Online review manipulation by asymmetrical firms: Is a firm’s manipulation of online reviews always detrimental to its competitor?

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Online review manipulation by asymmetrical firms: Is a firm’s manipulation of online reviews always detrimental to its competitor? Huanhuan Cao School of Management, Zhejiang University of Technology, 18thChaowang Road, Hangzhou, Zhejiang, 310014, China

ARTICLE INFO

ABSTRACT

Keywords: Online review manipulation Online reviews Asymmetrical firms Competing market Search products

Online reviews have a significant influence on consumers, and consequently firms are motivated to manipulate online reviews to promote their own products. This paper develops an analytical model to systematically explore the impact of online review manipulation on asymmetrical firms who sell substitutable search products in a competing market. Results show that a firm’s manipulation of online reviews is not necessary to hurt its competitor’s profit. In addition, if firms are free to choose whether to manipulate online reviews, both firms will always choose to manipulate online reviews. Moreover, there exists a prisoner’s dilemma in which online reviews are overmanipulated.

1. Introduction Online reviews are becoming important sources of information for consumers to learn more about products before purchase, and these reviews play an increasingly significant role in consumers’ purchasing decisions [1–8]. A 10 % improvement in an online rating on Ctrip (i.e., the largest travel website in China) translates to a 4.4 % increase in a hotel’s revenue [9], and a drop of one star in an online rating on Yelp decreases a restaurant’s revenue by 5%–9% [10]. The monetary effects of online reviews motivate firms to manipulate online reviews [11]. It has been reported that 15%–30% of online reviews are manipulated despite the filtering algorithms in place [10,12]. The central focus of this paper is to determine the implications of competing firms’ self-promotion efforts in the form of manipulating online reviews. While prior research [13,14] has studied firms’ strategic manipulation efforts in a monopoly context, this paper accounts for the fact that firms may actually act differently in a competing market. Empirical research [10] confirms that firms with lower reputations are more likely to engage in online review manipulation, which means that the motivations for a superior firm and an inferior firm to manipulate online reviews can also differ. Moreover, Mayzlin et al. [11] suggest that the benefits from online review manipulation are likely to be highest for independent hotels that are owned by single-unit owners and lowest for branded chain hotels that are owned by multi-unit owners, which means that the benefit from manipulating online reviews may differ between superior and inferior firms. Thus, this paper allows for asymmetry of the competing firms. This paper addresses the following research questions:

1) Does a firm’s manipulation of online reviews always hurt its competitor? Or, who gains from the manipulation of online reviews (e.g., the inferior firm, superior firm, or both)? 2) Who manipulates online reviews (e.g., the inferior firm, superior firm, or both)? To address these questions, this paper develops an analytical model in which two asymmetrical firms sell substitutable search products through a common platform. Although the products differ in both quality and fit to consumers’ needs, this paper focuses on the quality dimension, which plays a dominant role in determining consumers’ perceived utility differences between the two products. Each consumer has her own assessment of the quality difference between the two products, which follows a uniform distribution, and online reviews are public and common to all consumers. Consumers combine their own assessment and the public common assessment from online reviews to form their judgments. This paper models that the two products are the same in their true quality but differ in their quality as revealed by unmanipulated online reviews. The firm with higher quality revealed by unmanipulated online reviews is referred to as the superior firm, and the other firm is referred to as the inferior firm. This paper stipulates in the model that the manipulation of online reviews reduces the credibility of online reviews, which, in turn, reduces consumers’ confidence in online reviews. This paper uses the scenario with no firm manipulation as the benchmark to analyze the impacts of manipulation in the scenarios with manipulation by only the inferior firm, by only the superior firm, and by both firms. The results show that a firm’s manipulation of online reviews is not necessary to hurt its competitor’s profit regardless of scenarios (i.e.,

E-mail address: [email protected]. https://doi.org/10.1016/j.im.2019.103244 Received 30 October 2018; Received in revised form 28 November 2019; Accepted 30 November 2019 0378-7206/ © 2019 Elsevier B.V. All rights reserved.

Please cite this article as: Huanhuan Cao, Information & Management, https://doi.org/10.1016/j.im.2019.103244

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with manipulation by only the inferior firm, by only the superior firm, or by both firms). Interestingly, if firms are free to choose whether to manipulate online reviews, both firms will always choose to manipulate online reviews. This paper also identifies two interesting special cases. First, if the quality of the two products revealed by unmanipulated online reviews is the same, both firms could still be better off if they both manipulate reviews, even though both firms will implement the same manipulation efforts, which cancel each other out. Second, if firms are free to choose whether to manipulate online reviews, there exists a prisoner’s dilemma in which online reviews are overmanipulated. To the best of our knowledge, this study is one of the first to analyze whether firms can benefit from online review manipulation in a competing market. The premise of this work is to understand the different influences of online review manipulation on firms that implement manipulation and on their competitors. In particular, this paper builds on empirical and analytical works, which are discussed below. Several empirical works have found some evidence of online review manipulation on many platforms, and these studies have empirically investigated the economic impacts of online review manipulation on firms. Lee et al. [15] studied the manipulation of online sentiment in the context of movie tweets and confirmed that firms might be actively managing online sentiment in a strategic manner. Mayzlin et al. [11] examined hotel reviews on Expedia.com and TripAdvisor.com and found that the hotels that were more likely to engage in online review manipulation were those that were owned by non-chain or small owners, were independent and were managed by small management companies. Luca and Zervas [10] investigated online reviews on the Yelp platform and found that a restaurant was more likely to commit review fraud when its reputation was weak or when it faced increased competition. Lappas et al. [12] focused on the impact of fake reviews on the vulnerability of individual businesses and found that even limited injections of fake reviews could have a significant effect on the visibility of individual businesses. Nie [16] empirically studied the impact of Airbnb’s presence on conventional hotels’ manipulation strategies and found that low-end hotels did not increase their review manipulation activities, whereas high-end hotels demoted their competing hotels less and promoted themselves more in the presence of higher levels of competition. On the other hand, a few analytical works have studied the effect of firms’ manipulation strategies. In a monopoly context, Mayzlin [13] argued that producers with lower quality expended more resources on manipulating reviews, but Dellarocas [14] showed that there was an equilibrium in which the high-quality producer invested more resources into review manipulation. Nian et al. [17] analyzed the effect of manipulating online reviews under two pricing regimes (i.e., wholesale pricing and agency pricing) in a competing market and found that in both pricing regimes, an increase in the cost of manipulation reduced the manipulation level of high-quality manufacturers and increased the manipulation level of low-quality manufacturers. Aköz et al. [18] studied the case in which firms manipulate online reviews by inserting bias into online reviews when the price is uninformative about quality and found that there was wasteful spending on manipulation by both highand low-quality types. The main innovation of this paper, compared to previous analytical works, is the development of a modeling framework for the manipulation of online reviews. In the research by Dellarocas [14], even though consumers were aware of firms’ manipulations of online reviews, consumers treated manipulated online reviews and unmanipulated online reviews identically and updated their perception through Bayesian learning. Nian et al. [17] considered only the positive effect for firms that manipulate online reviews, which uniformly changed consumers’ perceived quality favorably toward the manipulating firm. However, in this paper, in addition to the positive effect for firms that manipulate online reviews, it also considers the negative effect of manipulation on the credibility of online reviews. Therefore,

this study identifies two effects of manipulating online reviews: the mean-shifting effect and the variance-increasing effect. The meanshifting effect refers to the uniform changes in each consumer's perceived quality difference between the two products under the manipulation of online reviews. The variance-increasing effect refers to the increased heterogeneity of consumers’ perceived quality difference due to the reduced credibility of online reviews under manipulation. The rest of the paper is organized as follows. Section 2 describes the model. Section 3, Section 4, and Second 5 describe the derivation of the equilibrium solutions and discuss the effect of manipulation by only the inferior firm, only the superior firm, and by both firms, respectively. Section 6 discusses firms’ manipulation decisions if firms are free to choose whether to manipulate online reviews. Section 7 concludes the paper. 2. The model 2.1. Consumer utility This study considers two competing firms (Firm A and Firm B) and a continuum of consumers with heterogeneous preferences. This paper assumes that the two competing firms sell substitutable products through a common platform. Firm A sells product A, and firm B sells product B. Each product is characterized by a quality attribute and a fit attribute. The quality of a product determines the maximum value that a consumer can derive from the product, which is denoted as x i , i {A, B} . The products have different degrees of misfit to different consumers. In particular, this paper assumes that the products are located at the two end points of a hoteling line of unit length, with product A at 0, product B at 1, and consumers uniformly distributed along the line. The distance between a product and a consumer measures the degree of misfit of the product to the consumer. The misfit cost is the degree of misfit times a unit misfit cost t . A consumer’s net utility for product x i , i {A, B} , is equal to the maximum value of the product that a consumer can derive from the product net the misfit cost and product price pi . Specifically, for a consumer with a degree of misfit to product A, the net utilities derived from product A and product B as follows:

VA = xA

t

VB = xB

(1

pA )t

pB

(1)

Therefore, for a consumer with a degree of misfit to product A, the net utility difference between product A and product B is

VA

VB = (xA

xB ) + (1

2 )t

(pA

pB )

(2)

