Channel Choice via On-Line Platform

Abstract

Several major on-line platforms operate two channels: An agency channel in which suppliers retain control over prices and quantities and pay a portion of sales revenue to the platform, and a reselling channel in which the platform purchases goods from the supplier and resells them to consumers. These two channels run in parallel and many suppliers interact with only one of them. Although it is quite easy for a supplier to sell through a platform’s agency channel, they must typically be invited to participate in the reselling channel. We develop a model of a powerful platform that can offer a supplier a two-part contract to induce it to participate in its reselling channel instead of its agency channel. When the supplier sells through the platform’s agency channel, we find that if the competition among the traditional resellers is at least moderate and the on-line platform is a close enough substitute for traditional resale channel, then the equilibrium quantities sold through the on-line and traditional channels both exceed the first best quantities. This would not occur if the supplier sold through either the on-line or the traditional channel in isolation. Nor would it occur if the supplier sold through the platform’s reselling channel. As a consequence, we find that when competition among traditional resellers is at least moderate, and both the commission rate and the substitutability between the on-line platform and the traditional resale channel are sufficiently high, there is a Pareto improving reselling contract between the supplier and the platform.

1. Introduction

It is now well understood that the interactions between a supplier and a reseller(s) can be dramatically altered when the supplier can encroach upon the market served by the reseller(s) by selling directly to consumers. This understanding has been developed by Chiang et al. (2003), Hendershott and Zhang (2006), Huang and Swaminathan (2009), Cattani et al. (2006), and Arya et al. (2007), among others. With the emergence of on-line agency/marketplace platforms, such as eBay, Amazon, Craig’s List, etc., supplier encroachment has become increasingly common. Indeed, many suppliers would be unable to sell directly without using a platform’s agency channel to facilitate the transactions. Yet nearly all of the research on encroachment ignores the facilitating role that these channels play. Moreover, because several of the largest on-line platforms operate both reselling and agency channels, we investigate when and why a supplier and an on-line platform would agree to have the supplier use the platform’s reselling channel instead of selling directly through its agency channel.

We use the term agency ¹ to refer to the business model in which the intermediary facilitates transactions but never takes ownership of the products. Under an agency model, suppliers retain ownership until the point of sale and control the selling price/quantity for their product, but then pay the intermediary a sales commission that is most commonly a percentage of revenue. These agency channel operations are distinct from traditional reselling where the intermediary takes ownership of the product, and controls the quantity/selling price.

Although many platforms operate solely as agencies, including Alibaba, eBay, Etsy, and Poshmark, several of the most prominent on-line platforms, such as Walmart, JD, and Amazon, operate as both agencies and resellers. The platforms often display the products from the reselling channel next to those from the agency channel, so it is not always obvious to a consumer which channel they are purchasing from. In practice, it is relatively easy for a supplier to sell through an on-line platform’s agency channel, but only a small subset of suppliers are invited to participate in its reselling channel. For example, for a non-negotiable monthly fee of $39.99 and a share of revenue, anyone can sign-up to be a third-party seller via Amazon’s agency channel ² . However, a supplier must be invited to become a first-party seller, and sell through the reselling channel. According to Webretailer ³ , Amazon negotiates hard for reselling contracts, and may ask for significant slotting fees.

While it is commonly understood that high sales volume is a prerequisite for a supplier to participate in platform’s reselling channel, we show that this may not be the only driver of how the platform and a supplier agree to interact with one another. In particular, we focus on two key factors: The number of traditional resellers, which measures the intensity of competition among them, and the substitutability between the on-line platform and the traditional resale channel. We assume that there is no difference between the physical product that is sold through the on-line channel and the one sold through the traditional resale channel, so that the substitutability between the two channels is determined entirely by the perceived differences in the purchasing and delivery process. The on-line platform allows consumers the convenience of not having to leave home to order and receive products. However, even though most on-line platforms can now deliver in less than 24 hours, they will never match the instantaneous fulfillment of a traditional reseller, nor do they allow a consumer to experience the touch and feel of a product prior to purchase.

The extent to which these differences matter to consumers may depend on the type of product. Consider, for example, branded consumer packaged goods such as Gillette razor blades, Huggies diapers, etc. These are products that consumers purchase repeatedly, so they have little need to touch and feel prior to purchase. They also tend to be available at traditional resellers that consumers visit regularly, minimizing any inconvenience associated with purchasing in a traditional reseller. So while some consumers may have slight preference for purchasing on-line or at traditional resellers, the substitutability between the channels should be relatively high for products like these. However, for other products, the inter-channel substitutability may be weaker. For example, for a product like a set of wind-chimes, some customers may have much more desire to be able to touch and feel them prior to purchase while others may value much more highly the convenience of completing their purchase without leaving the couch. Alternatively, for a product that is available through traditional resellers only in specific geographic regions, preference between the on-line and the traditional reselling channel may vary considerably, depending on a consumer’s location. In either of these two situations, some consumers may have a strong preference for one of the two channels, so that the amount of substitutability between them is reduced.

We consider a setting in which a supplier sells through $n$ traditional resellers and can additionally sell her product through an on-line platform that operates both reselling and agency channels in parallel. We assume that consumers are indifferent between the on-line platform’s agency and reselling channels, but the substitutability between either of these on-line channels and the traditional resale channel is imperfect. Motivated by our observations of Amazon, we assume that the supplier can sell through the platform’s agency channel at an exogenous commission rate unless it and the platform agree to a two-part reselling contract, involving a fixed slotting fee and a per-unit wholesale price, which can be dictated by the platform.

Our contributions are as follows: First, we recognize the unique set of interactions and balance of power that may exist between an on-line platform and a supplier that also sells through a traditional reselling channel. For many manufacturers, the only practical way that they can encroach upon the market of traditional resellers is by selling through an on-line agency. In addition, several of the major platforms operate both agency and reselling channels, and while they make it easy for a supplier to participate in their agency channel, they selectively invite suppliers to participate in their reselling channel and dictate the terms of trade to those invited. We are unique in capturing the complex operational detail of these interactions in a relatively simple model that yields useful managerial insights. Second, we show that when a supplier simultaneously sells through both the platform’s agency channel and a traditional reselling channel, the dynamics can be very different from what happens when the supplier sells through either of these channels in isolation. As shown by Adida and DeMiguel (2011), when a supplier sells through only a traditional reselling channel, the equilibrium quantity sold is less than the first-best quantity, and approaches it from below only as the number of resellers becomes arbitrarily large. Similarly, when a supplier sells through only an agency channel, the equilibrium quantity sold does not exceed the first-best quantity, and is equal to it only when the marginal cost of production is zero. Yet we show that when a supplier sells through both channels simultaneously, it is possible for the quantities sold through both channels to exceed the first-best quantities. This happens when the intensity of competition among traditional resellers, cross-channel substitutability, and commission rate in the agency channel are all relatively high. Third, based on this insight, we show how the selling format in the on-line platform may depend upon the nature of the traditional reselling channel. In particular we derive the optimal Pareto improving two-part reselling contract for the platform to offer to the supplier, and show that such a contract exists at commission rates as low as 15–20% when both the intensity of competition among the traditional resellers and cross-channel substitutability are sufficiently high. To put this in perspective, according to Market Pulse ⁴ , the total cost of selling for Amazon’s third-party agency channel sellers, including referral, advertising, and fulfillment, can be as much as 50–60 of sales revenue which is well above the threshold above which we find that Pareto improving reselling contracts exist.

After reviewing existing literature and its relationship to our work in Section 2, we describe our model in Section 3 along with a benchmark of a vertically integrated supply chain in which a single decision maker controls all quantity/price decisions. In Section 4, we first characterize the equilibrium for the case in which the supplier uses the platform’s agency channel. Then, after solving the platform’s optimization problem for a two-part reselling contract that requires that each firm earn as much as it would when the supplier sells through the platform’s agency channel, we characterize the conditions under which the supplier and the platform can both benefit from the supplier selling through the reselling channel. In Section 5, we discuss two extensions to our basic model. Finally, in Section 6, we provide concluding remarks and directions for future research.

2. Literature Review

Our work is at the intersection among the literature on supplier encroachment, agency selling, and dual channels. Sibley and Weisman (1998) recognize the issue of supplier encroachment by investigating how the input prices to the firms that serve a downstream market are affected when a monopolistic supplier introduces its own direct channel. Motivated by industries such as telecommunications, electric power, and natural gas, they provide conditions for which the wholesale prices of a monopolistic supplier decrease when it introduces a direct channel.

