receiver surplus depending on cuto¤ Q which is maximized at Q = q̄ 0 for c = 0 Fix [GREEN] p > λ [RED] then [BLACK DASHED] q̄ 0 > q̃ neutral signal [YELLOW] 2's surplus 0.08 0.06 0.04 0.02 0.00 0.0 0.5 1.0 Q fH (q̄ 0 ) q̄ 0 =signal that turns prior λ into posterior =p: 1 λ λ f (q̄ 0 ) = 1 p p L Basic intuition related to Meyer’s (1991) optimal biased information Luciana Nicollier & Marco Ottaviani () Production and Manipulation of Reviews December 19, 2014 16 / 37 1. Receiver Surplus Depending on Cuto¤ Q: Mass Market Fix [GREEN] p < λ [RED], then [BLACK DASHED] q̄ 0 < q̃ [YELLOW] 2's surplus 0.4 0.2 0.0 0.0 0.2 0.4 0.6 0.8 1.0 Q Again, indi¤erence at optimal cuto¤ q̄ 0 Luciana Nicollier & Marco Ottaviani () Production and Manipulation of Reviews December 19, 2014 17 / 37 1. Receiver Surplus Depending on Cuto¤ Q: Mass Market Fix [GREEN] p < λ [RED], then [BLACK DASHED] q̄ 0 < q̃ [YELLOW] 2's surplus 0.4 0.2 0.0 0.0 0.2 0.4 0.6 0.8 1.0 Q Again, indi¤erence at optimal cuto¤ q̄ 0 q̄ 0 =signal such that posterior=price: Luciana Nicollier & Marco Ottaviani () 0 λ fH (q̄ ) 1 λ fL (q̄ 0 ) Production and Manipulation of Reviews = p 1 p December 19, 2014 17 / 37 1. Now Introduce Cost of Reviews Sender trades o¤ receiver’s surplus with review cost Marginal info bene…t: λfH (Q ) (1 p ) + (1 λ) fL (Q ) ( p ) [BLACK for Q q̄ 0 ] MB,MC 0.4 0.2 0.0 0.0 0.5 Example: linear signal, λ = 23 , p = 34 , c = Luciana Nicollier & Marco Ottaviani () 1.0 Q 1 5 ) qc = Production and Manipulation of Reviews 11 29 & q̄ c = December 19, 2014 19 21 18 / 37 1. Now Introduce Cost of Reviews Sender trades o¤ receiver’s surplus with review cost Marginal info bene…t: λfH (Q ) (1 p ) + (1 λ) fL (Q ) ( p ) [BLACK for Q q̄ 0 ] For Q q̄ 0 complaint equilibrium [RED]=-[BLACK] MB,MC 0.4 0.2 0.0 0.0 0.5 Example: linear signal, λ = 23 , p = 34 , c = Luciana Nicollier & Marco Ottaviani () 1.0 Q 1 5 ) qc = Production and Manipulation of Reviews 11 29 & q̄ c = December 19, 2014 19 21 18 / 37 1. Now Introduce Cost of Reviews Sender trades o¤ receiver’s surplus with review cost Marginal info bene…t: λfH (Q ) (1 p ) + (1 λ) fL (Q ) ( p ) [BLACK for Q q̄ 0 ] For Q q̄ 0 complaint equilibrium [RED]=-[BLACK] Marginal review cost: [λfH (Q ) + (1 [GREEN] λ) fL (Q )] c = f (Q ) c MB,MC 0.4 0.2 0.0 0.0 0.5 Example: linear signal, λ = 23 , p = 34 , c = Luciana Nicollier & Marco Ottaviani () 1.0 Q 1 5 ) qc = Production and Manipulation of Reviews 11 29 & q̄ c = December 19, 2014 19 21 18 / 37 1. Now Introduce Cost of Reviews Sender trades o¤ receiver’s surplus with review cost Marginal info bene…t: λfH (Q ) (1 p ) + (1 λ) fL (Q ) ( p ) [BLACK for Q q̄ 0 ] For Q q̄ 0 complaint equilibrium [RED]=-[BLACK] Marginal review cost: [λfH (Q ) + (1 λ) fL (Q )] c = f (Q ) c [GREEN] % Q for λ > 1/2 because high signals are more likely MB,MC 0.4 0.2 0.0 0.0 0.5 Example: linear signal, λ = 23 , p = 34 , c = Luciana Nicollier & Marco Ottaviani () 1.0 Q 1 5 ) qc = Production and Manipulation of Reviews 11 29 & q̄ c = December 19, 2014 19 21 18 / 37 1. Now Introduce Cost of Reviews Sender trades o¤ receiver’s surplus with review cost Marginal info bene…t: λfH (Q ) (1 p ) + (1 λ) fL (Q ) ( p ) [BLACK for Q q̄ 0 ] For Q q̄ 0 complaint equilibrium [RED]=-[BLACK] Marginal review cost: [λfH (Q ) + (1 λ) fL (Q )] c = f (Q ) c [GREEN] % Q for λ > 1/2 because high signals are more likely then q̄ c q 0 > q 0 q c , as in …gure [opposite for λ < 1/2] MB,MC 0.4 0.2 0.0 0.0 0.5 Example: linear signal, λ = 23 , p = 34 , c = Luciana Nicollier & Marco Ottaviani () 1.0 Q 1 5 ) qc = Production and Manipulation of Reviews 11 29 & q̄ c = December 19, 2014 19 21 18 / 37 1. Receiver Preferred Equilibrium Now, receiver cares only about info value, disregarding info cost Luciana Nicollier & Marco Ottaviani () Production and Manipulation of Reviews December 19, 2014 19 / 37 1. Receiver Preferred Equilibrium Now, receiver cares only about info value, disregarding info cost Receiver’s preferred equilibrium is Luciana Nicollier & Marco Ottaviani () Production and Manipulation of Reviews December 19, 2014 19 / 37 1. Receiver Preferred Equilibrium Now, receiver cares only about info value, disregarding info cost Receiver’s preferred equilibrium is Complaint Eq. for prior λ > λ̄R (λ̄R = 1/2 in example) 2's surplus 0.10 0.08 0.06 0.04 0.02 0.00 0.0 Luciana Nicollier & Marco Ottaviani () 0.2 0.4 Production and Manipulation of Reviews 0.6 0.8 1.0 Q December 19, 2014 19 / 37 1. Receiver Preferred Equilibrium Now, receiver cares only about info value, disregarding info cost Receiver’s preferred equilibrium is Complaint Eq. for prior λ > λ̄R (λ̄R = 1/2 in example) 2's surplus 0.10 0.08 0.06 0.04 0.02 0.00 0.0 0.2 0.4 0.6 0.8 1.0 Q Praise Eq. for λ < λ̄R Luciana Nicollier & Marco Ottaviani () Production and Manipulation of Reviews December 19, 2014 19 / 37 1. Receiver Preferred Equilibrium Now, receiver cares only about info value, disregarding info cost Receiver’s preferred equilibrium is Complaint Eq. for prior λ > λ̄R (λ̄R = 1/2 in example) 2's surplus 0.10 0.08 0.06 0.04 0.02 0.00 0.0 0.2 0.4 0.6 0.8 1.0 Q Praise Eq. for λ < λ̄R [for λ = λ̄R two equilibria give same payo¤] Luciana Nicollier & Marco Ottaviani () Production and Manipulation of Reviews December 19, 2014 19 / 37 1. Sender Preferred Equilibrium Preferences across equilibria for Sender: CE %S PE , λ λ̄S p, c + where λ̄S R λ̄R (= q̃ ) , p R λ̄R (= q̃ ) Intuitively, for high λ bad