In recent years, there has been a notable increase in the popularity of ecommerce. According to forecasts, the whole retail e-commerce sales are projected to increase by 20.1% in 2024 and maintain a steady growth trend until 2027¹. Despite the convenience and efficiency of online shopping, customers have reservations about the perceived value of products, particularly those that provide experiential value ( Feng et al., 2023 ). Practically, numerous consumers read online reviews to reduce ambiguity before purchasing. According to the survey², a significant majority of customers, specifically 90%, check online reviews before they decide to visit a business; additionally, a high percentage of customers, 88%, attribute the same degree of confidence in online reviews as they do in personal recommendations. A newly published study reveals that the global quantity of online reviews doubled in the year after the start of COVID-19³, suggesting that businesses should heed consumer reviews. Online businesses typically make dynamic adjustments to not only prices but also inventory in response to the effects of online reviews. Within scholarly circles, a multitude of researchers have emphasized the significance of online consumer reviews in the context of inventory management ( Yang & Zhang, 2019 ; Vahdani & Sazvar, 2022 ; Cheung et al., 2022 ). When retailers recognize that the subsequent appearance of online reviews can assist in alleviating consumers’ uncertainty regarding the product, thereby increasing sales, they are equipped with a fresh opportunity to maintain strategic inventory early on. Strategic inventory refers to a business practice wherein retailers deliberately acquire a greater quantity of products than they can sell during the current period, and the excess inventory is then transferred to the subsequent sales period. Two possible explanations exist for why retailers may choose to maintain strategic inventory. On the one hand, strategic inventory can assist retailers in mitigating the risk of shortages. A lack of inventory results in financial losses for retailers. Upon its introduction to the market in 2023, Mate 60 was met with significant consumer enthusiasm, propelled mainly by online reviews praising its exceptional camera capabilities. As a result, retailers encountered challenges related to inventory shortages due to the increased level of demand, and those who proactively maintain strategic inventories have the potential to generate substantial financial gains. On the other hand, strategic inventory can improve the retailers’ bargaining power concerning forthcoming wholesale prices. Researchers have shown that implementing strategic inventory can effectively motivate upstream manufacturers to decrease their future wholesale pricing ( Anand et al., 2008 ). When manufacturers cannot provide an optimal price, retailers will instead choose to sell the pre-owned inventory. A case in point is CELSA, an iron and steel corporation that pre-accumulates significant volumes of raw materials, thereby compelling its suppliers to decrease their prices.

In practice, information asymmetries in the supply chain are pervasive. While downstream retailers and upstream manufacturers agree on the advantages of information sharing, achieving information symmetry throughout the entire supply chain remains a challenge. Generally, retailers exhibit reluctance to disclose confidential information to manufacturers. An example is the home appliance industry, where manufacturers frequently face challenges in obtaining critical data, including negotiated retail pricing, sales figures, and inventory information. This is because, to protect their interests, retailers typically maintain the privacy of this information. Due to the inventory information asymmetry, manufacturers could not observe retailers’ strategic inventory behavior. Hence, manufacturers encounter difficulties in effectively adjusting wholesale pricing due to the lack of precise knowledge regarding retailers’ inventory levels and sales despite being provided with order quantity information. As a result, a question arises: in light of the subsequent consequences of online evaluations, is it advantageous for retailers to maintain strategic inventory levels if they conceal inventory information?

Typically, retailers of household appliances, cell phones, and vehicles tend to place large orders before the start of the sales season not only to minimize the possibility of running out of stock after the appearance of online reviews but also to enhance their negotiating leverage with upstream manufacturers. In contrast, retailers rarely disclose confidential inventory data to manufacturers. Expanding upon prior investigations concerning strategic inventory, we augment our analysis by integrating the effects of information asymmetry and online reviews. This research addresses the questions below: 1) How do online reviews affect the strategic inventory? What are the implications of information asymmetry on strategic inventory that is based on online reviews? Furthermore, what are the differences in strategic inventory between information symmetry and asymmetry? 2) How do online reviews affect the prices over the two periods under strategic inventory? How does information asymmetry affect the prices? 3) Does the manufacturer suffer from an information disadvantage?

