Retailer Information Sharing With Upstream Product Line Flexibility

Abstract

With the rise of the digital economy, many firms are enhancing product line flexibility (i.e., the ability to adjust product line length or depth) to better manage demand uncertainties brought about by disruptive technologies. Concurrently, the booming digital economy has widened the information gap in supply chains. Retailers/platforms can now gather more detailed data to predict demand, but such data remains unavailable to manufacturers. This article studies how a manufacturer’s product line flexibility influences a retailer’s incentive to voluntarily share private demand information. We show that upstream product line flexibility encourages a retailer to voluntarily share information when product substitutability is low and the product line extension fee is moderate. This insight challenges the conventional belief that retailers should keep demand information private to maintain an advantage over manufacturers. Our work is the first to suggest that upstream product line flexibility can significantly motivate retailer information sharing. Additionally, we show that, although a social planner might prefer to withhold demand information from the manufacturer in the absence of product line flexibility, sharing this information becomes preferable when the manufacturer can adjust the product line length. The retailer’s decision on information sharing can align with the social planner’s in such scenarios. Furthermore, we demonstrate that, given upstream product line flexibility, except when product substitutability is not sufficiently high and the product line extension fee is moderate, the retailer’s information sharing decision is unaffected by whether the manufacturer determines the product line design before or after demand is realized and shared accordingly.

Keywords

Product line flexibility information sharing social welfare product line design

1. Introduction

Consumer products are often sold in product lines rather than as single product variants. For example, the iPhone 15 Pro is avaiable in four colors and four storage capacities.¹ Offering an extended product line can have numerous benefits for stakeholders, such as facilitating sales growth and enhancing social welfare. However, product line extensions are not always beneficial. A notorious example of a failed product line extension is Crystal Pepsi’s failure in the 1990s, recognized as one of the 10 worst product flops post-1950 by TIME in 2014.² Despite calls for learning from Crystal Pepsi, product line failures persist, as seen with Coca-Cola’s Sprite Remix³ and Burger King’s Satisfries.⁴ These cases highlight that product line design is a risky decision requiring careful consideration. Therefore, discussions on lessons from Crystal Pepsi’s failure are ongoing.⁵ Firms are eager to decode for the success of a product line design, with one key factor being comprehensive market knowledge (Baskin, 2016; Xiong and Chen, 2014). Due to their distance from end customers, manufacturers find it challenging to obtain accurate market information independently (Li et al., 2021). As a potential solution, manufacturers may rely on retailers’ demand information. Retailers, being closer to consumers, often have better access to market conditions. Advances in electronic data interchange technology have made it easier for retailers to share credible market information with suppliers. For instance, in 2017, the Tmall Innovation Center (TMIC) was established. As a market research division of Tmall, TMIC aims to enable firms make more informed decisions by providing accurate demand information. To date, TMIC has shared market information with over 80 manufacturers from various industries, including Estee Lauder, Shiseido, Johnson & Johnson, and Samsung.⁶ Firms may strategically change product line designs based on this information. For example, after information collaboration with TMIC in 2018, Mars Inc. added a new variant to its product line of Snickers candy bars.⁷

Existing management theories offer substantial insights into how retailers make information sharing decisions. Conventionally, information sharing is believed to harm the retailer’s profit margin by enabling the manufacturer to make strategic decisions, thereby undermining the retailer’s profitability (Narayanan and Raman, 2004). This conventional wisdom contrasts with the real-world observation that retailer information sharing is common in business practice. To explain this discrepancy, previous literature has attempted to understand the incentives behind retailer information sharing by identifying the conditions under which a retailer voluntarily shares information with a manufacturer. However, most extant works focus on scenarios where manufacturers sell only a single product variant to retailers, with limited attention to the product line scenario. Despite the prevalence of selling in product lines, the mechanisms behind retailer information sharing remain unclear. Firms’ operations and marketing strategies can differ significantly with varying product line lengths (Dong et al., 2019). Therefore, the managerial implications derived from current literature may not adequately guide firms’ information-sharing strategies in product line scenarios. As more firms improve their product line flexibility⁸ to better handle demand uncertainty (Yayla-küllü et al., 2021), it is necessary and urgent to develop theoretical guidance to help retailers optimize their information sharing strategies.

Motivated by the above discussion, this article studies how a manufacturer’s product line flexibility affects a retailer’s incentive to voluntarily share demand information. We apply a stylized model widely used in product line design literature (Dong et al., 2019) to characterize the manufacturer’s product line flexibility. The manufacturer can choose to produce either one or two product variants, incurring an exogenous constant product line extension fee when producing two variants. We also employ a classic characterization of information asymmetry between the manufacturer and the retailer (Huang et al., 2018). The manufacturer holds a prior belief about the demand distribution, while the retailer can privately access precise demand information. The sequence of events in this paper is as follows. Initially, the retailer makes commitments on whether to voluntarily share demand information with the manufacturer. As selling season approaches, the retailer realizes the demand information and then shares it (or not) as committed. Based on this result,⁹ the manufacturer determines the product line design (i.e., the length of the product line) and decides the wholesale price for each product variant. Finally, the retailer sets the retail price.

We aim to answer the following research questions. First, how does upstream product line flexibility affect a retailer’s information sharing strategy? Will the retailer have more incentives to voluntarily share demand information with the manufacturer when the product line design is uncertain? If so, what drives the retailer to share information voluntarily? Second, how does upstream product line flexibility affect the alignment between a retailer’s and a social planner’s preferences for retailer information sharing? Will the retailer’s information sharing decision align with the social planner’s in the presence of upstream product line flexibility? If so, under what conditions does this alignment occur? Third, how does the timing of the product line design choice affect the retailer’s incentive to share information? Does the retailer have more incentives to voluntarily share information when the manufacturer determines the product line design before or after demand is realized and information is shared? If so, under what conditions does this outcome occur?

Our work provides several interesting findings as follows. First, we show that upstream product line flexibility (i.e., an uncertain product line design) incentivizes a retailer to voluntarily share information when product substitutability is low and the product line extension fee is moderate. This insight contrasts with the conventional belief that retailers should keep demand information private to maintain an advantage over manufacturers. Our work uniquely highlights the critical role of upstream product line flexibility in motivating downstream information sharing. To our knowledge, this is the first attempt to examine how product line flexibility affects downstream information sharing. This finding complements the literature on information sharing by providing a new theoretical explanation for the discrepancy between the prevalence of information sharing in practice and the traditional academic prediction of non-sharing (Huang et al., 2018; Li et al., 2021). Our finding helps explain why downstream firms that do not face upstream encroachment or co-opetition may still voluntarily disclose private information in real-world business. When the manufacturer faces upstream product line flexibility, its product line design is uncertain when the retailer determines the information-sharing strategy. This uncertainty has conflicting effects (one negative and one positive) on the retailer’s profit from disclosing information. The negative effect is that information sharing may increase the retailer’s costs, as the manufacturer can make efficient pricing decisions with exact demand information, leading to higher wholesale prices. The positive effect is that information sharing may offer the retailer more chances to benefit from the upstream product line extension. Information sharing motivates the manufacturer to extend the product line when market demand is favorable, and the product line extension fee is moderate. Thus, the trade-off between these conflicting effects determines the retailer’s optimal information-sharing strategy. When product substitutability is low, the retailer may be more inclined to share information if the manufacturer determines the product line design after demand is realized and shared, as this timing can increase the probability of benefiting from product line extension under favorable demand conditions.

Second, we show that the retailer’s information sharing decision aligns with the social planner’s if product substitutability is sufficiently high or the product line extension fee is not moderate. Otherwise, inconsistencies arise between the retailer’s and the social planner’s decisions. When the product line extension fee is not moderate, the manufacturer’s product line decision is less likely to be influenced by the retailer’s information sharing strategy, making the positive effect of retailer information sharing inoperative. Therefore, neither the retailer nor the social planner prefers retailer information sharing under these circumstances, and inconsistency arises only if the product line extension fee is moderate. To the best of our knowledge, this finding is the first in the literature to highlight the critical role of product line extension cost in optimizing social welfare. It implies that, in addition to subsidies, the government can assist manufacturers in lowering the product line extension cost so that retailers may voluntarily make a socially optimal decision on information sharing. Therefore, our work complements the existing literature by revealing that, besides directly extending agility and adaptability (Yayla-küllü et al., 2021), product line flexibility can indirectly impact achieving PPP (Profit, People, and Planet) goals via retailer information sharing. For product substitutability, as it increases, the positive effect of product line extension on the retailer’s profit diminishes, making the negative effect of information sharing more significant. Consequently, both the retailer and the social planner prefer withholding information when product substitutability is high.

Third, we show that the timing of the product line design decision has no impact on the retailer’s information-sharing decision unless product substitutability is not sufficiently high, and the product line extension fee is moderate. This finding contributes to the ongoing debate on when downstream firms should disclose private information (Tang et al., 2023). Extant literature mainly considers encroachment or channel selection, while our paper examines this issue from the perspective of product line flexibility. When the product line extension fee is very large or very small, the manufacturer tends to produce a short or long product line, respectively, regardless of the retailer’s information sharing decision. In such cases, the positive effect of information sharing on the retailer’s profit becomes irrelevant, leading the retailer to withhold information. Therefore, if the product line extension cost is not moderate, the retailer’s incentive to share information is unaffected by the timing of product line design decision. As product substitutability increases, the positive effect of information sharing diminishes. Consequently, when product substitutability is sufficiently high, the negative impact of information sharing outweighs the positive effect on the retailer’s profit. In this scenario, regardless of whether the manufacturer decides on the product line design before or after demand is realized and shared, the retailer is likely to withhold information. Thus, when product substitutability is high, the retailer’s incentive to share information remains independent of the timing of the product line design choice. Specifically, when product substitutability is low, the retailer may have more incentives to share information if the manufacturer sets the product line design after demand is realized and shared. If the manufacturer determines the product line design before demand is realized and shared, the retailer’s decision to share information will always lead the manufacturer to extend the product line. However, if the manufacturer determines the product line design after demand is realized and shared, the retailer’s choice to share information does not always lead to extension of the manufacturer’s product line. In cases of sufficiently low market demand, the manufacturer may decide not to extend the product line even if the retailer shares information. When product substitutability is low enough, it can motivate the manufacturer to extend the product line even in the face of unfavorable market demand. Therefore, when the manufacturer determines the product line design after demand is realized and shared, low product substitutability increases the likelihood that the retailer would benefit from the positive effects of information sharing, making the retailer more inclined to voluntarily share information.

The remain in part of this article is organized as follows: Section 2 reviews the related literature, and Section 3 lays out the model. The main findings are presented in Sections 4 and 5. Section 6 considers several model extensions, and Section 7 concludes the article.

