Sales volume and online reviews in a sequential game

Abstract In the age of e-commerce, consumers tend to base their purchasing decisions on online information, including the sales volume and the online reviews of products. To investigate the impact of such behaviour on firms’ competition strategy, we built a two-period model, which includes a leader firm that exists in the market for both periods and a follower firm that only enters the market in the second period. We consider three circumstances of online information: with no information, with sales volume information only, and with both sales volume and online reviews information. We show that when only sales volume information is available, the leader firm can always gain a competitive advantage over the follower firm in the second period. However, with the availability of both sales volume and online reviews, under certain conditions, the follower firm will be more competitive in the second period. Furthermore, neither sales volume information nor online reviews can guarantee the leader firm a higher profit.


Introduction
With the development of information technology and the digital economy, the Internet has become an important channel for consumers to obtain product information.In particular, online reviews are becoming more influential as consumers tend to believe that this source of information is more trustworthy (e.g., Burtch et al., 2018).According to the research conducted by Dixa, a marketing company, 93% of customers read online reviews before purchasing a product, and 47% would spread the word about a positive experience while 95% would leave comments about a negative experience.Moreover, online reviews lead to an 18% increase in sales on average (Loiselle, 2022).Therefore, e-retailers have tried hard to incentivize consumers to leave online reviews (e.g., Cao, 2020).Meanwhile, even before the advent of the e-commerce era, firms have realised that consumers also take product sales into account when they make purchase decisions (e.g., Hu et al., 2021).Specifically, many studies have shown that when sellers' reputation is unknown, consumers prefer to buy from those with more customers.This so-called "herding effect" has been extensively studied (e.g., Ding & Li, 2019;Godinho de Matos et al., 2016).
The demand side impacts of these two types of information are obvious and have attracted a lot of attention.However, there also exist supply side effects, as competing companies also adjust their strategies according to such information.For example, Li and Hitt (2010) suggest that online product reviews have a significant effect on the price as firms may benefit by reducing the prices for products of intermediate quality to boost their reviews/ratings.Feng et al. (2019) further point out that firms' manipulation of prices to influence online reviews and the resultant demand for the products can be done dynamically.For sales volume, many studies have also analysed why firms should, or should not change their price when they face a large number of sales (e.g., Becker, 1991).
The existing operations literature has rarely investigated the joint influence of these two types of information on the competition between companies.As far as we know, Liu et al. (2017) is the first and only study that establishes a duopoly competition model to discuss the joint influence of sales volume data and online reviews on the pricing decisions of two differentiated products.However, the game that Liu et al. (2017) study is simultaneous and unsuitable for the analysis of sequential decisions.In reality, companies usually compete in a sequential manner.For example, when a company enters a new market, the sales data and the online reviews of the incumbent companies can potentially play a critical role in the competitive strategies that the newcomer decides to adopt.The existing literature offers little insight regarding how such cases unfold.This article attempts to explore, for the first time, the combined influence of sales volume information and online reviews on the pricing decisions of leaders and followers in a two-period model.In particular, we discuss the pricing decisions of one leader firm and one follower firm under three different scenarios of information: no information, only sales information, and both sales and online reviews information.We study how the "first mover advantage" of leaders (Robinson & Fornell, 1985;Lieberman & Montgomery, 1988) and the "late mover advantage" of followers (Golder & Tellis, 1993;L opez & Roberts, 2002) are affected by the information of sales volume and product reviews.
We find that in a market with only sales volume information, if consumers are not sufficiently optimistic about its product, the leader firm will set a low price so as to increase sales volume in the first period and induce a herding effect.By doing so, the leader can enhance its competitiveness in the second period, enabling it to set a high price to make up for the losses from the first period.Meanwhile, the competitiveness of the follower will be weakened, and the follower will need to reduce its price and settle with a lower profit.On the other hand, in a market with both sales volume and online reviews information, if consumers have high prior beliefs in a product's quality, the leader firm will charge a high price in the first period.In the second period, if the combined effect of prior beliefs, sales information, and online reviews gives consumers a perception of high product quality, the leader will further increase its price.Otherwise, the leader will lower its price as the competitiveness of the follower is enhanced.We also show that neither sales volume information nor online reviews can always improve the leader's profit level.
The solution approach in this article follows the rational expectations hypothesis first proposed by Muth (1961), which suggests that economic outcomes do not differ systematically from what people expect them to be.Applying this concept to the present setting, we analyse the model above by looking for rational expectations (RE) equilibria, which satisfy the following: (1) Consumers anticipate the influence of sales volumes and online reviews and thereby make their purchase decision, (2) given the expectations of consumers' willingness to pay, firms make their pricing decisions, and (3) everyone's expectations are consistent with actual outcomes.If these criteria are met, the firm and consumers reach the RE equilibrium.In this way, equilibrium outcomes can be studied using our framework.
The contributions of this article are two-fold.From a theoretical perspective, it is the first paper to study the influence of sales volume information and online reviews on the sequential competition between firms, which complements earlier findings using a simultaneous competition model.In addition, our results also add new insights to the studies on the "first mover advantage" of leaders and the "late mover advantage" of followers in Stackelberg games.From a practical perspective, we show that for a market leader that faces incoming competition, releasing information to the market is not always beneficial.In particular, neither sales volume information nor online reviews can guarantee the profit improvement of the leader firm.This lesson can potentially serve as a guide for the market leader's decisions to publish certain information or not.Besides, our results also provide suggestions to the leader firms in terms of their pricing decisions under different information disclosure scenarios.
The remainder of this article is as follows.Section 2 reviews the relevant literature.Section 3 presents the model setup, while Section 4 analyses the results.Finally, the last section concludes and discusses policy implications.