This paper refers to xA xB as the true quality difference of the two products and to as the true degree of misfit. This paper also assumes that the true quality difference between the two products is zero (i.e., xA xB = 0 ) [19]. A continuum of consumers of measure 1 has a different true degree of misfit, which satisfies a uniform distribution. There are two types of products discussed widely in the economics literature: search products and experience products [20–22]. According to Kwark et al. [23], search products (e.g., digital camera, GPS, and hardware) that are evaluated based on objective indices, such as product performance, reliability, and durability, are likely to be qualitydominant-fit cases [21], whereas experience products (e.g., jewelry and video games) that are evaluated based on subjective consumer-specific indices, such as features and esthetics, are more fit-dominant-quality cases [22]. The quality-dominant-fit case refers to the case in which the quality dimension plays a dominant role in determining consumers’ perceived utility, which means there are consumers who have the lowest fit with product A but derive a higher net utility from it than they do from product B because their assessment on the quality dimension is favorable toward product A [23]. Similarly, the fit-dominant-quality case refers to the case in which the fit dimension plays a dominant role in determining consumers’ perceived utility. This paper 2

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focuses on search products (i.e., the quality-dominant-fit case) for two reasons. First, firms’ manipulations are always focused on the quality dimension. Firms’ self-promoting manipulations of online reviews always exert efforts to improve average review ratings, which reflect the quality of the product [11,16]. Manipulation of the quality dimension has little effect on consumers’ perceived utility in the fit-dominantquality case. This trend occurs because consumers who have perfect fit with a product always derive a higher net utility from that product, regardless of their assessment of the quality dimension [23]. Second, firms’ manipulations of fit dimension may increase the fit of some consumers but must decrease the fit of other consumers. This pattern occurs because consumers always prefer high quality to low quality but differ in the fit dimension [23].

online reviews to improve their own quality, as revealed by online reviews. eA is denoted as the quality improvement attained by firm A through manipulating online reviews and eB is denoted as the quality improvement attained by firm B through manipulating online reviews. Therefore, under manipulation by only the superior firm, the quality difference revealed by online reviews is xR + eA ; under manipulation by only the inferior firm, the quality difference revealed by online reviews is xR eB ; and under manipulation by both firms, the quality difference revealed by online reviews is xR + eA eB . ei can also be referred to as the manipulation effort. A manipulation effort of ei by firm i costs µei2 , where µ measures the unit cost of manipulating online reviews. In the presence of online review manipulation, the credibility of online reviews is jeopardized. In most cases, consumers know that online reviews are manipulated, but they cannot tell specifically which of the online reviews have been manipulated. As a result, consumers’ confidence in online reviews is reduced, and consumers will rely more on their own assessment of products. In the presence of online review manipulation, M ( M > C ) is denoted as the confidence in their own assessments. Therefore, in the presence of online review manipulation (i.e., xR + 1 eA 2 eB ), the expected net utility difference between product A and product B for the consumer with perceived quality difference x C is

2.2. Product uncertainty and unmanipulated online reviews Consumers are uncertain about the quality of both products. In the absence of online reviews, based on the product description and other information sources, each consumer has formed her own assessment of the quality difference between the two products.x C is denoted as a consumer’s own assessment of the quality difference based on her own information sources other than online reviews. Different consumers perceive different x C values. This paper assumes that at the aggregate level, consumers’ perceived quality differences satisfy a uniform distribution over [ , ]. For simplicity, we normalize to 1. Online reviews provide public information about products, and consumers can use this information in addition to their own assessments to evaluate the products. xR is denoted as the perceived quality difference revealed by unmanipulated online reviews, and this quality is common to all consumers. In the presence of unmanipulated online reviews, consumers combine the public common assessment xR and their own assessment x C to form their judgement of the quality difference. Using the minimum variance estimation [24], the consumer’s expected quality difference becomes C xC + (1 C, C ) xR , where (0,1) , depends on the relative precisions of the two information C sources. Intuitively, consumers adjust their quality assessments because of the additional information from unmanipulated online reviews, and the extent to which unmanipulated online reviews affect consumers’ assessments depends on the relative confidence between their own assessments and unmanipulated online reviews. When xR = 0 , the quality of firm A revealed by unmanipulated online reviews is equal to that of firm B. When xR > 0 , the quality of firm A revealed by unmanipulated online reviews is higher than that of firm B. Because of the symmetry, this paper considers only xR 0 , and refers to firm A as the superior firm and to firm B as the inferior firm. Note that even though the true qualities of products from the two firms are identical, it is possible that unmanipulated online reviews of the two products could reveal different levels of quality. This is because unmanipulated online reviews are not determined by only the quality of products but also by other factors, such as prior consumers’ expectation [2] and previous online reviews [25]. Even the same product can receive different online ratings, e.g., the same book sold on Amazon.com and on BN.com [1] and the same hotel reserved through Ctrip.com and eLong.com [26]. Then, in the presence of unmanipulated online reviews (i.e., xR ), the expected net utility difference between product A and product B for the consumer with perceived quality difference x C is

E (VA

VB x C ) =

C xC

+ (1

C ) xR

+ (1

2 )t

(pA

pB )

E (VA

VB x c ) =

M xC

+ (1

(pA

M )(xR

+

1 eA

2 eB )

+ (1

2 )t (4)

pB )

in which ( 1, 2 ) {(0,1), (1,0), (1,1)} , where (0,1) corresponds to the scenario with manipulation by only the inferior firm, (1,0) corresponds to the scenario with manipulation by only the superior firm, and (1,1) corresponds to the scenario with manipulation by both firms. 2.4. Timing of the game The sequence of events is as follows. In stage 1, firms decide whether to manipulate online reviews. In stage 2, firms set the price pi and manipulation effort ei (if firm i decides to manipulate online reviews) simultaneously. In stage 3, consumers make their purchase decisions. Four scenarios are considered: the scenario with no firm manipulation, the scenario with manipulation by only the inferior firm, the scenario with manipulation by only the superior firm, and the scenario with manipulation by both firms. This paper uses the scenario with no firm manipulation as the benchmark to analyze the impacts of online review manipulation. Table 1 summarizes the main notations used in the paper. 2.5. Demand function In the last stage of the game, consumers learn the expected utility differences between two products. Based on Eqs. (3) and (4), we can uniformly formulate a consumer’s expected net utility difference as

E (VA

VB x C ) = x C + (1 (pA

pB )

)(xR +

1 eA

2 eB )

+ (1

2 )t (5)

in which ( , 1, 2 ) {( C , 0,0), ( M , 0,1), ( M , 1,0), ( M , 1,1)}, where ( C , 0,0) corresponds to the scenario with no firm manipulation, ( M , 0,1) corresponds to the scenario with manipulation by only the inferior firm, ( M , 1,0) corresponds to the scenario with manipulation by only the superior firm, and ( M , 1,1) corresponds to the scenario with manipulation by both firms. In our model, we assume that the two firms sell substitutable search products through a common platform. Therefore, the quality dimension plays a dominant role in determining consumers’ perceived utility differences between the two products. According to Eq. (5), if her perceived quality difference is higher than [(pA pB ) (1 2 ) t (1 )(xR + 1 eA 2 eB )]/ , she derives a higher net utility from product A; otherwise, she derives a higher net

(3)

2.3. The manipulation of online reviews Firms can manipulate online reviews to change the quality difference between the two products revealed by online reviews. This paper assumes that posting negative reviews about one’s competitor is qualitatively equivalent to posting positive reviews about oneself [13,14]. Therefore, this paper considers only the case in which firms manipulate 3

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Table 1 Summary of Notations. Notation

Definition and comments

i xi

Index for products/firms True quality of product i The degree of misfit between a consumer and product A Unit misfit cost Price of product i A consumer’s net utility derived from product i Firm i ’s manipulation effort The unit cost of manipulation A consumer’s perceived quality difference between products A and B in the absence of online reviews The quality difference between products A and B revealed by unmanipulated online reviews The weight assigned to consumers’ own assessments of the quality difference in the absence of manipulation The weight assigned to consumers’ own assessments of the quality difference in the presence of manipulation Demand for product i Demand for product i with no firm manipulation Firm i ’s profit with no firm manipulation Demand for product i with manipulation by only the inferior firm Firm i ’s profit with manipulation by only the inferior firm Demand for product i with manipulation by only the superior firm Firm i ’s profit with manipulation by only the superior firm Demand for product i with manipulation by both firms Firm i ’s profit with manipulation by both firms

t pi Vi ei µ xC xR C

M

Di DiN iN

DiI iI

DiS iS

DiB iB

1 0

1 [(pA pB ) (1 2 ) t (1

1 [p 2 A 1

DB =

0

pB

)(xR + 1 eA

(1

)(xR +

[(pA pB ) (1 2 ) t (1

2 eB )]

)(xR + 1 eA

1

1 + [p 2 A

pB

(1

)(xR +

1 eA

DBN

1 1 = + [p 2 2C A

pB pB

(1 (1

pi

iN

= =

C ) xR

3

(3

+ (1

C

C ) xR )

18 (3

2

C

(1 18

C

1 2

DAI = DBI =

C ) xR)

2

C

1

[pA

pB

(1

M )(xR

eB )]

1 1 + [p 2 2M A

pB

(1

M )(xR

eB )]

2

M

In stage 2 of the game, the firms maximize their profits by choosing the optimal prices and the optimal manipulation effort; that is,

max

AI

=pA DAI

max

BI

=pB DBI

pA

pB , eB

(8)

µeB2

On the basis of the first-order conditions, the equilibrium manipulation effort for the inferior firm and the equilibrium price for each firm are obtained. The following lemma summarizes the equilibrium )2

(1

2 eB )]

(6)

Lemma 2. When only the inferior firm manipulates online reviews, the equilibrium prices, the equilibrium manipulation effort for the inferior firm, and the seller profits are as follows when µ >

0

xR <

3 M 1

:

M

(1

M)

6M

2

and

(a) Prices:

C ) xR]

* pAI =2

C ) xR]

* pBI

=pi DiN

3

outcomes. Notice that the conditions µ > 6 M and 0 xR < 1 M are M M to ensure that both firms play a role in the equilibrium, and that the inferior firm that manipulates online reviews cannot drive the superior firm out of the market.