The work of Chiang et al. (2003) and Hendershott and Zhang (2006) recognize that the introduction of such a direct channel can mitigate double marginalization and improve supply chain performance. Others, including Huang and Swaminathan (2009) and Cattani et al. (2006), focus on how different policies on pricing in the reselling channel affect the interactions with the direct channel. Although the coexistence of a direct channel creates additional competition for traditional reselling, Arya et al. (2007) find that the reseller can benefit from encroachment if the supplier’s cost premium for selling directly is sufficiently large. This benefit arises because the supplier’s ability to encroach causes her to offer a lower wholesale price. The framework from Arya et al. (2007) has been extended to allow for endogenized quality, Ha et al. (2016); investment spillovers, Yoon (2016); information asymmetry, Li et al. (2014, 2015); Huang et al. (2018); Gao et al. (2021); strategic inventory, Guan et al. (2019); competition among resellers, Liu et al. (2021); and nonexclusive reselling, Hotkar and Gilbert (2021).

Among this literature on encroachment, our work is closest to Liu et al. (2021) who show that the ability to sell directly can be harmful to a supplier when the competition among resellers is sufficiently intense. But our work is distinct from theirs in a couple of key ways. First, we recognize that the only practical way for most suppliers to sell directly is by using an on-line agency channel, and that the major ones, for example, Amazon, Walmart, and JD, are highly efficient. Thus, instead of a per-unit cost premium for direct selling, which is assumed by the vast majority of literature on encroachment, including Liu et al. (2021), we assume that the supplier must share an exogenous fraction of revenue with the platform’s agency channel. Second, we assume that the on-line platform operates both agency and reselling channels in parallel, and can invite the supplier to interact with it through its reselling channel. In an extension of their main model, Liu et al. (2021) allow for the possibility that the supplier could choose between selling directly and selling to an additional independent reseller. However, this is quite different from our setting where the on-line platform must invite the supplier to participate in its reselling channel, and the supplier’s ability to alternatively sell through the platform’s agency channel is an outside option for herself as well as for the platform.

Compared to reselling, the agency model assigns more operational control to the supplier. Jerath and Zhang (2010) were among the first to study the issue of an intermediary ceding control of operational decisions to a supplier. In the context of a traditional department store allowing suppliers to set up stores-within-store and control prices and service levels, they find that the increased demand in the store from traffic associated with service from the store-within-store can moderate inter-store competition and benefit both sides. Several other studies address the decision of an intermediary to operate as a reseller or as an agency. Hagiu and Wright (2015) demonstrate that decision rights for allocating marketing resources should be assigned to either the supplier or the intermediary, depending on who has better information. Several other papers focus more on pricing/quantity decisions. Abhishek et al. (2016) considers a single manufacturer who sells through two competing intermediaries, each of whom can choose to operate as a reseller or as an agency. They find that the equilibrium formats chosen by the intermediaries can be either agency or selling, depending upon the spillover effects upon the manufacturer’s traditional channels. Tian et al. (2018) studies a similar question but in the context of two manufacturers distributing through a single intermediary. They find that the intermediary prefers the pure agency (reselling) model when substitutability is high (low), while for moderate substitutability and moderate fulfillment costs, the intermediary may prefer hybrid mode. Tan and Carillo (2017) study the use of the agency model to distribute digital products in the media industry and the effects upon the sale of traditional physical products. Recently, Lai et al. (2022) show how the “Fulfilled by Amazon” program can help the platform to manage the price and service competition in its reselling and agency channels. Our work is distinct from this literature in considering how the supplier’s interaction with an on-line platform affects its existing interactions with traditional resellers and in acknowledging the platform’s power to dictate the terms of trade for a reselling contract.

In a setup where a supplier sells to multiple retailers, Adida and DeMiguel (2011) show that double marginalization is alleviated as the number of competing retailers increases. However, for finite retailers, the complete elimination of double marginalization remains unattainable through a wholesale price contract. Moreover, Adida and DeMiguel (2011) demonstrate that the total supply never exceeds the first-best (what they call centralized) quantity. For a dual-channel setup, Chiang et al. (2003) establish that the presence of a direct channel mitigates double marginalization. A recent study by Ha et al. (2022) shows how the flexibility of two channels successfully reduces double marginalization. While the literature has explored the mitigation of the double marginalization effect through dual-channel selling and retailer competition, the phenomenon of overproduction—characterized by sales surpassing the vertically integrated first-best quantity—has not been observed. Our study demonstrates that a combination of an agency-operated direct channel and competing retailers can induce overproduction, thereby reducing the overall profit of the supply chain.

Our work is also related to the dual-channels literature that studies settings in which a supplier sells through both traditional retailers and through on-line channels. For example, Yoo and Eunkyu (2011) study a supplier selling through two traditional retailers and an internet channel. Like Cattani et al. (2006), they allow for consumers to be differentiated in the relative inconvenience that they experience from the two channels, but they assume that the internet channel operates like a traditional reseller rather than as an agency platform. Both Shen et al. (2019) and Ha et al. (2022) study settings in which a supplier sells through both a traditional reselling channel and an agency platform. Shen et al. (2019) is similar to us in acknowledging that while the supplier can unilaterally choose a linear wholesale price for the traditional reseller, the platform has power to influence the terms of trade through both a fixed and variable component. Different from us, they do not consider competition in the traditional resale channel, and assume that the platform operates purely as an agency. Also different from us, they focus on the implications of whether the platform can unilaterally dictate both the fixed and variable components of the contract versus having to negotiate over one or both of these components. Ha et al. (2022) is similar to us in studying the interactions between a supplier and a platform that operates a reselling and an agency channel in parallel. However, their setting differs from ours in several key dimensions. First, they do not consider the supplier’s interactions with traditional resellers; second, they do allow for the platform to exert demand enhancing effort; and third, they allow the supplier to unilaterally dictate a linear wholesale price to the platform’s reselling channel. Because of the platform’s demand enhancing effort and the supplier’s ability to dictate the wholesale price, they find conditions when it is optimal for the supplier to sell through both channels simultaneously.

3. Model

We consider the interactions among a supplier, an arbitrary number of traditional resellers, and an on-line platform that operates both an agency and a reselling channel. Throughout the paper, we adopt the convention of referring to the supplier with female pronouns and to resellers with male pronouns. The on-line platform is referred to as it. We assume that the channels compete in quantities (Cournot), such that the market-clearing price is determined by the quantities sold through the two channels. This assumption is appropriate in settings where, due to production lead times, firms have more flexibility to adjust prices than to adjust their quantities in the short term. The per-unit costs of production and sales are normalized to zero.

We assume that there are $n$ traditional resellers, and that the on-line platform and the traditional reselling channel are imperfect substitutes for one another. Let $\theta \in [0,1]$ be the substitutability parameter between the on-line and the traditional resale channels, where $\theta =1$ implies that the two channels are perfect substitutes, and $\theta =0$ implies that they are independent. To focus on the difference between the purchasing experience through an on-line platform versus that at a traditional reseller, we assume that the traditional resellers are perfect substitutes for one another and that consumers are indifferent about whether the product is sold through the on-line platform’s agency or reselling channels. Because the traditional resellers are perfect substitutes for one another, the intensity of competition among them is measured by $n$ .

Let $y$ denote the quantity that is sold through the on-line platform, either through its agency or reselling channel, and let $q_i$ be the quantity chosen by traditional reseller $i\in \{1,\dots ,n\}$ . Define $Q=\sum _{i=1}^n{q}_i$ as the aggregate quantity of all of the traditional resellers, and $\mathbf{\text{q}}:=[q_1,\dots ,q_n]$ as the vector of quantities for the $n$ traditional resellers. Let $p_r$ and $p_p$ be the market clearing prices for the traditional resellers and the platform, respectively. Following the model described in the appendix of Chapter one of Ingene and Parry (2004) we assume that the utility of a representative consumer is a quadratic function of $Q$ and $y$ :

$$U(Q,y):=a_{r}Q+a_{p}y-\frac{Q^2+y^2}{2}-Qy\theta$$

(1)

where $a_r$ and $a_p$ are the representative consumer’s (maximum) marginal utility for the product via the traditional reselling and on-line channels, respectively. For symmetry, we take $a_r=a_p$ , and without further loss of generality, we normalize $a_r=a_p=1$ . It is easy to confirm that the prices that clear the market for any $Q$ and $y$ are:

$$\begin{array}{rl}{p}_r& :=a_r-Q-\theta y:=1-Q-\theta y\\ p_p& :=a_p-y-\theta Q:=1-y-\theta Q\end{array}$$

Linear inverse demand models are common in the literature on interactions involving more than one channel, including Arya et al. (2007), Li et al. (2014), Hotkar and Gilbert (2021), Shen et al. (2019), among others. By normalizing the intercept of both of these inverse demand functions to 1, we are assuming that the maximum marginal utility that the representative consumer gets from the product through the on-line channel is the same as their maximum marginal utility via the traditional resellers.

