The Impact of Planogram Design and Display Fees on Retail Category Management

Abstract

We study the impact of planogram design (i.e., placement of products on shelves) and display fees (i.e., fees manufacturers pay retailers for prime shelf space) on a retailer’s category management strategy and interactions with national brand manufacturers (NBMs). We consider a game-theoretic model with one retailer and multiple NBMs. Each NBM offers one product. In addition, the retailer has the option to introduce a store brand (SB) product. If the retailer decides to introduce its SB, it needs to drop one of the national brand (NB) products from its assortment because it has limited shelf space. The retailer’s planogram has one prime shelf space and multiple nonprime shelf spaces. The prime shelf space has a demand-stimulating impact. The NBMs determine their wholesale prices and how much they are willing to pay for the prime shelf space. The retailer makes SB introduction and planogram decisions. It also sets the quantities for each product in its assortment, resulting in market-clearing retail prices. Our analysis leads to three key findings: first, the presence of a prime shelf space may not only prevent the retailer from introducing its SB but also lead to sizable changes in the retail and wholesale prices in the category. For example, an extensive numerical study reveals that receiving the prime shelf space increases an NB product’s retail price by 5.48%, on average. The average increase in the same product’s wholesale price is 2.52%, as the prospect of charging a higher wholesale price incentivizes its manufacturer to pay a display fee for securing the prime shelf space. Second, there are cases in which the retailer uses SB introduction as a strategic lever to intensify the competition for the prime shelf space and thereby increase its revenue from display fees. Third, despite being an additional expense, display fees can increase the NBMs’ profits by allowing them to influence the retailer’s assortment and planogram decisions in their favor. We discuss the implications of these findings for managers and researchers.

1. Introduction

Many retailers group products with similar characteristics into categories (e.g., canned vegetables, laundry detergent, yogurt) and treat each category as a strategic business unit (ACNielsen, 2005). A category typically consists of products owned and marketed by national brand manufacturers (NBMs) and may also include store brands (SBs)—also known as private labels—offered by retailers (Kumar and Steenkamp, 2007). For example, in the laundry detergent category, many retailers carry several national brands (NBs), including Tide (marketed by Procter & Gamble) and Persil (marketed by Henkel), in addition to their own SBs. SBs have become increasingly popular in recent years. In 2024, SB sales in the United States reached an all-time high dollar volume of $271 billion, which translates into 24% growth over a 4-year period and a market share of 20.7% in dollars and 23.1% in units (Private Label Manufacturers Association, 2025).

The practice of treating a product category as a strategic business unit, referred to as category management, enables retailers to maximize the overall category performance by coordinating marketing and operational decisions (e.g., assortment selection, pricing, shelf design) across different brands (ACNielsen, 2005; Basuroy et al., 2001; Zenor, 1994). The category management literature indicates that making assortment and pricing decisions at the category level requires a retailer to consider several factors, including demand substitution patterns in the category (e.g., Besanko et al., 2005), category-level constraints such as limited shelf space (e.g., Rooderkerk et al., 2013), and NBMs’ strategic responses to the retailer’s actions (e.g., Dukes et al., 2009). Given the strategic importance of SBs for retailers, category management studies have also explored how SB presence in a category affects a retailer’s assortment and pricing decisions as well as interactions with its channel partners (e.g., Chintagunta et al., 2002; Nasser et al., 2013).

Placement of products on a retailer’s shelves, referred to as planogram design, is another important component of category management (e.g., Dreze et al., 1994; Nielsen, 2020). In particular, displaying a product in a prime shelf location (e.g., eye level) can increase its visibility, which in turn leads to an increase in its demand (e.g., Chandon et al., 2009; van Nierop et al., 2008). By contrast, nonprime shelves (e.g., stoop level) are less desirable because they are either difficult to reach or outside consumers’ field of vision while walking through the store (Ebster and Garaus, 2015). Indeed, consumers perceive products displayed on nonprime shelves to be of lower quality (Valenzuela and Raghubir, 2015).

Because of the positive impact of prime shelves on consumer demand, some NBMs make side payments to retailers to display their products in prime shelf locations (Rivlin, 2016). Hereinafter, we refer to such payments as display fees. ¹ The trade literature suggests that display fees can have a sizable impact on a retailer’s category profit. For example, a Wall Street Journal article (Haddon and Nassauer, 2018) reports that Whole Foods’ suppliers pay $300,000 to secure a prime shelf for several weeks. Indeed, an NBM can pay a retailer as much as $1 million a year to place a single product on a prime shelf location (Rivlin, 2016). Such fees can also have a significant impact on NBMs’ profits. In particular, according to Rivlin (2016, p. 23), trade fees, which include display fees, can constitute 15% to 20% of a manufacturer’s costs, “the second largest expense for many food manufacturers, behind only the cost of creating the product itself.”

Motivated by the practical importance of planogram design, we examine the impact of planogram considerations (e.g., allocation of prime shelf space, display fees) on a retailer’s category management strategy and interactions with NBMs. We study three research questions. First, we study the impact of planogram considerations on the retailer’s assortment and pricing decisions. The trade literature provides retailers with planogram design recommendations. For example, a Nielsen (2020) study recommends that retailers give their prime shelves to products that generate high sales volumes and/or high gross profits. Similarly, Ebster and Garaus (2015, p. 27) state that “eye level is the ideal zone for placing products with a high profit margin.” Although these recommendations aim to monetize the demand-stimulating impact of prime shelf spaces, they overlook how planogram design affects a retailer’s category management decisions and NBMs’ responses to such decisions, leading to our first research question: how does the presence of prime shelf space in a retailer’s planogram affect the retailer’s category management decisions and strategic interactions with NBMs?

Second, we study the impact of planogram considerations on the retailer’s SB introduction decisions. The analytical SB literature shows that a retailer’s decision to add an SB product to its assortment can play an important role in its strategic interactions with NBMs (e.g., Alan et al., 2019; Nasser et al., 2013; Ru et al., 2015). While these studies generate insights into retailers’ SB introduction decisions and NBMs’ strategic responses (e.g., wholesale price adjustments), they omit the interplay between a retailer’s SB- and planogram-related decisions, leading to our second research question: how do planogram considerations (e.g., allocation of prime shelf space, display fees) impact a retailer’s SB introduction decision?

Third, we study the impact of planogram considerations on the NBMs. Within the scope of planogram considerations, a retailer’s decision to collect display fees can influence an NBM’s profit through its sales revenue and operational costs. On the one hand, display fees may enable an NBM to secure a prime shelf space, leading to an increase in its sales. On the other hand, these fees may constitute a significant proportion of an NBM’s costs, as Rivlin (2016) documents. Thus, it is unclear whether the increase in sales offsets the display fee expense an NBM incurs. In addition, an NBM’s display fee payment may have an indirect impact on the other NBMs’ profits through the retailer’s actions. Thus, our third research question is: how do display fees affect NBMs’ profits?

Our study builds on category management literature to incorporate planogram considerations into a setting in which the retailer makes assortment and pricing decisions in the presence of an SB. Specifically, we analyze a game-theoretic model with one retailer and multiple NBMs, each offering one product. In addition, the retailer has the option to carry its own SB product. If the retailer decides to carry its SB, it needs to drop one of the NB products from its assortment due to limited shelf space. Thus, in our setting, the retailer’s assortment decision corresponds to an SB introduction decision. The retailer’s planogram has one prime (e.g., eye-level) and multiple nonprime (e.g., stoop-level or stretch-level) shelf spaces, where appearing in the prime shelf space increases a product’s demand. As such, the retailer needs to determine which product in its assortment will receive the prime shelf space.

In our model, both the retailer and the NBMs maximize their profits. The retailer’s profit has two components. The first component, which we refer to as gross profit, captures the profit the retailer generates from product sales. The second component, which we refer to as display revenue, captures the profit the retailer generates by collecting a display fee from the NBM that receives the prime shelf space. Similarly, an NBM’s profit equals its gross profit (profit from product sales) less the display fee it pays. The NBMs determine the manufacturer margins for their products as well as how much they are willing to pay for the prime shelf space, while the retailer makes SB introduction and planogram decisions and sets the quantities for each product it carries in its assortment. The NBMs’ manufacturer margin decisions determine the wholesale prices, whereas the retailer’s stocking decisions lead to market-clearing retail prices.

Characterizing the equilibrium assortment, manufacturer margins, retail quantities, and NBMs’ display fee offers sheds light on the retailer’s planogram choices. Specifically, when the retailer does not offer an SB product, the most attractive NB (i.e., the NB with the highest demand) receives the prime shelf space. When the retailer carries the SB in its assortment, it either gives the prime shelf space to the most attractive NB or its SB. When the retailer gives the prime shelf space to its SB, it forgoes display revenue. Notably, there are also cases when the most attractive NB receives the prime shelf space without paying a display fee. Such cases emerge both in the absence and presence of the SB in the retailer’s assortment.

Comparing our main model with alternative models leads to three key findings. First, we compare our main model with an alternative model in which the retailer’s planogram has only nonprime shelves. This comparison demonstrates that the presence of the prime shelf space can prevent the retailer from introducing its SB, while also leading to sizable changes in the retail and wholesale prices in the category. For example, an extensive numerical study shows that receiving the prime shelf space increases an NB product’s retail price by 5.48%, on average. Similarly, the average increase in the same product’s wholesale price is 2.52%, providing its manufacturer with an incentive to pay a display fee to secure the prime shelf space. Second, comparing our main model with an alternative model in which the retailer does not have an SB shows that there are cases when the retailer can use its SB as a strategic lever to intensify the competition for the prime shelf space and thereby increase its display revenue. Third, comparing our main model with an alternative model in which the retailer does not collect display fees reveals that there are cases when NBMs can benefit from display fees. These cases arise when display fees serve as an entry deterrence mechanism that prevents the retailer from carrying the SB in its assortment.

In summary, we contribute to the literature by analyzing the impact of planogram considerations on a retailer’s category management strategy and interactions with NBMs. The rest of the article proceeds as follows: Section 2 provides an overview of the relevant literature. Section 3 presents our model, and Section 4 characterizes the equilibrium outcomes. Section 5 focuses on a special case of our model in which the retailer carries a narrow assortment with three products and presents our key findings. Section 6 demonstrates the robustness of our findings by numerically analyzing wider assortments with more than three products. Section 7 concludes with a discussion of the implications of our findings for managers and researchers.

2. Literature Review

Our study is related to the category management literature and the SB literature. Because these research streams are vast, we focus on the studies that are most relevant to ours.

Assortment studies in the category management literature indicate that finding the right assortment is a challenging task for retailers (Mantrala et al., 2009). On the one hand, when a retailer carries a large assortment, consumers are more likely to find a product that matches their needs (Boatwright and Nunes, 2001). On the other hand, carrying a large assortment increases a retailer’s operational costs (Rooderkerk et al., 2013). A stream of assortment studies focuses on the strategic implications of a retailer’s assortment decisions (e.g., Alan et al., 2019; Dukes et al., 2009; Nasser et al., 2013). The number of available products is relatively small in these studies (typically two to three), which facilitates a game-theoretic analysis of a retailer’s interactions with other channel constituents (e.g., NBMs, competing retailers, and consumers) in both the absence and presence of SBs in the category.

Another stream of assortment studies focuses on deriving structural properties and developing heuristics to simplify the complexity of the assortment selection problem (e.g., Gaur and Honhon, 2006; Nakkas et al., 2020; Rooderkerk et al., 2013). A common feature of these studies is that they consider an arbitrarily large number of products a firm can include in its assortment. Some of these studies have a cost term that increases as the assortment size increases (e.g., Gaur and Honhon, 2006; Nakkas et al., 2020), while others impose a constraint, such as limited shelf space, on the assortment size (e.g., Rooderkerk et al., 2013) to match practice in which a firm typically cannot include all available products in its assortment. We follow the latter approach and capture the impact of limited shelf space on a retailer’s assortment by considering a setting in which the retailer needs to remove an NB product to introduce its SB product. Our study contributes to both streams of the assortment literature by shedding light on the impact of planogram considerations on a retailer’s assortment decisions and strategic interactions with NBMs.

The category management literature also examines retailers’ shelf planning decisions, such as the location and number of shelf facings a retailer assigns to each product and the horizontal and vertical positioning of products in its planogram (e.g., Chandon et al., 2009; Dreze et al., 1994; Jalali et al., 2023; Pak et al., 2020; van Nierop et al., 2008). Although these studies generate insights into a retailer’s planogram decisions, they typically do not consider a retailer’s strategic interactions with NBMs. Our study contributes to this literature by shedding light on how the demand-stimulating impact of prime shelf space and strategic channel interactions affect the retailer’s planogram decisions.