Literature review
This article is related to two streams of literature.The first relevant stream of literature is about social learning, which involves online product reviews or consumer information updating (for example, sales volumes), that informs consumers about product/ service attributes.Chen and Xie (2008) argue that consumer reviews provide product-matching information that reduces consumers' uncertainty about products and helps consumers find products that match their needs.Some studies find that product types (experiential or utilitarian) moderate the effect of review features on perceived review helpfulness (Mudambi & Schuff, 2010;Pan & Zhang, 2011).Some recent studies find that earlier reviews affect later reviews (Li & Hitt, 2010;Wu & Huberman, 2008) and that social dynamics affect online reviews (e.g., Trusov et al., 2009;Moe & Trusov, 2011;Samiei & Tripathi, 2014).There are also studies exploring how to develop social learning systems to induce truthful reporting (Fan et al., 2005) and how user reporting habits may bias ratings (Hu et al., 2009).This stream offers evidence that, on the demand side of the market, user-generated online product reviews play a very important role in informing consumers' purchase decisions.Jing (2011) examines the strategic interaction between consumer learning and the firm's pricing strategies, assuming that customers can learn product characteristics either from friends' experiences or from a firm's information revelation.However, existing papers do not study how consumer learning affects the price competition between substitutable products when firms enter the market sequentially.This article contributes to the investigation of the interplay between online product reviews and firms' competitive strategies.
The second relevant stream of the literature focuses on firms' competition and pricing.First, as static models may not capture the intricacies of the market in many situations (Zhang & Feng, 2011;Mehra et al., 2012), we focus on dynamic pricing.When a firm enters a market, there are two commonly observed pricing strategies for the new products: penetration pricing and skimming pricing (Hotler & Armstrong, 2012).A penetration pricing strategy is helpful for building the consumer learning of a (perceived) uninformed product (Shapiro, 1983).Skimming pricing is effective when the market is highly differentiated, and consumers are not price sensitive (Noble & Gruca, 1999).Papanastasiou and Savva (2017) investigate how the presence of social learning through Bayes updating between customers affects the firm's dynamic policy within a two-period model, including preannounced pricing and responsive pricing.Crapis et al. (2017) analyse the social learning mechanism and its effect on the seller's pricing decision in a market of customers with heterogeneous quality preferences.Ajorlou et al. (2018) study the problem of optimal dynamic pricing for a monopolist selling a product to customers in a social network where customers' knowledge of the product is only through friends who already know about the product's existence.Feldman et al. (2019) provide a dynamic model to examine a firm's quality and pricing decisions for its new experience goods where the customers can learn product quality after purchase and share that information with later customers.We follow this line of research and study the firm's pricing decision in the presence of consumer learning.However, different from the previous studies, we aim to investigate the combined influence of sales volume information and online reviews on the pricing decisions of leaders and followers in a two-period model.In particular, we study how the "first mover advantage" of leaders is affected by the information of sales volume and product reviews.