We assume that the supplier is sufficiently powerful with respect to the traditional resellers that it can unilaterally announce a per-unit wholesale price, denoted by $w_r$ , at which it will sell to them. On the other hand, major on-line platforms typically have enough market power to dictate the terms of trade to suppliers. In particular, we assume that the supplier can sell through either the platform’s agency or reselling channels, but must be invited to use the reselling channel.

To clarify the distinction between the agency and reselling channels, we assume that the supplier sells through either the platform’s agency or reselling channels, but not through both of them. In our e-companion, we confirm that, whenever there is a Pareto-improving reselling contract that prohibits the supplier from simultaneously selling through the agency’s agency channel, it would dominate a reselling contract that permits the supplier to sell through both channels.

Based on the observation that on-line platforms typically use the same commission rate for broad product categories, we assume that the commission rate $r$ , which represents the platform’s share of revenue in the agency channel, is exogenous. Noting that any fixed fees for participating in a platform’s agency channel are nominal and rarely discourage suppliers from participating, we avoid unnecessary complication by normalizing any such fixed fees to zero. These assumptions are similar to Ha et al. (2022), and Lai et al. (2022) among others.

To represent the platform’s power to invite a supplier to participate in its reselling channel, we allow it to offer the supplier a two-part reselling contract, in which the supplier would sell to the platform at wholesale price, $w_p$ , and additionally pay a fixed slotting fee, $F$ . Because there is no evidence of fixed fees being paid by platforms to suppliers, we require $F\ge 0$ . Of course, the supplier need not accept the proposed contract. If she declines, she can alternatively sell through the platform’s agency channel, where she must share fraction $r$ of her revenue with the platform, keeping fraction $1-r$ for herself.

Because the issue of whether the supplier uses the platform’s agency or its reselling channel is relatively long-term, we assume that this happens up-front. Before anything else happens, the platform decides whether to invite the supplier to participate in its reselling channels as described above. Depending upon whether the platform makes an invitation that is accepted by the supplier, there are two possible subgames.

If the platform and the supplier agree to interact in the platform’s reselling channel, then in stage 1 of this subgame, the supplier announces the wholesale price, $w_r$ , at which she will sell to the traditional resellers, and this price need not be the same as the wholesale price $(w_p)$ at which she has agreed to sell to the platform. Although the differential pricing that occurs between an on-line platform and traditional resellers may appear to be at odds with the Robinson Patman Act of 1936, differential wholesale pricing can be permissible if different intermediaries provide different services. Indeed, such differences in services played a key role in the 2019 California jury decision that found that Living Essentials, LLC was not in violation of Robinson-Patman when it offered discounts on its 5-Hour Energy product to Costco but not to other intermediaries ⁵ . Arguably, the difference between the shopping and product acquisition process that a consumer experiences at Costco versus at other intermediaries is smaller than the difference between the shopping and product acquisition process that they would experiences at an on-line platform vis-a-vis at a traditional reseller. Therefore, in our base model, we do not require that the supplier offer the same wholesale price to the traditional resellers that it gives to the on-line-platform. However, in our on-line appendix, we consider the implications of a requirement that the supplier offer the same per-unit wholesale price to the traditional resellers that it agrees to with the platform.

When inviting a supplier to participate in its reselling channel at a specific wholesale price, $w_p$ , the platform anticipates the wholesale price, $w_r$ , that the supplier would subsequently offer to the traditional resellers, as well as how both of these wholesale prices would affect the quantities that are sold. In stage 2 of this subgame, the traditional resellers choose their quantities $(q_i,\text{ for }i=1,\dots ,n)$ at the same time that the platform chooses its quantity $(y)$ to sell through its reselling channel.

Define ${\pi }_s^R$ , ${\pi }_i^R$ , and ${\pi }_p^R$ to be the profits of the supplier, reseller $i\in \{1,\dots ,n\},$ and the platform, respectively, when the supplier accepts an invitation from the platform to use its reselling channel.

$$\begin{array}{rl}{\pi }_s^R(F,w_p,w_r,\mathbf{\text{q}},y)& =w_r\sum _i{q}_i+w_{p}y-F\end{array}$$

(2)

$$\begin{array}{rl}{\pi }_i^R(F,w_p,w_r,\mathbf{\text{q}},y)& =(p_r-w_r)q_i,i=1,\dots ,n\end{array}$$

(3)

$$\begin{array}{rl}{\pi }_p^R(F,w_p,w_r,\mathbf{\text{q}},y)& =(p_p-w_p)y+F\end{array}$$

(4)

A summary of notation is provided in Table 1. If the supplier and the platform do not agree to interact through the platform’s reselling channel, then the supplier can sell through the platform’s agency channel. In stage 1 of this subgame, the supplier chooses the per-unit wholesale price, $w_r$ , to offer to the traditional resellers. Then in stage 2, the traditional resellers choose their quantities $(q_i,\text{ for }i=1,\dots ,n)$ at the same time that the supplier chooses her quantity $(y)$ to sell through the platform’s agency channel. This is an intentional departure from much of the encroachment literature that assumes that the supplier can post-pone her quantity decision until after she receives the orders from traditional reseller(s). For example, Arya et al. (2007), Ha et al. (2016), and Hotkar and Gilbert (2021), all allow for the supplier to respond to the reseller’s quantities by arguing that she has no way to commit not to respond. We have specifically not made this assumption in our base model for the following reasons: First, when the decisions are made sequentially, it means that the supplier’s quantity is a best response to the quantity(s) ordered by the traditional reseller(s), but that the quantity(s) chosen by the traditional reseller(s) are not necessarily (and in general will not be) best responses to the supplier’s quantity. This is reasonable in a one-shot game, that is, a product with a very short life-cycle, but may not be so reasonable in the context of a product with a long life-cycle where we would expect that in equilibrium they would each be making best-responses to the other’s quantities. Second, when the supplier sells through the platform’s reselling channel, it is the platform rather than the supplier who makes the quantity decision, and it is implausible that the platform would be able to observe the quantity(s) of the traditional reseller(s) before making its decision. By assuming that the quantity decisions are made simultaneously regardless of whether the supplier uses the platform’s agency or reselling channels, we can focus on the effects of who controls the quantity decision and whether the decision is guided by a wholesale price versus a revenue sharing arrangement without muddying the waters with a difference in the timing of when the quantity decisions are made. However, in an extension, we show that our results continue to hold qualitatively if the supplier can post-pone its quantity decision until after receiving the order(s) from the traditional reseller(s) when she uses the platform’s agency channel.

Table 1.

Notations.

Notation	Meaning
$n$	Number of resellers
$r$	The platform’s share of revenue from sales through its agency channel
$\theta$	Substitutability between the on-line and the traditional reselling channels
$w_p$	Wholesale price for platform in its reselling channel
$w_r$	Wholesale price for traditional resellers
$p_p$	Market-clearing price in agency channel
$p_r$	Market-clearing price in reselling channel
$q_i$	Quantity sold through reseller $i$
$Q$	Cumulative quantity sold through all resellers
$y$	Quantity sold through the platform
${\pi }_s$ , ${\pi }_i$ , ${\pi }_p$	Profit of supplier, reseller $i$ , and agency platform respectively

Define ${\pi }_s^A$ , ${\pi }_i^A$ , and ${\pi }_p^A$ to be the profits of the supplier, reseller $i\in \{1,\dots ,n\},$ and the platform, respectively, when the supplier uses the agency channel:

$$\begin{array}{rl}{\pi }_s^A(w_r,\mathbf{\text{q}},y)& =w_r\sum _i{q}_i+p_p(1-r)y\end{array}$$

(5)

$$\begin{array}{rl}{\pi }_i^A(w_r,\mathbf{\text{q}},y)& =(p_r-w_r)q_i,i=1,\dots ,n\end{array}$$

(6)

$$\begin{array}{rl}{\pi }_p^A(w_r,\mathbf{\text{q}},y)& =p_{p}ry\end{array}$$

(7)

3.1. Vertically Integrated Benchmark, the first-best solution

An important benchmark is the vertically integrated case in which a single firm chooses both the quantities $Q$ and $y$ to sell to maximize the total profit ${\mathrm{\Pi }}^{VI}:=p_{r}Q+p_{p}y$ . Using the superscript VI to indicate the Vertically Integrated solution, which also represents the first-best solution, it is easy to confirm that:

$$(Q^{VI},y^{VI})=(\frac{1}{2(1+\theta )},\frac{1}{2(1+\theta )})$$

At these optimal quantities, which are often referred to as the first-best solution, the total supply chain profit associated with the supplier’s product is:

$${\mathrm{\Pi }}^{VI*}=\frac{1}{2(1+\theta )}$$

4. Analysis of Supply Chain Interactions

We begin by considering the supply chain interactions when the supplier uses the platform’s agency channel. Subsequently, we consider these interactions when the supplier and platform instead agree to interact through the platform’s reselling channel.