To tackle these inquiries, we develop a two-period model including a manufacturer (he) and a retailer (she). The retailer can order an excessive number of items during the early period and maintain the surplus for future sales. Consumers who buy the products in Period 1 do not have access to online reviews because the products are newly launched, but they can post reviews after purchasing, which affects the purchasing decisions of consumers in Period 2. We first consider two benchmark cases where the retailer’s strategic inventory can be witnessed and then pay close attention to the scenario of information asymmetry, namely when the manufacturer cannot witness the retailer’s inventory. Analyzing the equilibrium outcomes, we deduce managerial insights for strategic inventory. The analysis is based on two effects under the impact of online reviews: the inventory expansion effect, which refers to the retailer’s tendency to store items in advance, and the demand-expansion effect, which means that the potential market is expected to expand. By analyzing the tradeoff between the two effects, one can understand how information asymmetry and online reviews affect strategic inventory.

This research complements the existing knowledge on strategic inventory by analyzing the intricate impacts of online reviews and information asymmetry. Our study focuses on the impact of review signals and consumers’ reliance on online reviews on strategic inventory. Our objective is to elucidate the distinctions between information symmetry and asymmetry, an area that has yet to be explored in the academic literature despite some researchers examining strategic inventory with online reviews or under information asymmetry independently.

The subsequent sections are structured as follows. Section 2 summarizes the relevant literature to fill the existing gap and align our study accordingly. In Section 3, we provide a detailed explanation of our model and give the fundamental assumptions. In Section 4 and Section 5, we provide the equilibrium solutions for strategic inventory when online reviews are present in Period 2, considering both information symmetry and asymmetry scenarios. In Section 6, we compare the results. Section 7 further analyze the overall supply chain, and welfare. Ultimately, in Section 8, we bring this paper to a conclusion and delineate possible avenues for further investigation. Refer to Appendix for comprehensive information on certification procedures.

This paper researches strategic inventory considering online reviews and information asymmetry. Our work is intimately connected to three primary areas of research: online reviews, strategic inventory, and information asymmetry.

We employ a two-period supply chain model, including a manufacturer (he) in charge of production and a retailer (she) responsible for procuring and reselling the products to end customers. As previously demonstrated, the retailer can procure additional products for sale in Period 2 in addition to those ordered for sale in Period 1. The main notations are shown in Table 2.

To simplify the process, we standardize the manufacturing and selling costs to zero. Following Li et al. (2021) and Guan et al. (2019) , it is assumed that both participants in the supply chain possess market information and that the potential demand remains constant throughout both periods. Besides, we assume that all consumers exhibit myopic behavior. In other words, we do not consider the case of consumers strategically comparing products from the two periods. This also ensures that the potential demand is identical in both periods, and we can focus more on the analysis of strategic inventory. The myopic consumer assumption is commonly adopted in prior scholarly works ( Wang et al., 2022a ; Liu et al., 2021 ).

Table 2. Notation list.

Generally, there are no reviews accessible for a newly launched product. Therefore, in Period 1, customers assess the product only based on their initial belief $v$, which is uniformly distributed in $\left[0,1\right]$. These preconceived notions may be from the content seen on a website, commercial advertising the product, or a company’s reputation. The customer’s utility is represented by the function $u_1=v-p_1$. Therefore, we can calculate the quantity sold in Period 1 as $s_1=1-p_1$. The inverse demand function is $p_1=1-s_1$.

Customers in Period 1 may post feedback about the product on the Internet after purchasing, allowing customers in Period 2 to browse and examine reviews online. Following Kwark et al. (2014) and Yang et al. (2021) , we denote $v_0$ as the product’s value indicated by reviews. More precisely, in Period 2, customers see a favorable signal from online reviews when $v_0>0$, and conversely, an unfavorable signal when $v_0<0$. Hence, the consumer’s expected evaluation is $\left(1-r\right)v+r{v}_0$, with $r$ denoting the customers’ emphasis on the information derived from online reviews. The utility function is defined as $u_2=\left(1-r\right)v+r{v}_0-p_2$. Therefore, the quantity

being sold could be calculated by $s_2=1-\frac{r{v}_0-p_2}{r-1}$. The inverse demand function

is $p_2=\left(1-s_2\right)\left(1-r\right)+r{v}_0$.

Additional assumptions for our research include:

1) Studies have discovered that sellers can distort consumer reviews ( Chen et al., 2022a ; Wu & Qiu, 2023 ). For simplicity, we assume that reviews posted by customers online reviews provide complete and accurate information ( Zhao et al., 2022 ).

2) To focus on the analysis of strategic inventory, following prior works regarding strategic inventory ( Roy et al., 2019 ; Miao et al., 2022 ), we do not consider safety inventory, pipeline inventory, or other related considerations.