Model setup
Consider two firms, A and B, selling similar products A and B in the same market, respectively.Without loss of generality, we assume that the marginal production costs of both products are zero.There are two types of consumers in the market: regular and irregular.Regular consumers make purchase decisions to maximise the utility from the product.Before the purchase, regular consumers have the same prior belief about the quality of product A or product B, which follows a normal distribution, q$Nðq, r 2 q Þ: Other than the quality of the product, another component in the regular consumers' utility is the preference for a certain product, which is assumed to be uniformly distributed over ½0, 1, with product A located at 0 while product B located at 1 (Hotelling, 1929).Let t represent the unit mismatch cost caused by the mismatch between the product and the consumer's preferences (0 < t < 1).Specifically, a regular consumer with a preference of y needs to pay ty or tð1 À yÞ mismatch costs if he/she buys product A or product B.These regular consumers are uncertain about the degree to which the product matches their own preferences before the purchase.Following Kwark et al. (2014) and Liu et al. (2017), we assume that a regular consumer believes that his/her preference is at y with probability 1/2, and at any other point on the line with equal probability (i.e., Ð 1 0 z=2dz ¼ 1=4).The two firms compete in price, which is the last component in the regular consumers' utility.Therefore, the expected utility from buying product A for a regular consumer is q À y=2 þ 1=4 À Á t À p A : On the other hand, the irregular consumers will always buy The mean or consumers' expectations of variable q The actual quality of product A and product B q i Quality of product A, updated based on past i information, i ¼ S, R, where S represents sales volume information, R represents online reviews and sales volume information p e 1 Consumers' expectations on the pricing of firm A in T1 x i j The weight of various information in product quality expectations, i ¼ S, R:j ¼ 1, 2, 3 r The quality of the product revealed by online reviews c The amount of online reviews information p i Ai Firm A's prices in each stage ði ¼ 1, 2Þ, i ¼ 0, S, R, where 0 represents no information from a certain firm, without considering the prices and the qualities of the products.Examples of such consumers include those who are loyal to a certain product, and consumers who have special preferences and special needs that only a certain product can fulfil.Such consumers have been investigated in many studies (e.g., Krishnamurthi & Raj, 1991;Iyer & Pazgal, 2003;Sinitsyn, 2008).The demand of the irregular consumers follows another normal distribution, i.e., d $ Nðd, r 2 d Þ: All the symbols involved in this article are shown in Table 1 and Table 2.

Game timing
The two firms are involved in a two-stage game (T1 and T2) throughout the sales cycle of the products.The game timing is shown in Figure 1.Consumers (including regular and irregular) enter the market in two batches, and every consumer demands at most one unit of product at each stage.In stage T1, firm A and the first batch of consumers enter the market first at time t 0 : Firm A chooses the price for product A and the information scenario (i.e., which information to disclose) at time t 1 : At t 2 , the two types of consumers make purchase decisions based on their own value judgments.Then at t 3 , the first batch of consumers review on the quality of product A (if firm A decides to disclose consumer reviews), and then withdraw from the market.In stage T2, at t 4 , firm B and the second batch of consumers enter the market.Firm B provides product B and competes with firm A on the basis of T1: At t 5 , based on the information disclosed in T1, regular consumers update their belief about the quality of product A: At t 6 , the two firms set their prices for T2: Finally, at t 7 , consumers make purchase decisions based on the updated utilities.
It should be noted that the following assumptions are made: (1) Consumers cannot see irregular consumers' demand information, i.e., consumers can see the previous sales of the product if this information is disclosed, but they cannot distinguish whether these sales are from regular consumers or irregular consumers (Liu et al., 2017;(2) The second batch of consumers can only see the current prices of the firms.However, the large amount of information in the market makes it easier for consumers to infer the previous price even if they cannot observe it accurately; (3) Firms obtain information regarding regular consumers' prior beliefs in products and irregular consumers' demand distribution through past sales history, experience, and reports on product marketing research (Liu et al., 2017).