2. Literature Review

This article is related to the vast literature on information sharing. In recent years, there are two main streams in this research area. One examines the effect of information sharing. For example, Jiang et al. (2016) examined three formats of upstream information sharing: no information sharing, voluntary information sharing, and mandatory information sharing. They show that the retailer prefers no information sharing while the manufacturer prefers mandatory information sharing. Clottey and Benton (2020) analyzed the value of a supplier sharing information about the quality-distribution of components with an assembler. Tsunoda and Zennyo (2021) explored how platform information sharing affects third-party suppliers and offline retailers, showing that the platform’s information sharing capability makes the agency model more likely to be adopted. Guan et al. (2023) examined the value of the manufacturer’s information acquisition and sharing in a supply chain with manufacturer encroachment. The other research stream explores how other operations and marketing strategies affect information sharing. For example, Huang et al. (2018) showed that a retailer may voluntarily share demand information in anticipation of supplier encroachment. Li et al. (2021) find that agency contracts may incentivize an online retailer to share information with the manufacturer. Ha et al. (2022) showed that encroachment and information sharing are complementary and suggest managers should not ignore the impact of one decision on the other, even when the latter is not a primary motivation of the former. Li and Zhang (2023) proposed a new wholesale pricing mechanism that promotes information sharing between a relatively weaker retailer and a more powerful manufacturer, benefiting both parties.

This article is also related to the broad literature on product line design. In recent years, papers in this literature have focused mainly on how other operations management and marketing factors affect product line design. For example, Jing (2016) analyzes the interactions between consumer evaluation costs and product differentiation under duopoly when firms can adopt customer learning investment to lower consumer evaluation costs. Dong et al. (2019) examined the effects of how demand risk is contractually allocated on product line length and stocking quantities. Kuksov and Liao (2019) analyzed how a firm should adjust its product variety in the presence of social communication, showing that such adjustments may be either upward or downward. Lu et al. (2019) showed that, for co-products, the length of the product line is smaller in an indirect channel than in a direct channel. Zou et al. (2020) demonstrated that the quality difference in a product line will be larger (smaller) if consumers’ anticipated regret increases (reduces) profit. Ji et al. (2022) examined how social communications affect an upstream firm’s product line design in the platform economy and find that social communications can increase product line length while decreasing product price and quality. Huh and Li (2023) analyzed product-line pricing while considering the dual objective of profit and consumer surplus.

Unlike existing studies, our work contributes to the literature in the following three ways. First, the extant works in the literature on information sharing consider mainly a manufacturer selling only a single product variant to the retailer, and few of them pay attention to the product line scenario. To the best of our knowledge, our paper is the first to suggest that upstream product line flexibility can significantly impact retailer information sharing. Our analysis shows that when product substitutability is low and the product line extension fee is moderate, upstream product line flexibility incentivizes a retailer to share information voluntarily. Second, unlike the current literature on product line design, our work focuses on an asymmetric information setting in a supply chain, where the retailer possesses superior demand information. We aim to explore the retailer’s information-sharing strategy with upstream product line flexibility. Our work sheds light on how to resolve the supply chain information asymmetry problem in the context of consumer products being sold in product lines rather than in single product variants. Third, our work identifies the conditions under which a retailer’s decision on information sharing is also socially optimal in the presence of upstream product line flexibility. Thus, our work provides policymakers with an alternative solution for optimizing social welfare besides subsidies: to lower the product line extension cost so that the retailers may voluntarily make the socially optimal decision on information sharing.

3. Model

Consider an upstream manufacturer selling a horizontally differentiated product line through an intermediate retailer. The market consists of a continuum of consumers. To illustrate the main results and mechanisms, we follow the extant literature (Dong et al., 2019) by assuming that the product line length $N$ is no more than 2; that is, the manufacturer can produce either a single product variant or two substitutive variants. The key notations are summarized in Table 1.

Table 1.
Parameters and decision variables.

Symbol Definition

$N$ Product line length

$w_{s}$ Wholesale price for the single variant

$w_{i}$ Wholesale price for variant $i$

$p_{s}$ Retail price for the single variant

$p_{i}$ Retail price for variant $i$

$θ$ Random market size due to uncertainty

$u$ Expectation of random market size due to uncertainty

$f$ Product line extension fee

$β$ Product substitutability

$D_{s}$ Consumer demand for the single product variant

$D_{i}$ Consumer demand for variant $i$ in the product line

Symbol	Definition
$N$	Product line length
$w_{s}$	Wholesale price for the single variant
$w_{i}$	Wholesale price for variant $i$
$p_{s}$	Retail price for the single variant
$p_{i}$	Retail price for variant $i$
$θ$	Random market size due to uncertainty
$u$	Expectation of random market size due to uncertainty
$f$	Product line extension fee
$β$	Product substitutability
$D_{s}$	Consumer demand for the single product variant
$D_{i}$	Consumer demand for variant $i$ in the product line

3.1. Manufacturer and Retailer

The manufacturer sets wholesale price $w_{s}$ for the single product variant when $N = 1$ or $w_{i}$ for each product variant $i$ when $N = 2$ . Subsequently, the retailer charges consumers $p_{s}$ for the single product variant when $N = 1$ or $p_{i}$ for each product variant $i$ when $N = 2$ . For mathematical simplicity and without loss of generality, we normalize the manufacturer’s marginal production cost to zero. Additionally, the manufacturer incurs an exogenous and constant product line extension fee $f$ when choosing $N = 2$ .

3.2. Market

In line with the literature (Dong et al., 2019), we consider a continuum of consumers of the same type with a utility function that is separable and linear in a numeraire good. If $N = 1$ , the representative consumer maximizes $(1 + θ) D_{s} - \frac{1}{2} D_{s}^{2} - p_{S} D_{s}$ , where $D_{s}$ is the demand and $θ$ captures market uncertainty, uniformly distributed on $[0, 2 u]$ with $u ⩽ 1$ . It represents the random market size due to uncertainty. If $N = 2$ , the representative consumer maximizes $U (D_{1}, D_{2}) - p_{1} D_{1} - p_{2} D_{2}$ , where $D_{i}$ ( $i = 1, 2$ ) is the demand for product variant $i$ , and $U (D_{1}, D_{2}) = (1 + θ) (D_{1} + D_{2}) - \frac{1}{2} (D_{1}^{2} + D_{2}^{2} + 2 β D_{1} D_{2})$ . The term $0 < β < 1$ measures product substitutability.

3.3. Model Timing

In real-world business, the retailer typically has more advantages than the manufacturer in resolving consumer uncertainty before demand materializes, as the retailer is often closer to consumers in major supply chain systems. Accordingly, we assume that the retailer can privately obtain the exact demand information $θ$ before demand materializes, while the manufacturer maintains its initial belief on consumer demand. This assumption is consistent with previous literature (Guo, 2009; Mittendorf et al., 2013). We model the interaction between the manufacturer and the retailer using a stylized Stackelberg game. In the game, the retailer moves first as a leader to determine whether to share realized demand information with the manufacturer. Then, the manufacturer moves as a follower to choose between offering a short ( $N = 1$ ) or long ( $N = 2$ ) product line. In line with the related literature, such as Arya and Mittendorf (2011) and Huang et al. (2018), the retailer’s information sharing decision is assumed to be binding and irreversible. Figure 1 illustrates the model timing. As illustrated in Figure 1, the sequence of events unfolds as follows:

In the first stage, the retailer decides whether to share information before privately obtaining the exact demand information in the second stage.

In the third stage, the manufacturer makes the product line decision.

Depending on the decisions made by the retailer and the manufacturer, four possible scenarios, or subgames, can arise, each differing in terms of pricing:

If the retailer chooses to not share information and the manufacturer produces only one product variant (i.e., $N = 1$ ), the manufacturer first sets wholesale price $w_{s}^{N}$ , followed by the retailer setting the retail price $p_{s}^{N}$ .

If the retailer chooses to not share information and the manufacturer produces two product variants (i.e., $N = 2$ ), the manufacturer first sets wholesale price $w_{i}^{N}$ for each variant, and then the retailer sets the retail price $p_{i}^{N}$ .

If the retailer chooses to share information and the manufacturer produces only one product variant (i.e., $N = 1$ ), the manufacturer first sets wholesale price $w_{s}^{S}$ , followed by the retailer setting the retail price $p_{s}^{S}$ .

If the retailer chooses to share information and the manufacturer produces two product variants (i.e., $N = 2$ ), the manufacturer first sets wholesale price $w_{i}^{S}$ for each variant, and then the retailer sets the retail price $p_{i}^{S}$ .

Finally, in the fifth stage, consumers make their purchase decisions.

4. Results

In this section, we analyze the manufacturer’s product line design and the retailer’s contract choice sequentially. The analysis of social welfare is presented at the end of the section.

4.1. Manufacturer’s Product Line Design

We begin by examining the manufacturer’s product line design in scenarios where the retailer chooses to either keep its information private or share it. First consider the case where the retailer opts to keep the information private. The following lemma summarizes the equilibrium prices and profits.

Lemma 1
Given that the retailer chooses not to share the information: (1)
When the manufacturer chooses to produce only one product variant ( $N = 1$ ), it sets the wholesale price $w_{s}^{N} = \frac{1 + u}{2}$ . The retailer charges consumers a retail price $p_{s}^{N} = \frac{3 + 2 θ + u}{4}$ . The manufacturer’s and the retailer’s profits are $π_{s M}^{N} = \frac{(1 + u)^{2}}{8}$ and $π_{s R}^{N} = \frac{(1 + 2 θ - u)^{2}}{16}$ , respectively.
(2)
When the manufacturer chooses to produce two product variants ( $N = 2$ ), it sets wholesale prices $w_{1}^{N} = w_{2}^{N} = \frac{1 + u}{2}$ . The retailer charges consumers retail prices $p_{1}^{N} = p_{2}^{N} = \frac{3 + 2 θ + u}{4}$ . The manufacturer’s and the retailer’s profits are $π_{t M}^{N} = \frac{(1 + u)^{2}}{4 (1 + β)} - f$ and $π_{t R}^{N} = \frac{(1 + 2 θ - u)^{2}}{8 (1 + β)}$ , respectively.
(3)
The manufacturer chooses to produce two product variants ( $N = 2$ ) if and only if the product line extension fee $f ⩽ \frac{(1 + u)^{2} (1 - β)}{8 (1 + β)}$ . Otherwise, the manufacturer chooses to produce only one product variant ( $N = 1$ ).

For ease of readability, we leave all proofs of this article to the Appendix. According to Lemma 1, when the retailer opts to keep its realized demand information private, the manufacturer chooses to produce two product variants if and only if the product line extension fee $f$ is sufficiently low. It is easy to verify that $\frac{(1 + u)^{2} (1 - β)}{8 (1 + β)}$ increases in the expectation of the random market size $u$ but decreases in product substitutability $β$ . Thus, Lemma 1 implies that when the retailer does not share information with the manufacturer, increasing the expected market size or reducing product substitutability can incentivize the manufacturer to extend the product line. The rationale behind this finding is as follows. Offering a longer product line enables the manufacturer to serve more consumers. However, if the market size is limited, efforts to increase demand through product line extension may not be successful. Therefore, market expansion can encourage the manufacturer to extend the product line. When the manufacturer does not recieve the exact demand information from the retailer, it bases its decision on expected demand. Consequently, the anticipation of a large random market size boosts the manufacturer’s incentive to extend the product line. Conversely, when product substitutability is high, consumers are more likely to choose between the two variants, which reduces the positive impact of product line extension on demand expansion. As a result, the manufacturer may opt for a shorter product line when product substitutability is high.