1 1 dxd = 2 2

In stage 2 of the game, the firms maximize their profits by choosing the optimal prices; that is,

max

(1

In the scenario with only the inferior firm’s manipulation, from Eq. (6), we know the demand for each product is

In the scenario with no firm manipulation, from Eq. (6), we know that the demand for each product is

1 [p 2C A

C ) xR

3

3.2. Manipulation by only the inferior firm

3.1. Benchmark (no firm manipulation)

1 2

(1

+

Proof: All proofs are in the Appendix.

3. The impact of manipulation by only the inferior firm

DAN =

C

* BN

2 eB )] 2 eB )]

* pBN =

* AN

1 1 dxd = 2 2

1 eA

C

(a) Seller profits:

utility from product B. Then, we can formulate the demand for each product as

DA =

* pAN =

=

12µ M

2 M

4µ

12µ

12µ

2 M

4µ

12µ

M

M (1

M ) xR 2 M)

M ) xR 2 M)

(1

M

M (1

(1

(a) Manipulation effort for the inferior firm: * eBI =

(7)

On the basis of the first-order conditions, the equilibrium price for each firm is botained. The following lemma summarizes the equili3 brium outcome. Note that the condition 0 xR < 1 C in the following C lemma is to ensure that both firms play a role in the equilibrium.

(1

M )(3 M

12µ

M

(1

M ) xR) 2 M)

(1

(a) Seller profits: * AI

Lemma 1. When no firms manipulate online reviews, the equilibrium 3 prices and seller profits are as follows when 0 xR < 1 C :

* BI

C

(a) Prices:

= =

2

M (2µ (1

M ) xR

(12µ µ (8µ

M

(1 (12µ

M M) M

+ 6µ

M

2)(3

(1

(1

M)

2)2

2 2 M) )

(1

(1

M M

M ) xR)

2

) 2) 2

Now this paper analyzes the manipulation decision of the inferior firm if the superior firm does not manipulate online reviews and the 4

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H. Cao

(1 eB ) ). The second source is the change in conto 2 C )(xR 2C sumers’ confidence in their own assessments. Therefore, under manipulation by only the inferior firm, relative to the scenario without considering the change in consumers’ confidence in their own assessments, the superior firm’s potential market size changes by 1 1 1 + 2 (1 eB ) (M eB ) (from to C )(xR C )(xR 2 2 1

1 2

1

C

C

+

1 2C

M )(xR 1 firm changes by 2 C 1 1 (1 M )(xR 2 2

eB ) ), and the potential market size of the inferior

(1

C

superior 1 [(1 2

(

firm’s M ) eB + (

C

C )(xR

M

eB ) (from

1 2

1 2C

(1

eB ) to

C )(xR

eB ) ). Overall, through the mean-shifting effect, the potential market size changes by M C ) xR], and the inferior firm’s potential

market size changes by 2 [(1 M ) eB + ( M C ) xR]. C Second, in evaluating the utility difference between the two products, each consumer combines her own assessment with the quality difference assessment revealed by online reviews. Under manipulation by only the inferior firm, the credibility of online reviews is reduced, and consumers’ confidence in their own assessments is increased. Because consumers’ own assessments follow a uniform distribution over [ 1,1] and the quality difference revealed by online reviews is common to all consumers, the manipulation by the inferior firm increases the heterogeneity of consumers' perceived quality difference, which means that the distribution of consumers' perceived quality difference between the two products is more diverse. This effect is called the variance-increasing effect (as shown in Fig. 2(b) and (d)). Mathematically, the su(1 M )( M C )(xR eB ) perior firm’s potential market size changes by 2

Fig. 1. Impact of manipulation by only the inferior firm on profits.

impact of manipulation by only the inferior firm on the superior firm. The results are summarized in the following proposition.

1

(from

(a) The inferior firm will always manipulate online reviews (i.e., * * BI > BN ); * (b) Both firms will be better off (i.e., iI* > iN ) compared to no firm manipulation if and only if

(1 eB ) ). (1 eB ) to 2 (from 2 M )(xR M )(xR 2 M 2C The intuitions of Proposition 1(a) are straightforward. The inferior firm largely benefits from the mean-shifting effect under the manipulation by only the inferior firm. When xR eB , which means that the quality difference revealed by unmanipulated online reviews is large, the inferior firm benefits from both the mean-shifting effect (i.e., 1 [(1 0 ) and the variance-increasing effect M ) eB + ( M C ) xR] 2

0

xR < min{x1, 36µ

3 1

C

1

} )

3

(2

)(1

C

)2

M C M C C M C M where x1 = 2 . 12µ ( M (1 C ) (1 M ) C M ) (1 C )(1 M) Proposition 1(a) shows that manipulating online reviews is always profitable for the inferior firm if the superior firm does not manipulate online reviews. Proposition 1(b) reveals that manipulation by only the inferior firm will not always hurt the superior firm’s profit. When xR is low (as shown in Fig. 1 Region 1), manipulation by only the inferior firm benefits not only the inferior firm but also the superior firm. When xR is relatively high (as shown in Fig. 1 Region 2), manipulation by only the inferior firm benefits only the inferior firm but hurts the superior firm. Under the manipulation of only the inferior firm, relative to the scenario with no firm manipulation, two things change. First, the inferior firm exerts manipulation efforts (i.e., eB > 0 ). Second, under manipulation by only the inferior firm, the credibility of online reviews is reduced, and a consumer places more weight on her own assessment and less weight on online reviews (i.e., from C to M ). These two changes generate two effects under manipulation by only the inferior firm. First, the manipulation by the inferior firm uniformly changes each consumer's perceived quality difference between the two products favorably toward the inferior firm. We call this the mean-shifting effect (as shown in Fig. 2(a) and (c)). Mathematically, the mean-shifting effect comes from two sources. The first source is the manipulation effort (i.e., eB ) by the inferior firm without considering the change in consumers’ confidence in their own assessments. Therefore, under manipulation by only the inferior firm, relative to the scenario with no firm manipulation, the superior firm’s potential market size changes by 1 1 1 1 1 (1 eB ) ), C ) eB (from 2 + 2 (1 C ) xR to 2 + 2 (1 C )(xR 2

C

C

and the inferior firm’s changes by

1 2C

C

(1

C ) eB

(from

1 2

1 2C

(1

+

1 2C

(1

M )(xR

1 2

+

1 2 M

(1

M )(xR

the inferior firm’s potential market changes by

C (

1 2

eB ) to

C M

Proposition 1. Suppose that the superior firm does not manipulate online reviews,

(1

1

1

)(

)(x

(1

eB ) ). However,

M )( M

C )(xR

eB )

2C M

1

e )

B M M C R 0 ). Therefore, the inferior firm will always (i.e., 2C M benefit from the manipulation by only the inferior firm. When xR < eB , which means that the quality difference revealed by unmanipulated online reviews is small, the inferior firm will benefit from the mean1 0 ), but will be hurt shifting effect (i.e., 2 [(1 M ) eB + ( M C ) xR] C

(1

)(

)(x

e )

B M M C R < 0 ). by the variance-increasing effect (i.e., 2C M However, the benefit from the mean-shifting effect will be stronger than the negative impact caused by the variance-increasing effect. This result occurs because, compared to the quality difference revealed by the unmanipulated online reviews (i.e., xR ), the changes in each consumer's perceived quality difference by the inferior firm’s manipulation (i.e., eB ) are greater. Therefore, overall, the inferior firm will always benefit if it is the only firm to use manipulation. The intuitions of Proposition 1(b) are as follows. Under manipulation by only the inferior firm, the superior firm will always suffer from the mean-shifting effect. By the variance-increasing effect, both firms will lose their high valuation consumers and gain more low valuation consumers (as shown in Fig. 1(b) and (d)). However, the gain of low valuation consumers for both the inferior firm and the superior firm is the same. Therefore, whether the superior firm could benefit from the variance-increasing effect depends on the relative reduction of high valuation consumers between the inferior firm and the superior firm. When xR eB , which means that mean-shifting effect caused by the inferior’s manipulation is small relative to the mean-shifting effect caused by the unmanipulated online reviews, the loss of high valuation consumers for the superior firm is greater than that for the inferior firm (1 M )( M C )(xR eB ) 0 ) (as shown in Fig. 1(d)). When xR < eB , (i.e., 2

C ) xR

C M

5

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Fig. 2. The mean-shifting effect and variance-increasing effect under manipulation by only the inferior firm (t= 0.2 , eB = 0.2 ,

which means mean-shifting effect caused by the inferior’s manipulation is largely relative to the mean-shifting effect caused by the unmanipulated online reviews, the loss of high valuation consumers for the superior firm is smaller than that for the inferior firm (i.e., (1 M )( M C )(xR eB ) > 0 ) (as shown in Fig. 1(b)). To make the benefit 2C M from the variance-increasing effect larger than the hurt from the meanshifting effect, xR must be sufficiently small. Therefore, in this case, when xR is low enough, the superior firm will be able to benefit from manipulation by only the inferior firm. Overall, combining the results from Proposition 1(a), it is straightforward that when xR is low enough, both firms will be better off under manipulation by only the inferior firm if the superior firm does not manipulate online reviews.