reviews are rare, so CE is cheap for sender Luciana Nicollier & Marco Ottaviani () Production and Manipulation of Reviews December 19, 2014 20 / 37 1. Sender Preferred Equilibrium Preferences across equilibria for Sender: CE %S PE , λ λ̄S p, c + where λ̄S R λ̄R (= q̃ ) , p R λ̄R (= q̃ ) Intuitively, for high λ bad reviews are rare, so CE is cheap for sender consider λ approaching λ̄R , CE Luciana Nicollier & Marco Ottaviani () R PE Production and Manipulation of Reviews December 19, 2014 20 / 37 1. Sender Preferred Equilibrium Preferences across equilibria for Sender: CE %S PE , λ λ̄S p, c + where λ̄S R λ̄R (= q̃ ) , p R λ̄R (= q̃ ) Intuitively, for high λ bad reviews are rare, so CE is cheap for sender consider λ approaching λ̄R , CE R PE now Sender pays review costs, relatively lower in a PE if p is high Luciana Nicollier & Marco Ottaviani () Production and Manipulation of Reviews December 19, 2014 20 / 37 1. Sender Preferred Equilibrium Preferences across equilibria for Sender: CE %S PE , λ λ̄S p, c + where λ̄S R λ̄R (= q̃ ) , p R λ̄R (= q̃ ) Intuitively, for high λ bad reviews are rare, so CE is cheap for sender consider λ approaching λ̄R , CE R PE now Sender pays review costs, relatively lower in a PE if p is high intuitively: p ") Q ") Pr (P ) # & Pr (C ) ") c (PE ) # & c (CE ) " Luciana Nicollier & Marco Ottaviani () Production and Manipulation of Reviews December 19, 2014 20 / 37 1. Sender Preferred Equilibrium Preferences across equilibria for Sender: CE %S PE , λ λ̄S p, c + where λ̄S R λ̄R (= q̃ ) , p R λ̄R (= q̃ ) Intuitively, for high λ bad reviews are rare, so CE is cheap for sender consider λ approaching λ̄R , CE R PE now Sender pays review costs, relatively lower in a PE if p is high intuitively: p ") Q ") Pr (P ) # & Pr (C ) ") c (PE ) # & c (CE ) " so, Sender switches to PE to save on reviews at λ̄S > λ̄R Luciana Nicollier & Marco Ottaviani () Production and Manipulation of Reviews December 19, 2014 20 / 37 1. Sender Preferred Equilibrium Preferences across equilibria for Sender: CE %S PE , λ λ̄S p, c + where λ̄S R λ̄R (= q̃ ) , p R λ̄R (= q̃ ) Intuitively, for high λ bad reviews are rare, so CE is cheap for sender consider λ approaching λ̄R , CE R PE now Sender pays review costs, relatively lower in a PE if p is high intuitively: p ") Q ") Pr (P ) # & Pr (C ) ") c (PE ) # & c (CE ) " so, Sender switches to PE to save on reviews at λ̄S > λ̄R E.g., λ = 2/3, p = 3/4, c = 1/10: CE V&C R PE but PE S CE 0.10 0.05 0.00 0.0 Luciana Nicollier & Marco Ottaviani () 0.5 Production and Manipulation of Reviews 1.0 Q December 19, 2014 20 / 37 1. Baseline with Fixed Price & No Manipulation: Summary With unobservable reviewing strategy, 3 equilibrium outcomes Luciana Nicollier & Marco Ottaviani () Production and Manipulation of Reviews December 19, 2014 21 / 37 1. Baseline with Fixed Price & No Manipulation: Summary With unobservable reviewing strategy, 3 equilibrium outcomes NE (no reviews), PE (praise), & CE (complaint) Luciana Nicollier & Marco Ottaviani () Production and Manipulation of Reviews December 19, 2014 21 / 37 1. Baseline with Fixed Price & No Manipulation: Summary With unobservable reviewing strategy, 3 equilibrium outcomes NE (no reviews), PE (praise), & CE (complaint) Let’s focus on Sender’s preferred equilibrium Luciana Nicollier & Marco Ottaviani () Production and Manipulation of Reviews December 19, 2014 21 / 37 1. Baseline with Fixed Price & No Manipulation: Summary With unobservable reviewing strategy, 3 equilibrium outcomes NE (no reviews), PE (praise), & CE (complaint) Let’s focus on Sender’s preferred equilibrium this equilibrium also results when reviewing strategy is observable Luciana Nicollier & Marco Ottaviani () Production and Manipulation of Reviews December 19, 2014 21 / 37 1. Baseline with Fixed Price & No Manipulation: Summary With unobservable reviewing strategy, 3 equilibrium outcomes NE (no reviews), PE (praise), & CE (complaint) Let’s focus on Sender’s preferred equilibrium this equilibrium also results when reviewing strategy is observable Sender’s preferred equilibrium PE %S CE , λ Luciana Nicollier & Marco Ottaviani () λ̄S (p, c ) & p Production and Manipulation of Reviews p̄S (λ, c ) December 19, 2014 21 / 37 1. Baseline with Fixed Price & No Manipulation: Summary With unobservable reviewing strategy, 3 equilibrium outcomes NE (no reviews), PE (praise), & CE (complaint) Let’s focus on Sender’s preferred equilibrium this equilibrium also results when reviewing strategy is observable Sender’s preferred equilibrium PE %S CE , λ λ̄S (p, c ) & p p̄S (λ, c ) PRAISE Eq. when p high relative to λ (typical!) Luciana Nicollier & Marco Ottaviani () Production and Manipulation of Reviews December 19, 2014 21 / 37 1. Baseline with Fixed Price & No Manipulation: Summary With unobservable reviewing strategy, 3 equilibrium outcomes NE (no reviews), PE (praise), & CE (complaint) Let’s focus on Sender’s preferred equilibrium this equilibrium also results when reviewing strategy is observable Sender’s preferred equilibrium PE %S CE , λ λ̄S (p, c ) & p p̄S (λ, c ) PRAISE Eq. when p high relative to λ (typical!) Example: When λ = 1/2, CE R PE and CE %S PE , p Luciana Nicollier & Marco Ottaviani () 1/2 = λ Production and Manipulation of Reviews December 19, 2014 21 / 37 1. Baseline with Fixed Price & No Manipulation: Summary With unobservable reviewing strategy, 3 equilibrium outcomes NE (no reviews), PE (praise), & CE (complaint) Let’s focus on Sender’s preferred equilibrium this equilibrium also results when reviewing strategy is observable Sender’s preferred equilibrium PE %S CE , λ λ̄S (p, c ) & p p̄S (λ, c ) PRAISE Eq. when p high relative to λ (typical!) Example: When λ = 1/2, CE R PE and CE %S PE , p 1/2 = λ Next, preferences of Firm for …xed prices? Luciana Nicollier & Marco Ottaviani () Production and Manipulation of Reviews December 19, 2014 21 / 37 1. Baseline with Fixed Price & No Manipulation: Summary With unobservable reviewing strategy, 3 equilibrium outcomes NE (no reviews), PE (praise), & CE (complaint) Let’s focus on Sender’s preferred equilibrium this equilibrium also results when reviewing strategy is observable Sender’s preferred equilibrium PE %S CE , λ λ̄S (p, c ) & p p̄S (λ, c ) PRAISE Eq. when p high relative to λ (typical!) Example: When λ = 1/2, CE R PE and CE %S PE , p 1/2 = λ Next, preferences of Firm for …xed prices? More sales in CE , so always CE Luciana Nicollier & Marco Ottaviani () F PE Production and Manipulation of Reviews December 19, 2014 21 / 37 1. Enough Uncertainty about Previous Sale Kills CE Suppose Sender is present with probability α < 1 Luciana Nicollier & Marco Ottaviani () Production and Manipulation of Reviews December 19, 2014 22 / 37 1. Enough Uncertainty about Previous Sale Kills CE Suppose Sender is present with probability α < 1 posterior after no review λ? now closer to prior λ Luciana Nicollier & Marco Ottaviani () Production and Manipulation of Reviews December 19, 2014 22 / 37 1. Enough Uncertainty about Previous Sale Kills CE Suppose Sender is present with probability α < 1 posterior after no review λ? now closer to prior λ To preserve value of info: in PE need λ? Luciana Nicollier & Marco Ottaviani () p Production and Manipulation of Reviews December 19, 2014 22 / 37 1. Enough Uncertainty about Previous Sale Kills CE Suppose Sender is present with probability α < 1 posterior after no review λ? now closer to prior λ To preserve value of info: in PE need λ? p As α decreases, λ? increases toward prior λ (less bad news) Luciana Nicollier & Marco Ottaviani () Production and Manipulation of Reviews December 19, 2014 22 / 37 1. Enough Uncertainty about Previous Sale Kills CE Suppose Sender is present with probability α < 1 posterior after no review λ? now closer to prior λ To preserve value of info: in PE need λ? p As α decreases, λ? increases toward prior λ (less bad news) Niche Mkt, p > λ: no problem Luciana Nicollier & Marco Ottaviani () Production and Manipulation of Reviews December 19, 2014 22 / 37 1. Enough Uncertainty about Previous Sale Kills CE Suppose Sender is present with probability α < 1 posterior after no review λ? now closer to prior λ To preserve value of info: in PE need λ? p As α decreases, λ? increases toward prior λ (less bad news) Niche Mkt, p > λ: no problem Mass Mkt, p < λ: for small α constraint λ? p binds, then q̄ c is reduced from unconstrained level so that λ? = Luciana Nicollier & Marco Ottaviani () FH (q̄ c ) λ =p F (q̄ c ) Production and Manipulation of Reviews December 19, 2014 22 / 37 1. Enough Uncertainty about Previous Sale Kills CE Suppose Sender is present with probability α < 1 posterior after no review λ? now closer to prior λ To preserve value of info: in PE need λ? p As α decreases, λ? increases toward prior λ (less bad news) Niche Mkt, p > λ: no problem Mass Mkt, p < λ: for small α constraint λ? p binds, then q̄ c is reduced from unconstrained level so that λ? = FH (q̄ c ) λ =p F (q̄ c ) To preserve value of info: in CE need λ? > p Luciana Nicollier & Marco Ottaviani () Production and Manipulation of Reviews December 19, 2014 22 / 37 1. Enough Uncertainty about Previous Sale Kills CE Suppose Sender is present with probability α < 1 posterior after no review λ? now closer to prior λ To preserve value of info: in PE need λ? p As α decreases, λ? increases toward prior λ (less bad news) Niche Mkt, p > λ: no problem Mass Mkt, p < λ: for small α constraint λ? p binds, then q̄ c is reduced from unconstrained level so that λ? = FH (q̄ c ) λ =p F (q̄ c ) To preserve value of info: in CE need λ? > p As α decreases, λ? decreases toward prior λ (less good news) Luciana Nicollier & Marco Ottaviani () Production and Manipulation of Reviews December 19, 2014 22 / 37 1. Enough Uncertainty about Previous Sale Kills CE Suppose Sender is present with probability α < 1 posterior after no review λ? now closer to prior λ To preserve value of info: in PE need λ? p As α decreases, λ? increases toward prior λ (less bad news) Niche Mkt, p > λ: no problem Mass Mkt, p < λ: for small α constraint λ? p binds, then q̄ c is reduced from unconstrained level so that λ? = FH (q̄ c ) λ =p F (q̄ c ) To preserve value of info: in CE need λ? > p As α decreases, λ? decreases toward prior λ (less good news) Niche Mkt, p > λ: for small α, receiver of ? does not buy, so no CE! Luciana Nicollier & Marco Ottaviani () Production and Manipulation of Reviews December 19, 2014 22 / 37 1. Enough Uncertainty about Previous Sale Kills CE Suppose Sender is present with probability α < 1 posterior after no review λ? now closer to prior λ To preserve value of info: in PE need λ? p As α decreases, λ? increases toward prior λ (less bad news) Niche Mkt, p > λ: no problem Mass Mkt, p < λ: for small α constraint λ? p binds, then q̄ c is reduced from unconstrained level so that λ? = FH (q̄ c ) λ =p F (q̄ c ) To