Next, we consider the scenario where the retailer chooses to share information. The equilibrium results are summarized in Lemma 2.
Lemma 2
Given that the retailer chooses to share information: (1)
When the manufacturer chooses to produce only one product variant ( $N = 1$ ), it sets the wholesale price $w_{s}^{S} = \frac{1 + θ}{2}$ . The retailer charges consumers a retail price $p_{s}^{S} = \frac{3 + 3 θ}{4}$ . The manufacturer’s and the retailer’s profits are $π_{s M}^{S} = \frac{(1 + θ)^{2}}{8}$ and $π_{s R}^{S} = \frac{(1 + θ)^{2}}{16}$ , respectively.
(2)
When the manufacturer chooses to produce two product variants ( $N = 2$ ), it sets wholesale prices $w_{1}^{S} = w_{2}^{S} = \frac{1 + θ}{2}$ . The retailer charges consumers retail prices $p_{1}^{S} = p_{2}^{S} = \frac{3 + 3 θ}{4}$ . The manufacturer’s and the retailer’s profits are $π_{t M}^{S} = \frac{(1 + θ)^{2}}{4 (1 + β)} - f$ and $π_{t R}^{S} = \frac{(1 + θ)^{2}}{8 (1 + β)}$ , respectively.
(3)
The manufacturer chooses to produce two product variants ( $N = 2$ ) if and only if the product line extension fee $f ⩽ \frac{(1 + θ)^{2} (1 - β)}{8 (1 + β)}$ . Otherwise, the manufacturer chooses to produce only one product variant ( $N = 1$ ).

Lemma 2 shows that when the retailer shares the realized demand information, the manufacturer chooses to produce two product variants ( $N = 2$ ) if and only if the product line extension fee $f ⩽ \frac{(1 + θ)^{2} (1 - β)}{8 (1 + β)}$ . Since $\frac{(1 + θ)^{2} (1 - β)}{8 (1 + β)}$ increases with the random market size $θ$ but decreases with product substitutability $β$ , Lemma 2 implies that when the retailer discloses the realized demand information, the manufacturer’s incentive to extend the product line can be enhanced by increasing the random market size or reducing product substitutability. The difference between the no-information-sharing and the information-sharing scenarios is that when the retailer commits to sharing the realized demand information, the manufacturer’s product line decision becomes independent of the expectation of the random market size $u$ . The rationale is that when the retailer chooses to share information, the manufacturer obtains the exact demand information before product line design. This acquisition of exact demand information allows the manufacturer to evaluate the benefits of product line extension more efficiently, thus eliminating the risk of potential loss due to consumer uncertainty.

In addition, Lemma 2, in conjunction with Lemma 1, shows that when there is unfavorable market demand (i.e., $θ < u$ ), retailer information sharing may incentivize the manufacturer to offer a short product line. Specifically, when $θ < u$ , a manufacturer with a moderate product line extension fee (i.e., $\frac{(1 + θ)^{2} (1 - β)}{8 (1 + β)} < f < \frac{(1 + u)^{2} (1 - β)}{8 (1 + β)}$ ) chooses to produce two product variants in the no-information-sharing scenario but opts for only one product variant in the information-sharing scenario. This finding suggests that when the manufacturer’s product line design is determined after the retailer’s observation of the exact demand information, information sharing cannot lead to product line extension if the market demand is unfavorable.
4.2. Retailer’s Information-Sharing Decision

In this section, we examine the retailer’s information sharing decision. As shown in Section 3.3, the retailer decides on the information-sharing strategy based on the expected profit. According to Lemma 1, when the retailer does not share information, its expected profit is

E [π_{R}^{N}] = {\begin{cases} \int_{0}^{2 u} \frac{(1 + 2 θ - u)^{2}}{16 (1 + β) u} d θ, & if f ⩽ \frac{(1 + u)^{2} (1 - β)}{8 (1 + β)}, \\ \int_{0}^{2 u} \frac{(1 + 2 θ - u)^{2}}{32 u} d θ, & otherwise . \end{cases}

(1)

According to Lemma 2, when sharing the information, the retailer’s expected profit is

\begin{aligned} E [π_{R}^{S}] & = \int_{0}^{min {[\arg {h (x) = f}]^{+}, 2 u}} \frac{(1 + θ)^{2}}{32 u} d θ \\ + \int_{min {[\arg {h (x) = f}]^{+}, 2 u}}^{2 u} \frac{(1 + θ)^{2}}{16 (1 + β) u} d θ, \end{aligned}

(2)

where

h (x) = \frac{(1 + x)^{2} (1 - β)}{8 (1 + β)}

. Then, we have Proposition 1 below to characterize the retailer’s information-sharing decision. For convenience, we define

{\bar{f}}_{s 1} = \frac{(1 + 6 u + 12 u^{2} + \frac{2 - 14 β}{1 - β} u^{3})^{\frac{2}{3}} (1 - β)}{8 (1 + β)}

Proposition 1

The retailer voluntarily shares the realized demand information with the manufacturer if and only if $0 ⩽ β < \frac{3 + 9 u + u^{2}}{3 + 9 u + 13 u^{2}}$ and $\frac{(1 + u)^{2} (1 - β)}{8 (1 + β)} < f ⩽ {\bar{f}}_{s 1}$ .

Proposition 1 shows that when product substitutability is low (i.e., $0 ⩽ β < \frac{3 + 9 u + u^{2}}{3 + 9 u + 13 u^{2}}$ ) and the product line extension fee is moderate (i.e., $\frac{(1 + u)^{2} (1 - β)}{8 (1 + β)} < f ⩽ {\bar{f}}_{s 1}$ ), the retailer prefers to voluntarily share the realized demand information. Note that when the manufacturer’s product line decision (i.e., choice between $N = 1$ and $N = 2$ ) is predetermined, the retailer would withhold information regardless of the manufacturer’s choice. Therefore, Proposition 1 implies that when the upstream product line design is uncertain, the retailer’s incentive to share information can be enhanced if product substitutability is low and the product line extension fee is moderate. This finding uniquely underscores the critical role of upstream product line design in motivating retailer information sharing. While the conventional wisdom suggests that a retailer should keep private realized demand information to maintain an advantage over the manufacturer, we show that the retailer might prefer to voluntarily disclose this information to the manufacturer when the upstream product line design is uncertain. The rationale is as follows. When the manufacturer’s product line design is uncertain, sharing privately realized demand information to the manufacturer can have two conflicting (both negative and positive) effects on the retailer’s profit. The negative effect is that information sharing may increase the retailer’s cost. By disclosing information to the manufacturer, the retailer might face higher wholesale prices, as the manufacturer could make more efficient pricing decisions with precise demand information. The positive effect is that information sharing might provide the retailer with more opportunities to benefit from the upstream product line extension. Information sharing can incentivize the manufacturer to extend the product line under favorable conditions. As shown inSection 4.1, when market demand is favorable (i.e., $θ > u$ ), a manufacturer that would otherwise produce a short product line (i.e., $N = 1$ ) in the absence of retailer information sharing might produce a long product line (i.e., $N = 2$ ) under shared information if the product line extension fee is not very high (i.e., $\frac{(1 + u)^{2} (1 - β)}{8 (1 + β)} < f < \frac{(1 + θ)^{2} (1 - β)}{8 (1 + β)}$ ). Thus, the trade-off between these two conflicting effects of information sharing determines the retailer’s optimal information-sharing strategy.

When the upstream product line design is uncertain, the retailer’s primary motivation for sharing demand information is to influence the manufacturer’s product line decision, thereby facilitating product line extension. If the product line extension fee is sufficiently small, the manufacturer would offer a long product line even if the retailer withholds demand information. Conversely, if the product extension fee is sufficiently large, the manufacturer may prefer a short product line even if the retailer shares information. Thus, for a retailer, it is profitable to share the realized demand information only when the manufacturer’s product line extension fee is moderate. In addition, as product substitutability increases, the benefit of product line extension to the retailer is diminished. In this scenario, the positive effect of information sharing on the retailer’s profit may no longer outweigh the negative effect. Thus, it is advantageous for the retailer to share information only when product substitutability is sufficiently low.

Next, we analyze how the threshold values of product substitutability $β$ and the product line extension fee $f$ change along with other parameters. First, for the upper bound of product substitutability (i.e., $\frac{3 + 9 u + u^{2}}{3 + 9 u + 13 u^{2}}$ ), it is easy to verify that this value decreases with an increase in the expected random market size $u$ . This finding implies that, all else being equal, a higher expectation of random market size makes the retailer less likely to share information. As the expected random market size $u$ increases, the profit loss that because of product substitution in a long product line is magnified. Consequently, the positive impact that information sharing has on the retailer’s profit is diminished, weakening the retailer’s incentive to share information.

We then consider the threshold values of the product line extension fee. For the lower bound, (i.e., $\frac{(1 + u)^{2} (1 - β)}{8 (1 + β)}$ ), it is clear that this value increases with the expectation of random market size $u$ but decreases with product substitutability $β$ . This indicates that as the expectation of random market size increases or as product substitutability decreases, the retailer is less inclined to disclose information to a manufacturer with a relatively low product line extension cost. The rationale behind this finding is as follows. When the product line extension fee is relatively small, a higher expectation of random market size or lower product substitutability provides the manufacturer more incentives to extend the product line in the no-information-sharing scenario. Consequently, the positive effect of information sharing fails, and only the negative effect remains. Therefore, the retailer would choose to withhold the demand information. For the upper bound (i.e., ${\bar{f}}_{s 1}$ ), the results are summarized in Lemma 3 below.

Lemma 3

Suppose that $0 ⩽ β < \frac{3 + 9 u + u^{2}}{3 + 9 u + 13 u^{2}}$ . (1)

${\bar{f}}_{s 1}$ decreases in $β$ .

(2)

${\bar{f}}_{s 1}$ first increases and then decreases in $u$ , and obtains the maximum at $u = \frac{2 - 2 β + \sqrt{3} \sqrt{1 - β^{2}}}{7 β - 1}$ if $β > \frac{1}{2}$ . Otherwise, ${\bar{f}}_{s 1}$ increases in $u$ .