To examine the effects of information asymmetry, two benchmarks are established first: no strategic inventory with information symmetry and strategic inventory with information symmetry, denoted by $\bar{B}$ and $B$, respectively.

This section examines the strategic inventory with information asymmetry, considering the impact of online reviews (represented as N). Figure 2 illustrates the decision sequence when information is asymmetric. Initially, the manufacturer establishes the wholesale pricing denoted as $w_1^N$, and the retailer determines the order quantity represented as $q_1^N$ subsequently. The retailer then independently decides on the amount $s_1^N$ to sell and the inventory $I^N$ to hold for Period 2. Simultaneously, the manufacturer adjusts the wholesale price to $w_2^N$ without witnessing her inventory decisions. At this stage, customers who bought the items in Period 1 write comments, resulting in the realization of the signal $v_0$. In Period 2, the retailer determines the amount to orders ( $q_2^N$) and sells ( $s_2^N$).

Following backward induction, the retailer’s sale in Period 2 is discussed first. Given the inventory of $I^N>0$ carried over from Period 1 and knowledge of the wholesale price $w_2^N$, the retailer determines the optimal order quantity ( $q_2^N$) to maximize her profit:

${\pi }_{R2}^N=p_2^N{s}_2^N-w_2^N{q}_2^N=\left[\left(1-s_2^N\right)\left(1-r\right)+r{v}_0\right]s_2^N-w_2^N{q}_2^N,$ (1)

$\text{s}\text{.t}\text{.}{s}_2^N<q_2^N+I^N.$

It can be easily confirmed that:

$q_2^{N\text{*}}={\left[\frac{1-r\left(1-v_0\right)-w_2^N}{2\left(1-r\right)}-I^N\right]}^{+}.$ (2)

By substituting (2) to (1), we can derive her profit in Period 2 as:

${\pi }_{R2}^{N\text{*}}=\{\begin{array}{l}\frac{{\left(1-r\left(1-v_0\right)\right)}^2+w_2^N-2w_2^N\left(1-2I^N\left(1-r\right)-r\left(1-v_0\right)\right)}{4\left(1-r\right)}\\ \text{if}{w}_2^N\le \left(1-r\right)\left(1-2I^N\right)+r{v}_0,\\ I^N\left(\left(1-I^N\right)\left(1-r\right)+r{v}_0\right)\text{otherwise}.\end{array}$ (3)

Thus, the manufacturer’s profit in Period 2 is:

${\pi }_{M2}^{N\text{*}}=\{\begin{array}{ll}{w}_2^N\left(\frac{1-r\left(1-v_0\right)-w_2^N}{2\left(1-r\right)}-I^N\right)\hfill & \text{if}{w}_2^N\le \left(1-r\right)\left(1-2I^N\right)+r{v}_0,\hfill \\ 0\hfill & \text{otherwise}.\hfill \end{array}$ (4)

Information asymmetry prevents the manufacturer from witnessing the retailer’s inventory behavior while adjusting the wholesale price. Likewise, the retailer decides her order quantity $q_1^N$ and inventory $I^N$ with knowledge of this fact. Profit for the retailer upon procurement of $q_1^N$ is:

${\pi }_{R1}^N=p_1^N{q}_1^N+{\pi }_{R2}^{N\text{*}}-h{I}^N.$ (5)

Since both the manufacturer and the retailer could not observe each other’s decisions, they are considered to have made decisions simultaneously (i.e., he determines $w_2^N$, and she determines $I^N$ and $s_1^N$).

Lemma 3. A unique Nash equilibrium $\left(I^{N*},s_1^{N*},w_2^{N*}\right)$ exists as:

$\left(I^{N\text{*}},s_1^{N\text{*}},w_2^{N\text{*}}\right)=\{\begin{array}{l}\left(0,q_1^N,\frac{1}{2}\left(1+r{v}_0-r\right)\right)\text{if}{q}_1^N<{\underset{\_}{q_1}}^N,\\ \left(\frac{4q_1^N+r{v}_0-2h-r-1}{2\left(3-r\right)},\frac{2h-4q_1^N-r{v}_0+r+1}{2\left(3-r\right)}+q_1^N,\frac{\left(1-r\right)\left(h-2q_1^N+2\right)+r{v}_0}{3-r}\right)\\ \text{if}{\underset{\_}{q_1}}^N<q_1^N<{\bar{q}}_1{}^N,\\ \left(\frac{1-2h+r{v}_0-r}{2\left(1-r\right)},\frac{1}{2},h\right)\text{if}{q}_1^N>{\bar{q}}_1{}^N.\end{array}$ (6)

where ${\underset{\_}{q_1}}^N=\frac{1}{4}\left(2h+1+r-r{v}_0\right)$ and ${\bar{q}}_1{}^N=\frac{2\left(1-h\right)+r\left(v_0-2\right)}{2\left(1-r\right)}$.