DBS =

1 2

M

[pA

pB

(1

max

AS

=pA DAS

max

BS

=pB DBS

pA , eA

pB

(1

M )(xR

M

= 0.7 ).

+ eA)]

µeA2

(9)

On the basis of the first-order conditions, the equilibrium manipulation effort for the superior firm and the equilibrium price for each firm are obtained. The following lemma summarizes the equilibrium outcome.

Note

2 6µ M (1 M) 2µ (1 M)

0 xR < equilibrium.

In the scenario with manipulation by only the superior firm, from Eq. (6), we know the demand for each product is

1 2

pB

= 0.5,

In stage 2 of the game, the firms maximize their profits by choosing the optimal prices and optimal manipulation efforts; that is,

4. The impact of manipulation by only the superior firm

DAS =

1 1 + [p 2 2M A

C

that

the

conditions

µ>

(1

M)

2

and

6M

are to ensure that both firms play a role in the

Lemma 3. When only the superior firm manipulates online reviews, the equilibrium prices, the equilibrium manipulation effort for the superior

M )(xR + eA)]

firm, and the seller profits are as follows when µ > 6

(1

M)

6M

2

and

Information & Management xxx (xxxx) xxxx

H. Cao

0

xR <

(1 (1 C ) xR to 2 M )(xR + eA ) ). By the variance-in2C creasing effect (as shown in Fig. 4(b) and (d)), the superior firm’s po(M C )(1 M )(xR + eA) tential market size changes by (from 2 1 2

2 6µ M (1 M) : 2µ (1 M)

(a) Prices: * pAS =

12µ

2 M

+ 4µ

12µ

* pBS =2

M (1

(1

M

2 M

12µ M

M)

+ 4µ

12µ

1 2

M ) xR

M (1

(1

M )(3 M

12µ

+ (1 (1

M

M)

M ) xR 2

M)

M ) xR) 2

(a) Seller profits: * AS * BS

= =

µ (8µ

(1

M

M)

(12µ 2

M (2µ (1

2)(3

(12µ

+ (1

M

(1

M

M ) xR

M

6µ

M ) xR)

M

2

) 2) 2

+ (1

M

(1

M

M)

2) 2

)2)2

Now this paper analyzes the manipulation decision of the superior firm, if the inferior firm does not manipulate online reviews, and the impact of manipulation by only the superior firm on the inferior firm. The results are summarized in the following proposition. Proposition 2. Suppose that the inferior firm does not manipulate online reviews, (a) The superior firm will manipulate online reviews (i.e., only if

0

xR < min {x2 ,

3

C

1

6µ

,

(1

M

M)

2µ (1

C

max{

(1

M)

6

2

,

M

(1 12(

2

M)

(a) Both firms will be better off (i.e., ulation if and only if

µ

* iS

C)

* iN )

M)

(1

* AS

>

* AN )

if and

}

>

C )(1

M (1

compared to no manip-

2

M)

C M)

}

and

max{0, x3} < xR < min{x2 , where

x2 =

3

C

1

36µ M C ( M C) 12( M (1 C ) (1 M)

6µ

2 M) )

(1

(1

C )(1 C )(1

(1

M

2µ (1

2 M) )

C )(12µ M (1 3 C (2 M C M ) + (1

, C

3 M 18µ C (8µ M (1

M) 2

M)

2

M) M)

3 C (12µ M

2

}

(1

M ) 18µ C (8µ M

2 M) )

(1

2 M) )

,

+

1 2C

(1

C ) xR

to

1 2

+

1 2C

C

(1

potential market size changes

(1

M )(xR

+ eA ) to

1 2

+

1 2 M

C M

(1

M )(xR

( M

C )(1

M )(xR + eA)

2C M

1 2

1 2C

1

(from

In the scenario with manipulation by both firms, from Eq. (6), we know the demand for each product is

.

M )(xR + eA ) ), and 1 by 2 [( M C ) xR C

+ eA) ), and the inferior

5. The impact of manipulation by both firms

x3 =

Proposition 2(a) shows that manipulation by only the superior firm is profitable for the superior firm when the quality difference between the two products revealed by unmanipulated online reviews slightly favors product A. Proposition 2(b) reveals that manipulation by only the superior firm will not always hurt the profit of the inferior firm. When µ is large and xR is moderate (as shown in Fig. 3 Region 1), manipulation by only the superior firm benefits not only the superior firm but also the inferior firm. When µ is small and xR is small (as shown in Fig. 3 Region 2), manipulation by only the superior firm only benefits the superior firm. When xR is large (as shown in Fig. 3 Region 3), manipulation by only the superior firm benefits only the inferior firm. Under manipulation by only the superior firm, by the mean-shifting effect (as shown in Fig. 4(a) and (c)), the superior firm’s potential 1 (M market size changes by 2 [(1 (from M ) eA C ) xR] 1 2

1 2C

1

(1 (1 M )(xR + eA) ). M )(xR + eA ) to 2 M The intuitions of Proposition 2(a) are as follows. Under manipulation by only the superior firm, the superior firm always suffers from the (M C )(1 M )(xR + eA ) < 0 ) (as shown in variance-increasing effect (i.e., 2C M Fig. 4(b) and (d)). This is because, with the quality difference between the two products revealed by unmanipulated online reviews toward product A and the manipulation by only the superior firm, the loss of high valuation consumers for the superior firm is greater than that for the inferior firm. Then, whether the superior firm can benefit from the manipulation by only the superior firm depends on the mean-shifting effect. As mentioned in the previous section, the mean-shifting effect comes from two sources: the manipulation effort (i.e., eA ) by the superior firm and the change in consumers’ confidence in their own assessments. However, combining these two sources, the superior firm can either benefit or suffer from the mean-shifting effect. When (1 M ) eA xR < , the superior firm can benefit from the mean-shifting efM C fect. Therefore, only when xR is low enough will the superior firm benefit from manipulation under manipulation by only the superior firm. The intuitions of Proposition 2(b) are as follows. First, for the inferior firm to benefit from manipulation by the superior firm, µ cannot be too small. This is because we know that the manipulation effort by * the superior firm (i.e., eAS ) decreases with the unit cost of manipulation * (i.e., µ ). Therefore, when µ is small, eAS will be extremely high. Then, the profit for the inferior firm will decrease dramatically due to the mean-shifting effect that largely benefits the superior firm. Second, for the inferior firm to benefit from the superior firm’s manipulation, xR cannot be too low. Under manipulation by only the superior firm, the inferior firm will always benefit from the variance-increasing effect ( )(1 )(x + e ) (i.e., M C 2 M R A > 0 ) (as shown in Fig. 4(b) and (d)). FurtherC M more, the inferior firm will benefit from the mean-shifting effect when (1 M ) eA xR . Therefore, under manipulation by only the superior firm, M C the inferior firm will be better off only when xR is not too low. By combining the results from Proposition 2(a), it is clear that when µ is large and xR is moderate, both firms will be better off under manipulation by only the superior firm. 1 2

(a) Manipulation effort of the superior firm: * eAS =

+

1

firm’s potential market size changes by

2

(1

M

1 2C

DAB = DBB =

1 2

1

[pA

pB

(1

M )(xR

+ eA

eB )]

1 1 + [p 2 2M A

pB

(1

M )(xR

+ eA

eB )]

2

M

In stage 2 of the game, the firms maximize their profits by choosing the optimal prices and the optimal manipulation efforts; that is,

max

AB

=pA DAB

µeA2

max

BB

=pB DBB

µeB2

pA , eA

pB , eB

(10)

the inferior firm’s

On the basis of the first-order conditions, the equilibrium manipulation effort and the equilibrium price for each firm are obtained. The following lemma summarizes the equilibrium outcome.

(from

Lemma 4. When both firms manipulate online reviews, the equilibrium

(1

M ) eA]

7

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H. Cao

Fig. 3. Impact of manipulation by only the superior firm on profits.

Fig. 4. The mean-shifting effect and variance-increasing effect under manipulation by only the superior firm (t= 0.2 , eA = 0.2 , 8

C

= 0.5,

M

= 0.7 ).

Information & Management xxx (xxxx) xxxx

H. Cao

prices, the equilibrium manipulation efforts, and the seller profits are as follows: Conditions (1

µ>

M) 6 M

0

µ=

2

and

xR <

(1

M) 6 M

0

2

8 M

0

2 6µ M (1 M) 2µ (1 M)

and 3 M

xR <

2 M)

(1

Prices

1

<µ< xR <

M 2 M)

(1

6 M

(1

M) 2µ (1

2

Manipulation efforts

* pAB =

M

* pBB =

M

* pAB =

M

* pBB =

M

and

* pAB

=

M

6µ M

* pBB =

M

M)

always lower than that of the inferior firm. In this case, the intuition is similar to the scenario with manipulation by only the inferior firm.