Market model equilibrium of three information conditions
In the first period of the game, T1, firm A monopolises the market.Anticipating the consumers' response to the product sales volume and consumer online reviews information (if available) in T2, firm A may alter the introductory price that maximises its overall profit, and in turn, affect the competition state in T2: In order to investigate the influence of sales and reviews information on the competitive situation, we will analyse three information scenarios: a market without information; a market with only sales volume information; and a market with both sales volume and reviews information.

Without information
As a benchmark, we first consider the scenario where firm A does not disclose any information.In this case, without any additional market information, consumers can only infer the actual product quality based on their prior beliefs, i.e., q$Nðq, r 2 q Þ: The purchasing behaviour of the irregular consumers is by nature not affected by the firms' strategies, while the firms also do not need to consider these consumers as they will not affect regular consumers when no information is disclosed.We will only consider the relationship between the purchasing behaviour of the regular consumers and the pricing decisions of firms in this subsection.The cases when firms need to take the purchasing behaviour of the irregular consumers into account will be presented in the following subsections.In those cases, although irregular consumers are still not affected by the strategies of the firms, due to the existence of sales volume information and online reviews, these consumers will have an impact on regular consumers' behaviour and then affect companies' decisions.We use the superscript " 0" to represent the market equilibrium under the scenario without information and omit the superscript on partial variables in the analysis process.
Regular consumers make purchase decisions based on their prior beliefs of product quality and the price.In T1, the utility of a regular consumer located at y and buying product A is From U A1 > 0, we can find that the regular consumers' demand for product A in T1 is y 2 ½0, D A1 , Table 2. Description of normal distribution.

Normal distribution
Meaning The prior belief of the regular consumers about the actual quality of product A and product B r$Nð r, r 2 r Þ Online reviews on product quality where and the corresponding profit of firm A is: In T2, the utility of the regular consumer located at y and buying product A (B) is Letting U A2 ¼ U B2 , we can find out the critical consumer who is indifferent between purchasing product A and purchasing product B. Therefore, the demand functions for the two firms are , respectively, while the profit functions of the two firms are Solving ( 3), (6), and (7) yields the following Lemma 1.All the proofs are demonstrated in Appendix C.
Lemma 1.In the case with no information, the equilibrium prices and profits of the two firms in the two stages are 1.For firm A: Lemma 1 shows that in T1, firm A adopts monopoly pricing, which only depends on regular consumers' belief on quality q (Shapiro, 1983).Since there is no information disclosed in this case, the two stages, T1 and T2, are independent from each other.The game in T2 is played in a symmetric static Cournot fashion, so the two firms would set the same price, which depends on the unit mismatch cost t, and get the same profit.This is consistent with the classic microeconomic literature (Allaz & Vila, 1993).To avoid trivial cases, we assume that t and q are not too large, so the entire market is covered.The behaviour of irregular consumers has no effect on the prices of the two firms.As firm A's prices in the two stages are independent from each other, both firms share the same price and the same profit in T2: We can conclude that the leader firm cannot obtain the first mover advantage in the case without any information.