The pricing studies in the category management literature reveal that coordinating prices among all brands in a category is another important but challenging task for retailers (e.g., Basuroy et al., 2001; Zenor, 1994). Several factors complicate such coordination efforts. First, optimal retail prices depend on the strategic role of a category (e.g., loss leader vs. profit driver). For example, maximizing category sales may necessitate relatively low prices (Alan et al., 2017), while maximizing category profit may require high retail markups, leading to relatively high prices (Basuroy et al., 2001). Second, a retailer needs to consider cross-price effects because a product’s demand depends not only on its own price but also on the prices of the other products in the category (e.g., Besanko et al., 2005; Kadiyali et al., 2000). Third, SB presence in a category can have a significant impact on retail prices (e.g., Chintagunta et al., 2002). Our study incorporates these pricing dynamics and contributes to this literature stream by shedding light on the impact of planogram considerations on wholesale and retail prices.

The SB literature provides several reasons for the increasing importance of SBs for retailers (for an overview of this literature, see Sethuraman, 2009). Specifically, SBs typically have higher retail margins because of their lower acquisition and merchandizing costs (e.g., Ailawadi and Harlam, 2004). Furthermore, they enable a retailer to differentiate its assortment from its competitors (Corstjens and Lal, 2000) and improve consumer loyalty (Seenivasan et al., 2016). SBs also give retailers leverage in their negotiations with NBMs, allowing retailers to receive better terms of trade, such as lower wholesale prices (e.g., Chintagunta et al., 2002; Zheng et al., 2022). Other strategic considerations investigated in the SB literature include sourcing of SBs (e.g., Kumar et al., 2010), NBs’ strategic responses to SB introduction (e.g., Nasser et al., 2013), multitier SBs (e.g., Amaldoss and Shin, 2015), and cross-category demand spillover effects of SBs (e.g., Alan et al., 2019). Our study contributes to this literature by shedding light on the interplay between a retailer’s planogram and SB introduction decisions.

3. Model

We consider a distribution channel with a single retailer and $n$ competing NBMs, where each NBM offers a single product. In addition, the retailer has the option to offer an SB product. The retailer can carry $n$ products in its assortment. Restricting the retailer’s assortment size to $n$ means that the retailer can carry either $n$ NB products or $n-1$ NB products along with its SB. Our analysis focuses on a setting in which the retailer’s planogram has one prime and $n-1$ nonprime shelf spaces. This setting allows us to parsimoniously capture the competition between NB and SB products for limited shelf space, where one shelf position is more attractive than the rest of the planogram.

Let $\mathcal{A}$ denote the assortment (i.e., set of products the retailer carries). Furthermore, let ${\mathbf{I}}^{\mathcal{A}}$ denote a unit vector with $n$ elements, where the $i^{\text{th}}$ element, $I_i^{\mathcal{A}}$ , equals one if product $i\in \mathcal{A}$ receives the prime shelf space and zero if it receives a nonprime shelf space. Prior research documents that displaying a product in a prime shelf space has a positive impact on that product’s sales (e.g., Dreze et al., 1994; Jalali et al., 2023). We incorporate this positive link into a linear demand model as follows: for a given assortment, let $\mathbf{q}$ denote a vector, where each element, $q_i$ for $i\in \mathcal{A}$ , represents the quantity of product $i$ consumed by a representative consumer. Then, we define a representative consumer’s utility function as

$$U(\mathbf{q})=\sum _{i\in \mathcal{A}}({\alpha }_i+\beta I_i^{\mathcal{A}})q_i-\sum _{i\in \mathcal{A}}\sum _{j\in \mathcal{A}}{\theta }_{ij}{q}_i{q}_j,$$

(1)

where ${\alpha }_i$ , ${\theta }_{ii}$ , and ${\theta }_{ij}$ capture the marginal utility of product $i$ , diminishing marginal utility of product $i$ , and utility interaction between products $i$ and $j$ , respectively. In addition, $\beta >0$ captures the marginal utility boost associated with being displayed in the prime shelf space for product $i$ . That is, receiving the prime shelf space enhances product $i$ ’s marginal utility from ${\alpha }_i$ to ${\alpha }_i+\beta$ . As we formalize in Section 4, this enhancement implies that moving a product from a nonprime shelf space to the prime shelf space increases its equilibrium demand. When $\beta =0$ (i.e., when the retailer’s planogram does not have a prime shelf space), Equation (1) reduces to the classical quadratic utility function with $n$ products (e.g., Shubik and Levitan, 1980).

Let $p_i$ denote the retail price of product $i\in \mathcal{A}$ . Then, a representative consumer solves the following consumption problem:

$$\underset{\mathbf{q}\ge 0}{max}\sum _{i\in \mathcal{A}}({\alpha }_i+\beta I_i^{\mathcal{A}})q_i-\sum _{i\in \mathcal{A}}\sum _{j\in \mathcal{A}}{\theta }_{ij}{q}_i{q}_j-\sum _{i\in \mathcal{A}}{p}_i{q}_i,$$

(2)

where $\sum _{i\in \mathcal{A}}{p}_i{q}_i$ captures the total consumption expenditure. For ease of exposition, we set ${\theta }_{ii}=1/2$ for $i\in \mathcal{A}$ and ${\theta }_{ij}=1/4$ for $j\in \mathcal{A}\setminus \{i\}$ . Solving Equation (2) after this simplification leads to the following inverse demand function for product $i$ :

$$p_i={\alpha }_i+\beta I_i^{\mathcal{A}}-q_i-\frac{1}{2}\sum _{j\in \mathcal{A}\setminus \{i\}}{q}_j.$$

(3)

In Equation (3), ${\alpha }_i+\beta I_i^{\mathcal{A}}$ can be interpreted as the perceived quality of product $i$ (e.g., Choné and Linnemer, 2020). This formulation is consistent with the findings in the literature that consumers find products displayed on nonprime shelves to be of lower quality (e.g., Valenzuela and Raghubir, 2015), as moving product $i$ from the prime shelf space to a nonprime shelf space would lower its perceived quality from ${\alpha }_i+\beta$ to ${\alpha }_i$ .

In practice, some manufacturers make display fee payments to retailers for prime shelf positions (Bloom et al., 2000; Federal Trade Commission, 2003; Rivlin, 2016). To this end, let $w_i$ and $b_i$ denote the wholesale price for product $i$ and manufacturer $i$ ’s display fee offer, respectively. Accordingly, for a given assortment $\mathcal{A}$ and planogram ${\mathbf{I}}^{\mathcal{A}}$ , we define the retailer’s total category profit as

$${\mathrm{\Pi }}_r\left({\mathbf{I}}^{\mathcal{A}}\right)=\sum _{i\in \mathcal{A}}((p_i-w_i)q_i+b_i{I}_i^{\mathcal{A}}).$$

(4)

The inverse demand function in Equation (3) allows us to rewrite Equation (4) as

$$\begin{array}{rl}{\mathrm{\Pi }}_r\left({\mathbf{I}}^{\mathcal{A}}\right)& =\sum _{i\in \mathcal{A}}({\alpha }_i+\beta I_i^{\mathcal{A}}-q_i-\frac{1}{2}\sum _{j\in \mathcal{A}\setminus \{i\}}{q}_j-w_i)q_i\\ & +\sum _{i\in \mathcal{A}}{b}_i{I}_i^{\mathcal{A}}.\end{array}$$

(5)

Let $c_i$ denote the unit production cost of product $i$ . In addition, let $a_i\equiv {\alpha }_i-c_i$ and $m_i\equiv w_i-c_i$ denote the attractiveness of product $i$ and manufacturer $i$ ’s unit margin, respectively. Accordingly, we can rewrite the retailer’s profit function as

$$\begin{array}{rl}{\mathrm{\Pi }}_r\left({\mathbf{I}}^{\mathcal{A}}\right)& =\underset{\text{Retailer's gross profit},{\pi }_r({\mathbf{I}}^{\mathcal{A}})}{\underbrace{\sum _{i\in \mathcal{A}}\underset{\text{Retailer's unit margin for product}i,r_i({\mathbf{I}}^{\mathcal{A}})}{\underbrace{(a_i+\beta I_i^{\mathcal{A}}-q_i-\frac{1}{2}\sum _{j\in \mathcal{A}\setminus \{i\}}{q}_j-m_i)}}{q}_i}}\\ & +\underset{\text{Display revenue},b_r({\mathbf{I}}^{\mathcal{A}})}{\underbrace{\sum _{i\in \mathcal{A}}{b}_i{I}_i^{\mathcal{A}}}},\end{array}$$

(6)

where $r_i({\mathbf{I}}^{\mathcal{A}})$ is the retailer’s unit margin for product $i$ , ${\pi }_r({\mathbf{I}}^{\mathcal{A}})$ is the gross profit the retailer generates by selling products to consumers, and $b_r({\mathbf{I}}^{\mathcal{A}})$ is the display fee it collects from the NBM that receives the prime shelf space. Note that the retailer’s display fee revenue is zero when it gives the prime shelf space to its own SB or to an NBM that does not offer a display fee.

The NBMs set their unit margins $m_i$ (equivalently, their wholesale prices, $w_i=m_i+c_i$ ) to maximize their profits. Manufacturer $i$ ’s profit function for a given planogram is

$${\mathrm{\Pi }}_i({\mathbf{I}}^{\mathcal{A}})=m_i{q}_i-b_i{I}_i^{\mathcal{A}},$$

(7)

which equals zero if product $i$ is not in the assortment, $m_i{q}_i$ if product $i$ is in the assortment and receives a nonprime shelf space, and $m_i{q}_i-b_i$ if product $i$ is in the assortment and receives the prime shelf space. The first part of the manufacturer’s profit function, ${\pi }_i({\mathbf{I}}^{\mathcal{A}})\equiv m_i{q}_i$ , captures the gross profit it generates by selling its product to the retailer. The second part, $b_i{I}_i^{\mathcal{A}}$ , captures the display fee it pays. In this formulation, the manufacturer’s display fee offer, $b_i$ , may be zero, capturing the possibility that it receives the prime shelf space without paying a display fee.

The sequence of events is as follows: in stage 1, the retailer selects its assortment, $\mathcal{A}$ , by deciding whether to carry $n$ NB products or $n-1$ NB products along with its SB. In stage 2, the NBMs simultaneously determine their display fee offers for the prime shelf space, $b_i$ . In stage 3, the retailer decides on its planogram depending on the NBMs’ display fee offers. In stage 4, the NBMs simultaneously determine their unit margins, $m_i$ . Finally, in stage 5, the retailer sets the quantities $q_i$ for all $i\in \mathcal{A}$ , which lead to the retail prices on the basis of Equation (3). All model parameters and objective functions are common knowledge.

This sequence mimics the sequence of assortment and planogram decisions in practice. That is, many retailers follow a hierarchical approach in which they first determine the assortment and then finalize the planogram (Bianchi-Aguiar et al., 2021). This sequential approach simplifies the retailer’s planogram decisions by enabling it to focus on finding the best way to display its assortment, rather than trying to build a planogram from the entire set of products it can include in its assortment. Furthermore, both assortment and planogram decisions affect the demand structure in the category. Therefore, having the manufacturers’ margin and the retailer’s quantity decisions in the last two stages of the game enables the channel members to adjust their prices depending on the retailer’s assortment and planogram decisions. In the assortment stage of our setting, the retailer’s decision to carry $n$ NBs or $n-1$ NBs along with its SB translates into an SB introduction decision. As such, having the assortment stage precede the manufacturers’ margin (wholesale price) decisions allows NBMs to respond to the retailer’s SB introduction decision. This feature makes our model consistent with the empirical findings in the SB literature, which show that NBMs adjust their wholesale prices after a retailer introduces its SB (e.g., Chintagunta et al., 2002; Pauwels and Srinivasan, 2004).