4.1. Supplier uses the Platform’s Agency Channel

For a given wholesale price and commission rate, it is easy to confirm from the first-order conditions for (5) and (6) that the quantities chosen satisfy the following:

$$\begin{array}{rl}{q}_i^A(w_r,r)& ={\left[\frac{2-2w_r-\theta }{2+n(2-{\theta }^2)}\right]}^{+},i\in \{1,\dots ,n\}\end{array}$$

(8)

$$\begin{array}{rl}{y}^A(w_r,r)& =\{\begin{array}{ll}\frac{(1+n)-n(1-w_r)\theta }{2+n(2-{\theta }^2)}& w_r\le 1-\frac{\theta }{2}\\ \frac{1}{2}& w_r\ge 1-\frac{\theta }{2}\end{array}\end{array}$$

(9)

where $[x{]}^{+}:=Max\{x,0\}$ . Interestingly, while $q_i^A(w_r,r)$ and $y^A(w_r,r)$ are decreasing and increasing, respectively, in the wholesale price, neither of these two quantities depends directly upon the commission rate. The existence of a threshold wholesale price, above which the traditional resellers stop selling the product is intuitive. However, notice that this threshold, $1-\frac{\theta }{2}$ , is independent of the number of resellers and is decreasing in $\theta$ . When the platform is a closer substitute for the traditional resale channel, traditional resellers stop selling at lower wholesale prices.

In stage 2, the supplier chooses a wholesale price to offer to the traditional resellers in anticipation of the quantities that will be chosen in response to this wholesale price.

Lemma 1

When the supplier sells through the platform’s agency channel, the wholesale price that maximizes her profits is:

$$w_r^A:=\frac{(4-2r\theta )(1+n)-2n(2-r){\theta }^2+n{\theta }^3}{8+2n(4-(3-r){\theta }^2)}\le 1-\frac{\theta }{2}$$

(10)

where the fact that $w_r^A\le 1-\frac{\theta }{2}$ ensures that there are positive sales through both the traditional resellers and through the platform’s agency channel. By substituting this equilibrium wholesale price into (8) and (9) and then substituting back into the profit functions we can obtain the equilibrium quantities and profits as shown in Table 2.

Table 2.

Equilibrium values when supplier sells through the platform’s agency channel.

$w_r^{A*}$	${\displaystyle \frac{(4-2r\theta )(1+n)-2n(2-r){\theta }^2+n{\theta }^3}{8+2n(4-(3-r){\theta }^2)}}$
$q_i^{A*}$	${\displaystyle \frac{2-(2-r)\theta }{4+n(4-(3-r){\theta }^2)}}$
$y^{A*}$	${\displaystyle \frac{4(1+n)-(2+\theta )n\theta }{8+2n(4-(3-r){\theta }^2)}}$
${\pi }_s^{A*}$	${\displaystyle \frac{4n+(4(1+n)(1-r)-4n\theta (2-r)+n{\theta }^2)}{16+4n(4-(3-r){\theta }^2)}}$
${\pi }_p^{A*}$	${\displaystyle \frac{r(2n\theta -(4+n(4-{\theta }^2)){)}^2}{4(4+n(4-(3-r){\theta }^2){)}^2}}$
${\pi }_i^{A*}$	${\displaystyle \frac{(2-(2-r)\theta {)}^2}{(4+n(4-(3-r){\theta }^2){)}^2}}$

By taking first-derivatives of $w_r^{A*}$ , it is easy to confirm that it is decreasing in both $r$ and $n$ for all $\theta \in [0,1]$ . Recall that $r$ is the commission rate charged by the platform, and $n$ , which represents the number of traditional resellers, is a measure of the intensity of competition among these resellers. As either of these parameters increase, the relative attractiveness of selling through traditional resellers increases, and the supplier reduces her wholesale price. However, the effect of substitutability parameter, $\theta$ , upon the equilibrium wholesale price is a bit more nuanced. For large values of $r$ , $w_r^{A*}$ is strictly decreasing in $\theta$ , while for sufficiently small $r$ , it is decreasing and then increasing. This is illustrated in Figure 1, where we plot $w_r^{A*}$ as a function of $\theta$ . In both the left and right plots, where $n=5$ and $n=100$ respectively, we can see that $w_r^{A*}$ is decreasing and then increasing in $\theta$ for $r=0.1$ , but is strictly decreasing for $r=0.5$ . When the commission rate is high, the supplier responds to greater substitutability by decreasing the wholesale price to shift more sales to the traditional resellers. But when the commission rate is small enough that the supplier keeps a large enough portion of the revenue from the agency channel, the effect of a small increase in $\theta$ depends on the baseline amount of substitutability. When the baseline substitutability is low, a small increase causes the supplier to reduce her wholesale price. The intensified competitive pressure upon the traditional resellers dominates the adverse impact upon agency channel sales, and this causes the supplier to reduce her wholesale price. However, when substitutability increases from an already high baseline, it becomes more important for the supplier to protect her profits in the agency channel by increasing, instead of decreasing, her wholesale price.

Figure 1.

Equilibrium wholesale price for traditional resellers when supplier sells through the platform’s agency channel. (a) $n=5$ ;(b) $n=100$ .

It is also of interest to compare the equilibrium quantities that are sold in equilibrium when the supplier sells through the platform’s agency channel to the first-best quantities.

Proposition 1

(i) The equilibrium quantity sold through the platform’s agency channel always exceeds the first best quantity for that channel, that is, $y^{A*}\ge y^{VI}$ ; and (ii) there exists a threshold, $r_Q^A:=\frac{4+n{\theta }^2}{(2+\theta )n\theta }$ , such that the equilibrium quantity sold through the traditional resale channel exceeds the first-best quantity for that channel, that is, $Q^{A*}\ge Q^{VI}$ , if and only if $r\ge r_Q^A$ .

The above proposition shows that when a supplier sells through both traditional reselling and agency channels, the dynamics are different than when it sells exclusively through either reselling or agency channels. When the supplier sells exclusively through reselling channels, the equilibrium quantity(s) is (are) strictly less than the first-best quantity(s), approaching it (them) from below as the intensity of competition among the resellers grows large. Similarly, when a supplier sells exclusively through agency channels, regardless of the intensity of competition among the agencies, the equilibrium quantity(s) is (are) less than or equal to the first-best quantity(s), and is (are) equal to it (them) only when the marginal cost of production is zero. However, Proposition 1 shows that these relationships can be reversed when a supplier sells through both a reselling and an agency channel simultaneously, and they are at least partially substitutable, that is, $\theta >0$ . This happens because, when the supplier chooses the quantity to sell through the agency channel, she takes the quantity sold through the traditional reselling channels as given, and seeks to maximize her share of revenue in the on-line agency channel. This causes her to choose a quantity that always exceeds the first-best for that channel. The supplier chooses $w_r$ in anticipation of how she will subsequently sell through the agency channel, and as the commission rate increases, she reduces $w_r$ to push more volume through the traditional reselling channels. When the commission rate is sufficiently large, this results in the quantities in both channels exceeding the first-best simultaneously.

From the perspective of total supply chain profits, it is easy to confirm that, for any quantity, $Q$ , sold through the traditional reselling channel, the conditionally optimal quantity, $y$ , to sell through the agency channel is decreasing in $Q$ , and vice-versa. Therefore, if the quantity in one channel exceeds the first-best quantity for that channel, this can be partially mitigated by having the quantity in the other channel be less than its first-best quantity. But when both quantities exceed the first-best, it is unequivocal that the supply chain profits would be increased if either or both quantities could be reduced.

Corollary 1

If and only if $n>2$ , there exists $\theta <1$ for which $r_Q^A:=\frac{4+n{\theta }^2}{(2+\theta )n\theta }<1$ , so that the quantity sold through the traditional resellers exceeds the first-best quantity for that channel when $r\in (r_Q^A,1]$ .