We first examine how the upper bound of the product line extension fee (i.e., ${\bar{f}}_{s 1}$ ) changes with product substitutability $β$ . Lemma 3 shows that the upper bound of the product line extension fee decreases as product substitutability increases. Recall from Proposition 1 that the retailer would not share demand information when the manufacturer’s product line extension fee $f$ exceeds ${\bar{f}}_{s 1}$ . Thus, Lemma 3 suggests that high product substitutability discourages the retailer from sharing demand information with a manufacturer whose product line extension fee is relatively large. When product substitutability is high, a manufacturer with a relatively large product line extension fee has less incentive to offer a long product line due to the loss of profit from product substitution. Conversely, all else being equal, an increase in product substitutability reduces the retailer’s additional profit from the product line extension. Due to these two factors, the negative effect of information sharing outweighs the positive effect in this scenario, leading the retailer to withhold demand information. We illustrate this finding graphically in Figure EC.1, which is included in the e-companion.

Next, we analyze how the upper bound of the product line extension fee (i.e., ${\bar{f}}_{s 1}$ ) changes with the expectation of random market size $u$ . As shown in Lemma 3, if product substitutability $β$ is sufficiently high (i.e., $β > \frac{1}{2}$ ), the upper bound of the product line extension fee increases with the expectation of random market size when $u ⩽ \frac{2 - 2 β + \sqrt{3} \sqrt{1 - β^{2}}}{7 β - 1}$ but decreases when $u > \frac{2 - 2 β + \sqrt{3} \sqrt{1 - β^{2}}}{7 β - 1}$ . If product substitutability is sufficiently low (i.e., $β ⩽ \frac{1}{2}$ ), the upper bound of the product line extension fee increases with the expectation of random market size. Recall from in Proposition 1 that the retailer would not share information with a manufacturer whose product line extension fee exceeds ${\bar{f}}_{s 1}$ . Thus, Lemma 3 implies that increasing the expectation of random market size does not always lead to retailer information sharing for manufacturers with a larger product line extension fee. The rationale behind this finding is as follows. The higher product substitutability is, the less attractive it is for a manufacturer to produce a long product line. Consequently, higher product substitutability makes it harder for the retailer benefit from the positive effects of information sharing. On the other hand, as the expectation of random market size increases, the retailer’s expected profit from withholding information also increases. Consequently, due to these two effects, the retailer is less likely disclose information to a manufacturer with a high product line extension fee when both product substitutability and the expectation of random market size are sufficiently large. We provide two graphical illustrations of this finding in Figures EC.2 and EC.3, which are included in the e-companion.

Next, we analyze the equilibrium strategies for the retailer’s information sharing and the manufacturer’s product line design. For convenience, we use IS-i (resp., NS-i) to represent the case in which the retailer chooses information sharing (resp., no information sharing) and the manufacturer chooses $N = i$ . According to Proposition 1, when product substitutability is sufficiently high (i.e., $β ⩾ \frac{3 + 9 u + u^{2}}{3 + 9 u + 13 u^{2}}$ ), the retailer always withholds information. In this scenario, the equilibrium strategy is NS-1 if $f > \frac{(1 + u)^{2} (1 - β)}{8 (1 + β)}$ , and is NS-2 if $f ⩽ \frac{(1 + u)^{2} (1 - β)}{8 (1 + β)}$ . When product substitutability is sufficiently low (i.e., $β < \frac{3 + 9 u + u^{2}}{3 + 9 u + 13 u^{2}}$ ), the retailer voluntarily discloses the information if and only if the product line extension fee is moderate (i.e., $\frac{(1 + u)^{2} (1 - β)}{8 (1 + β)} < f ⩽ {\bar{f}}_{s 1}$ ). In this circumstance, the equilibrium strategy is IS-1 if $\frac{(1 + u)^{2} (1 - β)}{8 (1 + β)} < f ⩽ {\bar{f}}_{s 1}$ and $f > \frac{(1 + θ)^{2} (1 - β)}{8 (1 + β)}$ , IS-2 if $\frac{(1 + u)^{2} (1 - β)}{8 (1 + β)} < f ⩽ {\bar{f}}_{s 1}$ and $f < \frac{(1 + θ)^{2} (1 - β)}{8 (1 + β)}$ , NS-1 if $f > {\bar{f}}_{s 1}$ , and NS-2 if $f < \frac{(1 + u)^{2} (1 - β)}{8 (1 + β)}$ . We illustrate the above results in Figures 2 and 3 with $θ = 0.4$ . Figure 2 represents the case with low product substitutability ( $β = 0.25$ ), while Figure 3 represents the case with high product substitutability ( $β = 0.75$ ). As shown in Figure 3, as $u$ increases, IS-1 and IS-2 disappear becauses $β = 0.75$ becomes larger than the threshold value at that point.

4.3. Social Welfare

In this section, we consider a scenario where a social planner determines the retailer’s information-sharing policy with the objective of maximizing social welfare. Our goal is to identify the conditions under which the retailer’s decision to share information aligns with the social planner’s decision.

Similar to previous studies (Liu and Cui, 2010), we calculate social welfare by summing the supply chain profit and consumer welfare. According to Lemmas 1 and 2, social welfare is defined as follows:

When the retailer does not share information and the manufacturer produces a short product line ( $N = 1$ ), social welfare is $\frac{(1 + 2 θ - u) (7 + 6 θ + u)}{32}$ .

When the retailer does not share information and the manufacturer produces a long product line ( $N = 2$ ), social welfare is $\frac{(1 + 2 θ - u) (7 + 6 θ + u)}{16 (1 + β)} - f$ .

When the retailer shares information and the manufacturer produces a short product line ( $N = 1$ ), social welfare is $\frac{7 (1 + θ)^{2}}{32}$ .

When the retailer shares information and the manufacturer produces a long product line ( $N = 2$ ), social welfare is $\frac{7 (1 + θ)^{2}}{16 (1 + β)} - f$ .

We first explore the conditions under which a social planner would prefer the retailer to share information. The results are summarized in Proposition 2 below.

Proposition 2
A social planner would prefer the retailer to share demand information with the manufacturer if and only if $β < \frac{9 + 39 u + 27 u^{2}}{9 + 39 u + 47 u^{2}}$ and $\frac{(1 + u)^{2} (1 - β)}{8 (1 + β)} < f ⩽ {\bar{f}}_{s s}$ , where ${\bar{f}}_{s s}$ satisfies
$\begin{aligned} \int_{0}^{min {[\arg {h (x) = \bar{f}}]^{+}, 2 u}} \frac{7 (1 + θ)^{2}}{64 u} d θ \\ + \int_{min {[\arg {h (x) = \bar{f}}]^{+}, 2 u}}^{2 u} {\frac{7 (1 + θ)^{2}}{16 (1 + β)} - \bar{f}} \frac{d θ}{2 u} \\ = \int_{0}^{2 u} \frac{(1 + 2 θ - u) (7 + 6 θ + u)}{64 u} d θ . \end{aligned}$
(3)

Proposition 2 shows that when product substitutability is low (i.e., $β < \frac{9 + 39 u + 27 u^{2}}{9 + 39 u + 47 u^{2}}$ ) and the product line extension fee is moderate (i.e., $\frac{(1 + u)^{2} (1 - β)}{8 (1 + β)} < f ⩽ {\bar{f}}_{s s}$ ), the social planner prefers the retailer to share demand information with the manufacturer. Note that when the manufacturer’s product line decision (i.e., choice between $N = 1$ and $N = 2$ ) is exogenously deterministic, the social planner always prefers the retailer to keep the information private. Thus, Proposition 2 implies that when the social planner faces an uncertain upstream product line design, the incentive to make the retailer share demand information is strengthened if product substitutability is small and the product line extension fee is moderate. The rationale is as follows. When the manufacturer’s product line design is uncertain, allowing the retailer to share demand information with the manufacturer can have two conflicting effects on social welfare, one negative and one positive. The negative effect is that making the retailer share information may intensify double marginalization. With the exact demand information, the manufacturer can make more efficient price decisions to optimize its profit. As a consequence, the retailer may need to raise the retail price to avoid excessive profit loss, intensifying double marginalization. The positive effect is that making the retailer share information is likely to increase consumer welfare by adding product variety. Retailer information sharing can motivate the manufacturer to provide the socially optimal product line length under certain conditions. When market demand is favorable (i.e., $θ > u$ ), the manufacturer’s incentive to provide the socially optimal product line length is strengthened by retailer information sharing. Specifically, as shown inSection 4.1, a manufacturer who would produce a short product line (i.e., $N = 1$ ) without retailer information sharing will produce a long product line (i.e., $N = 2$ ) when the information is shared if the product line extension fee is not very high (i.e., $\frac{(1 + u)^{2} (1 - β)}{8 (1 + β)} < f < \frac{(1 + θ)^{2} (1 - β)}{8 (1 + β)}$ ). Thus, the trade-off between these two conflicting effects determines whether the social planner should make the retailer share demand information with the manufacturer. When the upstream product line design is uncertain, the main reason for a social planner to make the retailer share demand information is to influence the manufacturer’s product line decision, facilitating the socially optimal product line length. If the product line extension fee is sufficiently small, the manufacturer would offer a long product line even if the retailer withholds demand information. Conversely, if the product extension fee is sufficiently large, the manufacturer may prefer a short product line even if the retailer shares information. Therefore, only when the product line extension fee is moderate should a social planner make the retailer share demand information with the manufacturer. In addition, since consumer welfare decreases with product substitutability when the manufacturer offers a long product line, the positive effect of retailer information sharing on social welfare may not offset the negative effect. Thus, the social planner should only make the retailer share information when product substitutability is sufficiently low.

Figure 4.
Illustration of retailer’s and social planner’s preference on retailer information sharing ( $β = 0$ ).

A graphic illustration of Proposition 2 is given in Figure 4. In this figure, we set $β = 0$ , and there are four types of lines. The solid line represents ${\bar{f}}_{s s}$ , as defined in Proposition 2. The densely dotted line represents $\frac{(1 + u)^{2} (1 - β)}{8 (1 + β)}$ , and the densely dashed line represents $\frac{(1 + 2 u)^{2} (1 - β)}{8 (1 + β)}$ . The loosely dotted line represents ${\bar{f}}_{s 1}$ , which is defined in Proposition 1. According to Proposition 1, when $\frac{(1 + u)^{2} (1 - β)}{8 (1 + β)} < f ⩽ {\bar{f}}_{s 1}$ , the retailer voluntarily shares demand information with the manufacturer. In Figure 4, the area between the loosely dotted line and the densely dotted line represents the case where $\frac{(1 + u)^{2} (1 - β)}{8 (1 + β)} < f ⩽ {\bar{f}}_{s 1}$ . As shown in Figure 4, the area between the loosely dotted line and the densely dotted line is contained in the area between the solid line and the densely dotted line. This indicates that when $β = 0$ , the retailer’s decision on information sharing aligns with the decision of a social planner if the product line extension fee is either very small (i.e., $f ⩽ {\bar{f}}_{s 1}$ ) or very large (i.e., $f > {\bar{f}}_{s s}$ ). Conversely, if the product line extension fee is moderate (i.e., ${\bar{f}}_{s 1} < f ⩽ {\bar{f}}_{s s}$ ), according to Propositions 1 and 2, the retailer opts not to share information with the manufacturer even if the social planner prefers information sharing. This finding implies that when $β = 0$ , the social planner shows more preference for retailer information sharing than the retailer does.