4. Analysis

In this section, we first analyze the subgame in which the retailer carries $n$ NB products in its assortment. Then, we analyze the other subgame in which the retailer carries $n-1$ NBs and its own SB. Finally, we compare the retailer’s total category profits in the two subgames to characterize the full equilibrium. Without loss of generality, we sort the NB products in descending order of their attractiveness levels (i.e., $a_1\ge a_2\ge \cdots \ge a_n$ ) so that an NBM with a lower index offers a more attractive product. However, we do not impose a condition on the attractiveness level of the SB product, $a_s={\alpha }_s-c_s$ , to allow the possibility that it may be more attractive than some NB products because of its relatively high marginal utility, ${\alpha }_s$ , or relatively low production cost, $c_s$ . We let $\mathrm{\Omega }\equiv \{(a_1,\dots ,a_n,a_s,\beta )\in {\mathbb{R}}^{n+2}:a_1\ge \cdots \ge a_n\ge 0,a_s\ge \beta \ge 0,(n^2+n+1)a_n\ge n\sum _{i=1}^{n-1}{a}_i+(n+1{)}^2\beta ,(n^2+2n+2)a_{n-1}\ge n\sum _{i=1}^{n-2}{a}_i+(2n+1)(a_s+\beta ),(n^2+n+1)a_s\ge n\sum _{i=1}^{n-1}{a}_i+n\beta \}$ denote the set of feasible parameter values. The conditions in the definition of $\mathrm{\Omega }$ ensure that we focus on the practically relevant cases in which a product has positive demand when the retailer includes it in its assortment. We use $\varphi =(a_1,\dots ,a_n,a_s,\beta )$ to refer to an element of $\mathrm{\Omega }$ .

4.1. Planogram Design Without the SB

In this subsection, we use backward induction to solve the subgame in which the retailer carries $n$ NB products. Let $\mathcal{N}=\{1,2,\dots ,n\}$ denote the assortment with $n$ NB products. We first analyze the fourth and fifth stages of the game in which the NBMs and the retailer determine the wholesale prices and quantities, respectively.

In the last stage of the game, for a given planogram ${\mathbf{I}}^{\mathcal{N}}=(I_1^{\mathcal{N}},\dots ,I_n^{\mathcal{N}})$ , the retailer solves

$$\underset{\mathbf{q}\ge 0}{max}\sum _{i\in \mathcal{N}}(a_i+\beta I_i^{\mathcal{N}}-q_i-\frac{1}{2}\sum _{j\in \mathcal{N}\setminus \{i\}}{q}_j-m_i)q_i+b_i{I}_i^{\mathcal{N}}.$$

(8)

Solving the first-order conditions of the retailer’s objective function with respect to $q_i$ leads to

$${\check{q}}_i\left({\mathbf{I}}^{\mathcal{N}}\right)=a_i+\beta I_i^{\mathcal{N}}-m_i-\frac{\sum _{j\in \mathcal{N}}(a_j+\beta I_j^{\mathcal{N}}-m_j)}{n+1}.$$

(9)

In the fourth stage of the game, anticipating ${\check{q}}_i({\mathbf{I}}^{\mathcal{N}})$ , the NBMs simultaneously solve $\underset{m_i\ge 0}{max}{m}_i{\check{q}}_i({\mathbf{I}}^{\mathcal{N}})$ . Lemma 1 characterizes the subgame equilibrium outcomes for a given planogram. We present all proofs in Section A of the e-companion.

Lemma 1

When $\mathcal{A}=\mathcal{N}$ with a given planogram ${\mathbf{I}}^{\mathcal{N}}$ , the manufacturer margin for product $i$ is

$$\begin{array}{rl}{\hat{m}}_i({\mathbf{I}}^{\mathcal{N}})& =\frac{n+1}{2n+1}(a_i+\beta I_i^{\mathcal{N}})\\ & -\frac{n}{(n+1)(2n+1)}(\beta +\sum _{j\in \mathcal{N}}{a}_j).\end{array}$$

(10)

In addition, the quantity (demand) for product $i$ is ${\hat{q}}_i({\mathbf{I}}^{\mathcal{N}})=\frac{n}{n+1}{\hat{m}}_i({\mathbf{I}}^{\mathcal{N}})$ , and the retail margin for product $i$ is ${\hat{r}}_i({\mathbf{I}}^{\mathcal{N}})=\frac{1}{2}(a_i+\beta I_i^{\mathcal{N}}-{\hat{m}}_i({\mathbf{I}}^{\mathcal{N}}))$ . Consequently, manufacturer $i$ ’s profit is ${\hat{\mathrm{\Pi }}}_i({\mathbf{I}}^{\mathcal{N}})={\hat{\pi }}_i({\mathbf{I}}^{\mathcal{N}})-b_i{I}_i^{\mathcal{N}}={\hat{m}}_i({\mathbf{I}}^{\mathcal{N}}){\hat{q}}_i({\mathbf{I}}^{\mathcal{N}})-b_i{I}_i^{\mathcal{N}}$ , and the retailer’s profit is ${\hat{\mathrm{\Pi }}}_r({\mathbf{I}}^{\mathcal{N}})={\hat{\pi }}_r({\mathbf{I}}^{\mathcal{N}})+\sum _{i=1}^n{b}_i{I}_i^{\mathcal{N}}=\sum _{i=1}^n{\hat{r}}_i({\mathbf{I}}^{\mathcal{N}}){\hat{q}}_i({\mathbf{I}}^{\mathcal{N}})+\sum _{i=1}^n{b}_i{I}_i^{\mathcal{N}}$ .

Lemma 1 implies that having the prime shelf space has a positive impact on a product’s demand. Formally, let ${\mathbf{I}}_i^{\mathcal{N}}$ denote a unit vector, indicating that product $i\in \mathcal{N}$ receives the prime shelf space. For example, ${\mathbf{I}}_1^{\mathcal{N}}$ means that the first product in the assortment receives the prime shelf space and the remaining $n-1$ products receive nonprime shelf spaces (i.e., $I_1^{\mathcal{N}}=1$ and $I_j^{\mathcal{N}}=0$ for all $j\in \mathcal{N}\setminus \{1\}$ ). Then, for $j\ne i$ , we have ${\hat{q}}_i({\mathbf{I}}_i^{\mathcal{N}})-{\hat{q}}_i({\mathbf{I}}_j^{\mathcal{N}})=\frac{n}{2n+1}\beta \ge 0$ . In addition, the retail price for product $i$ is ${\hat{p}}_i({\mathbf{I}}^{\mathcal{N}})={\hat{r}}_i({\mathbf{I}}^{\mathcal{N}})+{\hat{m}}_i({\mathbf{I}}^{\mathcal{N}})+c_i$ . Accordingly ${\hat{p}}_i({\mathbf{I}}_i^{\mathcal{N}})-{\hat{p}}_i({\mathbf{I}}_j^{\mathcal{N}})=\frac{3n+2}{2(2n+1)}\beta \ge 0$ . Having ${\hat{q}}_i({\mathbf{I}}_i^{\mathcal{N}})-{\hat{q}}_i({\mathbf{I}}_j^{\mathcal{N}})\ge 0$ and ${\hat{p}}_i({\mathbf{I}}_i^{\mathcal{N}})-{\hat{p}}_i({\mathbf{I}}_j^{\mathcal{N}})\ge 0$ implies that the retailer can sell more units of product $i$ at a higher retail price when product $i$ receives the prime shelf space.

In the third stage of the game, the retailer makes its planogram decision. Specifically, for given display fee offers, $b_i$ , the retailer solves $\underset{i\in \{1,2,\dots ,n\}}{max}{\hat{\mathrm{\Pi }}}_r({\mathbf{I}}_i^{\mathcal{N}})$ . Solving this problem requires us to analyze how the NBMs determine their display fee offers. Lemma 1 indicates that manufacturer $i$ ’s profit is ${\hat{\pi }}_i({\mathbf{I}}_i^{\mathcal{N}})-b_i$ when it receives the prime shelf space. Lemma 1 also implies that when manufacturer $i$ does not receive the prime shelf space, its profit does not depend on which competing manufacturer in the assortment receives the prime shelf space. Formally, ${\hat{\pi }}_i({\mathbf{I}}_j^{\mathcal{N}})={\hat{\pi }}_i({\mathbf{I}}_k^{\mathcal{N}})$ for all $j,k\in \mathcal{A}\setminus \{i\}$ . Accordingly, manufacturer $i$ ’s display fee offer must ensure that ${\hat{\pi }}_i({\mathbf{I}}_i^{\mathcal{N}})-b_i\ge {\hat{\pi }}_i({\mathbf{I}}_j^{\mathcal{N}})$ because it would be better off receiving a nonprime shelf space otherwise. Thus, manufacturer $i$ ’s maximum display fee offer is ${\eta }_i^{\mathcal{N}}={\hat{\pi }}_i({\mathbf{I}}_i^{\mathcal{N}})-{\hat{\pi }}_i({\mathbf{I}}_j^{\mathcal{N}})$ . Lemma 2 shows two structural properties related to ${\eta }_i^{\mathcal{N}}$ .

Lemma 2

For $\mathcal{A}=\mathcal{N}$ , ${\eta }_1^{\mathcal{N}}\ge {\eta }_2^{\mathcal{N}}\ge \cdots \ge {\eta }_n^{\mathcal{N}}$ . In addition, ${\hat{\pi }}_r({\mathbf{I}}_1^{\mathcal{N}})+{\eta }_1^{\mathcal{N}}\ge {\hat{\pi }}_r({\mathbf{I}}_2^{\mathcal{N}})+{\eta }_2^{\mathcal{N}}\ge \cdots \ge {\hat{\pi }}_r({\mathbf{I}}_n^{\mathcal{N}})+{\eta }_n^{\mathcal{N}}$ .

The first part of Lemma 2 shows that the first NBM, which offers the most attractive product, has the highest willingness to pay for the prime shelf space. The second part implies that if each NBM were to set its display fee offer to the maximum display fee offer it could afford (i.e., if $b_i={\eta }_i^{\mathcal{N}}$ for all $i\in \mathcal{N}$ ), the first NBM would receive the prime shelf space. These properties imply that the first NBM competes with the second NBM for the prime shelf space. The first NBM receives the prime shelf space if its display fee offer, $b_1$ , is such that ${\hat{\pi }}_r({\mathbf{I}}_1^{\mathcal{N}})+b_1\ge {\hat{\pi }}_r({\mathbf{I}}_2^{\mathcal{N}})+{\eta }_2^{\mathcal{N}}$ . Proposition 1 characterizes the subgame equilibrium outcomes for $\mathcal{A}=\mathcal{N}$ .

Proposition 1

Let ${\overline{a}}_1\equiv (1+2\frac{n^2+1}{n(n+3)})a_2+\frac{n^2+1}{n(n+3)}\beta -\frac{2}{n+3}\sum _{j=3}^n{a}_j$ . When $\mathcal{A}=\mathcal{N}$ , the first NBM receives the prime shelf space. If $\varphi \in {\mathrm{\Omega }}_1^{\mathcal{N}}\equiv \{\varphi \in \mathrm{\Omega }:a_1<{\overline{a}}_1\}$ , it pays a display fee of ${\hat{b}}_1^{\mathcal{N}}={\hat{\pi }}_r({\mathbf{I}}_2^{\mathcal{N}})+{\eta }_2^{\mathcal{N}}-{\hat{\pi }}_r({\mathbf{I}}_1^{\mathcal{N}})$ . If $\varphi \in {\mathrm{\Omega }}_2^{\mathcal{N}}\equiv \{\varphi \in \mathrm{\Omega }:a_1\ge {\overline{a}}_1\}$ , it does not pay a display fee (i.e., ${\hat{b}}_1^{\mathcal{N}}=0$ ). In both cases, $b_k^{\mathcal{N}}={\eta }_k^{\mathcal{N}}$ for all $k\ge 2$ .

Proposition 1 reveals that if ${\hat{\pi }}_r({\mathbf{I}}_1^{\mathcal{N}})\ge {\hat{\pi }}_r({\mathbf{I}}_2^{\mathcal{N}})+{\eta }_2^{\mathcal{N}}$ , the maximum total category profit the retailer can generate by giving the prime shelf space to the second NBM is no greater than the gross profit it can generate by giving the prime shelf space to the first NBM. Consequently, the first NBM sets its display fee offer to zero and receives the prime shelf space without paying a display fee. By contrast, if ${\hat{\pi }}_r({\mathbf{I}}_1^{\mathcal{N}})<{\hat{\pi }}_r({\mathbf{I}}_2^{\mathcal{N}})+{\eta }_2^{\mathcal{N}}$ , the first NBM needs to make a positive display fee offer to receive the prime shelf space. Setting ${\hat{\pi }}_r({\mathbf{I}}_1^{\mathcal{N}})={\hat{\pi }}_r({\mathbf{I}}_2^{\mathcal{N}})+{\eta }_2^{\mathcal{N}}$ and solving for $a_1$ leads to the threshold we define in Proposition 1, ${\overline{a}}_1$ . This threshold increases in $a_2$ and $\beta$ and decreases in $\sum _{k=3}^n{a}_k$ . Intuitively, when $a_2$ becomes more attractive, the range in which the first NBM pays a display fee expands because, all else being equal, a higher $a_2$ intensifies the competition between the first and second NBMs for the prime shelf space. Similarly, when $\beta$ increases, the set in which the first NB pays a display fee, ${\mathrm{\Omega }}_1^{\mathcal{N}}$ , expands as the prime shelf space becomes more valuable. When $\sum _{k=3}^n{a}_k$ increases, the second NBM’s willingness to pay for the prime shelf space decreases, shrinking the set in which the first NB pays a display fee.