+

2µxR (1 M) M 2 6µ M (1 M) 2µxR (1 M) M 2 6µ M (1 M) (1

+

2µxR (1

M) M 2 6µ (1 M) M 2µxR (1 M) M 2 6µ (1 ) M M

+

(1

* eBB =

(1

(1

M)

8 M

when µ >

2

* eAB =

* eBB =

(1

M)

2

6 M

)2

)2

the (1

equilibrium

M)

2

when

2

8M

)2

(1

M)

(1

<µ

M)

2

6M

.

However,

(1

(b) µ = (c) min

{

M)

2

C)

,

(1

M) 6 M

and 0

and 0

x < min { 1

R 6M 2 2 (1 (1 M) M) , 6 8( M C) M

an d 0

2

}

xR < min {x5 ,

<µ<

(1

M)

2µ (1

2

xR < min {x 4 , 3C

(1

M

C M

1+

C M

(1

=

M

when

(1

M)

6M

2

, in Region 2 when )2

(1

(1

M)

2

M

};

M)

8M

2

<µ<

(1

M)

6M

2

=

* BB

=

(1

M)

2

6M

M ))

2 M ) + 2µxR (1 22 M) )

M ))

2 2µx (1 R M) 22 M) )

M ))

2

(8µ M

(8µ M

(1

(1

2 M ) )(6µ M 16µ (6µ M

(1

2 M ) )(6µ M 16µ (6µ M

(1

(1

(1

2

2

, both firms will be better off if xR is small )2

C

1 2

1 2C

1 2C

1 2C

C

M

1 2

1 2C

(M

[(

C ) xR]

M

C )(1

M ) xR

2C M

1

+

(1

M ) xR

3

xR ) 3

C )(1

M

(from

(from

C

+

(1

C ) xR

to

3

), which decreases with xR , and the price for the inferior (1

x

(1

M)

2

6 M

(1

)x

)x

, both firms implement the same level of manip-

* * = eBB = ulation effort (i.e., eAB

<µ<

2 2µx (1 R M) 22 M) )

2

2 (3 M + (1 M ) xR ) 18 M 2 (3 M (1 M ) xR) 18 M

C

(a) when µ >

(1

(1

M ))

Corollary 1. Under manipulation by both firms, in the presence of the symmetric quality revealed by unmanipulated online reviews (i.e., xR = 0 ),

2 M) )

.

(1

M)

6M

2

(1

when µ

max { 8(

(b) when µ =

(1

M)

6 M

2

M)

2

C)

M

,

(1

(1

M)

6M

2

M)

4µ

), but both firms are better off

};

, both firms implement the same level of manip-

* * = eBB = 0 ), but both firms are better off; ulation effort (i.e., eAB

(c) when

, and along

(1

M)

8M

2

<µ<

(1

M)

6M

2

, both firms implement the same level of

* * = eBB = manipulation effort (i.e., eAB

Line 1 when µ = 6 M . M The intuitions of Proposition 3 are as follows. First, when (1

* AB

(1

2 M ) + 2µxR (1 22 M) )

R C R M R to M ), firm increases by ( M C )(1 + 3 ) (from C 3 3 which increases with xR . Therefore, for both firms to benefit from the scenario in which both firms use manipulation, xR must be sufficiently small. Now this paper turns to the symmetric case with xR = 0 . xR = 0 means that the quality difference revealed by unmanipulated online reviews is symmetric to firms. The following corollary summarizes the interesting results in the symmetric case with xR = 0 .

2 6µ M (1 3 M) , 1 C }; 2µ (1 M) C

8µ

8 M

=

2 M ) )(6µ M 16µ (6µ M

(1

)2

perior firm increases by (

Proposition 3 implies that both firms could be better off under manipulation by both firms than when no firm manipulates online reviews (as shown in Fig. 5). In Fig. 5, both firms are better off in Region 1 when µ >

* BB

(1

(1 (1 M ) xR ). In this case, the changes in M ) xR to 2 M demands cannot dominate the results. As the confidence in the consumers’ own assessments increases from C to M , the price for the su1 2

, )2)

9(8µ M

M 6µ M )

2C M

6 M

1)

2

=

(1

2 M ) )(6µ M 16µ (6µ M

inferior firm’s potential market size decreases by

6µ M 3 , 1 C }; M) C

(6µ M (1 M C 2µ (1 (1 C )(6µ M M) 2 6µ )(1 3 ((1 ) M) M C x5 = , 2 6µ ) 2µ (1 (1 C )((1 M) M) M

M)

6µ M ) )2

* AB

(8µ M

(1

(1 (1 (from M ) xR ). Through the varianceC ) xR to increasing effect, the superior firm’s potential market size increases by 1 1 1 1 (M C )(1 M ) xR (1 (from 2 + 2 (1 M ) xR ), and the M ) xR to 2 + 2

)2

)2)(3

where x 4 =

3

,

C

xR (1 2((1

1 2

Proposition 3. When both firms manipulate online reviews in equilibrium, both firms are better off compared to when no firm manipulates online reviews when (1

+

2

=

C

M <µ , under manipulation by only the inferior firm, the 6M inferior firm drives the superior firm out of the market, and under manipulation by only the superior firm, the superior firm will drive the inferior firm out of the market (see Appendix). Now this paper analyzes the impact of manipulation by both firms on the superior firm and the inferior firm. The results are summarized in the following proposition.

8( M 2 M)

M) 4µ

M)

* BB

(8µ M

the inferior firm’s potential market size increases by

8M

(a) µ > max

2((1

=

(1

However, when µ = 6 M , both firms implement the same but zero M manipulation efforts. To understand this case, we could imagine a scenario in which firms claim that they manipulate online reviews but do not truly implement any efforts to manipulate. In doing so, they can still influence the credibility of online reviews and increase C to M . Third, under manipulation by both firms, both firms still play a role in (1

4µ

2 M)

* AB

enough. This is because when µ = 6 M , both firms will implement M the same but zero manipulation efforts (i.e., eA = eB = 0 ). Through the mean-shifting effect, the superior firm’s potential market size decreases 1 1 1 1 1 by 2 [( M C ) xR] (from 2 + 2 (1 M ) xR ), and C ) xR to 2 + 2 (1

than that of the inferior firm; when 8 M < µ < 6 M , the manipM M ulation effort of the inferior firm is higher than that of the superior firm. (1

xR (1

Second, when µ =

)2

(1

M)

(1

, the manipulation effort of the superior firm is higher (1

M)

2 xR (1 M) 2 2(6µ M (1 M) ) 2 xR (1 M) 2 2(6µ M (1 M) )

When µ > 6 M , the manipulation effort of the superior firm is alM ways higher than that of the inferior firm. In this case, the intuition is similar to the scenario with manipulation by only the superior firm.

ensures that both firms can make positive profits. Second,

(1

+

4µ

(1

There are three things to notice. First, the conditions of µ and xR ensure that both firms play a role in the equilibrium, and that either of the two firms can drive the other firm out of the market. The condition

µ>

M) 4µ

* * eAB = eBB =0

M ) xR 3 M ) xR 3

(1

* eAB =

Seller profits

better off when min

, the manipulation effort of the superior firm is

9

{

(1 8( M

2 M) C)

,

(1

2 M)

6 M

(1

M)

4µ

), but both firms are

}<µ<

(1

M)

6 M

2

.

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Fig. 5. Impact of manipulation by both firms on profits.

Corollary 1 reveals two interesting things about both firms’ manipulations of online reviews in the symmetric case with xR = 0 . First, we notice that in the symmetric case with xR = 0 , both firms will always implement the same level of manipulation effort. This is because both firms try to eliminate the mean-shifting effect to maximize their own profit. Second, even though both firms will always implement the same level of manipulation effort and the manipulation efforts of both firms will cancel out, both firms could still be better off in the symmetric case with xR = 0 .

reduce the damage brought by the inferior firm’s manipulation on the mean-shifting effect. Therefore, the best strategy for both firms is to always manipulate online reviews simultaneously. From this result, we can see that the motivations for the inferior firm and for the superior firm to manipulate online reviews are very different. For the inferior firm, the motivation to manipulate online reviews is to improve its profit. However, for the superior firm, the motivation to manipulate online reviews is to reduce the damage caused by the manipulation by the inferior firm. In many cases, the equilibrium is not necessarily Pareto optimal because there are some nonequilibrium outcomes of the game that would be better for both firms. The following corollary provides the condition under which the firms are caught in the prisoner’s dilemma, in which each firm chooses to manipulate online reviews, even though no manipulation of online reviews would generate higher profits for both firms.

6. Firms’ manipulation decisions In this part, this paper analyzes the market equilibrium if firms are free to choose whether to manipulate online reviews. Proposition 4 summarizes the market equilibrium when µ >

(1

M)

8M

2

.

Proposition 4. (Firms’ Manipulation Decisions) If firms are able to choose whether to manipulate online reviews, both firms will always choose to manipulate online reviews.