Next, we investigate whether the finding observed in Figure 4 (i.e., the case of $β = 0$ ) holds for an arbitrary $β$ . Before proceeding, we present Lemma 4 below.
Lemma 4
Given that $\bar{f} \in (\frac{(1 + u)^{2} (1 - β)}{8 (1 + β)}, \frac{(1 + 2 u)^{2} (1 - β)}{8 (1 + β)})$ is the solution to
$\begin{aligned} \int_{0}^{min {[\arg {h (x) = \bar{f}}]^{+}, 2 u}} \frac{7 (1 + θ)^{2}}{64 u} d θ \\ + \int_{min {[\arg {h (x) = \bar{f}}]^{+}, 2 u}}^{2 u} {\frac{7 (1 + θ)^{2}}{16 (1 + β)} - \bar{f}} \frac{d θ}{2 u} \\ = \int_{0}^{2 u} \frac{(1 + 2 θ - u) (7 + 6 θ + u)}{64 u} d θ, \end{aligned}$
(4)
where $h (x) = \frac{(1 + x)^{2} (1 - β)}{8 (1 + β)}$ . Then, ${\bar{f}}_{s s} > {\bar{f}}_{s 1}$ if and only if $8 u^{3} (1 + β) > 3 (2 u + 1 - K) (1 - β) K^{2}$ , where $K = \sqrt[3]{1 + 6 u + 12 u^{2} + \frac{2 - 14 β}{1 - β} u^{3}}$ .

Recall that when $β < \frac{3 + 9 u + u^{2}}{3 + 9 u + 13 u^{2}}$ , the retailer voluntarily shares information if and only if $\frac{(1 + u)^{2} (1 - β)}{8 (1 + β)} < f ⩽ {\bar{f}}_{s 1}$ , and when $β < \frac{9 + 39 u + 27 u^{2}}{9 + 39 u + 47 u^{2}}$ , the social planner prefers the retailer to share information if and only if $\frac{(1 + u)^{2} (1 - β)}{8 (1 + β)} < f ⩽ {\bar{f}}_{s s}$ . Lemma 4 shows that for $\forall β < \frac{3 + 9 u + u^{2}}{3 + 9 u + 13 u^{2}}$ , if product substitutability $β$ and the expectation of random market size $u$ satisfy $8 u^{3} (1 + β) > 3 (2 u + 1 - K) (1 - β) K^{2}$ , the social planner prefers retailer information sharing, but the retailer would not voluntarily disclose information when the product line extension fee is moderate (i.e., ${\bar{f}}_{s 1} < f ⩽ {\bar{f}}_{s s}$ ). In fact, when $β < \frac{3 + 9 u + u^{2}}{3 + 9 u + 13 u^{2}}$ , the inequality $8 u^{3} (1 + β) > 3 (2 u + 1 - K) (1 - β) K^{2}$ strictly holds for $\forall u \in [0, 1]$ . Thus, Lemma 4 implies that when product substitutability is sufficiently low (i.e., $β < \frac{3 + 9 u + u^{2}}{3 + 9 u + 13 u^{2}}$ ), the retailer’s decision on information sharing is not consistent with the decision of the social planner if and only if the product line extension is medium (i.e., ${\bar{f}}_{s 1} < f ⩽ {\bar{f}}_{s s}$ ). Specifically, when $β < \frac{3 + 9 u + u^{2}}{3 + 9 u + 13 u^{2}}$ and ${\bar{f}}_{s 1} < f ⩽ {\bar{f}}_{s s}$ , the social planner prefers retailer information sharing, but the retailer would not voluntarily share information with the manufacturer. In contrast, if product substitutability is moderate (i.e., $\frac{3 + 9 u + u^{2}}{3 + 9 u + 13 u^{2}} ⩽ β < \frac{9 + 39 u + 27 u^{2}}{9 + 39 u + 47 u^{2}}$ ), according to Proposition 2, the social planner prefers the retailer to share information when the product line extension fee is moderate (i.e., $\frac{(1 + u)^{2} (1 - β)}{8 (1 + β)} < f ⩽ {\bar{f}}_{s s}$ ). However, in this circumstance, as shown in Proposition 1, the retailer would not voluntarily disclose information regardless of the product line extension fee. Thus, when $\frac{3 + 9 u + u^{2}}{3 + 9 u + 13 u^{2}} ⩽ β < \frac{9 + 39 u + 27 u^{2}}{9 + 39 u + 47 u^{2}}$ , the retailer’s decision on information sharing is not consistent with the decision of the social planner if and only if $\frac{(1 + u)^{2} (1 - β)}{8 (1 + β)} < f ⩽ {\bar{f}}_{s s}$ . Last, we consider the scenario where product substitutability is sufficiently high (i.e., $β ⩾ \frac{9 + 39 u + 27 u^{2}}{9 + 39 u + 47 u^{2}}$ ). In this case, as shown in Propositions 1 and 2, neither the retailer nor the social planner prefers retailer information sharing. Thus, the retailer’s decision on information sharing is consistent with the decision of the social planner when $β ⩾ \frac{9 + 39 u + 27 u^{2}}{9 + 39 u + 47 u^{2}}$ .

Based on the above discussion, we can determine the conditions under which the social planner has a greater preference for retailer information sharing than the retailer. The results are summarized in Proposition 3 below.
Proposition 3
(1)
When product substitutability is sufficiently low (i.e., $β < \frac{3 + 9 u + u^{2}}{3 + 9 u + 13 u^{2}}$ ), the retailer’s decision on information sharing aligns with the decision of the social planner if the product line extension fee is very small (i.e., $f ⩽ {\bar{f}}_{s 1}$ ) or very large (i.e., $f > {\bar{f}}_{s s}$ ). Otherwise, the social planner has a greater preference for retailer information sharing than the retailer.
(2)
When product substitutability is moderate (i.e., $\frac{3 + 9 u + u^{2}}{3 + 9 u + 13 u^{2}} ⩽ β < \frac{9 + 39 u + 27 u^{2}}{9 + 39 u + 47 u^{2}}$ ), the retailer’s decision on information sharing aligns with the decision of the social planner if the product line extension fee is very large (i.e., $f > {\bar{f}}_{s s}$ ) or sufficiently small (i.e., $f ⩽ \frac{(1 + u)^{2} (1 - β)}{8 (1 + β)}$ ). Otherwise, the social planner has a greater preference for retailer information sharing than the retailer.
(3)
When product substitutability is sufficiently high (i.e., $β ⩾ \frac{9 + 39 u + 27 u^{2}}{9 + 39 u + 47 u^{2}}$ ), the retailer’s decision on information sharing aligns with the decision of the social planner.

Proposition 3 shows that inconsistencies between the retailer’s and the social planner’s decisions on retailer information sharing arise only when product substitutability is not sufficiently high and the product line extension fee is moderate. When the product line extension fee is not moderate, the manufacturer’s product line decision is less likely to be influenced by whether the retailer discloses information, making the positive effect of retailer information sharing inoperative. Thus, in this scenario, neither the retailer nor the social planner prefers retailer information sharing, and inconsistency arises only if the product line extension fee is moderate. Recall that product substitutability increases, the positive effect of retailer information sharing weakens when product substitutability is sufficiently high (i.e., $β ⩾ \frac{9 + 39 u + 27 u^{2}}{9 + 39 u + 47 u^{2}}$ ), the negative effect of information sharing dominates the positive effect on both the retailer’s profit and social welfare. At this time, neither the retailer nor the social planner prefers retailer information sharing, making the retailer’s and the social planner’s decisions on retailer information sharing consistent. Specifically, when inconsistency between the retailer’s and the social planner’s decisions arises, the social planner always prefers retailer information sharing, but the retailer does not. Proposition 3 suggests that when the social planner (e.g., government) aims to encourage the retailer to adopt a desirable information-sharing strategy, potential solutions include reducing product substitution or adjusting product line extension costs (either reducing or increasing them), in addition to offering subsidies.

Figure 5.
Illustration of consistency between retailer’s and social planner’s information sharing decisions.

A graphic illustration of Proposition 3 is given in Figure 5. In this figure, we set the expectation of random market size $u = 1$ . There are two dashed lines in Figure 5. The left panel represents $β = \frac{3 + 9 u + u^{2}}{3 + 9 u + 13 u^{2}} |_{u = 1}$ , and the right panel represents $β = \frac{9 + 39 u + 27 u^{2}}{9 + 39 u + 47 u^{2}} |_{u = 1}$ . As shown in the figure, an inconsistency between the retailer’s and the social planner’s decisions on retailer information sharing exists only in the shaded area. The unshaded area represents a “win-win” scenario where the retailer’s decision on information sharing aligns with the decision of the social planner. In Figure 5, the shaded area consists of two parts. One part is to the left side of the left dashed line (i.e., line $β = \frac{3 + 9 u + u^{2}}{3 + 9 u + 13 u^{2}} |_{u = 1}$ ), and the other is to the right side. In the shaded area on the left, the product line extension fee is so large that the manufacturer is more likely to offer a short product line if the retailer discloses information. This situation makes the positive effect of retailer information sharing on the retailer’s profit not work, leading the retailer to withhold information. In the shaded area on the right, product substitutability is so high that the negative effect of information sharing outweighs the positive effect on the retailer’s profit, again causing the retailer to withhold information.