preserve value of info: in CE need λ? > p As α decreases, λ? decreases toward prior λ (less good news) Niche Mkt, p > λ: for small α, receiver of ? does not buy, so no CE! Mass Mkt, p < λ: equilibrium with higher demand (as α decreases) Luciana Nicollier & Marco Ottaviani () Production and Manipulation of Reviews December 19, 2014 22 / 37 1. Summary of Baseline Model Baseline model stresses information content of silence Luciana Nicollier & Marco Ottaviani () Production and Manipulation of Reviews December 19, 2014 23 / 37 1. Summary of Baseline Model Baseline model stresses information content of silence Interpretation of silence depends on equilibrium (CE/PE) Luciana Nicollier & Marco Ottaviani () Production and Manipulation of Reviews December 19, 2014 23 / 37 1. Summary of Baseline Model Baseline model stresses information content of silence Interpretation of silence depends on equilibrium (CE/PE) When prior is favorable, CE with negative reviews: silence is good news Luciana Nicollier & Marco Ottaviani () Production and Manipulation of Reviews December 19, 2014 23 / 37 1. Summary of Baseline Model Baseline model stresses information content of silence Interpretation of silence depends on equilibrium (CE/PE) When prior is favorable, CE with negative reviews: silence is good news So increase in λ reduces rating Luciana Nicollier & Marco Ottaviani () Production and Manipulation of Reviews December 19, 2014 23 / 37 1. Summary of Baseline Model Baseline model stresses information content of silence Interpretation of silence depends on equilibrium (CE/PE) When prior is favorable, CE with negative reviews: silence is good news So increase in λ reduces rating When price is high, PE with positive reviews becomes cheaper Luciana Nicollier & Marco Ottaviani () Production and Manipulation of Reviews December 19, 2014 23 / 37 1. Summary of Baseline Model Baseline model stresses information content of silence Interpretation of silence depends on equilibrium (CE/PE) When prior is favorable, CE with negative reviews: silence is good news So increase in λ reduces rating When price is high, PE with positive reviews becomes cheaper So increase in p increases rating Luciana Nicollier & Marco Ottaviani () Production and Manipulation of Reviews December 19, 2014 23 / 37 2. Fixed Price & Costly MANIPULATION: Timing 1. SENDER a. decides whether to buy b. after buying, observes noisy signal of quality q c. releases review at cost c Luciana Nicollier & Marco Ottaviani () Production and Manipulation of Reviews FL , FH December 19, 2014 24 / 37 2. Fixed Price & Costly MANIPULATION: Timing 1. SENDER a. decides whether to buy b. after buying, observes noisy signal of quality q c. releases review at cost c FL , FH 2. Firm observes review r & manipulates it to r̂ (COST next) Luciana Nicollier & Marco Ottaviani () Production and Manipulation of Reviews December 19, 2014 24 / 37 2. Fixed Price & Costly MANIPULATION: Timing 1. SENDER a. decides whether to buy b. after buying, observes noisy signal of quality q c. releases review at cost c FL , FH 2. Firm observes review r & manipulates it to r̂ (COST next) 3. RECEIVER sees manipulated review r̂ & decides whether to buy Luciana Nicollier & Marco Ottaviani () Production and Manipulation of Reviews December 19, 2014 24 / 37 2. Assumption about Manipulation Cost Firm manipulates at cost by ∑ Γr (σrr ) with γm0 > 0 and γm00 > 0, 0 r where σr̂r = Pr(r̂ jr ) for r̂ , r 2 fB, ?, G g probability with which receiver observes review r̂ when …rm observed review r Luciana Nicollier & Marco Ottaviani () Production and Manipulation of Reviews December 19, 2014 25 / 37 2. Assumption about Manipulation Cost Firm manipulates at cost by ∑ Γr (σrr ) with γm0 > 0 and γm00 > 0, 0 r where σr̂r = Pr(r̂ jr ) for r̂ , r 2 fB, ?, G g probability with which receiver observes review r̂ when …rm observed review r Thus, Receiver observes r̂ 2 fB, ?, G g, garbling of original review Luciana Nicollier & Marco Ottaviani () Production and Manipulation of Reviews December 19, 2014 25 / 37 2. Assumption about Manipulation Cost Firm manipulates at cost by ∑ Γr (σrr ) with γm0 > 0 and γm00 > 0, 0 r where σr̂r = Pr(r̂ jr ) for r̂ , r 2 fB, ?, G g probability with which receiver observes review r̂ when …rm observed review r Thus, Receiver observes r̂ 2 fB, ?, G g, garbling of original review Firm’s optimal manipulation strategy is increasing Luciana Nicollier & Marco Ottaviani () Production and Manipulation of Reviews December 19, 2014 25 / 37 2. Assumption about Manipulation Cost Firm manipulates at cost by ∑ Γr (σrr ) with γm0 > 0 and γm00 > 0, 0 r where σr̂r = Pr(r̂ jr ) for r̂ , r 2 fB, ?, G g probability with which receiver observes review r̂ when …rm observed review r Thus, Receiver observes r̂ 2 fB, ?, G g, garbling of original review Firm’s optimal manipulation strategy is increasing either, eliminate B transformed into ? in Complaint Eq. Luciana Nicollier & Marco Ottaviani () Production and Manipulation of Reviews December 19, 2014 25 / 37 2. Assumption about Manipulation Cost Firm manipulates at cost by ∑ Γr (σrr ) with γm0 > 0 and γm00 > 0, 0 r where σr̂r = Pr(r̂ jr ) for r̂ , r 2 fB, ?, G g probability with which receiver observes review r̂ when …rm observed review r Thus, Receiver observes r̂ 2 fB, ?, G g, garbling of original review Firm’s optimal manipulation strategy is increasing either, eliminate B transformed into ? in Complaint