Corollary 2. (Prisoner’s Dilemma) When both firms choose to manipulate online reviews in equilibrium, both firms will enjoy higher profits when both do not manipulate online reviews when

Proposition 4 reveals that if both firms are free to choose whether to manipulate online reviews or not, both firms will manipulate online reviews. First, when the unit cost of manipulation is relatively small

(a)

(1

(b)

(1

(1

M)

2

(1

)2

M <µ (i.e., 8 ), if the inferior firm manipulates online re6M M views, the superior firm will also manipulate online reviews. This is because if the superior firm does not manipulate online reviews and the inferior firm does manipulate online reviews, the superior firm will be driven out of the market. For the same reason, if the superior firm manipulates online reviews, the inferior firm will also manipulate online reviews.

(1

M)

6 M M)

8 M

in { x 7 ,

2 2

<µ<

(1

M)

8( M

< µ < min

{

2

C)

an d 0

(1

M)

2

8( M C) 2 6µ (1 3C M) M , } ; 2µ (1 1 C M) (6µ M

where x 6 =

(1

(1

M)

6 M

2 M ) )(3 C 2 M) )

(1 C )(6µ M (1 2 6µ )(3 ((1 1) M) M C 2 6µ ) + 2µ (1 (1 C )((1 M) M

x7 =

,

xR < min {x 6 ,

M)

2

}

2 6µ M (1 3 M) , 1 C }; 2µ (1 M) C

and

1) 2µ (1

M)

0

xR < m

,

.

Corollary 2 implies that in some cases, online reviews are overmanipulated, and both firms will be better off when no firm manipulates online reviews (as shown in Fig. 6). In Fig. 6, the prisoner’s di-

)2

Second, when the unit cost is high (i.e., µ > 6 M ), regardless of M whether the superior firm chooses to manipulate online reviews or not, it is always profitable for the inferior firm to manipulate online reviews. This is because the inferior firm can largely benefit from the meanshifting effect by choosing to manipulate online reviews. This result is consistent with the research of Luca & Zervas [10], who showed that firms with low reputations are more likely to engage in online review manipulation because they can easily improve their profits by manipulation. When the inferior firm chooses to manipulate online reviews, it is also always profitable for the superior firm to manipulate online reviews. If the superior firm chooses to manipulate online reviews under manipulation by only the inferior firm, the superior firm can always

lemma exists in Region 3 when µ > (1

M)

2

(1

M)

2

(1

M)

6M

2

and in Region 4 when

<µ< 6 . Moreover, from Fig. 6(a) and (b), we can see 8 M M that, overall, when the unit cost of manipulation is small, both firms are more likely to be caught in the prisoner’s dilemma than they are when the unit cost is large. From each firm’s perspective, it is easier to manipulate online reviews at a low cost of manipulation. However, when both firms choose to manipulate online reviews in this case, the benefits from the mean-shifting effect for each firm would be reduced. Therefore, the benefits from manipulating online reviews are not as 10

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H. Cao

Fig. 6. Prisoner’s dilemma.

effect under manipulation by the inferior firm. Third, this paper also identifies two interesting special cases. When unmanipulated online reviews are symmetric for both firms, both firms could still be better off under manipulation by both firms compared to the scenario with no firm manipulation, even though the manipulation efforts of both firms will cancel out. This result occurs because both firms still have a chance to benefit from the variance-increasing effect. Moreover, if firms are free to choose whether to manipulate online reviews, there is a prisoner’s dilemma in which online reviews are overmanipulated, which means that both firms choose to manipulate online reviews even though no firm manipulation would generate higher profits for both firms. The results of this paper have several interesting implications for practice. First, the manipulation of online reviews is a useful tool to reduce the credibility of online reviews and, as a result, it increases uncertainty about products and firms when shopping online. Without online reviews, consumers face significant uncertainty about products and firms, which is also known as the “lemon market” [27]. With online reviews, the uncertainty between firms and consumers is significantly reduced. However, in a competitive market, reduced uncertainty is not always a good thing for firms. Second, contrary to intuition, this analysis of this paper shows that one firm’s manipulation is not necessary to hurt its competitor’s profit. Therefore, when a firm observes its competitor’s manipulation of online reviews, it does not necessarily rush into manipulation, and it may be better off because of its competitor’s manipulation. Third, the results show that both firms could still be better off under manipulation by both firms when unmanipulated online reviews are symmetric for both firms. Thus, even though the unmanipulated online reviews do not suggest any quality difference between the two products, firms can still adopt an online review manipulation strategy to increase their profits. Finally, the results also show that there is a prisoner’s dilemma in which online reviews are overmanipulated. Such a prisoner’s dilemma is more likely to exist when the unit cost of manipulation is relatively low. Thus, firms should be careful when deciding to manipulate online reviews in cases where the unit cost of manipulation is low. There are several promising directions for future research. First, this paper analyzes two competing firms that sell products on a common platform. However, we do not consider the role of the platform in our model. Many platforms, such as Yelp, adopt filtering systems to detect

significant as each firm’s expectations. 7. Conclusions Online reviews have a significant influence on consumers, which stimulates firms to manipulate online reviews to promote their own products. This paper offers an analytical model to systematically explore the impact of online review manipulation on asymmetric firms in a competing market. The principal results can be summarized as follows: First, this paper concludes that, counterintuitively, a firm’s manipulation of online reviews is not necessary to hurt its competitor’s profit regardless of scenarios (i.e., with manipulation by only the inferior firm, with manipulation by only the superior firm, or with manipulation by both firms). Intuitively, we believe that a firm’s manipulation of online reviews will hurt its competitor’s profit. However, the findings of this paper suggest that this is not always the case. In this paper, the manipulation of online reviews has two effects: the mean-shifting effect and the variance-increasing effect. One firm’s manipulation effort or one firm’s higher manipulation effort may or may not hurt its competitor by the mean-shifting effect. However, its competitor can benefit from the variance-increasing effect. This result occurs because manipulation reduces the credibility of online reviews, and consumers therefore place more weight on their own assessment. As a result, the distribution of consumers’ evaluations of products is more heterogeneous. Therefore, its competitor may benefit from the increased heterogeneity of consumers’ evaluations of products by acquiring more consumers, charging higher prices, or both. Second, if firms are free to choose whether to manipulate online reviews, both firms will choose to manipulate online reviews. When the unit cost of manipulation is small, either firm’s manipulation of online reviews will drive the other firm out of the market. When the unit cost of manipulation is high, for the inferior firm, it is always better to manipulate online reviews regardless of whether the superior firm chooses to manipulate or not. This result occurs because the inferior firm always benefits from the mean-shifting effect under manipulations compared to a scenario with no firm manipulation. For the superior firm, it is always better to manipulate online reviews when the inferior firm uses manipulation. This effect occurs because by manipulating, the superior firm reduces the damage caused to it by the mean-shifting 11

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H. Cao

fake online reviews [10]. It would be an interesting research question to consider the incentives of platforms to launch such filtering systems. Second, in this paper, we do not specify the types of online reviews, and generally assume that firms manipulate online reviews to improve the quality revealed by online reviews. However, different types of online reviews (i.e., third-party online reviews and first-party online reviews) have different impacts on consumers. Manipulation of different types of online reviews may have different influences on firms’ profits. Finally, this paper looks at single-period settings, and we assume that manipulation will reduce the overall credibility of online reviews. However, the manipulation of online reviews may have other impacts on consumers. For example, in the long run, manipulation runs the risk of being seen by consumers as having dire consequences for a firm’s reputation. The study of online review manipulation in multiperiod

settings is also an intriguing research topic worthy of further study. CRediT authorship contribution statement Huanhuan Cao: Conceptualization, Methodology, Software, Formal analysis, Writing-original draft, Writing-review & editing, Visualization, Supervision, Project administration, Funding acquisition. Acknowledgments This research was funded by the National Natural Science Foundation of China (Grant Nos. 71701184, 71702167, and 71572184) and Zhejiang Provincial Natural Science Foundation (Grant No. LY19G020011).

Appendix A A.1 Proof of Lemma 1 Proof: Firm's optimization problem is characterized by the first-order conditions of Eq. (7): AN

pA BN

pB

2pA + pB + (1 2C

=

=

pA

2pB

C ) xR

(1 2C

C ) xR

+

+

C

C

=0

=0

Based on these equations, the equilibrium is derived as follows: * pAN =

C

* pBN =

C

+

(1

C ) xR

3 (1

C ) xR

3

This paper is interested in cases where both firms play a role in the equilibrium. Therefore, the condition 0 xR < equilibrium prices are positive. Substituting the equilibrium prices into Eq. (7), the equilibrium profits are derived. □

3C 1

C

is to ensure that the

A.2 Proof of Lemma 2 Proof: Firm's optimization problem is characterized by the first-order conditions of Eq. (8): AI

pA BI

pB BI

eB

2pA + pB + (1

=

=

=

M ) xR

2

pA

2pB

(1

M ) xR

2

pB (1 2

M)

(1

M ) eB

+

M

=0

M

+ (1

M ) eB

+

M

=0

M

2µeB = 0

M

Based on these equations, the equilibrium is derived as follows: * pAI =2 * pBI

* eBI =

= (1

12µ M

2 M

4µ

12µ

12µ

2 M

12µ

4µ M

(1

M )(3 M

12µ

M

M

M (1

(1

M (1

M ) xR 2 M)

(1 M ) xR 2 M)

M ) xR) 2 M)

(1

This paper is interested in cases where both firms play a role in the equilibrium and both firms can make a positive profit. Therefore, µ and xR )2

(1

3

need to satisfy conditions µ > 6 M and 0 xR < 1 M . Substituting the equilibrium prices and the equilibrium manipulation effort of the inferior M M firm into Eq. (8), the equilibrium profits are derived. (1

)2

)2

(1

M Notice that when 8 M < µ , the inferior firm can still make positive profit but the superior firm will be driven out of market by the 6M M inferior firm. Therefore, in this case, the demand of the superior firm is zero and the demand of the inferior firm is one. Then, the optimal price of the

inferior firm is derived as (1

M)

(

1

M

2µ

xR

)

M

and the optimal effort of the inferior firm as

superior firm is zero and the equilibrium profit for the inferior firm is (1 12

M)

(

1

M

2µ

xR

)

M.