In summary, when the retailer offers $n$ NB products, the first NBM, which has the most attractive product in the category, receives the prime shelf space. When its product’s attractiveness level is relatively high (i.e., when $a_1\ge {\overline{a}}_1$ ), it does not pay a display fee. However, when its product’s attractiveness level is lower (i.e., when $a_1<{\overline{a}}_1$ ), it pays a display fee to prevent the retailer from giving the prime shelf space to the second NBM, which has the second most attractive product. The next lemma formalizes a structural property of the retailer’s subgame equilibrium profit.

Lemma 3

Let ${\hat{\mathrm{\Pi }}}_r^{\mathcal{N}}\equiv {\hat{\pi }}_r({\mathbf{I}}_1^{\mathcal{N}})+{\hat{b}}_r^{\mathcal{N}}$ denote the retailer’s subgame equilibrium profit when it carries $\mathcal{A}=\mathcal{N}$ . Then, $\mathrm{\partial }{\hat{\mathrm{\Pi }}}_r^{\mathcal{N}}/\mathrm{\partial }{a}_i\ge 0$ for all $i\in \mathcal{N}$ .

Lemma 3 indicates that the retailer’s profit increases in the attractiveness levels of the products in its assortment. This finding implies that if we were to relax our assumption that the retailer had access to $n$ NB products by studying a setting with $m$ NB products with $m>n$ , the retailer would carry the $n$ most popular products (i.e., the products with the highest attractiveness levels). This finding is consistent with the broader assortment literature in which the retailer’s optimal assortment typically includes the most popular products (e.g., Anderson et al., 1992; Kök et al., 2015; van Ryzin and Mahajan, 1999).

4.2. Planogram Design with the SB

In this section, we analyze a setting in which the retailer replaces the least attractive NB with its own SB. Let $s$ and $\mathcal{S}=\{1,2,\dots ,n-1,s\}$ denote the SB product and the retailer’s assortment, respectively. In addition, let ${\mathbf{I}}^{\mathcal{S}}=(I_1^{\mathcal{S}},I_2^{\mathcal{S}},\dots ,I_{n-1}^{\mathcal{S}},I_s^{\mathcal{S}})$ denote a unit vector, where $I_i^{\mathcal{S}}=1$ if product $i\in \mathcal{S}$ receives the prime shelf space and $I_i^{\mathcal{S}}=0$ if it receives a nonprime shelf space.

In the last stage, the retailer solves

$$\begin{array}{rl}& \underset{\mathbf{q}\ge 0}{max}\sum _{i\in \mathcal{S}}(a_i+\beta I_i^{\mathcal{S}}-q_i-\frac{1}{2}\sum _{j\in \mathcal{S}\setminus \{i\}}{q}_j-m_i)q_i\\ & +\sum _{i\in \mathcal{S}\setminus \{s\}}{b}_i{I}_i^{\mathcal{S}}.\end{array}$$

(11)

In Equation (11), the second part of the retailer’s objective function, $\sum _{i\in \mathcal{S}\setminus \{s\}}{b}_i{I}_i^{\mathcal{S}}$ , indicates that the retailer does not collect a display fee from its SB (i.e., $b_s=0$ ). Solving Equation (11) leads to

$${\check{q}}_i\left({\mathbf{I}}^{\mathcal{S}}\right)=a_i+\beta I_i^{\mathcal{S}}-m_i-\frac{\sum _{j\in \mathcal{S}}(a_j+\beta I_j^{\mathcal{S}}-m_j)}{n+1}.$$

(12)

We follow the SB literature (e.g., Alan et al., 2019; Du et al., 2005; Raju et al., 1995; Sayman et al., 2002) and assume that the retailer acquires its SB at the marginal cost without double marginalization (i.e., $m_s=0$ , leading to $w_s=m_s+c_s=c_s$ ). As such, in the fourth stage of the game, anticipating ${\check{q}}_i({\mathbf{I}}^{\mathcal{S}})$ and $m_s=0$ , the NBMs simultaneously solve $\underset{m_i\ge 0}{max}{m}_i{\check{q}}_i({\mathbf{I}}^{\mathcal{S}})$ for $i=1,2,\dots ,n-1$ . Lemma 4 characterizes the subgame equilibrium outcomes for a given planogram.

Lemma 4

When $\mathcal{A}=\mathcal{S}$ with a given planogram ${\mathbf{I}}^{\mathcal{S}}$ , the manufacturer margin for product $i\in \mathcal{S}\setminus \{s\}$ is

$$\begin{array}{rl}{\hat{m}}_i({\mathbf{I}}^{\mathcal{S}})& =\frac{n+1}{2n+1}(a_i+\beta I_i^{\mathcal{S}})-\frac{n}{(n+2)(2n+1)}(\beta +\sum _{j\in \mathcal{S}}{a}_j)\\ & -\frac{n+1}{(n+2)(2n+1)}(a_s+\beta I_s^{\mathcal{S}}).\end{array}$$

(13)

In addition, the quantity (demand) for product $i$ is

$$\begin{array}{rl}{\hat{q}}_i({\mathbf{I}}^{\mathcal{S}})& =\{\begin{array}{ll}\frac{n+1}{n+2}(a_s+\beta I_s^{\mathcal{S}})-\frac{n}{(n+1)(n+2)}(\beta +\sum _{j\in \mathcal{S}}{a}_j)& \text{if }i=s,\\ \frac{n}{n+1}{\hat{m}}_i({\mathbf{I}}^{\mathcal{S}})& \text{if }i\in \mathcal{S}\setminus \{s\},\end{array}\end{array}$$

(14)

and the retail margin for product $i\in S$ is ${\hat{r}}_i({\mathbf{I}}^{\mathcal{S}})=\frac{1}{2}(a_i+\beta I_i^{\mathcal{S}}-{\hat{m}}_i({\mathbf{I}}^{\mathcal{S}}))$ , where ${\hat{m}}_s({\mathbf{I}}^{\mathcal{S}})=0$ . Consequently, manufacturer $i$ ’s profit is ${\hat{\mathrm{\Pi }}}_i({\mathbf{I}}^{\mathcal{S}})={\hat{\pi }}_i({\mathbf{I}}^{\mathcal{S}})-b_i{I}_i^{\mathcal{S}}={\hat{m}}_i({\mathbf{I}}^{\mathcal{S}}){\hat{q}}_i({\mathbf{I}}^{\mathcal{S}})-b_i{I}_i^{\mathcal{S}}$ , and the retailer’s profit is ${\hat{\mathrm{\Pi }}}_r({\mathbf{I}}^{\mathcal{S}})={\hat{\pi }}_r({\mathbf{I}}^{\mathcal{S}})+\sum _{i=1}^{n-1}{b}_i{I}_i^{\mathcal{S}}=\sum _{i=1}^n{\hat{r}}_i({\mathbf{I}}^{\mathcal{S}}){\hat{q}}_i({\mathbf{I}}^{\mathcal{S}})+\sum _{i=1}^{n-1}{b}_i{I}_i^{\mathcal{S}}$ .

Comparing Lemmas 1 and 4 reveals that the SB presence in the retailer’s assortment changes the structure of manufacturer margins. Intuitively, when the retailer carries the SB, the NBMs in the assortment compete with a product that is not subject to double marginalization, creating margin pressure for the NBMs. The lack of double marginalization for the SB also creates a difference between the functional forms of the NB and SB demands, as Equation (14) shows. Nevertheless, the prime shelf space continues to have a positive impact on a product’s performance. In other words, receiving the prime shelf space increases a product’s retail and wholesale prices and demand.

In the third stage, the retailer makes its planogram decision by solving $\underset{i\in \{1,2,\dots ,n-1,s\}}{max}{\hat{\mathrm{\Pi }}}_r({\mathbf{I}}_i^{\mathcal{S}})$ . When the retailer carries the SB, a focal NBM’s maximum display fee offer depends on whether the SB or another NB receives the prime shelf if the focal NBM does not receive it. In particular, when another NB receives the prime shelf space, the focal NBM’s profit does not depend on the receipient of the prime shelf space (i.e., ${\hat{\pi }}_i({\mathbf{I}}_j^{\mathcal{S}})={\hat{\pi }}_i({\mathbf{I}}_k^{\mathcal{S}})$ for all $j,k\in \mathcal{S}\setminus \{i,s\}$ ). Accordingly, we define ${\eta }_i^{\mathcal{S}}\equiv {\hat{\pi }}_i({\mathbf{I}}_i^{\mathcal{S}})-{\hat{\pi }}_i({\mathbf{I}}_j^{\mathcal{S}})$ for $j\in \mathcal{S}\setminus \{i,s\}$ and ${\nu }_i^{\mathcal{S}}\equiv {\hat{\pi }}_i({\mathbf{I}}_i^{\mathcal{S}})-{\hat{\pi }}_i({\mathbf{I}}_s^{\mathcal{S}})$ . Lemma 5 shows three structural properties related to ${\eta }_i^{\mathcal{S}}$ and ${\nu }_i^{\mathcal{S}}$ .

Lemma 5

For $i\in \mathcal{S}\setminus \{s\}$ , ${\nu }_i^{\mathcal{S}}\ge {\eta }_i^{\mathcal{S}}$ . In addition, ${\hat{\pi }}_r({\mathbf{I}}_1^{\mathcal{S}})+{\eta }_1^{\mathcal{S}}\ge {\hat{\pi }}_r({\mathbf{I}}_2^{\mathcal{S}})+{\eta }_2^{\mathcal{S}}\ge \cdots \ge {\hat{\pi }}_r({\mathbf{I}}_{n-1}^{\mathcal{S}})+{\eta }_{n-1}^{\mathcal{S}}$ . Last, ${\hat{\pi }}_r({\mathbf{I}}_1^{\mathcal{S}})+{\nu }_1^{\mathcal{S}}\ge {\hat{\pi }}_r({\mathbf{I}}_2^{\mathcal{S}})+{\nu }_2^{\mathcal{S}}\ge \cdots \ge {\hat{\pi }}_r({\mathbf{I}}_{n-1}^{\mathcal{S}})+{\nu }_{n-1}^{\mathcal{S}}$ .

The first part of Lemma 5 states that for an NBM, losing the prime shelf space to the SB is costlier than losing it to another NBM. The demand structure in the category shapes this outcome, as the absence of double marginalization allows the retailer to more aggressively increase its SB quantity when the SB receives the prime shelf space. Such an increase leads to a sharper decrease in an NBM’s profit compared to cases when another NBM receives the prime shelf space. Consequently, an NBM is willing to pay a higher display fee to prevent the SB from receiving the prime shelf space. The second and third parts of Lemma 5 imply that if the retailer decided to give the prime shelf space to an NBM, the first NBM would be the recipient. This is because the first NBM can outbid all the other NBMs in the assortment. That said, the retailer can give the prime shelf space to its SB. Mathematically, if ${\hat{\pi }}_r({\mathbf{I}}_s^{\mathcal{S}})\ge {\hat{\pi }}_r({\mathbf{I}}_1^{\mathcal{S}})+{\nu }_1^{\mathcal{S}}$ , the first NBM cannot afford to receive the prime shelf space. Consequently, the retailer gives the prime shelf to its SB. By contrast, when ${\hat{\pi }}_r({\mathbf{I}}_s^{\mathcal{S}})<{\hat{\pi }}_r({\mathbf{I}}_1^{\mathcal{S}})+{\nu }_1^{\mathcal{S}}$ , the first NBM receives the prime shelf space. The display fee it pays depends on whether the SB or the second NB poses a credible threat to the first NB. If neither the SB nor the second NB poses a credible threat (i.e., if neither product is attractive enough to receive the prime shelf space), the first NB receives the prime shelf space without paying a display fee. If the SB poses a stronger credible threat than the second NB, the first NB sets its display fee based on the total profit the retailer would earn by giving the prime shelf space to the SB. Last, if the second NB poses a stronger credible threat than the SB, the first NBM sets its display fee based on the total profit the retailer would earn by giving the prime shelf space to the second NB. Proposition 2 characterizes the parameter sets for each possible equilibrium outcome. For expositional clarity, we illustrate these sets in Figure 1(a).