Eq. or, create fake G out of ? in Praise Eq. Luciana Nicollier & Marco Ottaviani () Production and Manipulation of Reviews December 19, 2014 25 / 37 2. Review Manipulation by Firm: Preview In equilibrium, manipulation determined by p = Luciana Nicollier & Marco Ottaviani () Production and Manipulation of Reviews ∂Γ(σj ) ∂σj December 19, 2014 26 / 37 2. Review Manipulation by Firm: Preview In equilibrium, manipulation determined by p = ∂Γ(σj ) ∂σj in both CE and PE we are creating one additional purchase Luciana Nicollier & Marco Ottaviani () Production and Manipulation of Reviews December 19, 2014 26 / 37 2. Review Manipulation by Firm: Preview In equilibrium, manipulation determined by p = ∂Γ(σj ) ∂σj in both CE and PE we are creating one additional purchase DIRECT EFFECT, supposing sender does not react to manipulation, but receiver is rational: Luciana Nicollier & Marco Ottaviani () Production and Manipulation of Reviews December 19, 2014 26 / 37 2. Review Manipulation by Firm: Preview In equilibrium, manipulation determined by p = ∂Γ(σj ) ∂σj in both CE and PE we are creating one additional purchase DIRECT EFFECT, supposing sender does not react to manipulation, but receiver is rational: REVENUE component is positive (in relevant range) Luciana Nicollier & Marco Ottaviani () Production and Manipulation of Reviews December 19, 2014 26 / 37 2. Review Manipulation by Firm: Preview In equilibrium, manipulation determined by p = ∂Γ(σj ) ∂σj in both CE and PE we are creating one additional purchase DIRECT EFFECT, supposing sender does not react to manipulation, but receiver is rational: REVENUE component is positive (in relevant range) COST of manipulation clearly increases Luciana Nicollier & Marco Ottaviani () Production and Manipulation of Reviews December 19, 2014 26 / 37 2. Review Manipulation by Firm: Preview In equilibrium, manipulation determined by p = ∂Γ(σj ) ∂σj in both CE and PE we are creating one additional purchase DIRECT EFFECT, supposing sender does not react to manipulation, but receiver is rational: REVENUE component is positive (in relevant range) COST of manipulation clearly increases STRATEGIC EFFECT, due to crowding out reviews by sender Luciana Nicollier & Marco Ottaviani () Production and Manipulation of Reviews December 19, 2014 26 / 37 2. Review Manipulation by Firm: Preview In equilibrium, manipulation determined by p = ∂Γ(σj ) ∂σj in both CE and PE we are creating one additional purchase DIRECT EFFECT, supposing sender does not react to manipulation, but receiver is rational: REVENUE component is positive (in relevant range) COST of manipulation clearly increases STRATEGIC EFFECT, due to crowding out reviews by sender Strategic e¤ect is negative in a Praise Eq. Luciana Nicollier & Marco Ottaviani () Production and Manipulation of Reviews December 19, 2014 26 / 37 2. Review Manipulation by Firm: Preview In equilibrium, manipulation determined by p = ∂Γ(σj ) ∂σj in both CE and PE we are creating one additional purchase DIRECT EFFECT, supposing sender does not react to manipulation, but receiver is rational: REVENUE component is positive (in relevant range) COST of manipulation clearly increases STRATEGIC EFFECT, due to crowding out reviews by sender Strategic e¤ect is negative in a Praise Eq. Strategic e¤ect is positive in a Complaint Eq. Luciana Nicollier & Marco Ottaviani () Production and Manipulation of Reviews December 19, 2014 26 / 37 2. DIRECT E¤ect of Manipulation: PRAISE EQ. Without reviews demand ‡at at λ BLUE Luciana Nicollier & Marco Ottaviani () Production and Manipulation of Reviews December 19, 2014 27 / 37 2. DIRECT E¤ect of Manipulation: PRAISE EQ. Without reviews demand ‡at at λ BLUE Impact of reviews on demand: BLUE->BLACK, rotation Luciana Nicollier & Marco Ottaviani () Production and Manipulation of Reviews December 19, 2014 27 / 37 2. DIRECT E¤ect of Manipulation: PRAISE EQ. Without reviews demand ‡at at λ BLUE Impact of reviews on demand: BLUE->BLACK, rotation DIRECT e¤ect of manipulation on demand/revenue […xing sender’s q̄ c ]: BLACK->GREEN Luciana Nicollier & Marco Ottaviani () Production and Manipulation of Reviews December 19, 2014 27 / 37 2. DIRECT E¤ect of Manipulation: PRAISE EQ. Without reviews demand ‡at at λ BLUE Impact of reviews on demand: BLUE->BLACK, rotation DIRECT e¤ect of manipulation on demand/revenue […xing sender’s q̄ c ]: BLACK->GREEN manipulation reduces occurrence of ? Luciana Nicollier & Marco Ottaviani () Production and Manipulation of Reviews December 19, 2014 27 / 37 2. DIRECT E¤ect of Manipulation: PRAISE EQ. Without reviews demand ‡at at λ BLUE Impact of reviews on demand: BLUE->BLACK, rotation DIRECT e¤ect of manipulation on demand/revenue […xing sender’s q̄ c ]: BLACK->GREEN manipulation reduces occurrence of ? so, direct e¤ect positive (in relevant range) Luciana Nicollier & Marco Ottaviani () Production and Manipulation of Reviews December 19, 2014 27 / 37 2. STRATEGIC E¤ect of Manipulation: PRAISE EQ. Now, sender reacts to expected manipulation: GREEN->RED Luciana Nicollier & Marco Ottaviani () Production and Manipulation of Reviews December 19, 2014 28 / 37 2. STRATEGIC E¤ect of Manipulation: PRAISE EQ. Now, sender reacts to expected manipulation: GREEN->RED Crowding out: Sender sends less good reviews, making: Luciana Nicollier & Marco Ottaviani () Production and Manipulation of Reviews December 19, 2014 28 / 37 2. STRATEGIC E¤ect of Manipulation: PRAISE