With sales volume information only
We now consider the case where the sales volume information in T1 is available to consumers in T2: Consumers can see the previous sales of the product on the product web page, but they cannot identify whether these sales are from regular or irregular consumers, so consider the previous sales all from regular consumers.We use variables with a superscript " S" to identify this situation.We assume that the herding effect exists, and consumers always believe that products with higher sales volumes are of better quality (Chen, 2008;Simonsohn & Ariely, 2008;Cai et al., 2009).
In T2, regular consumers use DA1 , the total sales volume in T1, as a reference point to infer the quality of product A. As the consumers are differentiated by their mismatch preferences, y, the larger this value, the less the consumer is willing to purchase product A. There should exist a particular value, denoted by DA1 , and for the specific consumer with preference equal to this value, the utility from purchasing product A is zero.In other words, this consumer is indifferent between buying product A or not.As the consumers' preference is uniformly distributed, all consumers who have lower mismatch preference than this indifferent consumer will get positive utilities from purchasing product A, and would thus do so.Therefore, the number of consumers purchasing product A will be DA1 À 0 ¼ DA1 : It is worth noting that this is a very common way in literature to derive demand functions (Yu et al., 2016).For the consumer with y ¼ DA1 , there is no difference between buying product A or not, i.e., q s À p e A1 À tð DA1 =2 þ 1=4Þ ¼ 0: Therefore, the derived product quality, q s , is given by Note that the total sales volume, DA1 , and the expected price in T1, p e A1 , are both available to consumers.Furthermore, the variance of q s is Dðq s Þ¼Dðp e A1 þtð DA1 =2þ1=4ÞÞ¼ðt 2 =4Þr 2 d : Following Caminal and Vives (1996), sales volume information from the previous period influences the consumers' current valuations about products.Meanwhile, applying Bayesian rule (DeGroot, 1970), regular consumers update their beliefs in product quality using the weighted average of prior mean belief q and the derived quality value q s q s ¼E qq s ,q ð Þ¼x S 1 qþx S 2 q s (9) weights of the prior belief q and the derived quality value q s : It is obvious that the more accurate the sales volume information (i.e., the bigger r 2 q ), the higher x S 2 , the proportion of this information in the formation of consumers' expectations of the quality of product A: It should be noted that with D A1 being the sales volume from regular consumers, and d being that from irregular consumers which is only observable to firm A. Substituting (2) into (10), we have Substituting ( 8) and (11) into Equation (9), we can obtain We analyse this model by looking for Rational Expectation Equilibrium (REE) (Fudenberg & Tirole, 1991), that is, (1) given their expectations of future price, consumers make their purchase decisions, (2) given the expectations of consumers' willingness to pay, the firm makes their pricing decisions, and (3) everyone's expectations are consistent with actual outcomes.Thus, in the equilibrium, firm A must correctly anticipate and set a price equal to consumer expectations, that is, p e A1 ¼ p A1 , which is quite intuitive and helps to make explicit the deliberations of all parties (Su & Zhang, 2008).After simplifying Eq. ( 12), the quality of consumer update for product A is, It should be noted that as companies can observe the purchase number of irregular consumers, d, the companies will convert q s observed.It is straightforward that consumers' belief in product A's quality is higher than the prior belief q in this case because of the existence of irregular consumers, d > 0: By applying backward induction, we can obtain the demand function of product A in T2 as, , so the profits of the two firms are Solving ( 5)-( 6) yields In T1, firm A sets a price to maximise the total profit of the two stages, namely max Solving ( 13)-( 16) yields the following Lemma 2.
Lemma 2. In the case with only sales information, the equilibrium prices and profits of the two firms in the two stages are , and p Sp B2 ¼ tdx S 2 ðdx S 2 À6Þ=36: Lemma 2 implies that the sales volume (from irregular consumers) plays a role in signalling the product quality.The prices (profits) depend on both the consumers' prior belief and the sales volume information, which is expressed as the algebraic sum of the prices (profits) in the case with no information, and a sales volume information factor reflecting the impact of the sales information.
In order to ensure that the two firms can set positive prices and obtain positive profits, the parameters need to be constrained.In particular, to ensure p S A1 > 0, we need q > q a ¼ 1 , that is, consumers are required to have an optimistic a priori belief in the quality of the product.Otherwise, firm A will not enter the market in the first period.Furthermore, to ensure p S B2 > 0, we need dx S 2 < 3, that is, the sales volume information factor in the second period must not be too large, otherwise firm B will not be able to enter the market.
We then compare firms' prices in both stages and obtain Proposition 1 as follows: Proposition 1.In a market with only sales information, two firms have the following pricing decisions (1) When q > q 1 , for the price of firm A: p S A2 < p S A1 , where , and vice versa; (2) In 72, the pricing of the two firms satisfies: p S A2 > p S B2 : It can be seen from Proposition 1 (1) that when the consumer's prior belief q is sufficiently large (as q > q 1 ), while both the number of irregular consumers d and the weight of sales volume information x S 2 are small, the quality updated by the sales volume information in T2 is small.Under this situation, firm A does not need to charge a low price to expand its sales in T1: In other words, it can make full use of its monopoly advantage in T1 as the first mover.This strategy has been fully discussed in the literature (Tirole, 1988), that is, firms initially charge high prices when competition is weak, and as market competition intensifies, they reduce the prices to attract customers.
On the other hand, when the consumers do not have sufficient confidence in the product (when q < q 1 ), the firm wants to achieve a higher sales number in T1 to improve the reputation of the product through a lowered "introductory" price, which allows it to charge a higher price in T2: This is referred to as "lower introductory price strategy"(e.g., Papanastasiou & Savva, 2017), that is, p S A1 < p S A2 : By adopting this strategy, firm A obtains a large sales volume in T1, which boosts the subsequent demand and enables it to charge a substantially higher price in T2: Moreover, the more accurate the sales volume information, i.e., the higher the weight ( x S 2 ) that consumers place on sales volume information, the greater the incentive for firm A to reduce its T1 price to boost its sales volume.Papanastasiou and Savva (2017) have also reached a similar conclusion.
Proposition 1 (2) also suggests that firm A has an advantage in T2, as its price is higher than that in the case without information ( p SP A2 > 0).Recall that both firms share the same price and the same profit in T2 in the case without any information.However, in the case with sales volume information, we can see that p S A2 > p S B2 , showing the first mover advantage of firm A, i.e., the leader firm has a higher price and profit in a symmetric end market competition.
We can compare the equilibrium prices and profits of the two companies under the situations with and without sales volume information and summarise the results in the following Proposition 2.
Proposition 2. Comparing the cases with and without sales information, p , where p S A < p 0 A when d < d 1 : 2. For firm B: p S B2 < p 0 B2 , p S B2 < p 0 B2 : Proposition 2 states that in order to increase q s , consumers' quality perception for product A, firm A will always charge a relatively low price ( p S A1 < p 0 A1 ) in T1 to expand sales.The firm can raise the price in T2 ( p S A2 > p 0 A2 ) to make up for its losses in T1: We can see from Equation ( 11) that the larger the number of irregular consumers d, the larger the sales volume DA1 in T1: As irregular consumers always buy from a certain firm, the sales volume of firm A will increase with the number of irregular consumers.However, due to the fact that regular consumers use sales volume to infer the quality of a product, an increase of sales because of the increase of irregular consumer will be translated to quality perception for the product, leading to a higher willingness to pay and thus, increase profitability for the firm in T2: However, Proposition 2 also suggests that the presence of sales volume information is not always beneficial to firm A. It is not guaranteed that the profit of firm A will increase when the sales volume information becomes available.The lower introductory price strategy prevents firm A from taking full advantage of its monopoly power in T1, while the competition from firm B also deters firm A from extracting surplus in T2 if it cannot build a sufficiently high-quality perception in consumers' minds.
Although firms have no control over the realisation of sales volumes because of irregular consumers, in the presence of sales volumes information, firm A gets the chance to improve its profit through its first mover advantage, while Proposition 2 (2) shows that firm B does not, i.e., p S B2 < p 0 B2 :