Figure 1.

Illustration of Propositions 2 and 3. (a) Subgame equilibrium for $\mathcal{A}=\mathcal{S}$ and (b) Full equilibrium. Notes. We generate these figures by setting $n=3$ , $a_2=(31+a_1)/32$ , $a_3=1$ , and $\beta =0.05$ .

Proposition 2

For $\mathcal{A}=\mathcal{S}$ , there are four possible subgame equilibrium outcomes. Specifically, let $a_s^{(1)}$ , $a_s^{(2)}$ , $a_s^{(3)}$ , and $a_s^{(4)}$ denote the $a_s$ values that solve ${\hat{\pi }}_r({\mathbf{I}}_s^{\mathcal{S}})={\hat{\pi }}_r({\mathbf{I}}_1^{\mathcal{S}})+{\nu }_1^{\mathcal{S}}$ , ${\hat{\pi }}_r({\mathbf{I}}_s^{\mathcal{S}})={\hat{\pi }}_r({\mathbf{I}}_2^{\mathcal{S}})+{\eta }_2^{\mathcal{S}}$ , ${\hat{\pi }}_r({\mathbf{I}}_s^{\mathcal{S}})={\hat{\pi }}_r({\mathbf{I}}_1^{\mathcal{S}})$ , and ${\hat{\pi }}_r({\mathbf{I}}_1^{\mathcal{S}})={\hat{\pi }}_r({\mathbf{I}}_2^{\mathcal{S}})+{\eta }_2^{\mathcal{S}}$ , respectively.

• (i)

When $\varphi \in {\mathrm{\Omega }}_1^{\mathcal{S}}\equiv \{\varphi \in \mathrm{\Omega }:a_s\ge a_s^{(1)}\}$ , the SB takes the prime shelf space, which implies that the retailer has no display revenue (i.e., $b_r^{\mathcal{S}}=0$ ). In this case, $b_i^{\mathcal{S}}={\nu }_i^{\mathcal{S}}$ for all $i\in \mathcal{S}\setminus \{s\}$ .

(ii)

When $\varphi \in {\mathrm{\Omega }}_2^{\mathcal{S}}\equiv \{\varphi \in \mathrm{\Omega }:a_s^{(1)}>a_s\ge max\{a_s^{(2)},a_s^{(3)}\}\}$ , the first NBM receives the prime shelf space by paying a display fee of $b_r^{\mathcal{S}}=b_1^{\mathcal{S}}={\hat{\pi }}_r({\mathbf{I}}_s^{\mathcal{S}})-{\hat{\pi }}_r({\mathbf{I}}_1^{\mathcal{S}})$ . In this case, $b_i^{\mathcal{S}}={\eta }_i^{\mathcal{S}}$ for all $i\in \mathcal{S}\setminus \{1,s\}$ .

(iii)

When $\varphi \in {\mathrm{\Omega }}_3^{\mathcal{S}}\equiv \{\varphi \in \mathrm{\Omega }:a_s<min\{a_s^{(2)},a_s^{(4)}\}\}$ , the first NBM receives the prime shelf space by paying a display fee of $b_r^{\mathcal{S}}=b_1^{\mathcal{S}}={\hat{\pi }}_r({\mathbf{I}}_2^{\mathcal{S}})+{\eta }_2-{\hat{\pi }}_r({\mathbf{I}}_1^{\mathcal{S}})$ . In this case, $b_i^{\mathcal{S}}={\eta }_i^{\mathcal{S}}$ for all $i\in \mathcal{S}\setminus \{1,s\}$ .

(iv)

When $\varphi \in {\mathrm{\Omega }}_4^{\mathcal{S}}\equiv \{\varphi \in \mathrm{\Omega }:max\{a_s^{(2)},a_s^{(3)}\}>a_s\ge min\{a_s^{(2)},a_s^{(4)}\}\}$ the first NBM receives the prime shelf space without paying a display fee (i.e., $b_r^{\mathcal{S}}=0$ ). In this case, $b_i^{\mathcal{S}}={\eta }_i^{\mathcal{S}}$ for all $i\in \mathcal{S}\setminus \{1,s\}$ .

As Figure 1(a) shows, the retailer gives the prime shelf space to its own SB when the SB’s attractiveness is relatively high (i.e., when $\varphi \in {\mathrm{\Omega }}_1^{\mathcal{S}}$ ). Intuitively, solving ${\hat{\pi }}_r({\mathbf{I}}_s^{\mathcal{S}})={\hat{\pi }}_r({\mathbf{I}}_1^{\mathcal{S}})+{\nu }_1$ , which is the boundary that separates ${\mathrm{\Omega }}_1^{\mathcal{S}}$ from ${\mathrm{\Omega }}_2^{\mathcal{S}}$ , leads to a threshold for $a_s$ above which the retailer forgoes a display fee and gives the prime shelf space to its own SB to reap the full benefit of having an attractive SB product. The NBM receives the prime shelf space when $a_s$ is below that threshold. For moderate values of $a_s$ (i.e., when $\varphi \in {\mathrm{\Omega }}_2^{\mathcal{S}}$ ), the retailer gives the prime shelf space to thefirst NB, and the first NB determines its display fee offer based on whatthe retailer would earn by giving the prime shelf space to its own SB. For lower values of $a_s$ , there are two possibilities. When the first NB’s attractiveness is relatively low (i.e., when $\varphi \in {\mathrm{\Omega }}_3^{\mathcal{S}}$ ), the second NB poses a credible threat. Consequently, the first NBM determines its display fee based on what the retailer would earn by giving the prime shelf space to the second NB. When the first NB’s attractiveness is higher (i.e., when $\varphi \in {\mathrm{\Omega }}_4^{\mathcal{S}}$ ), neither the SB nor the second NB poses a credible threat. Consequently, the first NB receives the prime shelf space without paying a display fee. We provide the closed-form expressions for these set boundaries in the proof of Proposition 2.

In summary, when the retailer carries the SB, either the first NB or the SB receives the prime shelf space. The attractiveness levels of the first two NBs and the SB play important roles in determining the recipient of the prime shelf space and the retailer’s display fee revenue. Specifically, when the SB’s attractiveness is relatively high, it receives the prime shelf. When it is lower, the first NB receives the prime shelf space. If the first NB’s attractiveness is relatively high compared to the SB and the second NB, the first NBM does not pay a display fee. Otherwise, it pays a display fee, where the display fee depends on whether the SB or the second NB poses a stronger threat. Collectively, these possible outcomes indicate that the SB plays an important role in the retailer’s prime shelf space allocation decision and display fee revenue only when it is sufficiently attractive.

4.3. Equilibrium Characterization

In this section, we analyze the first stage of the game in which the retailer selects its assortment. Proposition 3 formalizes the retailer’s assortment choice.

Proposition 3

There exists a threshold ${\overline{a}}_s(a_1,\dots ,a_n,\beta )$ such that the retailer’s equilibrium assortment is ${\mathcal{A}}^{*}=\mathcal{N}$ if $\varphi \in {\mathrm{\Omega }}^{\mathcal{N}}\equiv \{\varphi \in \mathrm{\Omega }:a_s\le {\overline{a}}_s\}$ and ${\mathcal{A}}^{*}=\mathcal{S}$ if $\varphi \in {\mathrm{\Omega }}^{\mathcal{S}}\equiv \{\varphi \in \mathrm{\Omega }:a_s>{\overline{a}}_s\}$ . Propositions 1 and 2 characterize the equilibrium outcomes (i.e., the manufacturer margins, retailer’s quantity decisions and planogram choice), for ${\mathcal{A}}^{*}=\mathcal{N}$ (i.e., when $\varphi \in {\mathrm{\Omega }}^{\mathcal{N}}$ ) and ${\mathcal{A}}^{*}=\mathcal{S}$ (i.e., when $\varphi \in {\mathrm{\Omega }}^{\mathcal{S}}$ ), respectively.

The proof of Proposition 3 shows that when the retailer sets $\mathcal{A}=\mathcal{S}$ , its total profit increases in the attractiveness level of the SB product, $a_s$ . By contrast, the retailer’s profit does not depend on $a_s$ when it does not carry the SB in its assortment. Comparing the two profit functions reveals that there exists an SB attractiveness threshold, ${\overline{a}}_s$ , above which the retailer carries the SB product in its assortment. Figure 1(b) visualizes Proposition 3. Specifically, the retailer carries ${\mathcal{A}}^{*}=\mathcal{N}$ for relatively small values of $a_s$ (i.e., when $a_s\le {\overline{a}}_s$ ). The retailer carries the SB in its assortment for higher values of $a_s$ (i.e., when $a_s>{\overline{a}}_s$ ). The SB receives the prime shelf space only when its attractiveness level is relatively high. The first NB receives the prime shelf space for lower $a_s$ values. Indeed, when $a_1$ is relatively high, the first NB receives the prime shelf without paying a display fee both in the absence and presence of the SB (i.e., when $\varphi \in {\mathrm{\Omega }}_2^{\mathcal{N}}\cup {\mathrm{\Omega }}_4^{\mathcal{S}}$ in Figure 1(b)).

In summary, we find that the SB’s attractiveness must exceed a threshold for the retailer to replace the least attractive NB with its SB in the assortment. The SB’s attractiveness must exceed an even higher threshold for the retailer to display it in prime shelf space. When the SB’s attractiveness does not exceed that threshold, the first NB receives prime shelf space. In such cases, the first NB can receive the prime shelf space without paying a display fee only when its attractiveness is relatively high compared to the attractiveness levels of the SB and the second NB.

5. Results

When the retailer’s assortment size is $n$ , our model has $n+2$ parameters (i.e., $a_1,\dots ,a_n$ , $a_s$ , and $\beta$ ), making it difficult to study the role of each model parameter for a general assortment size. To this end, our analysis in this section focuses on a special case of our model in which the retailer’s planogram has three shelf spaces (i.e., $n=3$ ) and the NB products’ appeals are $(a_1,a_2,a_3)=(a_1,(1+a_1)/2,1)$ , leading to a linear appeal gap between the NBs (i.e., $a_1-a_2=a_2-a_3=(a_1-1)/2$ ). We refer to this special case as the narrow assortment case. Studying the narrow assortment case allows us to parsimoniously capture the essential elements of our main model, as the narrow assortment case facilitates (i) competition between the SB and the third NB for the retailer’s assortment and (ii) competition between the SB and first and second NBs for the prime shelf space. Nevertheless, we examine more general cases with $n\ge 3$ and non-linear appeal gaps in Section 6 to show the robustness of our findings. Proposition 4 characterizes the equilibrium outcomes of the narrow assortment case. Figure 2 illustrates the proposition.

Figure 2.

Illustration of Proposition 4. Notes. We generate this figure by setting $n=3$ , $a_2=(1+a_1)/2$ , $a_3=1$ , and $\beta =0.1$ .

