Download Production and Manipulation of Reviews

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