Next, we analyze which information scenario (i.e., the information-sharing scenario versus the no-information-sharing scenario) is more likely to lead the manufacturer to make a welfare-improving product line extension decision. Similar to the literature (Liu and Cui, 2010), if a profit-oriented manufacturer’s product line extension decision also maximizes the total social welfare, we say that the manufacturer makes a welfare-improving product line extension decision. Through a straightforward comparison, we show that when the expectation of random market size $u$ is sufficiently large (i.e., $u > \frac{3 - \sqrt{3}}{1 + \sqrt{3}}$ ), retailer information sharing can offer the manufacturer more incentives to provide the socially optimal product line length if there is sufficiently high demand (i.e., $θ > u$ ) or sufficiently low demand (i.e., $θ < \frac{\sqrt{3} (1 + u) + u - 3}{4}$ ). If the demand is relatively high (i.e., $\frac{2 \sqrt{7} (1 + u) - 7}{7} < θ < u$ ), retailer information sharing offers the manufacturer fewer incentives to provide the socially optimal product line length. For relatively low demand (i.e., $\frac{\sqrt{3} (1 + u) + u - 3}{4} < θ < \frac{2 \sqrt{7} (1 + u) - 7}{7}$ ), whether retailer information sharing strengthens or weakens the manufacturer’s incentive to provide the socially optimal product line length depends on the product line extension fee $f$ . When the product line extension fee is relatively small (i.e., $\frac{(1 + θ)^{2} (1 - β)}{8 (1 + β)} < f < \frac{(1 + 2 θ - u) (7 + 6 θ + u) (1 - β)}{32 (1 + β)}$ ), the manufacturer’s incentive is weakened. When the product line extension fee is relatively large (i.e., $\frac{7 (1 + θ)^{2} (1 - β)}{32 (1 + β)} < f < \frac{(1 + u)^{2} (1 - β)}{8 (1 + β)}$ ), the manufacturer’s incentive is strengthened. If the expectation of random market size decreases to a moderate range (i.e., $\frac{\sqrt{7} - 2}{2} < u < \frac{3 - \sqrt{3}}{1 + \sqrt{3}}$ ), retailer information sharing cannot strengthen the manufacturer’s incentive to provide the socially optimal product line length when there is sufficiently low demand unless the product line extension fee is relatively small. If the expectation of random market size is sufficiently small, retailer information sharing weakens the manufacturer’s incentive to provide the socially optimal product line length unless there is sufficiently high demand. In fact, when the retailer chooses to not share demand information, all else being equal, a larger expectation of random market size would give the manufacturer more incentives to produce a long product line. However, if there is sufficiently low demand, the market size would be very small such that even a very short product line could easily cover it. In such a case, it would not be profitable to offer a long product line. Thus, social welfare may not be improved by product line extension. Since retailer information sharing incentivizes the manufacturer to shorten the product line when facing sufficiently low demand, it leads the manufacturer to provide the socially optimal product line length. When there is sufficiently high demand, the market size is too large to be covered by a short product line. Thus, to improve social welfare, it is better to provide a longer product line. By endowing the manufacturer with more flexibility in making a suitable product line design, retailer information sharing incentivizes the manufacturer to provide the socially optimal product line length. If the demand is relatively high, the market may still be large enough for social welfare to be improved through the increase of product variety. However, as the random market size $θ$ decreases, the manufacturer is more likely to offer a short product line. Thus, in this circumstance, retailer information sharing weakens the manufacturer’s incentive to provide the socially optimal product line length.
5. Timing of Product Line Design Choice

In this section, we consider a scenario where the manufacturer decides on the product line strategy before demand is realized and shared by the retailer. We aim to analyze how the timing of the manufacturer’s product line design affects the retailer’s incentive to share information.

When determining product line design before demand is realized and shared, the manufacturer makes the decision based on its expected profit. If the retailer chooses not to share information, the manufacturer’s expected profit is $\frac{(1 + u)^{2}}{8}$ when producing only one product variant (i.e., $N = 1$ ) and is $\frac{(1 + u)^{2}}{4 (1 + β)} - f$ when producing two product variants (i.e., $N = 2$ ). Thus, when the retailer chooses not to share information, the manufacturer produces two product variants if and only if $f ⩽ \frac{(1 + u)^{2} (1 - β)}{8 (1 + β)}$ . If the retailer chooses to share information, the manufacturer’s expected profit is $\frac{3 + 6 u + 4 u^{2}}{24}$ when producing only one product variant (i.e., $N = 1$ ) and is $\frac{3 + 6 u + 4 u^{2}}{12 (1 + β)} - f$ when producing two product variants (i.e., $N = 2$ ). Thus, if the retailer chooses to share information, the manufacturer produces two product variants if and only if $f ⩽ \frac{(3 + 6 u + 4 u^{2}) (1 - β)}{24 (1 + β)}$ . This leads us to Proposition 4 which characterizes the retailer’s information sharing decision when the manufacturer’s product line design is set before demand is realized and shared by the retailer. For convenience, we define ${\bar{f}}_{s 2} = \frac{(3 + 6 u + 4 u^{2}) (1 - β)}{24 (1 + β)}$ .

Proposition 4
When the manufacturer determines the product line strategy before demand is realized and shared, the retailer voluntarily commits to sharing information if and only if $0 ⩽ β < \frac{3 + 6 u + u^{2}}{3 + 6 u + 7 u^{2}}$ and $\frac{(1 + u)^{2} (1 - β)}{8 (1 + β)} < f ⩽ {\bar{f}}_{s 2}$ .

Proposition 4 demonstrates that when the manufacturer decides the product line strategy before demand is realized and shared, the retailer prefers information sharing over withholding information when product substitutability is low (i.e., $0 ⩽ β < \frac{3 + 6 u + u^{2}}{3 + 6 u + 7 u^{2}}$ ) and the product line extension fee is moderate (i.e., $\frac{(1 + u)^{2} (1 - β)}{8 (1 + β)} < f ⩽ {\bar{f}}_{s 2}$ ). This result is similar to the scenario where the manufacturer determines the product line strategy after demand is realized and shared. Note that when the manufacturer’s product line decision (i.e., choice between $N = 1$ and $N = 2$ ) is exogenously deterministic, the retailer would withhold information regardless of the manufacturer’s choice. Therefore, Proposition 4 implies that when the retailer faces an uncertain upstream product line design, its incentive for information sharing can be strengthened if product substitutability is low and the product line extension fee is moderate, regardless of the timing of product line design choice. This is because when the upstream product line design is uncertain to the retailer, the positive effect of information sharing is significant regardless of whether the manufacturer determines the product line strategy before or after demand is realized and shared. The difference lies in the fact that when the manufacturer determines the product line strategy before demand is realized and shared, retailer information sharing always leads the manufacturer to extend its product line. If the manufacturer determines the product line strategy after demand is realized and shared, whether retailer information sharing leads to product line extension depends on how the random market size materializes (i.e., the value of $θ$ ). In fact, when determining the product line strategy before demand is realized and shared, the manufacturer extends its product line in the information-sharing scenario but not in the no-information-sharing scenario if $\frac{(1 + u)^{2} (1 - β)}{8 (1 + β)} < f ⩽ {\bar{f}}_{s 2}$ . For $f ⩽ \frac{(1 + u)^{2} (1 - β)}{8 (1 + β)}$ (resp., $f > {\bar{f}}_{s 2}$ ), the manufacturer chooses $N = 2$ (resp., $N = 1$ ) in both scenarios. Thus, the retailer would consider the information-sharing strategy only when the product line extension fee is moderate (i.e., $\frac{(1 + u)^{2} (1 - β)}{8 (1 + β)} < f ⩽ {\bar{f}}_{s 2}$ ). If the retailer’s expected profit is higher when facing a long product line in the information-sharing scenario than that when facing a short product line in the no-information-sharing scenario, the retailer voluntarily shares information with the manufacturer. Otherwise, the retailer chooses to withhold information.

Next, we explore whether the retailer has more incentives to voluntarily share information if the manufacturer determines product line design after demand is realized and shared, rather than before. We first demonstrate the following lemma. For convenience, we define $\bar{β} = \frac{9 + 54 u + 108 u^{2} + 18 u^{3} - \sqrt{3} \sqrt{(3 + 6 u + 4 u^{2})^{3}}}{9 + 54 u + 108 u^{2} + 126 u^{3} - \sqrt{3} \sqrt{(3 + 6 u + 4 u^{2})^{3}}}$ .
Lemma 5
Let $Δ = {\bar{f}}_{s 1} - {\bar{f}}_{s 2}$ . (1)
$Δ ⩾ 0$ if and only if $β ⩽ \bar{β}$ . Otherwise, $Δ < 0$ .
(2)
There exists a unique $\hat{β} < \frac{1}{2}$ such that $Δ$ obtains the maximum at $u = 1$ if $β ⩽ \hat{β}$ . Otherwise, that is, when $β > \hat{β}$ , $Δ$ obtains the maximum at $u \in (0, 1)$ .

According to Lemma 5, the inequality ${\bar{f}}_{s 1} > {\bar{f}}_{s 2}$ holds if product substitutability is sufficiently low (i.e., $β < \bar{β}$ ). Otherwise, we have ${\bar{f}}_{s 1} ⩽ {\bar{f}}_{s 2}$ . Recall that when the manufacturer determines the product line design after demand is realized and shared, the retailer voluntarily shares information if and only if $β < \frac{3 + 9 u + u^{2}}{3 + 9 u + 13 u^{2}}$ and $\frac{(1 + u)^{2} (1 - β)}{8 (1 + β)} < f ⩽ {\bar{f}}_{s 1}$ . When the manufacturer determines the product line design before demand is realized and shared, the retailer voluntarily shares information if and only if $0 ⩽ β < \frac{3 + 6 u + u^{2}}{3 + 6 u + 7 u^{2}}$ and $\frac{(1 + u)^{2} (1 - β)}{8 (1 + β)} < f ⩽ {\bar{f}}_{s 2}$ . In addition, notice that $\bar{β} < \frac{3 + 9 u + u^{2}}{3 + 9 u + 13 u^{2}} < \frac{3 + 6 u + u^{2}}{3 + 6 u + 7 u^{2}}$ for $\forall u \in (0, 1]$ . Then Lemma 5 implies that when product substitutability is sufficiently low (i.e., $β < \bar{β}$ ) and ${\bar{f}}_{s 2} < f ⩽ {\bar{f}}_{s 1}$ , the retailer voluntarily shares information if the manufacturer determines the product line design after demand is realized and shared. Conversely, if the manufacturer determines product line design before demand is realized and shared, the retailer would keep the information private in this circumstance. When product substitutability is relatively low (i.e., $\bar{β} ⩽ β < \frac{3 + 9 u + u^{2}}{3 + 9 u + 13 u^{2}}$ ) and ${\bar{f}}_{s 1} < f ⩽ {\bar{f}}_{s 2}$ , the retailer would keep the information private if the manufacturer determines the product line design after demand is realized and shared. However, if the manufacturer determines the product line design before demand is realized and shared, the retailer voluntarily shares information. When product substitutability is relatively high (i.e., $\frac{3 + 9 u + u^{2}}{3 + 9 u + 13 u^{2}} ⩽ β < \frac{3 + 6 u + u^{2}}{3 + 6 u + 7 u^{2}}$ ), according to Proposition 1, the retailer would always withhold information if the manufacturer determines the product line design after demand is realized and shared. If, on the other hand, the manufacturer determines the product line design before demand is realized and shared, according to Proposition 4, the retailer voluntarily shares information for $\frac{(1 + u)^{2} (1 - β)}{8 (1 + β)} < f ⩽ {\bar{f}}_{s 2}$ . When product substitutability is sufficiently high (i.e., $β ⩾ \frac{3 + 6 u + u^{2}}{3 + 6 u + 7 u^{2}}$ ), as shown in Propositions 1 and 4, the retailer never shares information if the manufacturer sets the product line design, regardless of whether demand is realized and shared beforehand or afterward.