Proposition 4

Let $\tilde{\mathrm{\Omega }}\equiv \{(a_1,a_2,a_3,a_s,\beta )\in {\mathbb{R}}^5:1\le a_1\le (23-32\beta )/9,a_2=(1+a_1)/2,a_3=1,3(3a_1+2\beta +1)/26\le a_s\le (11a_1-14\beta +17)/14,\beta \ge 0\}$ denote the parameter set for the special case in which $n=3$ with $a_2=(1+a_1)/2$ and $a_3=1$ . Furthermore, let ${\tilde{a}}_s^{(1)}\equiv (27a_1-2\beta )/31$ , ${\tilde{a}}_s^{(2)}\equiv (879a_1-80\beta +843)/2086$ , and ${\tilde{a}}_s^{(3)}\equiv 3(3a_1+2\beta +11)/56$ . Then,

• (i)

when $\varphi \in {\tilde{\mathrm{\Omega }}}_1^{\mathcal{S}}\equiv \{\varphi \in \tilde{\mathrm{\Omega }}:a_s\ge {\tilde{a}}_s^{(1)}\}$ , the retailer carries ${\mathcal{A}}^{*}=\mathcal{S}$ , and the SB receives the prime shelf space;

(ii)

when $\varphi \in {\tilde{\mathrm{\Omega }}}_2^{\mathcal{S}}\equiv \{\varphi \in \tilde{\mathrm{\Omega }}:{\tilde{a}}_s^{(1)}>a_s\ge {\tilde{a}}_s^{(2)}\}$ , the retailer carries ${\mathcal{A}}^{*}=\mathcal{S}$ , and the first NB receives the prime shelf space by paying a display fee of $b_1^{*}={\hat{\pi }}_r^{\mathcal{S}}({\mathbf{I}}_s^{\mathcal{S}})-{\hat{\pi }}_r^{\mathcal{S}}({\mathbf{I}}_1^{\mathcal{S}})$ ;

(iii)

when $\varphi \in {\tilde{\mathrm{\Omega }}}_3^{\mathcal{S}}\equiv \{\varphi \in \tilde{\mathrm{\Omega }}:{\tilde{a}}_s^{(2)}>a_s\ge {\tilde{a}}_s^{(3)}\}$ , the retailer carries ${\mathcal{A}}^{*}=\mathcal{S}$ , and the first NB receives the prime shelf space by paying a display fee of $b_1^{*}={\hat{\pi }}_r^{\mathcal{S}}({\mathbf{I}}_2^{\mathcal{S}})+{\hat{\pi }}_2^{\mathcal{S}}({\mathbf{I}}_2^{\mathcal{S}})-{\hat{\pi }}_2^{\mathcal{S}}({\mathbf{I}}_1^{\mathcal{S}})-{\hat{\pi }}_r^{\mathcal{S}}({\mathbf{I}}_1^{\mathcal{S}})$ ;

(iv)

when $\varphi \in {\tilde{\mathrm{\Omega }}}_1^{\mathcal{N}}\equiv \{\varphi \in \tilde{\mathrm{\Omega }}:a_s<{\tilde{a}}_s^{(3)}\}$ , the retailer carries ${\mathcal{A}}^{*}=\mathcal{N}$ , and the first NB receives the prime shelf space by paying a display fee of $b_1^{*}={\hat{\pi }}_r^{\mathcal{N}}({\mathbf{I}}_2^{\mathcal{N}})+{\hat{\pi }}_2^{\mathcal{N}}({\mathbf{I}}_2^{\mathcal{N}})-{\hat{\pi }}_2^{\mathcal{N}}({\mathbf{I}}_1^{\mathcal{N}})-{\hat{\pi }}_r^{\mathcal{N}}({\mathbf{I}}_1^{\mathcal{N}})$ .

Proposition 4 reveals that the first NB cannot receive the prime shelf space without paying a display fee in the narrow assortment case with $(a_1,a_2,a_3)=(a_1,(1+a_1)/2,1)$ . Intuitively, when there is a linear appeal gap between the NB products (i.e., when $a_1-a_2=a_2-a_3=(a_1-1)/2$ ), the first NB’s appeal is not high enough to receive the prime shelf space without paying a display fee. Figure 2 shows that the retailer carries ${\mathcal{A}}^{*}=\mathcal{N}$ when the SB’s appeal, $a_s$ , is relatively low (i.e., when $a_s<{\tilde{a}}_s^{(3)}=3(3a_1+2\beta +11)/56$ ) and ${\mathcal{A}}^{*}=\mathcal{S}$ for higher $a_s$ values (i.e., when $a_s\ge {\tilde{a}}_s^{(3)}$ ). For moderate (high) values of $a_s$ , the first NB receives the prime shelf space by setting its display fee based on what the retailer would earn by giving the prime shelf space to the second NB (the SB). In addition, when $a_s$ is very high, the SB takes the prime shelf space. Proposition 5 formalizes the impact of model parameters on the retailer’s equilibrium profit and display fee revenue.

Proposition 5

At equilibrium, the retailer’s total category profit increases, whereas its display fee revenue is non-monotone in $a_1$ , $a_s$ , and $\beta$ .

The first part of Proposition 5 is rather intuitive, as it shows that increasing product appeals ( $a_1$ and $a_s$ ) and strengthening the demand-stimulating impact of the prime shelf space (i.e., increasing $\beta$ ) translate into a higher total category profit for the retailer. The second part indicates that the retailer’s display fee revenue may increase or decrease as $a_1$ , $a_s$ , or $\beta$ increases. Intuitively, an increase in a model parameter affects not only each NBM’s display fee offer but also the retailer’s incentive to give the prime shelf space to its SB, leading to non-monotone relationships between the parameters and the retailer’s display fee revenue at equilibrium. For example, $\mathrm{\partial }{b}_r^{*}/\mathrm{\partial }{a}_1=-387\beta /1225<0$ when $\varphi \in {\tilde{\mathrm{\Omega }}}_2^{\mathcal{S}}$ . The first NB competes with the SB for the prime shelf space in this region. As such, an increase in $a_1$ strengthens the first NB’s position, leading to a decrease in the display fee it pays. By contrast, $\mathrm{\partial }{b}_r^{*}/\mathrm{\partial }{a}_1=3\beta /70>0$ when $\varphi \in {\tilde{\mathrm{\Omega }}}_3^{\mathcal{S}}$ . In this region, the first NB competes with the second NB for the prime shelf space. In this case, increasing $a_1$ intensifies the competition between the two NBs for the prime shelf space, resulting in an increase in the retailer’s display fee revenue. Collectively, these two cases indicate that the retailer’s display revenue may decrease or increase as $a_1$ increases. The other two model parameters, $a_s$ and $\beta$ , create similar competitive dynamics.

The remainder of this section examines three important features of our setting (i.e., a planogram with one prime shelf, SB presence, and display fees) more closely to answer our research questions.

5.1. Impact of Planogram Considerations on Assortment and Pricing Decisions

In this subsection, we focus on our first research question and study the impact of prime shelf space on the retailer’s assortment and pricing decisions. To this end, we first consider an alternative version of the narrow assortment model in which the retailer’s planogram has three nonprime shelf spaces rather than one prime and two nonprime shelf spaces. Comparing the equilibrium outcomes of this alternative model with those of our main narrow assortment model generates insights into the role of the prime shelf space.

The absence of a prime shelf space means that the NBMs no longer have the incentive to pay a display fee and that the retailer no longer needs to determine which product should receive the prime shelf space. Accordingly, the retailer solves an assortment problem in the presence of pricing considerations. This alternative model is a special case of our main narrow assortment model in which $\beta =0$ because eliminating the demand-stimulating impact of prime shelf space is equivalent to having a planogram with three nonprime shelf spaces. Corollary 1 characterizes the retailer’s equilibrium assortment.

Corollary 1

For $n=3$ and $(a_1,a_2,a_3)=(a_1,(1+a_1)/2,1)$ , when the retailer’s planogram does not have a prime shelf space, the retailer’s equilibrium assortment is $\overline{\mathcal{A}}=\mathcal{N}=\{1,2,3\}$ if $a_s\le 3(3a_1+11)/56$ and $\overline{\mathcal{A}}=\mathcal{S}=\{1,2,s\}$ if $a_s>3(3a_1+11)/56$ .

Comparing Proposition 4 and Corollary 1 reveals that the presence of prime shelf space can prevent the retailer from introducing its SB. Specifically, in the presence of a prime shelf space, the retailer introduces its SB when $a_s\ge 3(3a_1+11)/56+3\beta /28$ . By contrast, in the absence of the prime shelf space, $a_s\ge 3(3a_1+11)/56$ is sufficient for SB introduction. These thresholds imply that there are cases when the retailer’s equilibrium assortment changes from $\overline{\mathcal{A}}=\mathcal{S}$ to ${\mathcal{A}}^{*}=\mathcal{N}$ when the retailer switches from a planogram with three nonprime shelf spaces to a planogram with one prime and two nonprime shelf spaces. In such cases, the equilibrium manufacturer and retail margins and demands also change because of the change in the retailer’s assortment.

The presence of the prime shelf space affects the equilibrium manufacturer and retail margins and demands even in the absence of an assortment change. For example, when $a_s\le 3(3a_1+11)/56$ , the retailer carries $\mathcal{N}=\{1,2,3\}$ both in the absence and presence of prime shelf space. However, the presence of the prime shelf space increases the first NB’s retail price and demand by $p_1^{*}-{\overline{p}}_1=41\beta /56$ (from ${\overline{p}}_1=c_1+(79a_1-9)/112$ to $p_1^{*}=c_1+(79a_1-9)/112+41\beta /56$ ) and $q_1^{*}-{\overline{q}}_1=39\beta /112$ (from ${\overline{q}}_1=3(23a_1-9)/224$ to $q_1^{*}=3(23a_1-9)/224+39\beta /112$ ), respectively. Intuitively, giving the prime shelf space to the first NB allows the retailer to sell more units of that product at a higher retail price. As a specific example, when $a_1=1$ , $c_1=0.5$ , and $\beta =0.05$ , receiving the prime shelf space increases the first NB’s retail price and demand by 3.25% and 9.29%, respectively. By contrast, the presence of the prime shelf space decreases the second and third NBs’ retail prices and demands because receiving the nonprime shelf spaces puts these products at a disadvantage with respect to the first NB.

In summary, we find that planogram considerations have overarching implications for the retailer’s category management strategy. Specifically, the retailer’s planogram decisions can have a sizable impact on the retail and wholesale prices and product demands in the category. Furthermore, there are cases when the retailer does not introduce its SB to take full advantage of the demand-stimulating impact of prime shelf space. These findings suggest that fully monetizing the demand-stimulating impact of prime shelf space requires retailers to consider the interplay between planogram, assortment, and pricing decisions and the NBMs’ strategic responses to such decisions.

5.2. Impact of Planogram Considerations on SB Introduction

In this subsection, we focus on our second research question and examine the impact of planogram considerations on the financial consequences of the retailer’s SB introduction decision. To this end, we consider an alternative version of the narrow assortment model in which the retailer does not have the option to include the SB in its assortment. In the absence of the SB, the retailer’s problem simplifies to planogram design with the three NBs. Accordingly, comparing the subgame equilibrium outcomes in which $\mathcal{A}=\mathcal{N}=\{1,2,3\}$ with the full equilibrium outcomes we present in Proposition 4 allows us to shed light on the retailer’s SB introduction decision. Corollary 2 characterizes the equilibrium outcomes in the absence of the SB.

Corollary 2

In the absence of the SB with $n=3$ and $(a_1,a_2,a_3)=(a_1,(1+a_1)/2,1)$ , the retailer carries $\hat{\mathcal{A}}=\mathcal{N}=\{1,2,3\}$ , and the first NB receives the prime shelf space by paying a display fee of ${\hat{b}}_1^{\mathcal{N}}=3\beta (a_1+10\beta +13)/196$ .

Corollary 2 reveals that in the absence of the SB, the first NB receives the prime shelf space by paying a display fee. This is consistent with the full equilibrium characterization in Proposition 4. That is, when there is a linear appeal gap between the NB products (i.e., $a_1-a_2=a_2-a_3=(a_1-1)/2$ ), the first NB’s appeal is not high enough to receive the prime shelf space without paying a display fee, regardless of whether the retailer carries the SB or the third NB in its assortment. Following Proposition 4, let $\mathrm{\Delta }{\mathrm{\Pi }}_r\equiv {\mathrm{\Pi }}_r^{*}-{\hat{\mathrm{\Pi }}}_r^{\mathcal{N}}$ denote the difference between the retailer’s total category profit at equilibrium and its total category profit in the subgame in which $\hat{\mathcal{A}}=\mathcal{N}=\{1,2,3\}$ . The retailer introduces the SB only when it is profitable to do so (i.e., ${\mathcal{A}}^{*}=\mathcal{S}=\{1,2,s\}$ only when $\mathrm{\Delta }{\mathrm{\Pi }}_r={\hat{\mathrm{\Pi }}}_r^{\mathcal{S}}-{\hat{\mathrm{\Pi }}}_r^{\mathcal{N}}\ge 0$ ). Although carrying ${\mathcal{A}}^{*}=\mathcal{S}$ implies an increase in the retailer’s total category profit, whether such an increase is due to an increase in gross profit or display revenue or both is unclear. As such, for ${\mathcal{A}}^{*}=\mathcal{S}$ , we decompose $\mathrm{\Delta }{\mathrm{\Pi }}_r$ into two components as follows:

$$\begin{array}{rl}\mathrm{\Delta }{\mathrm{\Pi }}_r& =({\hat{\pi }}_r^{\mathcal{S}}+{\hat{b}}_r^{\mathcal{S}})-({\hat{\pi }}_r^{\mathcal{N}}+{\hat{b}}_r^{\mathcal{N}})\\ & =\underset{=\mathrm{\Delta }{\pi }_r}{\underbrace{{\hat{\pi }}_r^{\mathcal{S}}-{\hat{\pi }}_r^{\mathcal{N}}}}+\underset{=\mathrm{\Delta }{b}_r}{\underbrace{{\hat{b}}_r^{\mathcal{S}}-{\hat{b}}_r^{\mathcal{N}},}}\end{array}$$

(15)

where $\mathrm{\Delta }{\pi }_r={\hat{\pi }}_r^{\mathcal{S}}-{\hat{\pi }}_r^{\mathcal{N}}$ and $\mathrm{\Delta }{b}_r={\hat{b}}_r^{\mathcal{S}}-{\hat{b}}_r^{\mathcal{N}}$ denote the changes in the retailer’s gross profit and display revenue, respectively. Proposition 6 shows that the signs of $\mathrm{\Delta }{\pi }_r$ and $\mathrm{\Delta }{b}_r$ .