1

M

2µ

. As a result, the equilibrium profit for the

This paper considers this case only in Section 7.

Information & Management xxx (xxxx) xxxx

H. Cao

A.3 Proof of Proposition 1 Proof: (a) Suppose that the superior firm does not manipulate online reviews, the inferior firm will always manipulate online reviews only if )2

(1

3

6µ

> BN . The conditions µ> 6 M and 0 xR < min{ 1 C , 2Mµ (1 C M with the manipulation by only the inferior firm are comparable. BI

)2

(1

3

6µ

(1

M)

2

M)

} are to ensure the scenario with no firm manipulation and the scenario

)2

(1

M } , we know that BI is always higher than BN . Therefore, suppose that the Under the conditions µ > 6 M and 0 xR < min{ 1 C , 2Mµ (1 C M) M superior firm does not manipulate online reviews, then the inferior firm will always manipulate online reviews. (b) Under the manipulation by only the inferior firm, both firms will be better off only if BI > BN and AI > AN . From Proposition 2(a), BI is

always higher than

0

xR < min{x3 ,

BN .

Therefore, this paper only needs to consider

2 6µ M (1 3 M) , 1 C }. 2µ (1 M) C

(2

The condition µ >

C )(1

M

12 M (

only the inferior firm, both firms will be better off when 0

2 M)

We can derive that

AI

>

AN

when µ >

(2

C )(1

M

12 M (

M)

2

C)

M

and

is to ensure x3 is larger than zero. Therefore, under the manipulation by

C)

M

AN .

>

AI

xR < min{x3 ,

2 6µ M (1 3 M) , 1 C }. 2µ (1 M) C

Notice that the results in Proposition 1 still hold in the extreme case when µ=

. When µ=

* = , from eBI

(1

M )(3 M

12µ M

(1 (1

M ) xR) , 2

M)

we know that the

manipulation effort of the inferior firm will be extremely small, which is approaching zero. Therefore, taking the manipulation effort and the unit cost of manipulation into consideration, the inferior firm may still benefit from the manipulation by only the inferior firm. □ A.4 Proof of Lemma 3 Proof: Firm's optimization problem is characterized by the first-order conditions of Eq. (9): AS

AS

BS

2pA + pB + (1

M ) xR

2

pA (1

=

eA pB

eA

=

pA

M)

2

eA)

M

=0

2µeA = 0

M

pA

=

+ (1

M

2pB

eA (1

M)

2

(1

M ) xR

+

M

=0

M

Based on these equations, the equilibrium is derived as follows: * pAS = * pBS

12µ

+ 4µ

12µ

=2

* eAS =

2 M

M

2 M

12µ M

(1

M (1

+ 4µ

12µ M )(3 M

12µ

M ) xR 2 M)

(1

(1

M

+ (1

M

M ) xR )2

M ) xR) 2 M)

(1

M

M (1

This paper is interested in cases where both firms play a role in the equilibrium and both firms can make a positive profit. Therefore, µ and xR )2

(1

6µ

)2

(1

M need to satisfy conditions µ > 6 M and 0 xR < 2Mµ (1 . Substituting the equilibrium prices and the equilibrium manipulation effort for the M M) superior firm into Eq. (9), the equilibrium profits are derived.

)2

(1

)2

(1

M Notice that when 8 M < µ , the superior firm can still make a positive profit by manipulating, but the inferior firm will be driven out 6M M of market. Thus, the demand of the inferior firm is zero and the demand of the superior firm is one. The optimal price of the superior firm is derived

as (1

M)

(x

R

+

1

M

2µ

)

M

and the optimal effort of the superior firm as

the equilibrium profit for the superior firm is (1

M)

(x

1

+

R

M

2µ

)

1

M

2µ

M .This

. As a result, the equilibrium profit for the inferior firm is zero and

paper considers this case only in Section 7. □

A.5 Proof of Proposition 2 Proof: (a) Suppose that the inferior firm does not manipulate online reviews, the superior firm will manipulate online reviews only if )2

(1

3

6µ

The conditions µ > 6 M and 0 xR < min { 1 C , 2Mµ (1 C M manipulation by only the superior firm are comparable. Under the conditions µ >

(1

M)

2

and 0

6M

(1

xR < min { 1

M)

M)

3C C

,

2

2 6µ M (1 M) } 2µ (1 M)

and solving

AS

>

AN ,

0

2 6µ M (1 M) }. 2µ (1 M)

xR < min {x1, 1 , C (b) Under the manipulation by only the superior firm, both firms will be better off only if

already know that and 0

xR < min{ 1

AS 3C

and xR > x2 ; (2) µ >

µ > max{

(1

2 M)

6M

,

C

is higher than

,

(2

2 6µ M (1 M) } 2µ (1 M) 2 M C )(1 M)

12 M ( M (1 C )(1

12( M (1

AN

C)

(1

C) 2 M) M)

when µ >

and solving

(1

BS

M)

6M

>

2

and 0

BN ,

AN .

we have xR < x1. Therefore, suppose that the

inferior firm does not manipulate online reviews, then the superior firm will manipulate online reviews when µ > 3C

>

AS

} are to ensure that the scenario with no firm manipulation and the scenario with the

xR < min{x1,

3C

1

C

,

AS > AN and BS > BN . 2 6µ M (1 M) } . Moreover, under 2µ (1 M) 2 2 (1 (1 C )(1 M) M)

we have two cases: (1) max{

6M

,

12( M (1

C)

(1

M)

(1

M)

2

6M

and

From Proposition 3(a), we the conditions µ >

C M)

} <µ<

(2

M

12 M (

(1

C )(1 M

M)

6M M)

2

2

C)

and xR > 0 . Therefore, under the manipulation by only the superior firm, both firms will be better off when

C M)

} and max{0, x2 } < xR < min{x1,

3C 1

13

C

,

2 6µ M (1 M) }. 2µ (1 M)

Information & Management xxx (xxxx) xxxx

H. Cao

Notice that the results in Proposition 2 still hold in the extreme case when µ=

. When µ=

* = , from eAS

(1

M )(3 M + (1

12µ M

(1

M ) xR) , 2

M)

we know that the

manipulation effort of the superior firm will be extremely small, which is approaching zero. Therefore, taking the manipulation effort and the unit cost of manipulation into consideration, the superior firm may still benefit from the manipulation by only the superior firm. □ A.6 Proof of Lemma 4 Proof: Firm's optimization problem is characterized by the first-order conditions of Eq. (10): AB

pA AB

eA BB

pB BI

eB

2pA + pB + (xR + eA

=

=

=

=

2 pA (1 2 pA

M)

M)

+

M

=0

2µeA = 0

M

2pB

pB (1 2

eB )(1

M

(xR + eA eB )(1 2C

M)

M)

+

M

=0

2µeB = 0

M

Based on these equations, the equilibrium is derived as follows:

2µxR (1 6µ M (1 2µxR (1

* pAB =

M

* pBB =

M

6µ

(1

M)

* eAB = * eBB =

+

(1

M)

+

2

M) M

(1

M

4µ

M) M

M)

2

xR (1 2(6µ

M)

M)

(1

M

xR (1

4µ

2(6µ

2 M)

M

(1

M

2)

)2 M)

2)

This paper is interested in cases where both firms play a role in the equilibrium and both firms can make a positive profit. Thus, there are three )2

(1

cases. The first case is when µ > 6 M and 0 M Eq. (10), the equilibrium profits are derived. The second case is when

(1

M)

2

8M

<µ<

(1

xR < M)

2

6M

2 6µ M (1 M) . 2µ (1 M)

and 0

xR <

Substituting the equilibrium prices and the equilibrium manipulation efforts into

(1

M)

2µ (1

2

6µ M M)

. Substituting the equilibrium prices and the equilibrium manipulation (1

efforts into Eq. (10), the equilibrium profits are derived. Note that when µ (1

M)

M)

2

8 M

2

, both firms cannot make a positive profit from manipulation.