EQ. Now, sender reacts to expected manipulation: GREEN->RED Crowding out: Sender sends less good reviews, making: good reviews more favorable & Luciana Nicollier & Marco Ottaviani () Production and Manipulation of Reviews December 19, 2014 28 / 37 2. STRATEGIC E¤ect of Manipulation: PRAISE EQ. Now, sender reacts to expected manipulation: GREEN->RED Crowding out: Sender sends less good reviews, making: good reviews more favorable & bad reviews more favorable Luciana Nicollier & Marco Ottaviani () Production and Manipulation of Reviews December 19, 2014 28 / 37 2. STRATEGIC E¤ect of Manipulation: PRAISE EQ. Now, sender reacts to expected manipulation: GREEN->RED Crowding out: Sender sends less good reviews, making: good reviews more favorable & bad reviews more favorable Total e¤ect? Luciana Nicollier & Marco Ottaviani () Production and Manipulation of Reviews December 19, 2014 28 / 37 2. Impact of Review Manipulation: PRAISE EQ. Total e¤ect on demand is positive (if review cost c is low) or negative Luciana Nicollier & Marco Ottaviani () Production and Manipulation of Reviews December 19, 2014 29 / 37 2. Impact of Review Manipulation: PRAISE EQ. Total e¤ect on demand is positive (if review cost c is low) or negative Luciana Nicollier & Marco Ottaviani () Production and Manipulation of Reviews December 19, 2014 29 / 37 2. Impact of Review Manipulation: PRAISE EQ. Total e¤ect on demand is positive (if review cost c is low) or negative For high c, manipulation damages …rm in two ways: Revenue# &Cost" Luciana Nicollier & Marco Ottaviani () Production and Manipulation of Reviews December 19, 2014 29 / 37 2. Impact of Review Manipulation: COMPLAINT EQ. DIRECT e¤ect of manipulation on demand, positive: BLACK->GREEN Luciana Nicollier & Marco Ottaviani () Production and Manipulation of Reviews December 19, 2014 30 / 37 2. Impact of Review Manipulation: COMPLAINT EQ. DIRECT e¤ect of manipulation on demand, positive: BLACK->GREEN as complaints are deleted Luciana Nicollier & Marco Ottaviani () Production and Manipulation of Reviews December 19, 2014 30 / 37 2. Impact of Review Manipulation: COMPLAINT EQ. DIRECT e¤ect of manipulation on demand, positive: BLACK->GREEN as complaints are deleted Luciana Nicollier & Marco Ottaviani () Production and Manipulation of Reviews December 19, 2014 30 / 37 2. Impact of Review Manipulation: COMPLAINT EQ. DIRECT e¤ect of manipulation on demand, positive: BLACK->GREEN as complaints are deleted STRATEGIC e¤ect of manipulation on demand, positive: GREEN->RED Luciana Nicollier & Marco Ottaviani () Production and Manipulation of Reviews December 19, 2014 30 / 37 2. Impact of Review Manipulation: COMPLAINT EQ. DIRECT e¤ect of manipulation on demand, positive: BLACK->GREEN as complaints are deleted STRATEGIC e¤ect of manipulation on demand, positive: GREEN->RED crowding out of sender’s bad reviews increases demand! Luciana Nicollier & Marco Ottaviani () Production and Manipulation of Reviews December 19, 2014 30 / 37 2. Impact of Review Manipulation: COMPLAINT EQ. DIRECT e¤ect of manipulation on demand, positive: BLACK->GREEN as complaints are deleted STRATEGIC e¤ect of manipulation on demand, positive: GREEN->RED crowding out of sender’s bad reviews increases demand! Total e¤ect on demand & revenue is positive— but costs also go up Luciana Nicollier & Marco Ottaviani () Production and Manipulation of Reviews December 19, 2014 30 / 37 2. Existence of Review Equilibria with Manipulation Sender completes reviews only if receiver has positive value of info: Luciana Nicollier & Marco Ottaviani () Production and Manipulation of Reviews December 19, 2014 31 / 37 2. Existence of Review Equilibria with Manipulation Sender completes reviews only if receiver has positive value of info: Reviews sent only if receiver earns positive rent when buying: need λP > p in PE & λ? > p in CE Luciana Nicollier & Marco Ottaviani () Production and Manipulation of Reviews December 19, 2014 31 / 37 2. Existence of Review Equilibria with Manipulation Sender completes reviews only if receiver has positive value of info: Reviews sent only if receiver earns positive rent when buying: need λP > p in PE & λ? > p in CE Manipulation decreases λP & λ? toward prior λ Luciana Nicollier & Marco Ottaviani () Production and Manipulation of Reviews December 19, 2014 31 / 37 2. Existence of Review Equilibria with Manipulation Sender completes reviews only if receiver has positive value of info: Reviews sent only if receiver earns positive rent when buying: need λP > p in PE & λ? > p in CE Manipulation decreases λP & λ? toward prior λ In Niche Mkt (p > λ) review equilibrium can be sustained only if cost of manipulation is high or if cost of review is low— otherwise, …rm will want to manipulate to an extent that destroys value of info, thus killing review equilibria resulting in Luciana Nicollier & Marco Ottaviani () Production and Manipulation of Reviews December 19, 2014 31 / 37 2. Existence of Review Equilibria with Manipulation Sender completes reviews only if receiver has positive value of info: Reviews sent only if receiver earns positive rent when buying: need λP > p in PE & λ? > p in CE Manipulation decreases λP & λ? toward prior λ In Niche Mkt (p > λ) review equilibrium can be sustained only if cost of manipulation is high or if cost of review is low— otherwise, …rm will want to manipulate to an extent that destroys value of info, thus killing review