Proposition 6

For $n=3$ and $(a_1,a_2,a_3)=(a_1,(1+a_1)/2,1)$ , the retailer introduces its SB when $\varphi \in {\tilde{\mathrm{\Omega }}}^{\mathcal{S}}\equiv \{\varphi \in \tilde{\mathrm{\Omega }}:a_s\ge {\tilde{a}}_s^{(3)}\}$ . The SB introduction increases the retailer’s gross profit (i.e., $\mathrm{\Delta }{\pi }_r\ge 0$ ) for all $\varphi \in {\tilde{\mathrm{\Omega }}}^{\mathcal{S}}$ . The retailer’s display revenue increases (i.e., $\mathrm{\Delta }{b}_r\ge 0$ ) when $\varphi \in {\tilde{\mathrm{\Omega }}}_{+}^{\mathcal{S}}\equiv \{\varphi \in {\tilde{\mathrm{\Omega }}}^{\mathcal{S}}:(1623a_1-250\beta +1191)/3332\le a_s<(27a_1-2\beta )/31\}$ and decreases (i.e., $\mathrm{\Delta }{b}_r<0$ ) when $\varphi \in {\tilde{\mathrm{\Omega }}}^{\mathcal{S}}\setminus {\tilde{\mathrm{\Omega }}}_{+}^{\mathcal{S}}$ .

Proposition 6 reveals that the retailer’s SB introduction increases its gross profit, whereas the impact of the SB introduction on the retailer’s display fee revenue depends on the SB’s appeal. Figure 3 illustrates the proposition. When the SB’s appeal is relatively low (i.e., when $a_s<(1623a_1-250\beta +1191)/3332$ ), SB introduction lowers the retailer’s display fee revenue. In such cases, the SB is not strong enough to compete with the first NB for the prime shelf space. Consequently, the first NB lowers its display fee. When the SB has a moderate appeal (i.e., when $(1623a_1-250\beta +1191)/3332\le a_s\le (27a_1-2\beta )/31$ ), the SB introduction increases the retailer’s display fee revenue. In such cases, the first NB continues to receive the prime shelf space, but pays a higher display fee to prevent the retailer from giving the prime shelf space to the SB. For higher values of $a_s$ (i.e., when $a_s>(27a_1-2\beta )/31$ ), the retailer gives the prime shelf space to the SB to fully monetize the high appeal of its own product. Consequently, it no longer earns display fee revenue.

Figure 3.

Illustration of Proposition 6. Notes. We generate this figure by setting $n=3$ , $a_2=(1+a_1)/2$ , $a_3=1$ , and $\beta =0.1$ .

In summary, the analytical SB literature shows that a retailer can introduce an SB product to increase its gross profit (e.g., Raju et al., 1995; Zheng et al., 2022). Our findings conform to this line of thought. In addition, we identify cases when planogram considerations allow the retailer to use the SB as a strategic lever to intensify the competition for the prime shelf space and thereby increase its display fee revenue. That said, we also identify cases when the SB’s contribution to the retailer’s gross profit comes at the expense of lower display fee revenues. Collectively, these findings suggest that when retailers make SB introduction decisions in the presence of planogram considerations, they should take into account not only the gross profit impact of SBs but also how SBs may affect their planogram decisions and side payments they receive from the NBMs.

5.3. Impact of Display Fees on NBMs

Section 5.2 indicates that display fees play an important role in the retailer’s assortment and planogram decisions (e.g., whether the retailer should carry the SB in its assortment). In this subsection, we focus on our third research question and examine the impact of display fees on NBMs. To do so, we first consider an alternative version of the narrow assortment model in which the retailer does not accept display fees. Comparing the equilibrium outcomes of this alternative model with those of our main narrow assortment model allows us to shed light on the impact of display fees on the NBMs.

Recall that our setting has a five-stage game in which the retailer collects display fee offers in the second stage. Removing this stage leads to a four-stage game in which the last three stages (i.e., the retailer’s planogram selection, the NBMs’ margin optimization, and the retailer’s quantity optimization) are identical to those of our main model. Solving the last two stages through backward induction leads to the retailer’s gross profit for all possible planogram choices in both our main model and this alternative model. Furthermore, the first two stages of the game in the alternative model (i.e., the retailer’s assortment and planogram decisions) reduce to selecting the planogram that maximizes the retailer’s gross profit, which equals its total profit because of the absence of display fees. Proposition 7 characterizes the equilibrium outcomes in the absence of display fees.

Proposition 7

Let ${\tilde{a}}_s^{(0)}$ denote the $a_s$ value that solves ${\hat{\pi }}_r({\mathbf{I}}_s^{\mathcal{S}})={\hat{\pi }}_r({\mathbf{I}}_1^{\mathcal{N}})$ . In addition, let ${\tilde{a}}_s^{(1)}\equiv (387a_1-250\beta +54)/833$ , and ${\tilde{a}}_s^{(2)}\equiv 3(3a_1+2\beta +11)/56$ . In the absence of display fees with $n=3$ and $(a_1,a_2,a_3)=(a_1,(1+a_1)/2,1)$ , there are three possible equilibrium outcomes. Specifically,

• (i)

when $\varphi \in {\tilde{\mathrm{\Omega }}}_0^{(1)}\equiv \{\varphi \in \tilde{\mathrm{\Omega }}:a_s\ge max\{{\tilde{a}}_s^{(0)},{\tilde{a}}_s^{(1)}\}\}$ , the retailer carries ${\tilde{\mathcal{A}}}_0=\mathcal{S}$ , and the SB takes the prime shelf space;

(ii)

when $\varphi \in {\tilde{\mathrm{\Omega }}}_0^{(2)}\equiv \{\varphi \in \tilde{\mathrm{\Omega }}:max\{{\tilde{a}}_s^{(0)},{\tilde{a}}_s^{(1)}\}>a_s\ge min\{{\tilde{a}}_s^{(1)},{\tilde{a}}_s^{(2)}\}\}$ , the retailer carries ${\tilde{\mathcal{A}}}_0=\mathcal{S}$ , and the first NB receives the prime shelf space; and

(iii)

when $\varphi \in {\tilde{\mathrm{\Omega }}}_0^{(3)}\equiv \{\varphi \in \tilde{\mathrm{\Omega }}:a_s<min\{{\tilde{a}}_s^{(1)},{\tilde{a}}_s^{(2)}\}\}$ , the retailer carries ${\tilde{\mathcal{A}}}_0=\mathcal{N}$ , and the first NB receives the prime shelf space.

Figure 4(a) illustrates Proposition 7. Consistent with our main model, the retailer offers the SB only when the SB has a relatively high appeal. When the SB is in the retailer’s assortment, it receives the prime shelf space unless the first NB’s appeal is relatively high. Indeed, comparing Figure 2, which shows the equilibrium outcomes of our main narrow assortment model, and Figure 4(a) reveals that the region in which the retailer carries the SB in its assortment is larger in the absence of display fees. Proposition 8 formalizes this observation.

Figure 4.

Illustration of Propositions 7 and 9. (a) Illustration of Proposition 7 and (b) illustration of Proposition 9. Notes. Figure 4(a) shows the equilibrium outcomes in the absence of display fees. Figure 4(b) shows the set of parameters in which the display fees make all channel members strictly better off. We generate these figures by setting $n=3$ , $a_2=(1+a_1)/2$ , $a_3=1$ , and $\beta =0.1$ .

Proposition 8

The set of parameters in which the retailer carries the SB at equilibrium is larger in the absence of display fees. Formally, ${\tilde{\mathrm{\Omega }}}^{\mathcal{S}}\subset {\tilde{\mathrm{\Omega }}}_0^{\mathcal{S}}$ , where ${\tilde{\mathrm{\Omega }}}^{\mathcal{S}}\equiv {\tilde{\mathrm{\Omega }}}_1^{\mathcal{S}}\cup {\tilde{\mathrm{\Omega }}}_2^{\mathcal{S}}\cup {\tilde{\mathrm{\Omega }}}_3^{\mathcal{S}}$ and ${\tilde{\mathrm{\Omega }}}_0^{\mathcal{S}}\equiv {\tilde{\mathrm{\Omega }}}_0^{(1)}\cup {\tilde{\mathrm{\Omega }}}_0^{(2)}$ .

Proposition 8 implies that the NBMs can use display fees as an entry deterrence mechanism to prevent the retailer from including the SB in its assortment. Intuitively, display fees make the NBs more profitable for the retailer. Consequently, the introduction of display fees shrinks the region in which the retailer carries the SB in its assortment. More generally, introducing display fees can lead to several changes in the equilibrium outcomes. First, the retailer’s assortment and planogram may remain unchanged, but the retailer may begin collecting a display fee. For example, when $\varphi \in {\tilde{\mathrm{\Omega }}}_0^{(2)}\cap {\tilde{\mathrm{\Omega }}}_3^{\mathcal{S}}$ , introducing display fees does not lead to a change in the retailer’s planogram (i.e., the first NB receives the prime shelf space), but rather generates additional revenue for the retailer and an additional expense for the first NBM. Second, the retailer may change its planogram without changing its assortment. For example, when $\varphi \in {\tilde{\mathrm{\Omega }}}_0^{(1)}\cap {\tilde{\mathrm{\Omega }}}_2^{\mathcal{S}}$ , the retailer changes its planogram from ${\mathbf{I}}_s^{\mathcal{S}}$ to ${\mathbf{I}}_1^{\mathcal{S}}$ to collect a display fee from the first NBM. Third, the retailer may change its assortment and, therefore, its planogram. For example, when $\varphi \in {\tilde{\mathrm{\Omega }}}_0^{(1)}\cap {\tilde{\mathrm{\Omega }}}_1^{\mathcal{N}}$ , the retailer changes its assortment from $\mathcal{S}$ and $\mathcal{N}$ and its planogram from ${\mathbf{I}}_s^{\mathcal{S}}$ to ${\mathbf{I}}_1^{\mathcal{N}}$ to collect a display fee from the first NBM. Can one (or more) of these changes make all channel members strictly better off? Proposition 9 provides an answer to this question.

Proposition 9

When display fees do not lead to an assortment change, they cannot make all four channel members strictly better off. However, when they lead to an assortment change, they can make all four channel members strictly better off. More formally, there exists a nonempty set ${\tilde{\mathrm{\Omega }}}_w\subset {\tilde{\mathrm{\Omega }}}_0^{(1)}\cap {\tilde{\mathrm{\Omega }}}_1^{\mathcal{N}}$ such that ${\mathrm{\Pi }}_r^{*}>{\tilde{\mathrm{\Pi }}}_r$ , and ${\mathrm{\Pi }}_i^{*}>{\tilde{\mathrm{\Pi }}}_i$ , for i=1,2,3.

Keeping the same assortment implies that the retailer carries either $\mathcal{N}=\{1,2,3\}$ or $\mathcal{S}=\{1,2,s\}$ in both the absence and presence of display fees. When ${\tilde{\mathcal{A}}}_0={\mathcal{A}}^{*}=\mathcal{S}$ , the third NBM does not benefit from display fees because its total profit is zero in both the absence and presence of display fees. When ${\tilde{\mathcal{A}}}_0={\mathcal{A}}^{*}=\mathcal{N}$ , display fees intensify the competition for prime shelf space, so the NBMs cannot simultaneously benefit from display fees. Thus, display fees cannot make all four channel members (i.e., the retailer and three NBMs) strictly better off when they do not lead to an assortment change. Conversely, the second part of Proposition 9 indicates that all four players can benefit from display fees when these fees lead to an assortment change.