The third case is when µ = 6 . In this case, if both firms implement manipulation efforts, they will implement the same manipulation efforts. M As a result, their manipulation efforts are cancelled out, but they need to pay for their manipulation effort. Therefore, the best response for both firms is to implement zero manipulation effort. The equilibrium prices and profits for both firms are derived by replacing C with M in the scenario with no firm manipulation. □ A.7 Proof of Proposition 3 Proof: Under the manipulation by both firms, both firms are better off only if different values of µ . The first case is when µ >

0

xR < min{x 4 ,

3C 1

C

,

xR < min {x5 ,

3C 1

M)

C

,

M)

2µ (1 (1

The third case is when µ =

2

6µ M M) 2 M)

6 M

. Solving

AB

>

and

AN

BB

BN ,

>

(1

M)

2

6M

. Solving

AB

>

AN

and

BB

µ>

M)

6 M

2

. Second, when µ=

, from

AN

and

BB

>

BN .

There are three cases with regard to

we can derive that when µ > max

BN ,

>

we can derive that when min

{

(1

M)

8( M

2

C)

{ ,

8( M

2 2 (1 M) M) 2) , 6 M C

(1

M)

(1

6 M

2

}<µ<

} (1

and

M)

2

6 M

} , both firms are better off.

. Solving

AB

>

AN

and

BB

>

BN ,

we can derive that when 0

better off. Notice that the results in Proposition 3 still hold in the extreme case when µ= (1

>

both firms are better off.

<µ<

8M (1

2

6 M

2 6µ M (1 M) }, 2µ (1 M) 2 (1 M)

The second case is when and 0

(1

AB

* eAB

=

(1

M)

4µ

+

xR (1

2(6µ M

M)

(1

2

* 2 and eBB M) )

=

xR < min { 1

. First, the case when µ=

(1

M)

4µ

xR (1

2(6µ M

M)

(1

2

2 , M) )

3C C

,

3 1+

C M C M

} , both firms are

only happens in the first case when

we know that the manipulation effort of the

superior firm and the manipulation effort of the inferior firm will be extremely small, which are approaching zero. Therefore, taking the manipulation effort and the unit cost of manipulation into consideration, the superior firm and the inferior firm may still benefit from the manipulation by only the inferior firm. □ A.8 Proof of Corollary 1 Proof: There are three cases with regard to different values of µ . 14

Information & Management xxx (xxxx) xxxx

H. Cao

The first case is when µ > * eAB * AB * AN

=

* eBB

(1

=

=

* BB

=

* BN

=

4µ 8µ M

2

(1

M)

M)

2

firms, * AB

=

* BB

2

=

* eBB

=

8µ M

,

=

(1

M)

2

(1

M)

* AB

(1

M)

=

* BB

2

(1

<µ<

8M

=

8µ M

(1 16µ

M)

2

* AN

>

* BN

=

C

=

2

, we can derive both firms are better off when

M)

2

. Substituting xR = 0 into the equilibrium manipulation efforts under the manipulation by both

6M

. In addition, substituting xR = 0 into the equilibrium profits under no firm manipulation, * BB

=

=

The third case is when µ = * AB

* BB

=

is immediately direvied. Substituting xR = 0 into the equilibrium profits under the manipulation by both firms,

4µ

2 M)

* AB

}.

6 M

(1 16µ

Therefore, solving both firms,

. Substituting xR = 0 into the equilibrium manipulation efforts under the manipulation by both firms,

is also immediately derived. Furthermore, substituting xR = 0 into the equilibrium profits under no firm manipulation,

The second case is when * eAB

2

is immediately derived. Substituting xR = 0 into the equilibrium profits under the manipulation by both firms,

(1 16µ

C)

M

M)

6 M

is also derived. Therefore, solving

C

=

µ > max{ 8(

M)

(1

M

=

2

8µ M

(1

2 M)

(1 16µ M

6 M

)2

* AN

>

=

* BN

. From Lemma 4,

C

=

2

* eAB

=

, both firms are better off when min * eBB

{

2 M)

(1 8( M

C)

,

(1

2 M)

6 M

* AN

* BN

=

}<µ<

is also derived.

C

=

2

2 M)

(1

.

6M

= 0 . Substituting xR = 0 into the equilibrium profits under the manipulation by

is derived. Furthermore, substituting xR = 0 into the equilibrium profits under no firm manipulation,

also derived. Therefore, both firms are always better off because

* AB

* BB

=

=

M

2

>

* AN

* BN

=

C

=

2

* AN

.□

=

* BN

=

C

2

is

A.9 Proof of Proposition 4 Proof: We summarize 4 scenarios in the following Table. Firm A’s manipulation decision

Firm B’s manipulation decision

Firm B manipulates Firm B does not

With regard to different values of µ , we have two cases. )2

(1

1

6µ

Firm A manipulates

Firm A does not

( (

( (

AB ,

AS ,

BB )

BS )

AI ,

AN ,

BI )

BN )

)2

(1

M M } . In this case, if firm A does not manipulate online reviews, firm B’s The first subcase is when µ > 6 M and 0 xR < min { 3 C , 2µ (1 C M) M best response is to manipulate online reviews. This is because that BI is always higher than BN in this case. If firm A manipulates online reviews, firm B’s best response is also to manipulate online reviews because of the fact that BB is always larger than BS . Then, this paper checks firm A’s best response to firm B’s manipulation. If firm B manipulates online reviews, firm A will always choose to manipulate online reviews because AB is always higher than AI . Therefore, both firms will always choose to manipulate online reviews in equilibrium.

)2

(1

)2

(1

M . In this case, if firm B manipulates online reviews, firm A will always manipulate online reviews. The second case is when 8 M < µ 6M M This is because if firm A does not manipulate online reviews under the scenario with the manipulation by only the inferior firm, firm A will be driven out of the market by firm B and make zero profit. If firm B does not manipulate online reviews, firm A’s best response is to manipulate online reviews

)2

(1

)2

(1

M because AS is always larger than AN under 8 M < µ . Therefore, the best response for firm A is always to manipulate online reviews 6M M regardless of the manipulation decision of firm B. Then, this paper checks the best response of firm B to the manipulation by firm A. If firm A manipulates online reviews, firm B will always manipulate online reviews. This is because if firm B does not manipulate online reviews under the scenario with the manipulation by only the superior firm, firm B will be driven out of the market by firm A and make zero profit. Therefore, both firms will always choose to manipulate online reviews in equilibrium. □

A.10 Proof of Corollary 2 Proof: There are two cases where prisoner’s dilemma exists. (a) The first case is when µ > AB

0

<

AN

and

xR < min{x 6,

<

BB 3C 1

C

,

(1

0

xR < min{x 7 ,

AB

3C 1

C

,

BN .

2

and 0

8M

<

AN

xR < min {

Solving

2 6µ M (1 M) }. 2µ (1 M) 2 (1 ) M

(b) The second case is when worse off only if

M)

6 M

<µ<

and

(1

AB

M)

6M

BB

<

2

1

C

3C

<

and 0

BN .

,

2 6µ M (1 M) }. 2µ (1 M)

and

AN

xR < min {

Solving

AB

<

<

BB

1

C

3C AN

2 6µ M (1 M) }. 2µ (1 M)

Under the manipulation by both firms, both firms are worse off only if

,

BN ,

we

2 6µ M (1 M) }. 2µ (1 M)

and

BB

<

BN ,

have

(1

M)

2

< µ < max

6 M

{

(1 8( M

2 2 (1 M) M) 2 , 6M C)

}

and

Under the manipulation by both firms, both firms are we have

(1

M)

8 M

2

< µ < min

{

(1 8( M

M)

2

C)

,

(1

M)

6M

2

}

and

[2] Y. Liu, Word of mouth for movies: its dynamics and impact on box office revenue, J. Mark. 70 (3) (2006) 74–89. [3] C. Dellarocas, X.Q. Zhang, N.F. Awad, Exploring the value of online product reviews in forecasting sales: the case of motion pictures, J. Interact. Mark. 21 (4) (2007) 2–20.

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Working Paper, (2017). [19] L. Li, J. Chen, S. Raghunathan, Advertising role of recommender systems in electronic marketplaces: A boon or a bane for competing sellers? Mis Q. (2018) forthcoming. [20] P. Nelson, Information and consumer behavior, J. Polit. Econ. 78 (2) (1970) 311–329. [21] D.A. Garvin, What does product quality really mean? Sloan Manage. Rev. 26 (1) (1984) 25–43. [22] J. Sutton, Vertical product differentiation: some basic themes, Am. Econ. Rev. 76 (2) (1986) 393–398. [23] Y. Kwark, J. Chen, S. Raghunathan, Platform or wholesale? A strategic tool for online retailers to benefit from third-party information, Mis Q. 41 (3) (2017) 763–785. [24] J.M. Bates, C.W.J. Granger, The combination of forecasts, Oper. Res. Q. 20 (4) (1969) 451–468. [25] X. Li, L.M. Hitt, Self-selection and information role of online product reviews, Inf. Syst. Res. 19 (4) (2008) 456–474. [26] Q. Ye, B. Gu, W. Chen, Measuring the Influence of Managerial Responses on Subsequent Online Customer Reviews—A Natural Experiment of Two Online Travel Agencies. Working Paper, (2010). [27] G.A. Akerlof, The market for "lemons": quality uncertainty and the market mechanism, Q. J. Econ. 84 (3) (1970) 488–500. Huanhuan Cao is an assistant professor in the School of Management at Zhejiang University of Technology. She received her Ph.D. from the School of Management at Xi’an Jiaotong University. Her research interests concern diverse economic, operational, and marketing aspects of electronic commerce and how internet-enabled IT transforms consumer behavior and firm strategy.

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