Lemma 3 illustrates that when $q_1^N<{\underset{\_}{q_1}}^N$, the retailer is unable to deliver the inventory and can only satisfy the customer demand in Period 1. When the value of $q_1^N$ lies between the range of ${\underset{\_}{q_1}}^N$ and ${\bar{q}}_1{}^N$, the retailer has the ability to maintain inventory. In other words, the items procured during Period 1 can be utilized to satisfy inventory needs for the ongoing period and sales in the subsequent period. However, when $q_1^N>{\bar{q}}_1{}^N$, the retailer orders excessive goods in Period 1 (i.e., $q_1^N>I^N+s_1^N$), potentially leading to unnecessary wastage. Hence, the retailer must ensure that the amount of the order remains below the specified threshold of ${\bar{q}}_1{}^N$.

Then the retailer determines the order quantity ( $q_1^N$) based on the wholesale pricing ( $w_1^N$). The retailer’s profit throughout the two periods is

${\pi }_R^N={\pi }_{R1}^{N\text{*}}-w_1^N{q}_1^N.$ (7)

By substituting (6), (5) and (3) into (7), we can derive:

${\pi }_R^{N\text{*}}=\{\begin{array}{l}\frac{{\left(1-r\left(1-v_0\right)\right)}^2}{16\left(1-r\right)}+\left(1-q_1^N\right)q_1^N-w_1^N{q}_1^N\text{if}{q}_1^N<{\underset{\_}{q_1}}^N,\\ \frac{h^2\left(r-5\right)\left(r-1\right)-2h\left(r-1\right)\left(2q_1^N\left(r-5\right)+\left(r-4\right)r\left(v_0-1\right)+1\right)-4q_1^{N2}\left(1-r^2\right)\left(4-r\right)}{4\left(1-r\right){\left(3-r\right)}^2}\\ +\frac{4q_1^N\left(r-4\right)\left(r-1\right)\left(r\left(v_0-2\right)+2\right)+r\left(r\left(\left(r-5\right)r+5\right){\left(1-v_0\right)}^2+2v_0-3\right)+2}{4{\left(3-r\right)}^2\left(1-r\right)}-w_1^N{q}_1^N\\ \text{if}{\underset{\_}{q_1}}^N<q_1^N<{\bar{q}}_1{}^N,\\ \frac{h^2-2h\left(r\left(v_0-1\right)+1\right)+r\left(r{\left(v_0-1\right)}^2+2v_0-3\right)+2}{4\left(1-r\right)}-w_1^N{q}_1^N\text{if}{q}_1^N>{\bar{q}}_1{}^N.\end{array}$ (8)

From equation (8), ${\pi }_R^{N\text{*}}$ is continuous and piece-wise concave or monotonically decreasing in $q_1^N$ for a given $w_1^N$.

Lemma 4. The retailer determines $q_1^N$ based on the manufacturer’s wholesale pricing $w_1^N$ as:

$q_1^{N\text{*}}=\{\begin{array}{ll}\frac{h\left(r-5\right)+\left(4-r\right)\left(r\left(v_0-2\right)+2\right)-{\left(r-3\right)}^2{w}_1^N}{2\left(4-r\right)\left(1-r\right)}\hfill & \text{if}0<w_1^N<W_1^N,\hfill \\ \frac{1-w_1^N}{2}\hfill & \text{if}{W}_1^N<w_1^N<1.\hfill \end{array}$ (9)

The retailer will maintain the inventory when $w_1^N<W_1^N$, but will not maintain it when $w_1^N>W_1^N$.

Corollary 1. The retailer’s order amount $q_1^N$ experiences a discontinuity at the point when $w_1^N=W_1^N$ under information asymmetry. However, the manufacturer never selects $W_1^N$ as $w_1^N$ in equilibrium.