Figure 4(b) shows the parameter set in which display fees make all channel members strictly better off, ${\tilde{\mathrm{\Omega }}}_w$ . We provide the closed-form expressions for the boundaries of this set in the proof of Proposition 9. Table 1 illustrates the second part of Proposition 9 with an example. We generate this example by setting $n=3$ , $a_1=1.6$ , $a_2=(1+a_1)/2=1.3$ , $a_3=1$ , $a_s=0.85$ , and $\beta =0.1$ . In the absence of display fees, the retailer carries $\mathcal{S}=\{1,2,s\}$ , and the SB takes the prime shelf space. By contrast, in the presence of display fees, the retailer carries $\mathcal{N}=\{1,2,3\}$ , and the first NB receives the prime shelf space. In this example, all four channel members (i.e., the retailer and three NBMs) are strictly better off in the presence of display fees. Specifically, despite paying a display fee, the first NBM’s total profit increases because the retailer moves its product from a nonprime shelf space to the prime shelf space. The second NBM’s profit also increases because it no longer competes with the SB, which does not have double marginalization. The third NBM’s profit is also higher because it enters the retailer’s assortment without making a display fee payment. Last, the retailer’s total category profit increases because it receives a display fee from the high-quality NBM. In this example, display fees serve as an entry deterrence mechanism because the retailer carries the SB in its assortment in the absence but not in the presence of display fees.

Table 1.

Impact of display fees.

Equilibrium Outcome	Without Display Fees		With Display Fees
Assortment	$\mathcal{S}=\{1,2,s\}$		$\mathcal{N}=\{1,2,3\}$
Planogram	${\mathbf{I}}_s^{\mathcal{S}}$		${\mathbf{I}}_1^{\mathcal{N}}$
Retailer’s display revenue	0		0.0239
Retailer’s profit	0.4009		0.4215
First NBM’s profit	0.1697		0.1971
Second NBM’s profit	0.0694		0.0741
Third NBM’s profit	0		0.0153

Notes. We generate this example by setting $n=3$ , $a_1=1.6$ , $a_2=1.3$ , $a_3=1$ , $a_s=0.85$ , and $\beta =0.1$ .

In summary, our analysis leads to two important results regarding the impact of display fees on the equilibrium outcomes. First, the region in which the retailer carries the SB in its assortment is smaller in the presence of display fees because display fees make the NBs more profitable for the retailer. Second, there are cases in which display fees can make all four channel members strictly better off. These cases arise when display fees serve as an entry deterrence mechanism that prevents the retailer from carrying the SB in its assortment. This finding indicates that display fees do not necessarily erode NBMs’ profits. In other words, NBMs can benefit from display fees by using them to influence retailers’ assortment and planogram decisions in their favor.

6. Robustness Checks

Section 5 leads to three key findings regarding the impact of planogram considerations on a retailer’s category management strategy and interactions with NBMs. First, the presence of the prime shelf space can not only prevent the retailer from introducing its SB but also have a sizable impact on the retail and wholesale prices in the category. Second, in some cases, the retailer uses its SB as a strategic lever to increase its display revenue by intensifying the competition for the prime shelf space. Third, NBMs can benefit from display fees because display fees enable them to influence the retailer’s assortment and planogram decisions in their favor. We obtain these findings from a special case of our main model in which the retailer carries three products, where there is a linear appeal gap between the NB products. Analytical tractability is challenging for more general versions of our main model with larger assortment sizes (i.e., $n>3$ ) and less structured product appeals (e.g., non-linear appeal gaps between products). Accordingly, we numerically study wider assortments with more general NB product appeals to test the robustness of our findings.

In our numerical study, we generate unique scenarios (parameter combinations) as follows: we consider three different $\beta$ values: $\beta =0.05$ , $\beta =0.1$ , and $\beta =0.25$ . We vary $a_s$ between 0.5 and 1.25 in increments of 0.01 and $a_1$ between 1 and 2.5 in increments of 0.01. We consider four different assortment sizes: $n=3$ , $n=5$ , $n=10$ , and $n=25$ . For a given $n$ and $a_1$ , we set $a_n=1$ and $a_i=a_n+(\frac{n-i}{n-1}{)}^{\gamma }(a_1-a_n)$ for $i=1,\dots ,n$ with $\gamma \ge 0$ . For a given assortment size, this structure allows us to control the NB products’ appeals (i.e., $a_1,\dots ,a_n$ ) with two parameters, $a_1$ and $\gamma$ . We consider four different $\gamma$ values: $\gamma =0.5$ , $\gamma =1$ , $\gamma =2$ , and $\gamma =5$ . Among these four $\gamma$ values, $\gamma =1$ implies a linear appeal gap between the NB products (i.e., $a_1-a_2=a_2-a_3=\cdots =a_{n-1}-a_n=\frac{a_1-a_n}{n-1}$ ). By contrast, $\gamma =0.5$ implies increasing appeal gaps (i.e., $a_1-a_2<a_2-a_3<\cdots <a_{n-1}-a_n$ ), whereas $\gamma =2$ and $\gamma =5$ imply decreasing appeal gaps (i.e., $a_1-a_2>a_2-a_3>\cdots >a_{n-1}-a_n$ ). Last, we set $c_s=a_s/2$ and $c_i=a_i/2$ for all $i=1,\dots ,n$ .

Following the above steps and removing parameter combinations that do not belong to the set of feasible parameter values, $\mathrm{\Omega }$ , result in 220,636 unique scenarios (i.e., combinations of $a_1$ , $a_s$ , $\beta$ , $\gamma$ , and $n$ ). The retailer carries ${\mathcal{A}}^{*}=\mathcal{N}$ in 40.65% of the scenarios and ${\mathcal{A}}^{*}=\mathcal{S}$ in the remaining scenarios. The SB receives the prime shelf space in 15.02% of the scenarios, and the first NB receives the prime shelf without a display fee in 3.87% of the scenarios. In other words, the retailer does not generate a display fee revenue in 18.89% of the scenarios. The first NB receives the prime shelf space by paying a display fee in the remaining scenarios.

Figure 5 illustrates how relaxing our assumption of linear appeal gaps affects the equilibrium outcomes. Figures 5(a), 5(b), and 5(c) have $\gamma =0.5$ , $\gamma =1$ , and $\gamma =5$ , respectively. When $\gamma =0.5$ and $\gamma =1$ , the first NB cannot receive the prime shelf space without paying a display fee. Intuitively, when $\gamma$ is relatively small, the second NB poses a credible threat to the first NB, forcing the first NB to pay a display fee. By contrast, Figure 5(c) illustrates that when $\gamma =5$ , the first NB can receive the prime shelf space without paying a display fee. Intuitively, a relatively high $\gamma$ value leads to a large appeal gap between the first and second NBs, preventing the second NB from posing a credible threat to the first NB for the prime shelf space.

Figure 5.

Role of Product Appeals. (a) $\gamma =0.5$ , (b) $\gamma =1$ and (c) $\gamma =5$ . Notes. We generate this figure by setting $\beta =0.05$ , $n=3$ , $a_2=1+(a_1-1)/2^{\gamma }$ , and $a_3=1$ .

Figure 6 illustrates the equilibrium outcomes for three different assortment sizes, where $n=3$ in Figure 6(a), $n=5$ in Figure 6(b), and $n=10$ in Figure 6(c). A key takeaway emerging from Figure 6 is that the retailer’s SB and planogram choices are robust to its assortment size. That is, the retailer carries ${\mathcal{A}}^{*}=\mathcal{N}$ when the SB’s appeal, $a_s$ , is relatively low. The SB enters the retailer’s assortment, but the first NB receives the prime shelf space for moderate $a_s$ values. The SB receives the prime shelf space when its appeal is relatively high. An additional insight emerging from Figure 6 is that the regions in which the SB enters the retailer’s assortment and receives the prime shelf space expand as the assortment size increases. Intuitively, the SB puts margin pressure on more NBMs, as the retailer’s assortment size grows. Consequently, replacing an NB with the SB becomes more attractive in larger assortments.

Figure 6.

Role of assortment size. (a) $n=3$ , (b) $n=5$ and (c) $n=10$ . Notes. We generate this figure by setting $\beta =0.05$ , $a_n=1$ , $a_i=1+\left(\frac{n-i}{n-1}\right)(a_1-1)$ for $i=1,\dots ,n$ .

Consistent with the findings in Section 5.1, the presence of the prime shelf space affects not only the retailer’s SB introduction decision but also the retail and wholesale prices in the category. For example, in scenarios in which the first NB receives the prime shelf space at equilibrium, the presence of the prime shelf space increases the retailer and wholesale prices of the first NB by 5.48% and 2.52%, on average. Similarly, when the SB receives the prime shelf space, the average increase in its retail price is 6.02%. More generally, the profit benefit of the prime shelf space increases in $\beta$ and decreases in $n$ . For example, the average increase in the retailer’s profit due to the presence of the prime shelf space is 4.52% when $\beta =0.05$ and 9.42% when $\beta =0.1$ . In addition, the average increase in the retailer’s profit due to the presence of the prime shelf space is 8.84% when $n=10$ and 6.41% when $n=25$ .

Focusing on the 130,897 scenarios in which the retailer carries the SB in its assortment, we find that SB introduction increases the retailer’s display revenue in 28.55% of such scenarios. Lastly, focusing on the 97,904 scenarios in which the SB and the first NB respectively receive the prime shelf space in the absence and presence of display fees, we find that display fees make all channel members (i.e., the retailer and all $n$ NBMs) better off in 10.61% of such scenarios by allowing the NBMs to influence the retailer’s assortment and planogram decisions in their favor. Collectively, these findings show that our results continue to hold when the retailer carries wider assortments with more general (i.e., non-linear) appeal gaps between the NB products.

7. Discussion and Conclusion

We contribute to the literature by investigating how planogram considerations affect a retailer’s category management strategy and interactions with NBMs. Our findings have important implications for retailers, manufacturers, and researchers. The implications of our study for retailers are twofold. First, our findings imply that fully monetizing the prime shelf spaces requires retailers to go beyond determining which products should receive prime shelf spaces and consider the interplay between planogram, assortment, and pricing decisions. Second, a retailer should pay close attention to the NBMs’ strategic responses to SB introduction. For example, our findings suggest that an NBM’s display fee offer depends on whether it competes with another NB or the SB for the prime shelf space. Consequently, a retailer should assess when SB introduction (and, more generally, increasing SB presence in its stores) allows it to extract more money from NBMs. On the flip side, the main implication of our study for NBMs is that they should be aware that the role of display fees may extend beyond determining which product receives the prime shelf space. This is because display fees may indirectly affect the retailer’s assortment and pricing decisions. For example, our study shows that an NBM’s display fee payment may prevent the retailer from introducing the SB to the category, thereby benefitting other NBMs in the category.

For researchers, the main implication of our study is that conclusions drawn from category management studies that overlook retailers’ planogram decisions and side payments from NBMs to influence such decisions should be treated with caution. For example, many empirical category management studies (e.g., Alan et al., 2017; Boatwright and Nunes, 2001; Pauwels and Srinivasan, 2004) examine how category management decisions (e.g., assortment reduction, SB introduction) affect a retailer’s category sales or gross profit. Understandably, data availability drives the choice of dependent variable in those studies. Nevertheless, our findings suggest that the omission of planogram considerations can have a significant impact on a retailer’s category management decisions and, therefore, total category sales and profit. Thus, it may be fruitful for future empirical studies to analyze how manufacturers’ side payments affect retailers’ planogram decisions.

We generate our insights from a stylized model that relies on several simplifying assumptions. Future research could extend our study by relaxing some of our assumptions. First, we assume an exogenous attractiveness level for each product. While NBMs in practice are unlikely to change the attractiveness levels of their products in response to a single retailer’s planogram decisions, retailers can optimally set the attractiveness levels of their SBs. For example, a retailer with a more efficient cost structure (i.e., a lower marginal cost) might be more likely to introduce a more attractive SB and display it in the prime shelf space. Second, we assume that the demand-stimulating impact of the prime shelf space is identical for all products in the category, whereas this impact may be stronger for some products in practice. Relaxing this assumption can lead to cases when a product with a relatively low attractiveness level can enter the retailer’s assortment and secure the prime shelf space because of its stronger response to the placement on the prime shelf space. Last, we assume that the retailer makes quantity decisions, resulting in market-clearing retail prices within a Cournot framework. Although a Cournot framework offers analytical tractability in our setting, a model in which the retailer directly sets retail prices based on market conditions (e.g., competition, promotional activities) may more accurately reflect retailers’ pricing decisions in practice. We hope that this article generates more interest in examining the channel implications of retailers’ planogram decisions.

Supplemental Material

sj-pdf-1-pao-10.1177_10591478251398330 - Supplemental material for The Impact of Planogram Design and Display Fees on Retail Category Management

Supplemental material, sj-pdf-1-pao-10.1177_10591478251398330 for The Impact of Planogram Design and Display Fees on Retail Category Management by Yasin Alan, Mümin Kurtuluş and Alper Nakkas in Production and Operations Management