As long as the intensity of competition among the traditional resellers is weak, $n\le 2$ , the equilibrium quantity sold through the traditional resellers is less than the first-best quantity. However, when there is at least moderate competition, that is, at least $n\ge 3$ , there will exist sufficiently large value of commission rate and inter-channel substitutability for which the equilibrium quantity sold through both the platform’s agency channel and the traditional resale channel both exceed the first-best quantities. It is easy to confirm that the threshold, $r_Q^A$ , is decreasing in $n$ and approaches $\frac{\theta }{2+\theta }$ as $n\to \mathrm{\infty }$ . Thus, as competition among the traditional resellers intensifies, there is a wide range of commission rates and inter-channel substitutability for which the equilibrium quantities sold through both channels exceed the first best quantities, dragging down the total supply chain profit.

The results of Proposition 1 are illustrated in Figure 2. In the left panel, where $n=5$ , and $\theta =0.9$ , we can see that, while the quantity sold through the platform’s agency channel, $y^{A*}$ , is larger than the first best quantity, $y^{VI}$ , for any commission rate, the equilibrium quantity sold through the traditional resellers, $Q^{A*}$ , is larger than the first-best quantity, $Q^{VI}$ , only for commission rates larger than about $r_Q^A\cong 0.62$ . In the panel on the right, we take $n=100$ , and we can see that the threshold commission rate above which both quantities exceed the first best decreases to $r_Q^A\cong 0.32$ .

Figure 2.

Equilibrium quantities when supplier sells through the platform’s agency channel versus first-best. (a) $\theta =0.9$ , $n=5$ ;(b) $\theta =0.9$ , $n=100$ .

4.2. Supplier uses the Platform’s Reselling Channel

While it is very easy for a supplier to sign-up to participate in an on-line platform’s agency channel, participation in the reselling channel is by invitation only. This endows the platform with considerable power to dictate the terms of interaction. We model this by allowing the platform to design a two-part contract, consisting of a fixed slotting fee, $F\ge 0$ , that the supplier must pay to the platform, and a per-unit wholesale price, $w_p$ , that the platform will pay to the supplier. Of course, the platform cannot require that a supplier participate in its reselling channel. To induce the acceptance of this invitation, it must ensure that the supplier would earn at least as much by selling through its reselling channel as she would by selling through the agency channel.

In designing this optimal two-part contract, the platform must account for the fact that, if the supplier agrees to participate, she will subsequently choose a wholesale price for the traditional resellers that maximizes her total profits. Let $w_r^{CO}(w_p)$ be the supplier’s conditionally optimal wholesale price for traditional resellers given any wholesale price, $w_p$ , that she agrees to accept from the platform. The platform must also account for how these two wholesale prices will impact the subsequent quantity setting subgame in stage 2. Let ${\mathbf{\text{q}}}^{\text{CO}}(w_p,w_r)$ and $y^{CO}(w_p,w_r)$ be the conditionally optimal quantities that are chosen in the equilibrium to the quantity setting subgame among the platform and the traditional resellers for wholesale prices $w_p$ and $w_r$ . The platform’s problem of designing a reselling contract to offer to the supplier that would allow itself and the supplier to earn at least as much as they would if the supplier were to use its agency channel is as follows:

$$\begin{array}{rl}& {\pi }_p^{R*}=\underset{F\ge 0,w_p\ge 0}{Max}\{{\pi }_p^R(F,w_p,w_r^{CO}\left(w_p\right),{\mathbf{\text{q}}}^{CO}(w_p,w_r^{CO}\left(w_p\right)),\\ & y^{CO}(w_p,w_r^{CO}\left(w_p\right)))\phantom{{\pi }_p^R}\}\end{array}$$

(11)

$$\begin{array}{rl}& {\pi }_s^R(F,w_p,w_r^{CO}\left(w_p\right),{\mathbf{\text{q}}}^{CO}(w_p,w_r^{CO}\left(w_p\right)),\\ & y^{CO}(w_p,w_r^{CO}\left(w_p\right)))\ge {\pi }_s^{A*}\end{array}$$

(12)

$$\begin{array}{rl}& {\pi }_p^R(F,w_p,w_r^{CO}\left(w_p\right),{\mathbf{\text{q}}}^{CO}(w_p,w_r^{CO}\left(w_p\right)),\\ & y^{CO}(w_p,w_r^{CO}\left(w_p\right)))\ge {\pi }_p^{A*}\end{array}$$

(13)

where ${\pi }_p^R(F,w_p,w_r,\mathbf{\text{q}},y)$ and ${\pi }_s^R(F,w_p,w_r,\mathbf{\text{q}},y)$ are defined in (4) and (2) respectively. If a solution to this optimization problem exists, it will be a combination of slotting fee and wholesale price that maximizes the platform’s profit from interacting with the supplier through its reselling channel subject to both the supplier and the platform earning as much as they would when the supplier sells through the platform’s agency channel.

To analyze the solution to the platform’s optimization problem above, we first need to characterize how the supplier will choose its wholesale price for the traditional resellers, contingent upon the price $(w_p)$ at which it agrees to sell to the platform. Following backward induction, the first order conditions for (4) and (3) imply that for a given combination of $w_p$ and $w_r$ , the quantities chosen by the platform and by the traditional resellers are as follows:

$$\begin{array}{rl}{q}_i^R(w_p,w_r)& ={\left[\frac{2-2w_r-\theta +w_p\theta }{2+n(2-{\theta }^2)}\right]}^{+},i\in \{1,\dots ,n\}\end{array}$$

(14)

$$\begin{array}{rl}{y}^R(w_p,w_r)& =\{\begin{array}{ll}{\left[\frac{1+n-n(1-w_r)\theta -w_p(1+n)}{2+n(2-{\theta }^2)}\right]}^{+}& w_r\le 1-\frac{\theta (1-2w_p)}{2}\\ {\left[\frac{1-w_p}{2}\right]}^{+}& w_r\ge 1-\frac{\theta (1-2w_p)}{2}\end{array}\end{array}$$

(15)

Where for $w_r\ge 1-\frac{\theta (1-2w_p)}{2}$ , we have $q_i^R(w_p,w_r)=0$ and the form of $y^R(w_p,q_p)$ switches from the upper to the lower branch of (15). Although both the upper and lower branches of (15) will be equal to zero for large enough $w_p$ , we restrict attention to wholesale prices that would induce the platform to sell a positive quantity for its reselling channel. Recall from (8) that, when the supplier sells through the platform’s agency channel, the traditional resellers are driven from the market when $w_r\ge 1-\frac{\theta }{2}$ , which is a lower threshold than we have here. Thus, the traditional resellers would sell positive quantities at a larger wholesale price when the supplier sells through the platform’s reselling channel than when she sells through its agency channel.

By substituting (14) and (15) into (2) we can now find the wholesale price that the supplier will set for her traditional resellers contingent upon the one at which she agrees to sell to the on-line platform.

Lemma 2

When the supplier sells through the platform’s reselling channel at wholesale price $w_p$ , the conditionally optimal wholesale price for her to offer to the traditional resellers is:

$$w_r^{RCO}\left(w_p\right)=\frac{2-\theta (1-2w_p)}{4}$$

(16)

Substituting this conditionally optimal wholesale price into (14) and (15) we can obtain the conditional equilibrium quantities that will be sold by each traditional reseller and by the platform respectfully given that the supplier agrees to sell to the platform at per-unit price $w_p$ . We can then obtain the profits for the supplier, each traditional reseller, and the platform by substituting back into (2), (3), and (4). The conditional equilibrium quantities and profits are as shown as functions of $w_p$ in Table 3. Note that, the conditional profits for both the supplier and the platform are shown as functions of both the fixed slotting fee, $F$ , and the per-unit wholesale price $w_p$ . Observe that the conditional equilibrium quantity that is sold by each traditional reseller, $q_i^{RCO}(w_p)$ , is independent of the wholesale price, $w_p$ , at which the supplier sells to the platform. Because the conditionally optimal price that the supplier offers to the traditional resellers, $w_r^{RCO}(w_p)$ , is increasing in $w_p$ , the profit of each traditional reseller is decreasing in $w_p$ , as can be confirmed from the expression for ${\pi }_i^{RCO}(w_p)$ . Hence, somewhat counter-intuitively, traditional resellers can benefit from the platform’s power to demand a lower wholesale price.

Table 3.

Conditional equilibrium when supplier sells through the reselling channel as a wholesale price of $w_p$ .