Corollary 1 demonstrates that when the retailer’s inventory behavior is unobservable, the order quantity function becomes discontinuous at $w_1^N=W_1^N$ (see Figure 3 ). This finding aligns with previous studies on strategic inventory that also consider information asymmetry ( Roy et al., 2019 ; Miao et al., 2022 ). However, the manufacturer never chooses the discontinuous point as the wholesale price as he would incur a loss of profit at $w_1^N=W_1^N$. Besides, by comparing Figure 3(a) and Figure 3(b) , it is apparent that the disparity between A and B is more significant than the disparity between C and D. In other words, $q_1^N$ experiences a larger jump at $W_1^N$ with positive reviews. In addition, $W_1^N$ under positive reviews is larger than that under negative reviews.

The manufacturer total profit can be derived as:

${\pi }_M^N=w_1^N{q}_1^N+{\pi }_{M2}^{N\text{*}}.$ (10)

By substituting (9) and (4) into (11), we can obtain the manufacturer’s profit:

${\pi }_M^{N\text{*}}=\{\begin{array}{l}\frac{h^2{\left(r-3\right)}^2+h\left(\left(r-3\right)r-2\right)w_1^N+w_1^N\left({\left(r-4\right)}^2\left(r\left(v_0-2\right)+2\right)+{\left(r-3\right)}^3{w}_1^N\right)}{2{\left(r-4\right)}^2\left(1-r\right)}\\ \text{if}0<w_1^N<W_1^N,\\ \frac{{\left(r\left(v_0-1\right)+1\right)}^2}{8\left(1-r\right)}-\frac{1}{2}\left(w_1^N-1\right)w_1^N\text{if}{W}_1^N<w_1^N<1.\end{array}$ (11)

The manufacturer determines $w_1^N$ to maximize his total profit as in (11), which is summarized as follows.

Lemma 5. The manufacturer’s decision on $w_1^N$ is:

$w_1^{N*}=\{\begin{array}{ll}\frac{h\left(2-\left(r-3\right)r\right)-{\left(r-4\right)}^2\left(r\left(v_0-2\right)+2\right)}{2{\left(r-3\right)}^3}\hfill & \text{if}\max \left\{0,h_1\right\}<h<h_2,\hfill \\ \frac{1}{2}\hfill & \text{otherwise}.\hfill \end{array}$ (12)

For simplicity, we denote $\bar{N}$ as the case where the retailer does not maintain strategic inventory under information asymmetry while $N$ as the case where the retailer maintains the inventory under information asymmetry. Hence, we obtain the following Lemma.

Lemma 6. (1) When $\max \left\{0,h_1\right\}<h<h_2$ (Scenario $N$), the equilibrium results are $w_1^{N*}=\frac{h\left(2-\left(r-3\right)r\right)-{\left(4-r\right)}^2\left(2+r\left(v_0-2\right)\right)}{2{\left(r-3\right)}^3}$, $w_2^{N*}=\frac{h\left(r\left(2r-11\right)+13\right)+\left(4-r\right)\left(2-r\left(2-v_0\right)\right)}{2{\left(3-r\right)}^2}$, $q_1^{N\text{*}}=\frac{h\left(3r-7\right)-\left(r-2\right)\left(2-r\left(2-v_0\right)\right)}{4\left(3-r\right)\left(1-r\right)}$, $q_2^{N\text{*}}=\frac{h\left(\left(11-2r\right)r-13\right)+\left(r-4\right)\left(2-r\left(2-v_0\right)\right)}{4{\left(3-r\right)}^2\left(r-1\right)}$, $s_1^{N\text{*}}=\frac{\left(r-4\right)r{v}_0-\left(h+2\right)\left(r-5\right)}{4{\left(r-3\right)}^2}$, $s_2^{N\text{*}}=\frac{h\left(r\left(2r-11\right)+13\right)-\left(r-2\right)r\left(2r-7\right)v_0-2\left(1-r\right)\left(5+\left(r-5\right)r\right)}{4\left(r-1\right){\left(3-r\right)}^2}$, $I^{N\text{*}}=\frac{h\left[r\left(2r-11\right)+13\right]+r\left(1-v_0\right)\left(\left(r-5\right)r+5\right)-1}{2{\left(r-3\right)}^2\left(r-1\right)}$, $p_1^{N\text{*}}=\frac{h\left(r-5\right)+r\left(4v_0-r\left(v_0-4\right)-22\right)+26}{4{\left(3-r\right)}^2}$, $p_2^{N\text{*}}=\frac{h\left(r\left(2r-11\right)+13\right)+r{v}_0\left(r\left(2r-13\right)+22\right)-2r\left(\left(r-8\right)r+20\right)+26}{4{\left(3-r\right)}^2}$,