With sales volume and online reviews information
This section discusses the case when both sales and online review information are available.In T2, consumers can see not only the previous sales information, but also the reviews from consumers who have purchased the product in T1: Therefore, consumer valuation of product quality will come from three sources: (1) consumers' prior beliefs; (2) sales volume information; (3) online reviews.
Online reviews help consumers update their expectation on the product from two aspects, i.e., both product quality and the preference mismatch (Chen & Xie, 2008).First, let r represent the component of product A's quality revealed by online reviews, which is a random variable, r $ Nðr, r 2 r Þ: Second, online reviews also help to reveal the degree to which the product meets their needs.We use c 2 ðÀ1, 1Þ to represent the informativeness of consumer online reviews.By reading reviews, a regular consumer updates his/her belief about the probability that his/her preference is at y from 1=2 to ð1 þ cÞ=2 (Chen & Xie, 2008).c captures two attributes of the online reviews, i.e., accuracy and content.Firstly, the sign of c represents the positive (or negative) content of signal.Secondly, a higher absolute value of c is related to better accuracy.In other words, the online review information is perfectly informative when c j j ¼ 1, and completely uninformative when c ¼ 0: As a result, the ex post belief on mismatch preference will range from 0 (with a significantly negative signal c ¼ À1) to y (with a significantly positive signal c ¼ 1).
Similar to Section 4.2, consumers update their beliefs following the Bayesian rule, that is, using the weighted sum of the prior belief q, the mean quality value from online reviews r, and the perceived quality value from sale volume q s as q We use variables with a superscript "R" to identify this situation, where