	Conditional equilibrium value
$w_r^{RCO}(w_p)$	${\displaystyle \frac{2-\theta +2\theta w_p}{4}}$
$q_i^{RCO}(w_p)$	${\displaystyle \frac{2-\theta }{4+2n(2-{\theta }^2)}}$
$y^{RCO}(w_p)$	${\displaystyle \frac{1+n-n\theta -w_p(1+n(1-\theta ))}{2+n(2-{\theta }^2)}}$
${\pi }_s^{RCO}(F,w_p)$	${\displaystyle \frac{2n+(1+n-2n\theta )}{8+4n(2-{\theta }^2)}}-\frac{(1-2w_p{)}^2}{8}-F$
${\pi }_p^{RCO}(F,w_p)$	${\displaystyle \frac{(2n\theta +n(1-2w_p){\theta }^2-4(1+n)(1-w_p){)}^2}{16(2-n(2-{\theta }^2){)}^2}}+F$
${\pi }_i^{RCO}(w_p)$	${\displaystyle \frac{(2-\theta -w_p(2-\theta ){)}^2}{(2-n(2-{\theta }^2){)}^2}}$

Using the results that are shown in Table 3, the platform’s problem of designing the optimal two-part contract for interacting with the supplier via its reselling channel that was previously defined in (11) and (12) can now be restated as follows:

$$\begin{array}{rl}& {\pi }_p^{R*}=\underset{F\ge 0,w_p\ge 0}{Max}\left\{{\pi }_p^{RCO}(F,w_p)\right\}\end{array}$$

(17)

$$\begin{array}{rl}& {\pi }_s^{RCO}(F,w_p)\ge {\pi }_s^{A*}\end{array}$$

(18)

$$\begin{array}{rl}& {\pi }_p^{RCO}(F,w_p)\ge {\pi }_p^{A*}\end{array}$$

(19)

By definition, if there exists a solution to this optimization problem, it will give both the platform and the supplier profits that are at least as large as those that they earn when the supplier sells through the platform’s agency channel. It follows that a necessary condition for some $(F,w_p)$ pair to be a solution to this problem is that it must result in combined profits of the platform and the supplier that are at least as large as their combined profits when the supplier uses the agency channel, that is, ${\pi }_s^{RCO}(F,w_p)+{\pi }_p^{RCO}(F,w_p)\ge {\pi }_s^{A*}+{\pi }_p^{A*}$ .

Before characterizing the solution to the platform’s problem of designing a reselling contract, if and when one exists, we introduce several important reference values for the per-unit wholesale price.

Lemma 3

(i) The per-unit wholesale price that maximizes the combined profit of the supplier and the platform, ${\pi }_s^{RCO}(F,w_p)+{\pi }_p^{RCO}(F,w_p)$ , is:

$$w^{S\mathrm{\&}P}:=\frac{(2-\theta )n\theta }{4+2n(2-{\theta }^2)}$$

(20)

(ii) The wholesale price for the platform that maximizes the supplier’s profit, ${\pi }_s^{RCO}(F,w_p)$ , is $w_p^S:=\frac{1}{2}$ , and $w_p^S\ge w^{S\mathrm{\&}P}$ for all $n$ and $\theta$ .

The above result confirms that, for a given value of the fixed slotting fee, $F$ , the wholesale price that maximizes the supplier’s profit from using the platform’s reselling channel is at least as large as the one that would maximize the combined profit of the platform and the supplier. Because $w^{S\mathrm{\&}P}$ maximizes the combined profits of the supplier and platform conditional upon the supplier using the reselling channel, it is a natural candidate for the platform and the supplier to agree upon. Of course, the commission rate in the platform’s agency channel plays an important role in determining the willingness of both the supplier and the platform to interact through the reselling channel instead of the agency channel.

Lemma 4

There exist two thresholds on the commission rate, denoted $r^s$ and $r^{sp}$ , respectively, such that: (i) ${\pi }_s^{RCO}(0,w^{S\mathrm{\&}P})\ge {\pi }_s^{A*}$ if and only if $r\ge r^s$ , while (ii) ${\pi }_s^{RCO}(F,w^{S\mathrm{\&}P})+{\pi }_p^{RCO}(F,w^{S\mathrm{\&}P})\ge {\pi }_s^{A*}+{\pi }_p^{A*}$ if and only if $r\ge r^{sp}$ .

Obviously, as the commission rate $r\to 0$ , the supplier would retain all of the revenue from her on-line platform sales via the agency channel, and would not be able to match those profits by selling through the reselling channel even at a wholesale price of $w_p=w_p^S$ and $F=0$ . However, her profit from selling through the agency channel is decreasing in the commission rate. For sufficiently large commission rates, the supplier could potentially earn more by selling through the platform’s reselling channel if the wholesale price is not too small.

Lemma 5

There exists a threshold on the commission rate, denoted $\ddot{r}$ , such that: For any $r\ge \ddot{r}$ , there exists a range of wholesale prices $(w_p)$ for which the supplier’s profit from selling through the platform’s reselling channel with $F=0$ is at least as large as it would be if she sold through the agency channel, and there exists a lower boundary of this range, ${\overline{w}}_p(r)$ .

As long as the commission rate is not too small, that is, $r\ge \ddot{r}$ , there exists a range of wholesale prices for which, prior to paying any slotting fees, the supplier could earn at least as much by selling through the supplier’s reselling channel as she would through its agency channel. With these preliminary results, we can now characterize how and when the platform can design an optimal reselling contract that allows both the supplier and the platform to earn at least as much as they could by interacting through its agency channel.

Proposition 2

(i) For $r\ge Max\{r^s,r^{sp}\}$ there exists an optimal solution to (17), (18), and (19) in which:

$$\begin{array}{rl}{w}_p^{R*}& =w^{S\mathrm{\&}P}\ge {\overline{w}}_p\left(r\right)\\ F^{R*}& ={\pi }_s^{RCO}(0,w_p^{S\mathrm{\&}P})-{\pi }_s^{A*}\ge 0\end{array}$$

(ii) If $r^{sp}<r^s$ then there exists a threshold commission rate, $\overline{r}\in (r^{sp},r^s)$ such that, for $r\in [\overline{r},r^s]$ , there exists an optimal solution to (17), (18), and (19) in which, $w_p^{R*}={\overline{w}}_p(r)\ge w^{S\mathrm{\&}P}$ , and $F^{R*}=0$ .

(iii) For all other values of commission rate, there does not exist a two-part contract with $F\ge 0$ for which both the supplier and the platform can earn at least as much by interacting through the platform’s reselling channel as they can by interacting through its agency channel.

Corollary 2

There exists a threshold, $r^R:=Min\{\overline{r},Max\{r^s,r^{sp}\}\}$ , such that the platform and the supplier will agree to interact through the platform’s reselling channel if and only if $r\ge \overline{r}$ . Otherwise, they will interact through the platform’s agency channel.

The equilibrium wholesale prices, quantities, and prices that result from this proposition are shown in Table 4. Note that although Table 4 shows the profits of the supplier and platform before the slotting fee is paid, we can find their equilibrium profits using the facts that ${\pi }_s^{R*}(F^{R*},w_p^{R*})={\pi }_s^{R*}(0,w_p^{R*})-F^{R*}$ and ${\pi }_p^{R*}(F^{R*},w_p^{R*})={\pi }_p^{R*}(0,w_p^{R*})+F^{R*}$ respectively.

Proposition 2 is illustrated in Figure 3 where we show the regions of $(\theta ,r)$ for which there exists an optimal two-part reselling contract that is Pareto improving. In the plot on the left, the competition among the traditional resellers is relatively weak $(n=5)$ , whereas in the plot on the right, it is far more intense $(n=100)$ . In each plot, the medium shaded region in the upper right represents $r\ge Max\{r^s,r^{sp}\}$ , for which the platform maximizes its profit at the wholesale price, $w_p=w^{S\mathrm{\&}P}$ , that maximizes the combined profits of the supplier and the platform, and the slotting fee is positive. Because we have assumed that the platform can design the terms of the contract, after paying the slotting fee of $F^{R*}$ , the supplier earns the same profit as she would by using the platform’s agency channel. Of course, at a smaller slotting fee, both firms could be strictly better off.

Figure 3.

Parameters where supplier sells through platform’s reselling channel for base model. (a) $n=5$ ; (b) $n=100$ .

Table 4.

Reselling channel equilibrium.