equilibria resulting in no sale for p Luciana Nicollier & Marco Ottaviani () λP̂ (q̂P , σ? ) in PE Production and Manipulation of Reviews December 19, 2014 31 / 37 2. Existence of Review Equilibria with Manipulation Sender completes reviews only if receiver has positive value of info: Reviews sent only if receiver earns positive rent when buying: need λP > p in PE & λ? > p in CE Manipulation decreases λP & λ? toward prior λ In Niche Mkt (p > λ) review equilibrium can be sustained only if cost of manipulation is high or if cost of review is low— otherwise, …rm will want to manipulate to an extent that destroys value of info, thus killing review equilibria resulting in no sale for p no sale for p Luciana Nicollier & Marco Ottaviani () λP̂ (q̂P , σ? ) in PE λ? (q̂C , σC ) in CE Production and Manipulation of Reviews December 19, 2014 31 / 37 2. Existence of Review Equilibria with Manipulation Sender completes reviews only if receiver has positive value of info: Reviews sent only if receiver earns positive rent when buying: need λP > p in PE & λ? > p in CE Manipulation decreases λP & λ? toward prior λ In Niche Mkt (p > λ) review equilibrium can be sustained only if cost of manipulation is high or if cost of review is low— otherwise, …rm will want to manipulate to an extent that destroys value of info, thus killing review equilibria resulting in no sale for p no sale for p λP̂ (q̂P , σ? ) in PE λ? (q̂C , σC ) in CE In a Mass Mkt (p < λ), there is always a review equilibrium with manipulation for any p because quality signal is unboundedly informative [provided that c < 1 p] Luciana Nicollier & Marco Ottaviani () Production and Manipulation of Reviews December 19, 2014 31 / 37 3. OPTIMAL PRICE & No Manipulation: Timing 1. Firm sets price p; product’s cost is C Luciana Nicollier & Marco Ottaviani () Production and Manipulation of Reviews December 19, 2014 32 / 37 3. OPTIMAL PRICE & No Manipulation: Timing 1. Firm sets price p; product’s cost is C Then as in baseline: 2. SENDER a. decides whether to buy b. after buying, observes noisy signal of quality q c. releases review at cost c FL , FH 3. RECEIVER observes review & decides whether to buy Luciana Nicollier & Marco Ottaviani () Production and Manipulation of Reviews December 19, 2014 32 / 37 3. Endogenous Price [NO Manipulation] Recall baseline without manipulation, …xing λ = 1/2 for illustration PE %S CE , p Luciana Nicollier & Marco Ottaviani () 1/2 = λ Production and Manipulation of Reviews December 19, 2014 33 / 37 3. Endogenous Price [NO Manipulation] Recall baseline without manipulation, …xing λ = 1/2 for illustration PE %S CE , p 1/2 = λ q̄ c With linear signal: = p + c; for c extracts sender’s rent: p = (2 c) c̆, optimal price with review q 2 (1 c) price 1.0 0.5 0.0 0.0 Luciana Nicollier & Marco Ottaviani () 0.5 Production and Manipulation of Reviews 1.0 c December 19, 2014 33 / 37 3. Endogenous Price [NO Manipulation] Recall baseline without manipulation, …xing λ = 1/2 for illustration PE %S CE , p 1/2 = λ q̄ c With linear signal: = p + c; for c extracts sender’s rent: p = (2 c) c̆, optimal price with review q 2 (1 c) price 1.0 0.5 0.0 0.0 0.5 1.0 c For high review cost c c̆, revenue maximizing p = min hc, 1/2i destroys value of information, inducing No Reviews Luciana Nicollier & Marco Ottaviani () Production and Manipulation of Reviews December 19, 2014 33 / 37 3. Endogenous Price [NO Manipulation] In CE, constraint p 1/2 binds: p = 1/2 revenues 1.0 0.5 0.0 0.0 Luciana Nicollier & Marco Ottaviani () 0.5 Production and Manipulation of Reviews 1.0 c December 19, 2014 34 / 37 3. Endogenous Price [NO Manipulation] In CE, constraint p 1/2 binds: p = 1/2 Maximized revenues p + 1 revenues F q p [RED] 1.0 0.5 0.0 0.0 Luciana Nicollier & Marco Ottaviani () 0.5 Production and Manipulation of Reviews 1.0 c December 19, 2014 34 / 37 3. Adding Product Cost Question: Does …rm pro…t from info contained in reviews? For example when C = 1/2 = λ (niche market), then CE when selected (p = 1/2) gives zero pro…ts! profits 0.20 0.15 Luciana Nicollier & Marco Ottaviani 0.10 () Production and Manipulation of Reviews December 19, 2014 35 / 37 3. Adding Product Cost Question: Does …rm pro…t from info contained in reviews? When marginal production cost C = 0, review info can only bene…t consumers but always damages …rm For example when C = 1/2 = λ (niche market), then CE when selected (p = 1/2) gives zero pro…ts! profits 0.20 0.15 Luciana Nicollier & Marco Ottaviani 0.10 () Production and Manipulation of Reviews December 19, 2014 35 / 37 3. Adding Product Cost Question: Does …rm pro…t from info contained in reviews? When marginal production cost C = 0, review info can only bene…t consumers but always damages …rm Need C > 0 (info with social value) for …rm to possibly pro…t from reviews For example when C = 1/2 = λ (niche market), then CE when selected (p = 1/2) gives zero pro…ts! profits 0.20 0.15 Luciana Nicollier & Marco Ottaviani 0.10 () Production and Manipulation of Reviews December 19, 2014 35 / 37 3. Adding Product Cost Question: Does …rm pro…t from info contained in reviews? When marginal production cost C = 0, review info can only bene…t consumers but always damages …rm Need C > 0 (info with social value) for …rm to possibly pro…t from reviews otherwise info is useful for consumer but reduces pro…ts For example when C = 1/2 = λ (niche market), then CE when selected (p = 1/2) gives zero pro…ts! profits 