Based on the above discussion, we obtain the conditions under which the retailer has more (resp., equal or less) incentive to voluntarily share information if the manufacturer determines the product line design after demand is realized and shared rather than before. The results are summarized in Proposition 5.
Proposition 5
(1)
For sufficiently low product substitutability (i.e., $β < \bar{β}$ ), the retailer voluntarily shares information when the manufacturer determines the product line design after demand is realized and shared, but not before, if ${\bar{f}}_{s 2} < f ⩽ {\bar{f}}_{s 1}$ . Otherwise, the retailer’s incentive to share information is independent of the timing of the product line design choice.
(2)
For relatively low product substitutability (i.e., $\bar{β} ⩽ β < \frac{3 + 9 u + u^{2}}{3 + 9 u + 13 u^{2}}$ ), the retailer voluntarily shares information when the manufacturer determines the product line design before demand is realized and shared, but not after, if ${\bar{f}}_{s 1} < f ⩽ {\bar{f}}_{s 2}$ . Otherwise, the retailer’s incentive to share information is independent of the timing of the product line design choice.
(3)
For relatively high product substitutability (i.e., $\frac{3 + 9 u + u^{2}}{3 + 9 u + 13 u^{2}} ⩽ β < \frac{3 + 6 u + u^{2}}{3 + 6 u + 7 u^{2}}$ ), the retailer voluntarily shares information when the manufacturer determines the product line design before demand is realized and shared, but not after, if $\frac{(1 + u)^{2} (1 - β)}{8 (1 + β)} < f ⩽ {\bar{f}}_{s 2}$ . Otherwise, the retailer’s incentive to share information is independent of the timing of the product line design decision.
(4)
For sufficiently high product substitutability (i.e., $β ⩾ \frac{3 + 6 u + u^{2}}{3 + 6 u + 7 u^{2}}$ ), the retailer’s incentive to share information is independent of the timing of the product line design choice.

Proposition 5 shows that unless product substitutability is not sufficiently high and the product line extension fee is moderate, the timing of when the manufacturer sets the product line design (before or after demand is realized and shared) has no impact on the retailer’s information-sharing decision. When the product line extension fee is very large (or very small), the manufacturer tends to produce a short (or long) product line regardless of whether the product line design is set before or after demand is realized and shared, and regardless of the retailer’s information-sharing decision. When the product line extension fee is very large (or very small), the manufacturer tends to produce a short (or long) product line regardless of whether the product line design is set before or after demand is realized and shared, and regardless of the retailer’s information-sharing decision. Therefore, when the product line extension fee is not moderate, the manufacturer’s product line design is less likely to be influenced by the retailer’s information-sharing decision. In this case, the positive effect of information sharing on the retailer’s profit becomes negligible, leading the retailer to withhold information. Consequently, if the product line extension cost is not moderate, the retailer’s incentive to share information is independent of the timing of the product line design decision. For product substitutability, recall that the positive effect of retailer information sharing weakens as product substitutability increases. Then, the negative effect of information sharing on the retailer’s profit dominates the positive effect when product substitutability is sufficiently high. At this point, regardless of whether the manufacturer determines the product line design before or after demand is realized and shared, the retailer tends not to disclose the information. Thus, when product substitutability is sufficiently high, the retailer’s incentive to share information is independent of the timing of the product line design choice. Specifically, when product substitutability is sufficiently low, the retailer may have more incentives to share information if the manufacturer sets the product line design after demand is realized and shared. When the manufacturer determines the product line design before demand is realized and shared, the retailer’s choice to share information always leads the manufacturer to extend the product line. However, if the manufacturer determines the product line design after demand is realized and shared, the retailer’s choice to share information does not always lead to an extension of the manufacturer’s product line. In case of sufficiently low market demand, the manufacturer may not extend the product line even if the retailer shares information. At this point, sufficiently low product substitutability can incentivize the manufacturer to extend the product line even if market demand is low. Therefore, when the manufacturer determines the product line design after demand is realized and shared, sufficiently low product substitutability increases the likelihood that the retailer will benefit from the positive effect of information sharing, making the retailer more likely to voluntarily share information.

Figure 6.
Illustration of how timing of product line design affects retailer information sharing.

Figure 6 provides a graphic illustration of Proposition 5. In this figure, we set the expectation of random market size to $u = 1$ . There are three dashed lines in Figure 6. The left dashed line represents $β ≜ β_{1} = \bar{β} |_{u = 1}$ , the middle one represents $β = \frac{3 + 9 u + u^{2}}{3 + 9 u + 13 u^{2}} |_{u = 1}$ , and the right one represents $β = \frac{3 + 6 u + u^{2}}{3 + 6 u + 7 u^{2}} |_{u = 1}$ . As shown in Figure 6, in the unshaded area, the retailer’s incentive to share information is independent of the timing of the product line design choice. The shaded area in Figure 6 consists of three parts. In the left shaded area, the retailer shares information if the manufacturer determines the product line design after demand is realized and shared, but not before. In the middle and right shaded areas, the retailer shares information if the manufacturer determines the product line design before demand is realized and shared, but not after. In the middle shaded area, the excessively large product line extension fee is the driving factor that makes the retailer withhold information when the manufacturer determines the product line design after demand is realized and shared. In the right shaded area, the excessively high product substitutability is the driving factor that makes the retailer withhold information when the manufacturer determines the product line design after demand is realized and shared.
6. Extensions

In this section, we extend our base model in several directions. First, we explore an alternative distribution contract, specifically the agency contract. Next, we examine the scenario where the retailer’s information acquisition cost is not negligible. Finally, we analyze the case in which the information sharing with the manufacturer is not a free but a paid service. Through these model variations, we demonstrate the robustness of our main results derived from the base model.

6.1. Agency Contract

In our base model, we consider the retailer as a reseller. However, in practice, supply chains often use not only the reselling model (i.e., wholesale contract) but also the agency model (i.e., agency contract). In this subsection, we explore the scenario where the retailer acts as an agent. Following the literature, we assume a commission rate denoted by $α$ . Under the agency contract, the power to set retail prices shifts from the retailer to the manufacturer. The retailer receives $α$ proportion of the revenue while the manufacture takes the remaining $1 - α$ proportion.

When the retailer does not share information, the expected profit under the agency contract is $\frac{α (1 + u)^{2}}{4}$ (resp., $\frac{α (1 + u)^{2}}{2 (1 + β)}$ ) if $f > \frac{(1 - α) (1 + u)^{2} (1 - β)}{4 (1 + β)}$ (resp., $f ⩽ \frac{(1 - α) (1 + u)^{2} (1 - β)}{4 (1 + β)}$ ). When the retailer shares information, the expected profit under the agency contract is given by the following equation:

\begin{aligned} \int_{0}^{min {[\arg {g (x) = f}]^{+}, 2 u}} \frac{α (1 + θ)^{2}}{8 u} d θ \\ + \int_{min {[\arg {g (x) = f}]^{+}, 2 u}}^{2 u} \frac{α (1 + θ)^{2}}{4 (1 + β) u} d θ, \end{aligned}

(5)

where

g (x) = \frac{(1 - α) (1 + x)^{2} (1 - β)}{4 (1 + β)}

. As

\int_{0}^{2 u} \frac{α (1 + θ)^{2}}{8 u} d θ > \frac{α (1 + u)^{2}}{4}

(resp.,

\int_{0}^{2 u} \frac{α (1 + θ)^{2}}{4 (1 + β) u} d θ > \frac{α (1 + u)^{2}}{2 (1 + β)}

), it is easy to verify that the retailer opts for voluntary information sharing when

f > \frac{(1 - α) (1 + 2 u)^{2} (1 - β)}{4 (1 + β)}

(resp.,

f < \frac{(1 - α) (1 - β)}{4 (1 + β)}

). For

\frac{(1 - α) (1 + u)^{2} (1 - β)}{4 (1 + β)} < f < \frac{(1 - α) (1 + 2 u)^{2} (1 - β)}{4 (1 + β)}

, as

\frac{α (1 + θ)^{2}}{8 u} < \frac{α (1 + θ)^{2}}{4 (1 + β) u}

, it is easy to show that the value of formula (5) is larger than

\frac{α (1 + u)^{2}}{4}

. Thus, the retailer chooses voluntary information sharing in this circumstance. Next, we examine the case of

\frac{(1 - α) (1 - β)}{4 (1 + β)} < f < \frac{(1 - α) (1 + u)^{2} (1 - β)}{4 (1 + β)}

. Here, the manufacturer chooses

N = 2

if the retailer withholds the information. To determine the retailer’s information sharing strategy, we should compare the value of formula (5) with

\frac{α (1 + u)^{2}}{2 (1 + β)}

. Similar to the proof of Proposition 1, we show that for

\frac{(1 - α) (1 - β)}{4 (1 + β)} < f < \frac{(1 - α) (1 + u)^{2} (1 - β)}{4 (1 + β)}

, the retailer voluntarily discloses the information if and only if

β < \frac{3 - u + u^{2}}{3 + 3 u + u^{2}}

and

f < \frac{(1 - α) (1 + \frac{4 u^{2}}{1 - β})^{\frac{2}{3}} (1 - β)}{4 (1 + β)}

The above results imply that under the agency contract, increased flexibility in the upstream product line can weaken the retailer’s incentive of voluntary information sharing for certain conditions. This finding is similar to what is observed under a wholesale contract. Indeed, it is profitable for an agent in a supply chain to voluntarily disclose information, as the agent’s profit is a proportion of the manufacturer’s profit. However, when the upstream product line length is uncertain, downstream information sharing may prompt the manufacturer to shorten the product line, making voluntary information sharing less attractive to the agent.

6.2. Information Acquisition Cost

In our base model, we assume that the retailer’s cost for acquiring information is negligible. However, in reality, it can be quite expensive for firms to make accurate demand predictions. In this extension, we relax this assumption by introducing an exogenous and constant information acquisition cost $c$ that the retailer incurs to obtain the exact demand information. To better understand the significant role of positive information acquisition costs in retailer information sharing with upstream product line flexibility, we assume $c > \frac{u^{2}}{6 (1 + β)}$ in this subsection. When $c$ is sufficiently small, not sharing the acquired information can be a profitable option for the retailer. In this case, the information acquisition cost would no longer influence the retailer’s decision to share information.

When the information acquisition cost is not negligible, if the retailer chooses to share information voluntarily, its expected profit is given by the following equation:

\begin{aligned} \int_{0}^{min {[\arg {h (x) = f}]^{+}, 2 u}} \frac{(1 + θ)^{2}}{32 u} d θ \\ + \int_{min {[\arg {h (x) = f}]^{+}, 2 u}}^{2 u} \frac{(1 + θ)^{2}}{16 (1 + β) u} d θ - c, \end{aligned}

(6)

where

h (x) = \frac{(1 + x)^{2} (1 - β)}{8 (1 + β)}

. Then, similar to the proof of Proposition 1, we show that the retailer voluntarily shares the information when

\frac{(1 + u)^{2} (1 - β)}{8 (1 + β)} < f ⩽ \frac{(1 + (6 - 96 c) u + 12 u^{2} + \frac{10 - 6 β}{1 - β} u^{3})^{\frac{2}{3}} (1 - β)}{8 (1 + β)}

0 ⩽ β < \frac{1 + 2 u - u^{2}}{1 + 2 u + u^{2}}

and

\frac{u^{2}}{6 (1 + β)} < c < min {\frac{3 + 6 u + 5 u^{2} - 3 (1 + u)^{2} β}{48 (1 + β)}, \frac{3 + 9 u + 9 u^{2} - (3 + 9 u + 5 u^{2}) β}{96 (1 - β)}}

. This finding is similar to that obtained from the base model (i.e., Proposition 1). Thus with upstream product line flexibility, regardless of whether the information acquisition cost is negligible or not, the retailer would not voluntarily disclose the information unless the product line extension fee is moderate and the product substitutability is low.