	$r\ge Max\{r^s,r^{sp}\}$	$r^{sp}<r^s$ and $r\in [\overline{r},r^s]$
$w_p^{R*}$	${\displaystyle \frac{(2-\theta )n\theta }{4+2n(2-{\theta }^2)}}$	${\overline{w}}_p(r)$
$w_r^{R*}$	${\displaystyle \frac{(2-\theta )(1+n)}{4+2n(2-{\theta }^2)}}$	$w_r^{RCO}({\overline{w}}_p(r))$
$q_i^{R*}$	${\displaystyle \frac{2-\theta }{4+2n(2-{\theta }^2)}}$	$q_i^{RCO}({\overline{w}}_p(r))$
$y^{R*}$	${\displaystyle \frac{1+n(1-\theta )}{2+n(2-{\theta }^2)}}$	$y^{RCO}({\overline{w}}_p(r))$
${\pi }_s^{R*}(0,w_p^{R*})$	${\displaystyle \frac{n(2-\theta )((2+\theta )(1+n)-2n{\theta }^2)}{4(2+n(2-{\theta }^2){)}^2}}$	${\pi }_s^{RCO}(F,{\overline{w}}_p(r))$
${\pi }_p^{R*}(0,w_p^{R*})$	${\displaystyle \frac{(1+n-n\theta {)}^2}{(2+n(2-{\theta }^2){)}^2}}$	${\pi }_p^{RCO}(F,{\overline{w}}_p(r))$
${\pi }_i^{RCO}(w_p^{R*})$	${\displaystyle \frac{(2-1\theta {)}^2}{4(2+n(2-{\theta }^2){)}^2}}$	${\pi }_i^{RCO}({\overline{w}}_p(r))$
$F^{R*}$	${\pi }_s^{R*}(0,w_p^{R*})-{\pi }_s^{A*}$	$0$

The darkly shaded region between $\overline{r}$ and $r^s$ in both of the plots in Figure 3 represents the region in which the optimal two-part contract for the platform to offer to the supplier has $F=0$ , that is, no slotting fee. In this region, the platform requests that the supplier sell to it at per-unit wholesale price of $w={\overline{w}}_p(r)\ge w^{S\mathrm{\&}P}$ , which is the smallest wholesale price at which the supplier’s profit is at least equal to her profit from selling through the agency channel. As long as $r\ge \overline{r}$ , this wholesale price is low enough that the platform is better off under this reselling arrangement than it would be if the supplier were selling through its agency channel. Because the expression for ${\overline{w}}_p(r)$ is quite complicated and does not provide any useful insight, we have not included it or the implied quantities or profits in Table 4. As we show in the proof of Proposition 2, when $r<\overline{r},$ the platform cannot earn as much by operating as a reseller at wholesale price ${\overline{w}}_p(r)$ as it could with the supplier selling through its agency channel. Consequently, there does not exist a two-part contract with $F\ge 0$ that both the platform and the supplier would accept. The lightly shaded region between $r^{sp}$ and $\overline{r}$ represents the region where, although the combined profits of the supplier and platform would be higher by having the supplier sell to the platform at $w_p=w^{S\mathrm{\&}P}$ than when the supplier uses the agency channel, there does not exist a two-part contract with $F\ge 0$ that would allow both firms to earn at least as much as they would with the supplier selling through the agency channel.

For the case where $r^{sp}<r^s$ , the definition of these two thresholds implies that for any $r\in [r^{sp},r^s]$ , at the wholesale price of $w_p=w^{S\mathrm{\&}P}$ , the combined profits of the platform and the supplier are larger when the supplier uses the platform’s reselling channel than when she uses its agency channel, but the supplier herself would be worse off for any $F\ge 0$ . For this situation, there are two possibilities. The first would be to allow a negative stocking fee, that is, the platform paying a fixed fee to the supplier for using its reselling channel. The second would be for the platform to offer $w_p>w^{S\mathrm{\&}P}$ . Because we do not observe negative stocking fees in practice, we require $F\ge 0$ . and focus on the second possibility. Instead of requesting the wholesale price, $w^{S\mathrm{\&}P}$ , that maximizes their combined profits, the platform instead waives the stocking fee and requests the smallest wholesale price, ${\overline{w}}_p(r)$ , that allows the supplier to earn at least as much as she would by selling through the agency channel.

From both the left and right plots in Figure 3, it is apparent that an arrangement in which the supplier uses the platform’s reselling channel instead of its agency channel can be Pareto improving when both the commission rate and the substitutability between the platform and traditional resellers are sufficiently high. Moreover, by comparing the left and right-hand plots, we can see that, as the intensity of competition among the traditional resellers $(n)$ increases, there is an expansion of the region of $(\theta ,r)$ for which the platform can induce the supplier to interact with it through its reselling channel.

To gain some insight into how the supplier and platform benefit from interacting via the platform’s reselling channel instead of its agency channel, recall the results of Proposition 1 and Corollary 1. When the supplier sells through the platform’s agency channel, as long as there is at least a moderate amount of competition among the traditional resellers, that is, $n>2$ , there are sufficiently large values of $\theta <1$ for which the quantities sold by both the traditional resellers and by the platform exceed the first-best quantities. In other words, the total profits earned by the supply chain would be larger if the quantity sold through each channel could be reduced. Let us now consider how the equilibrium quantities sold by the two channels when the supplier uses the platform’s reselling channel instead of its agency channel compare with the first-best quantities.

Proposition 3

When the supplier uses the platform’s reselling channel and sells to the platform at a per-unit wholesale price of $w_p=w^{P\mathrm{\&}S}$ , the equilibrium quantities satisfy $y^{R*}\ge y^{VI}$ and $Q^{R*}\le Q^{VI}$ if and only if $\theta \le {\theta }^{RVI}:=\frac{2}{n}$ , while $y^{R*}\le y^{VI}$ and $Q^{R*}\ge Q^{VI}$ if and only if $\theta \ge {\theta }^{RVI}:=\frac{2}{n}$ .

This is illustrated in Figure 4 where we compare the quantities that would be sold through the platform and through the traditional resellers with their first-best counterparts. To facilitate comparison with Figure 2, we take $n=5$ for the plot on the left while $n=100$ for the plot on the right. In contrast with what happens when the supplier sells through the platform’s agency channel, when the supplier sells through the reselling channel, either the quantity sold through the platform or the quantity sold by the traditional resellers exceeds the first-best quantity for that channel, but these quantities never both exceed their first-best counter-parts at the same time.

Figure 4.

Equilibrium quantities when the supplier sells through the platform’s reselling channel at $w_p=w^{S\mathrm{\&}P}$ versus first-best. (a) $n=5$ ; (b) $n=100$ .

The situations in which there exists an optimal solution to (17) subject to (18), and (19), that is, which implies that the platform and the supplier agree to interact through the platform’s reselling channel, are those in which the substitutability between the two channels is high, there is intense competition among the traditional resellers, and the platform’s commission rate is not too low. These are similar to the conditions that lead the platform and the traditional resellers to sell more than the first-best quantities when the supplier uses the platform’s agency channel, as identified in Proposition 1 and Corollary 1. From the perspective of maximizing the total supply chain profit ⁶ , the conditionally optimal quantity to sell in one channel is decreasing in the amount sold in the other. Therefore, it is far worse for both the platform and the traditional resale channel to sell more than the first-best quantities than if only one of them sells more while the other sells less. In these situations, if the supplier uses the platform’s reselling operations, the quantity sold through the traditional resale channel continues to exceed the first-best quantity, but the quantity sold through the platform’s reselling operations drops below the first-best quantity. This is what allows the combined profits of the supplier and platform to be larger with the supplier using the platform’s reselling operations than when she sells through its agency channel.

It is of interest to note that, when $\theta$ is large and the supplier uses the platform’s reselling operations, it is the traditional resellers that sell more than the platform. Although $w_p^{R*}<w_r^{R*}$ , that is, the wholesale price for the platform is lower than that offered to the traditional resellers, the intensity of competition among the traditional resellers dominates the higher wholesale price. The supplier exploits the competition among the traditional resellers by choosing $w_r>w_p$ , but still low enough to push enough volume through the traditional reselling channel that the platform ends up selling less than the first-best quantity in its reselling channel.

4.3. Discussion

Our results suggest that, at any given commission rate, when the competition among traditional resellers and the substitutability between the two channels are both high, the platform and the supplier both earn at least as much by interacting through the platform’s reselling channel under the platform’s optimal two-part contract as they would by interacting through its agency channel. Let us relate this to different products sold through Amazon’s reselling or agency channels. As previously discussed, for branded products that are purchased regularly and are readily available in traditional resellers that consumers visit often, the substitutability between the on-line channel and the traditional reselling channel is high. Both Gillette razor blades or Huggies diapers satisfy this criteria, and because they are available at nearly every grocery and convenience store, the competition among traditional resellers is strong for these two products. Consistent with the results of our model, both of these items are sold through Amazon’s reselling channel. In contrast, consider a product like the wind chimes sold by Sunin Yo, for which we argue the inter-channel substitutability is lower. In addition, because wind-chimes are not available in as many traditional resellers, $n$ should also be lower. The fact that the Sunin Yo wind-chimes are sold through Amazon’s agency channel, rather than in its reselling channel, is consistent with our results. Finally, noting that lower values of $\theta$ imply that the on-line platform attracts different consumers than do traditional resellers, our model provides insight into why Lammes Candies, a local supplier in Austin TX, uses Amazon’s agency channel. Most of Lammes’ traditional resellers are concentrated in Texas. Consequently, although there is relatively strong competition among traditional resellers, there are also consumers who can conveniently access their product only through the on-line platform. So for this situation, even though $n$ is relatively large, $\theta$ is small, and the fact that Lammes sells through Amazon’s agency channel is consistent with our results.