${\pi }_M^{N\text{*}}=\frac{h^2\left(r\left(\left(29-4r\right)r-70\right)+61\right)+2h\left(\left(r-3\right)r-2\right)\left(2-r\left(2-v_0\right)\right)+{\left(4-r\right)}^2{\left(2-r\left(2-v_0\right)\right)}^2}{8{\left(3-r\right)}^3\left(1-r\right)}$

and ${\pi }_R^{N\text{*}}=\frac{z_4{v}_0^2+z_5{v}_0+z_6}{16{\left(r-3\right)}^4\left(r-1\right)}$, where $z_4=r^2\left(\left(r\left(184-r\left(45-4r\right)\right)-320\right)r+196\right)$, $\begin{array}{c}{z}_5=2h\left(r\left(73-r\left(31-4r\right)\right)-50\right)\left(4-r\right)r\\ +4\left(\left(r\left(76-r\left(21-2r\right)\right)-104\right)r+34\right)\left(1-r\right)r\end{array}$ and $\begin{array}{c}{z}_6=h^2\left(r\left(r\left(r\left(4r-57\right)+278\right)-553\right)+376\right)\\ +4h\left(r-1\right)\left(r\left(r\left(r\left(2r-23\right)+89\right)-126\right)+38\right)\\ +4\left(r-1\right)\left(r\left(r\left(r\left(\left(r-11\right)r+43\right)-72\right)+57\right)-34\right).\end{array}$

(2) Otherwise (Scenario $\bar{N}$), the equilibrium results are: $w_1^{\bar{N}\text{*}}=\frac{1}{2}$, $w_2^{\bar{N}\text{*}}=\frac{1}{2}\left(1+r{v}_0-r\right)$, $q_1^{\bar{N}\text{*}}=s_1^{\bar{N}\text{*}}=\frac{1}{4}$, $q_2^{\bar{N}\text{*}}=s_2^{\bar{N}\text{*}}=\frac{1-r\left(1-v_0\right)}{4\left(1-r\right)}$, $p_1^{\bar{N}\text{*}}=\frac{3}{4}$, $p_2^{\bar{N}\text{*}}=\frac{3}{4}\left(1-r\left(1-v_0\right)\right)$, ${\pi }_M^{\bar{N}\text{*}}=\frac{{\left(1+r\left(v_0-1\right)\right)}^2+1-r}{8\left(1-r\right)}$ and ${\pi }_R^{\bar{N}\text{*}}=\frac{r\left(r{\left(1-v_0\right)}^2+2v_0-3\right)+2}{16\left(1-r\right)}$.

Proposition 7. Under information symmetry,

1) $w_2^{\bar{B}\text{*}}<w_1^{\bar{B}\text{*}}$, $p_2^{\bar{B}\text{*}}<p_1^{\bar{B}\text{*}}$, $w_2^{B\text{*}}<w_1^{B\text{*}}$, $p_2^{B\text{*}}<p_1^{B\text{*}}$;

2) $w_1^{B\text{*}}>w_1^{\bar{B}\text{*}}$, $w_2^{B\text{*}}<w_2^{\bar{B}\text{*}}$.

Part (1) of Proposition 7 demonstrates the simultaneous decrease of both wholesale and retail prices under information symmetry. This implies that to attract potential consumers who may read online reviews, the retailer should reduce prices, and the manufacturer should decrease wholesale prices.

Part (2) of Proposition 7 demonstrates that under information symmetry, the wholesale price increases (decreases) when the retailer is (not) capable of maintaining strategic inventory. This aligns with Anand et al. (2008) , which shows retailers employ strategic inventory to lower future wholesale pricing. As a response, manufacturers raise the first-period wholesale prices. Hence, part (2) of Proposition 7 establishes the continued validity of this assertion, considering the effects of online reviews. While the retailer may express concern about using strategic inventory in reaction to online ratings, she can utilize it to compel the manufacturer to lower future wholesale pricing, and he responds by raising the wholesale price during Period 1.

Proposition 8. Under information asymmetry,

1) $w_2^{\bar{N}\text{*}}<w_1^{\bar{N}\text{*}}$, $p_2^{\bar{N}\text{*}}<p_1^{\bar{N}\text{*}}$.