0.20 0.15 Luciana Nicollier & Marco Ottaviani 0.10 () Production and Manipulation of Reviews December 19, 2014 35 / 37 3. Adding Product Cost Question: Does …rm pro…t from info contained in reviews? When marginal production cost C = 0, review info can only bene…t consumers but always damages …rm Need C > 0 (info with social value) for …rm to possibly pro…t from reviews otherwise info is useful for consumer but reduces pro…ts Suppose C > 0, For example when C = 1/2 = λ (niche market), then CE when selected (p = 1/2) gives zero pro…ts! profits 0.20 0.15 Luciana Nicollier & Marco Ottaviani 0.10 () Production and Manipulation of Reviews December 19, 2014 35 / 37 3. Adding Product Cost Question: Does …rm pro…t from info contained in reviews? When marginal production cost C = 0, review info can only bene…t consumers but always damages …rm Need C > 0 (info with social value) for …rm to possibly pro…t from reviews otherwise info is useful for consumer but reduces pro…ts Suppose C > 0, For example when C = 1/2 = λ (niche market), then CE when selected (p = 1/2) gives zero pro…ts! PE is optimal with p > 1/2 = λ & …rm pro…ts from review information profits 0.20 0.15 Luciana Nicollier & Marco Ottaviani 0.10 () Production and Manipulation of Reviews December 19, 2014 35 / 37 4. OPTIMAL PRICE & MANIPULATION: Timing 1. Firm sets price p; product’s cost is C Luciana Nicollier & Marco Ottaviani () Production and Manipulation of Reviews December 19, 2014 36 / 37 4. OPTIMAL PRICE & MANIPULATION: Timing 1. Firm sets price p; product’s cost is C 2. SENDER a. decides whether to buy b. after buying, observes noisy signal of quality q c. releases review at cost c Luciana Nicollier & Marco Ottaviani () Production and Manipulation of Reviews FL , FH December 19, 2014 36 / 37 4. OPTIMAL PRICE & MANIPULATION: Timing 1. Firm sets price p; product’s cost is C 2. SENDER a. decides whether to buy b. after buying, observes noisy signal of quality q c. releases review at cost c FL , FH 3. Firm observes review r & manipulates it to r̂ (COST in next slide) Luciana Nicollier & Marco Ottaviani () Production and Manipulation of Reviews December 19, 2014 36 / 37 4. OPTIMAL PRICE & MANIPULATION: Timing 1. Firm sets price p; product’s cost is C 2. SENDER a. decides whether to buy b. after buying, observes noisy signal of quality q c. releases review at cost c FL , FH 3. Firm observes review r & manipulates it to r̂ (COST in next slide) 4. RECEIVER observes manipulated review r̂ & decides whether to buy Luciana Nicollier & Marco Ottaviani () Production and Manipulation of Reviews December 19, 2014 36 / 37 4. WRAPPING UP: Endogenous Price & Manipulation! Now, price also acts as commitment device for manipulation, in addition to extracting surplus Luciana Nicollier & Marco Ottaviani () Production and Manipulation of Reviews December 19, 2014 37 / 37 4. WRAPPING UP: Endogenous Price & Manipulation! Now, price also acts as commitment device for manipulation, in addition to extracting surplus When product cost C high relative to λ, …rm can only make money for relatively high price (p > λ, niche market) but it has to make sure sender experiments & transmits info to receiver (who then buy at relatively high prices) Luciana Nicollier & Marco Ottaviani () Production and Manipulation of Reviews December 19, 2014 37 / 37 4. WRAPPING UP: Endogenous Price & Manipulation! Now, price also acts as commitment device for manipulation, in addition to extracting surplus When product cost C high relative to λ, …rm can only make money for relatively high price (p > λ, niche market) but it has to make sure sender experiments & transmits info to receiver (who then buy at relatively high prices) But for …xed price, when p > λ we saw that (cheap enough) manipulation destroys value of information and thus the market Luciana Nicollier & Marco Ottaviani () Production and Manipulation of Reviews December 19, 2014 37 / 37 4. WRAPPING UP: Endogenous Price & Manipulation! Now, price also acts as commitment device for manipulation, in addition to extracting surplus When product cost C high relative to λ, …rm can only make money for relatively high price (p > λ, niche market) but it has to make sure sender experiments & transmits info to receiver (who then buy at relatively high prices) But for …xed price, when p > λ we saw that (cheap enough) manipulation destroys value of information and thus the market Then, …rm has incentive to commit to reduce manipulation by ∂Γ decreasing p (given ∂σ = p) Luciana Nicollier & Marco Ottaviani () Production and Manipulation of Reviews December 19, 2014 37 / 37 4. WRAPPING UP: Endogenous Price & Manipulation! Now, price also acts as commitment device for manipulation, in addition to extracting surplus When product cost C high relative to λ, …rm can only make money for relatively high price (p > λ, niche market) but it has to make sure sender experiments & transmits info to receiver (who then buy at relatively high prices) But for …xed price, when p > λ we saw that (cheap enough) manipulation destroys value of information and thus the market Then, …rm has incentive to commit to reduce manipulation by ∂Γ decreasing p (given ∂σ = p) Through this channel, when …rm can easily manipulate reviews, …rm has an incentive to lower prices (as commitment) to the bene…t of consumers Luciana Nicollier & Marco Ottaviani () Production and Manipulation of Reviews December 19, 2014 37 / 37