3
, and the equilibrium value for consumers to update the quality of product A is: Recall that in the case with only sales volume information, from we can see that due to the existence of irregular consumers d, the consumers raise their expectation by a strictly positive value, i.e., q S > q: However, from q x R 3 r we can see that it is possible to have q R < q due to the potential negative influence of r on q R as online reviews are less controllable (e.g., negative PR issues).Therefore, there are various relationships between q R , q S , and q in the presence of online reviews, as shown in Figure 2.

¼ 9Þ
In T2, the utility of the regular consumer located at y and buying product A or B is, , respectively.Note that the online review may decrease the mismatch cost from purchasing product A for consumers receiving a negative signal ðc < 0Þ, but it may also increase the mismatch cost for those receiving positive signal (c > 0).The profits of the two firms in T2 are: The following Lemma 3 is obtained with backward induction.
Lemma 3. In a market with sales volume and online reviews information, the equilibrium prices and profits of the two firms in the two stages are

For firm
where p RP Ai , p Rp Ai ði ¼ 1, 2Þ, p RP B2 , p Rp B2 are the sales volume and online reviews information factors, with À t 4 : Similar to Lemma 2, the prices (profits) in the case with sales volume and online reviews information can also be expressed as the sum of the prices (profits) in the no information case and a factor of these two types of information.At the same time, it can be found that when the quality of online reviews approaches the prior belief, while its proportion in quality perception x R 3 and the amount of reviews c approach 0, that is, when r !q, x R 3 !0, c ! 0, the sales and reviews information factors in Lemma 3 are the same as the sales volume information factors in Lemma 2. Under this situation, , which shows that Section 4.2 is in fact a special case of this section.
Again, we only pay attention to the situation where both firms can set positive price and obtain positive profit.We thus have the following constraints on the relevant parameters: to ensure p R A1 > 0, we need r < r a , q > q b ; to ensure p R A2 > 0, we need r > r b and q > q c ; to ensure p R B2 > 0, we need r < r c and q > q a : To summarise, we need q > max q a , q b , q c f g ¼ q c , which means that consumers' prior belief in product quality needs to be higher than a certain threshold, otherwise the firm will not be able to set a positive price, and thus cannot enter the market.From r a > r c > r b , we can get r b < r < r c : This means that the customer reviews cannot be too negative, as firm A will be squeezed out of the market in the second period.Among them, the values of r a , r b , r c , q b and q c are shown in Appendix A.
Proposition 3 summarises the pricing strategies of the two firms in the case with both sales volume and customer review information.Proposition 3. In the case with both sales and online reviews information, 1.When either of the following conditions is met, we Proposition 3 (1) specifies the two situations under which firm A would not adopt the low introductory pricing strategy.However, these situations are due to very different reasons.Part (i) suggests that when the consumers' prior belief q is sufficiently large, firm A can make full use of its monopoly power in T1 and charge a high price.It does not need to worry about losing out in its competition with firm B in T2 as a good sales volume can still be achieved even under the high price.Part (ii), on the other hand, is a combination of unfavourable conditions for firm A to adopt the low introductory price strategy.With all these conditions in place, it is not worthwhile for firm A to use a low introductory price in T1 to increase its competitiveness in T2: Proposition 3 (2) discusses the conditions under which firm A loses its first mover advantage while firm B gains a late mover advantage.The condition 2qx R 3 > tdx R 2 means that there are few irregular consumers in T1 (i.e., the quality perception of the product from the sales volume q s is small), and its proportion x R 2 is also small.These factors, coupled with the small expected quality perception from consumer reviews, r, lead to a small expectation of product A's quality.However, as consumers' expectation for product B's quality is completely determined by q, a large q is more beneficial to firm B. When the informativeness of the reviews is higher, the mismatch cost of product A is higher.The combination of all these factors causes the price of firm A to be lower than the price of firm B.
By the above analysis, we can see that, in the case with both sales and online reviews information, because firm A cannot control reviews, under certain conditions, firm A will lose the first-mover advantage in T2 and firm B will get the late-mover advantage.On this basis, we can further analyse the role of sales and online reviews, which provides additional insights and can be found in Appendix B.