2) When $h_{w1}^N<h<h_{w2}^N$, $w_2^{N\text{*}}>w_1^{N\text{*}}$; otherwise, $w_2^{N\text{*}}<w_1^{N\text{*}}$.

3) When $h>h_p^N$, $p_2^{N\text{*}}>p_1^{N\text{*}}$; otherwise, $p_2^{N\text{*}}<p_1^{N\text{*}}$.

Part (1) of Proposition 8 demonstrates that under information asymmetry, if the retailer does not maintain strategic inventory, both the wholesale and retail prices decrease over the two periods, which aligns with Part (1) of Proposition 7. This suggests that with the effects of online reviews, the prices decrease under the case without strategic inventory, regardless of whether she reveals her inventory information or not.

Parts (2) and (3) of Proposition 8 demonstrate that prices exhibit complex fluctuations when the retailer maintains strategic inventory when concealing her inventory information. Specifically, the retail price rises when the inventory cost is high, while the wholesale price increases when the cost is moderate. The rationale behind this circumstance is that information asymmetry leads to a need for transparency in the supply chain. In other words, upstream manufacturers adjust wholesale prices with a need for more crucial information (i.e., sales quantity and inventory amount owned by downstream retailers). Consequently, the wholesale price may be unreasonably elevated or reduced.

Proposition 9. The retailer will maintain strategic inventory when $h_1^B<h<h_2^B$ under information symmetry and $\max \left\{0,h_1\right\}<h<h_2$ under information asymmetry.

Proposition 9 proposes that the retailer will maintain strategic inventory as long as the holding cost is below acceptable limits. The reason is simple: a high holding cost negatively impacts the retailer’s profitability. Contrary to intuition, information symmetry establishes a threshold ${\bar{h}}_1^B$ below which the retailer rejects to maintain inventory. A plausible reason for this contradiction is that the retailer perceives the manufacturer as being responsible for predicting demand when the retailer’s inventory level is readily apparent, and the minimal cost associated with holding inventory does not prompt the retailer to hold excess inventory in advance. As a result, the retailer tends to procure the quantity that aligns with the selling quantity in Period 1 rather than investing significant effort in pre-stocking. Nevertheless, an increase in holding costs signals the retailer that maintaining strategic inventory has the potential to generate profits. If this is the situation, the retailer will proceed with this action strategy.

Figure 4 visualize the conditions for strategic inventory in Proposition 9. It’s easy to confirm that there is no common region under the two cases. Specifically, under information symmetry, the retailer will maintain the inventory when customers attach little significance to online ratings, while under information asymmetry, the retailer will maintain the inventory when customers attach much importance. This contrasts with Roy et al. (2019) suggesting that retailers directly disclose inventory levels to upstream manufacturers when the holding cost falls within certain thresholds.

To further explore how online reviews affect strategic inventory under information symmetry (asymmetry), we analyze the range to hold inventory under the two cases. Specifically, we define the range of strategic inventory under information symmetry as $h_{range}^B=h_2^B-h_1^B$ and that under information asymmetry as $h_{range}^N=h_2-h_1$. We obtain the following Proposition.

Proposition 10. $\frac{d{h}_{range}^B}{d{v}_0}>0$; $\frac{d{h}_{range}^N}{d{v}_0}<0$.

Proposition 10 demonstrates that $h_{range}^D$ ( $h_{range}^N$) increases (decreases) with $v_0$ under information symmetry (asymmetry). This is attributed to the tradeoff between the inventory-expansion effect and the demand-expansion effect. The concept of the inventory-expansion effect claims that retailers tend to pre-stock items for future sales when online reviews become increasingly positive. By mitigating the risk of stock shortages, strategic inventory can assist the retailer in optimizing profits in this situation. On the other hand, the demand-expansion effect asserts that an improvement in online customer ratings will induce an expansion of the potential market.. A rise in the review signal corresponds to an enhanced propensity among consumers to buy the product; as a result, the retailer experiences a reduction in inventory and an upsurge in demand.

Figure 5(a) illustrates that when the retailer’s inventory is visible, the retailer is more likely to maintain the inventory as the review signal improves. Although the potential demand increases and hence accelerates inventory depletion, it is still more profitable for the retailer to hold some inventories in advance because she can have relatively strong bargaining power for future prices with the upstream manufacturer. As a result, the inventory-expansion effect dominates, and the retailer tends to store products in advance.