It should be noticed that a positive information acquisition cost does not necessarily reduce the retailer’s incentive for voluntary information sharing. As shown in Proposition 1, when the information acquisition cost is negligible, the condition the condition for the retailer’s voluntary information sharing, based on the product substitutability is $0 ⩽ β < \frac{3 + 9 u + u^{2}}{3 + 9 u + 13 u^{2}}$ . It is easy to verify that $\frac{1 + 2 u - u^{2}}{1 + 2 u + u^{2}} > \frac{3 + 9 u + u^{2}}{3 + 9 u + 13 u^{2}}$ if and only if $0 < u < \frac{3 + \sqrt{93}}{14}$ . Therefore, from the perspective of product substitutability, all else being equal, the retailer’s incentive for voluntary information sharing is strengthened (resp., weakened) by a positive information acquisition cost when the expected random market size is small (resp., large).

6.3. Paid Information Service

In our base model, we consider the retailer’s voluntary information sharing. However, in practice, information sharing may be offered by retailers (e.g., Tmall) as a paid service. In this extension, we explore such a paid information service scenario.

According to Proposition 1, when product line extension fee is either sufficiently large or sufficiently small (i.e., $f < \frac{(1 + u)^{2} (1 - β)}{8 (1 + β)}$ or $f > \frac{(1 + 6 u + 12 u^{2} + \frac{2 - 14 β}{1 - β} u^{3})^{\frac{2}{3}} (1 - β)}{8 (1 + β)}$ ), or when product substitutability is sufficiently high (i.e., $β > \frac{3 + 9 u + u^{2}}{3 + 9 u + 13 u^{2}}$ ), the retailer would not disclose the demand information unless being paid a service fee by the manufacturer. When $f < \frac{(1 - β)}{8 (1 + β)}$ , the manufacturer would always choose $N = 2$ . In this case, the minimum information service fee that would incentivize the retailer to share the information is $\frac{u^{2}}{8 + 8 β}$ . When $f > \frac{(1 + 2 u)^{2} (1 - β)}{8 (1 + β)}$ , as the manufacturer always chooses $N = 1$ , the minimum information service fee should be $\frac{u^{2}}{16}$ . While for $\frac{(1 - β)}{8 (1 + β)} < f < \frac{(1 + 2 u)^{2} (1 - β)}{8 (1 + β)}$ , if the retailer discloses the information, the manufacturer chooses $N = 2$ (resp., $N = 1$ ) when $f < \frac{(1 + θ)^{2} (1 - β)}{8 (1 + β)}$ (resp., $f > \frac{(1 + θ)^{2} (1 - β)}{8 (1 + β)}$ ). At this point, the retailer’s expected profit without the information service fee is given by formula (2). While if the retailer withholds the information, the manufacturer chooses $N = 2$ (resp., $N = 1$ ) when $f < \frac{(1 + u)^{2} (1 - β)}{8 (1 + β)}$ (resp., $f > \frac{(1 + u)^{2} (1 - β)}{8 (1 + β)}$ ). Denote $\int_{0}^{2 u} \frac{(1 + 2 θ - u)^{2}}{16 (1 + β) u} d θ - (2)$ and $\int_{0}^{2 u} \frac{(1 + 2 θ - u)^{2}}{32 u} d θ - (2)$ as $F_{1}$ and $F_{2}$ respectively. Then, the minimum information service fee should be $max {F_{1}, 0}$ (resp., $max {F_{2}, 0}$ ) when $\frac{(1 - β)}{8 (1 + β)} < f < \frac{(1 + u)^{2} (1 - β)}{8 (1 + β)}$ (resp., $\frac{(1 + u)^{2} (1 - β)}{8 (1 + β)} < f < \frac{(1 + 2 u)^{2} (1 - β)}{8 (1 + β)}$ ). The results are illustrated in Figures 7 and 8.

Figure 7 represents the case with low product substitutability ( $β = 0.25$ ), while Figure 8 represents the case with high product substitutability ( $β = 0.75$ ). As shown in Figure 7, with low product substitutability, the retailer may offer a free information service when the product line extension fee is moderate. In contrast, in Figure 8, with high product substitutability, the retailer would always charge a positive service fee. This result is consistent with Proposition 1.

7. Managerial Implications and Concluding Remarks

To the best of our knowledge, this article is the first to study how a manufacturer’s product line flexibility affects a retailer’s incentive to voluntarily share demand information. We address three main issues. First, does upstream product line flexibility affect a retailer’s information sharing strategy, and if so, how? We find that whether upstream product line flexibility strengthens a retailer’s incentives for voluntary information sharing depends significantly on both product substitutability and the product line extension fee. When product substitutability is sufficiently low and the product line extension fee is moderate, upstream product line flexibility encourages the retailer to voluntarily share information with the manufacturer. This finding uniquely highlights the critical role of upstream product line flexibility in motivating retailer information sharing. It also provides an alternative theoretical explanation for the discrepancy between the prevalence of information sharing in practice and the traditional academic prediction of nonsharing. In the presence of upstream product line flexibility, voluntarily sharing information with the manufacturer can have two conflicting effects on the retailer’s profit—one negative and one positive. The trade-off between these two effects determines the retailer’s information-sharing strategy.

This finding is managerially relevant for retailers engaged in information collaborations (i.e., sharing information) with their upstream manufacturers. The result suggests that to ensure that information collaboration is profitable, the retailer should encourage the manufacturer to maximize the differences between variants in a product line. This implication aligns with Alibaba’s recent information collaboration with Mars Inc. In 2018, using information shared from the Alibaba’s Tmall Innovation Center (TMIC), Mars Inc. introduced a new Snickers candy bar variant with an unconventional taste and spice. Our work provides a theoretical explanation for why some firms’ product line extensions, particularly when sold through online retailers like JD and Taobao, seem unusual and improbable. This finding also has managerial implications for manufacturers seeking informational assistance from retailers. These manufacturers should avoid excessively high or low product line extension costs to encourage retailers to voluntarily share information.

Second, does upstream product line flexibility affect the difference between the retailer’s and the social planner’s preferences on retailer information sharing, and if so, how? We find that the impact of product line flexibility on this difference depends significantly on product substitutability and the cost to an upstream manufacturer of extending the product line. If product substitutability is sufficiently high or if the product line extension fee is either large or small, a retailer’s information sharing decision aligns with the optimal social welfare perspective. In this case, there is no difference between the retailer’s and the social planner’s preferences on retailer information sharing. However, if product substitutability is low and the product line extension fee is moderate, the retailer’s decision on information sharing diverges from the social planner’s optimal decision. Our research has managerial implications for policymakers interested in optimizing social welfare. In addition to providing subsidies, policymakers should assist manufacturers in adopting advanced technologies to reduce the product line extension cost, encouraging retailers to voluntarily make socially optimal decisions on information sharing.

Third, in the presence of upstream product line flexibility, does the timing of product line design affect the retailer’s incentive to share information, and if so, how? We demonstrate that, unless product substitutability is not sufficiently high and the product line extension fee is moderate, the retailer’s decision on information sharing is not influenced by whether the manufacturer determines the product line design before or after demand is realized and shared accordingly. This finding identifies conditions under which the timing of the product line design choice impacts the retailer’s incentive to share information. Specifically, if product substitutability is sufficiently low, the retailer is more inclined to voluntarily share information when the manufacturer determines the product line design after demand is realized and shared accordingly than before. Conversely, if product substitutability is moderate, the retailer is more incentivized to voluntarily share information when the manufacturer determines the product line design before demand is realized and shared accordingly. The results theoretically confirm the complementary relationship between product substitutability and the timing of the product line design choice in strengthening the retailer’s incentive to voluntarily share information. This finding has managerial relevance for manufacturers seeking informational assistance from retailers. Our research suggests that these manufacturers can alternatively adjust the timing of their product line design choice or modify differences in their product lines. If the timing of the product line design decision is fixed, adjusting differences in product lines can enhance product substitutability in areas where the retailer has more incentives to voluntarily share information. If adjustments in product line differences are challenging, strategically changing the timing of the product line design choice may also incentivize the retailer to voluntarily share information.

We also aim to outline potential directions for future research by acknowledging a few limitations of this work. First, our analysis focuses solely on the flexibility of horizontally differentiated product lines. It would be valuable to explore how the flexibility of a vertically differentiated product line influences a retailer’s motivation to voluntarily share demand information. With vertical differentiation, one can delve into asymmetric demand uncertainty and examine scenarios involving partial information sharing. Second, our paper assumes that the retailer has access to precise information. Future studies can explore how the information accuracy and accuracy-dependent information acquisition cost impact retailer information sharing. Third, retailers like Wal-Mart commonly employ vendor-managed systems (VMIs) and directly provide point-of-sale data to manufacturers (e.g., P&G) for production and inventory management. It would be intriguing to explore how product line design interacts with information sharing under VMI arrangements.

Supplemental Material

sj-pdf-1-pao-10.1177_10591478241268244 - Supplemental material for Retailer Information Sharing With Upstream Product Line Flexibility

Supplemental material, sj-pdf-1-pao-10.1177_10591478241268244 for Retailer Information Sharing With Upstream Product Line Flexibility by Xiang Ji, Jie Wu, Zhixin Chen and Ruixia Shi in Production and Operations Management

Footnotes

Acknowledgements

We thank the Department Editor Subodha Kumar, the anonymous Senior Editor, and the three anonymous reviewers for their constructive comments that have greatly improved the paper. All authors contribute equally to this paper.

Declaration of Conflicting Interests

The authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The authors disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: Xiang Ji, Jie Wu, and Zhixin Chen are partially supported by the National Natural Science Foundation of China (Nos. 72171219, 72201264, 71971203, 72371232, and 71921001), the USTC Research Funds of the Double First-Class Initiative (FSSF-A-230104), and the Fundamental Research Funds for the Central Universities (WK2040000060, WK2040000027).

ORCID iDs

Xiang Ji

Zhixin Chen

Supplemental Material

Supplemental material for this article is available online ().

Notes

How to cite this article

Ji X, Wu J, Chen Z and Shi R (2024) Retailer Information Sharing With Upstream Product Line Flexibility. Production and Operations Management 33(10): 1961–1978.

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