Conclusion
In the age of e-commerce, consumers use online information to learn about the products before making purchase decisions.Knowing this, companies also adjust their pricing strategies.This article is the first study to build a two-period game model in which two firms sequentially enter a market with both regular and irregular consumers under different scenarios of two types of online information, i.e., sales volume and customer reviews.
We show that in the case with only sales information, if consumers are sufficiently optimistic about product quality, the leader firm will adopt monopoly pricing in the first period and lower its price to accommodate the competition from the follower firm in the second period.Conversely, if consumers are not optimistic about a product, the leader firm will charge a low price in the first period to increase its sales volume, increasing consumers' quality perception for its product, thereby allowing it to be more competitive relative to the follower firm in the second period (i.e., first-mover advantage).In the case with both sales volume and online reviews information, consumers' perception of the leader firm's product quality in the second period is affected by three factors: consumers' prior beliefs, sales information, and online reviews.Through the combined influence of these three factors, the leader firm may lose its first-mover advantage, and the follower firm will gain the late-mover advantage under certain conditions.This is because online reviews can be either positive or negative.The leader firm can control the sales volume of products, but, cannot control customer reviews.Therefore, in the case with only sales information, the leader can actively adjust two-period pricing to maximise the total profit.However, in the case with both sales volume and online reviews information, the leader can only determine its prices passively due to the subjectivity of reviews.
These results can provide managerial insights to e-retailers.With the development of e-commerce, the sales volume and the consumer reviews have become important sources for future consumers to obtain product information.If the products have higher quality, the firms can use promotions, discounts, rewards and other means to guide consumers to review the products.Alternatively, the operator can turn off the reviews, which effectively affects consumers' perception of product quality, thereby enhancing the competitiveness of products in the market.By doing so, it makes the firm's marketing strategy more effective to achieve the purpose of increasing profit.
Certain limitations exist in this study.First, we follow the literature in assuming that regular consumers are not aware of the existence of irregular consumers, which is a simplification and may not always hold true.Future studies can consider strategic consumers who are more sophisticated, thereby making the model more authentic, and improving the analysis.Second, we assume that the qualities of the products are a given and not a strategic variable.In reality, it is possible for the follower firm to determine the quality level of a product after observing the sales volume and customer reviews of the leader firm, so as to obtain more leverage in competition.Another direction of future research is to consider this strategic behaviour and see how it affects the competition dynamics.

Figure 2 .
Figure 2. The expected qualities under three parameter constellations.

Table 1 .
Notations.Position or preference of consumers in the market d Demand for product A from irregular consumers in T1 D Ai , D B2 Demand from regular consumers in each stage ði ¼ 1, 2Þ DA1 Firm A's total demand in T1 t Mismatch cost per unit distance ( 0 < t < 1) d