However, when the retailer conceals her inventory information, she is less likely to maintain the inventory as the reviews become more favorable, as shown in Figure 5(b) . This may appear paradoxical, given that retailers typically benefit from maintaining inventory in anticipation of favorable product evaluations. The rationale is that, under information asymmetry, the demand-expansion effect dominates the inventory-expansion effect. The prospective market demand is enhanced as the review signal improves. Nevertheless, when the retailer covertly organizes the stock for upcoming sales (i.e., the manufacturer cannot observe her inventory behavior), her bargaining power for future wholesale prices is weakened. In other words, the retailer’s ability to negotiate wholesale pricing is diminished when her inventory is not directly apparent. As a result, the inventory-expansion effect recedes under information asymmetry. According to Proposition 8, the wholesale price may increase when the retailer’s inventory is not visible. This further supports the notion that the inventory-expansion effect diminishes under information asymmetry from the perspective of price fluctuations.

Corollary 2. ${\pi }_R^{\bar{N}*}={\pi }_R^{\bar{B}*}$, ${\pi }_M^{\bar{N}*}={\pi }_M^{\bar{B}*}$.

Corollary 2 indicates that in the absence of strategic inventory, the manufacturer’s and retailer’s profits remain unaffected by the disclosure of inventory information. This suggests that supply chain members are not interested in divulging inventory data if the retailer ignores strategic inventory practices.

Proposition 11. ${\pi }_M^{N*}>{\pi }_M^{B*}$.

Proposition 11 shows that information asymmetry confers a benefit on the manufacturer, which is consistent with the results presented by Roy et al. (2019) and Miao et al. (2022) . The manufacturer anticipates a benefit from the retailer concealing its inventory behavior due to the sequence of decisions. As depicted in Figure 1 , under information symmetry, the manufacturer possesses the opportunity to modify the wholesale price by utilizing sufficient knowledge (i.e., $w_2^D$ is determined after $I^D$ is set). In contrast, under information asymmetry (see Figure 2 ), both parties make decisions simultaneously (i.e., $w_2^N$, $s_1^N$ and $I^N$ are determined at the same time). Consequently, information asymmetry has led to the retailer relinquishing her leadership role in the subgame, a change that benefits the manufacturer.

Retailers are motivated to place large orders for items before the start of the sales season to minimize the possibility of running out of stock after the appearance of online reviews and enhance their negotiating leverage with upstream manufacturers. Simultaneously, retailers may conceal the inventory information to maintain an information advantage. Therefore, based on the two aspects, we formulate a conceptual framework to analyze the impact of information asymmetry on strategic inventory with online reviews. The results show that the retailer strategically maintains inventory under information symmetry (asymmetry) when consumers assign minimal (substantial) importance to online reviews. Counter-intuitively, information symmetry dictates the existence of a holding cost threshold below which retailers are prohibited from maintaining strategic inventory. Besides, as online reviews improve, the retailer’s propensity to maintain inventory is augmented (reduced) under information symmetry (asymmetry). Furthermore, in the context of online reviews, the implementation of strategic inventory could lead to a decrease in future pricing when information is symmetric. Nevertheless, prices might increase or decrease under information asymmetry. Finally, the manufacturer could gain an advantage from information asymmetry. Our research generates some managerial insights as follows.

For the retailer, online reviews significantly influence her decisions regarding strategic inventory. Specifically, given suitable holding costs, the retailer can store some stocks in advance and disclose her inventory information to the manufacturer when consumers rarely care about online reviews; on the other hand, she can secretly hold the inventory when consumers attach great importance to online reviews. However, the retailer should avoid carrying the inventory when consumers weigh moderately on online reviews. In addition, as online reviews become more favorable, stocking inventories in advance can bring more (less) profits to the retailer when she discloses (privately owns) her inventory information.

For the manufacturer, he will gain more profits if he cannot observe the retailer’s inventory. This underscores that when the manufacturer finds himself in an information-disadvantaged position, signing contracts with retailers may not be necessary to promote information sharing. Furthermore, if the retailer refuses to disclose information about her inventory, the manufacturer may consider raising the wholesale price.

There are some limitations in this paper. First, we simply assume that consumers are myopic in each period. However, anticipating future price reductions or online reviews, they may choose to delay their purchases, i.e., make decisions in the two-period setting. In addition, we solely focus on a straightforward two-echelon supply chain structure. Incorporating competition into the research would be an intriguing development.

This work was supported by National Natural Science Foundation of China No.71572154.