To avoid unnecessary complication we assume that the platform can unilaterally design the two-part contract and make a take-it or leave-it offer to the supplier. Given the market power of a platform like Amazon, this is not unreasonable, but it is not hard to see what would change if the platform and the supplier could bargain. In the region in which $r>Max\{r^{sp},r^s\}$ , the per-unit wholesale price of $w_p=w^{S\mathrm{\&}P}$ still maximizes their combined profit, so any form of generalized Nash bargaining should affect only the slotting fee. However the region in which $r\in [\overline{r},r^s]$ , where $F^{R*}=0$ and $w_p=\overline{w}(r)$ , if the supplier had some bargaining power, it could insist upon $w_p>\overline{w}(r)$ . This would have two effects. First, it would obviously give the supplier some profit in excess of what it would earn by selling through the agency channel. Second, noting that $\overline{w}(r)>w^{S\mathrm{\&}P}$ for $r<r^s$ , it follows that a larger wholesale price could potentially decrease the combined profit of the platform and the supplier, that is, benefit the supplier less than it hurts the platform. Thus, allowing for bargaining between the platform and the supplier over the terms of the reselling contract, would affect some of the specifics of the fixed fee and per-unit wholesale price, but should not change the fundamental characteristics of our results.

Finally, it is worth commenting on the fact that our analysis assumes that the supplier sells either through the platform’s reselling channel or its agency channel, but not through both of them. This is certainly the case for many suppliers, and our results highlight the trade-off between these two modes of interaction. However, there exist examples of suppliers who sell through both of the platform’s channels. Ha et al. (2022) study the implications of dual channel selling in the context of a bilateral monopoly between a supplier and a platform that operates both agency and reselling channels. By focusing on the platform’s ability to exert demand enhancing effort and the supplier’s ability to dictate the wholesale price for the reselling channel, they identify conditions for which it is optimal for the supplier to sell through both channels. In our setting, once the supplier sells to the platform’s reselling channel, she may have an ex-post incentive to also sell through the agency channel. However, as shown in our on-line appendix, because of how this ex-post incentive would be anticipated, neither the supplier nor the platform would benefit from the supplier being able to do this. Therefore, they would willingly agree to add a clause to any reselling arrangement that would specifically prohibit the supplier from selling through both channels.

5. Extensions

In our base model, we make two assumptions that merit further exploration. First, to ensure that the only difference between the supplier selling through the platform’s reselling versus agency channels is whether it is the platform or the supplier who controls the quantity, we assume that all quantity decisions are made simultaneously, regardless of which of the platform’s channels the supplier uses. However, when the supplier sells through the agency channel, there would be nothing to prevent her from waiting until after receiving orders from traditional resellers before choosing the quantity to sell on the platform’s agency channel, and this would be more consistent with the assumptions that are typically made in the supplier encroachment literature.

Second, our base model takes it as given that the supplier will have the ability to sell through the agency channel if she does not enter into a reselling contract with the platform. This is based on the fact that many suppliers have no credible way to commit that they will not sell through the agency channel and the observation that there are very few products that are not available in either Amazon’s reselling or its agency channel. Nevertheless, we consider the implications of a supplier who can credibly commit to not selling through an on-line platform’s agency channel when she would benefit from such a commitment.

5.1. Alternate Sequence of Events for Selling Through the Agency Channel

In much of the literature on supplier encroachment, it is assumed that the quantity decisions are made sequentially, that is, the supplier chooses her quantity after she receives the orders from the (traditional) reseller(s). For example, see Arya et al. (2007), Ha et al. (2016), Hotkar and Gilbert (2021), and Liu et al. (2021), among others. This is typically justified on the basis that the supplier has no credible means of committing to refrain from tailoring her quantity in response to the amount ordered by the reseller(s). A similar argument could be made that, for the case in our model where the supplier sells through the platform’s agency channel, she could postpone her own quantity decision until after receiving the orders from the traditional resellers.

As a robustness check, we now consider the possibility that, when the supplier uses the platform’s agency channel, she postpones her quantity decision until after she receives the orders from the traditional reseller(s). Using backward induction, we first consider how the supplier would respond to the orders that it receives from the traditional resellers. For a given wholesale price and commission rate, it is easy to confirm from the first-order conditions for (5) that the supplier’s best response to any order vector $\mathbf{\text{q}}$ is as follows:

$$y^{ABR}(w_r,r,\mathbf{\text{q}})={\left[\frac{1-\theta Q}{2}\right]}^{+}$$

(21)

where $Q:=\sum _{i=1}^n{q}_i$ . In anticipation of this best response, each of the $n$ traditional resellers attempts to maximize its own profits. Substituting (21) into the profit function for each traditional reseller (6), and simultaneously solving the $n$ first-order conditions, we find a unique equilibrium to the quantity setting subgame in which each reseller chooses:

$$q_i^{Ae1*}(w_r,r)={\left[\frac{2-2w_r-\theta }{(1+n)(2-{\theta }^2)}\right]}^{+}$$

(22)

where we append the superscript with “ $e1$ ” to distinguish the equilibrium values for the case where the quantity setting subgame is sequential (extension 1) from those where it is simultaneous. In stage 1, the supplier chooses the wholesale price for the traditional resellers in anticipation of both (21) and (22). Substituting both of these into the supplier’s profit function in (5), we can use the first-order conditions to find that the wholesale price that maximizes her profits is:

$$w_r^{Ae1*}=\frac{(4-2r\theta )(1+n)-2(1+n(2-r)){\theta }^2+(n+r){\theta }^3}{8(1+n)-2(2+n(3-r)){\theta }^2}$$

(23)

It can be verified that $w_r^{Ae1*}\le w_r^A$ , that is, the supplier chooses a smaller wholesale price for the sequential quantity setting subgame than in the simultaneous quantity setting subgame, but the difference is quite small. The equilibrium values for the game in which the supplier sells through the platform’s agency channel and the quantity setting subgame is sequential instead of simultaneous are shown in Table 5. As expected, these equilibrium values are slightly different than those for our base model. However, the qualitative results are unchanged. Just as in our base model, there exists a threshold on the commission rate, which we now denote by $r_Q^{Ae1}:=\frac{4+n{\theta }^2-2{\theta }^2}{(2+\theta )n\theta }$ that is analogous to the one in Proposition 1. In particular, $Q^{Ae1*}\ge Q^{VI}$ if and only if $r\ge r_Q^{Ae1}$ . It is easy to observe that $r_Q^{Ae1}<r_Q^A$ for all $\theta >0$ . With the new, lower threshold, it is only necessary that $n>1$ to have $\theta <1$ for which $r_Q^{Ae1}<1$ . Thus, when the supplier postpones her quantity decision until after the traditional resellers order, this expands the region of parameters for which both the quantity sold through the platform’s agency channel and the quantity sold by traditional resellers exceed the first best quantities for these channels.

Table 5.

Equilibrium when supplier sells through the platform’s agency channel and the quantity setting subgame is sequential.

$w_r^{Ae1*}$	${\displaystyle \frac{(4-2r\theta )(1+n)-2(1+n(2-r)){\theta }^2+(n+r){\theta }^3}{8(1+n)-2(2+n(3-r)){\theta }^2}}$
$q_i^{Ae1*}$	${\displaystyle \frac{2-(2-r)\theta }{4(1+n)-(2+n(3-r)){\theta }^2}}$
$y^{Ae1*}$	${\displaystyle \frac{4(1+n)-2n\theta -(2+n){\theta }^2}{8(1+n)-2(2+n(3-r)){\theta }^2}}$
${\pi }_s^{Ae1*}$	${\displaystyle \frac{4n+(4(1+n)(1-r)-4n\theta (2-r)+(n-2(1-r)){\theta }^2)}{16(1+n)-4(2+n(3-r)){\theta }^2}}$
${\pi }_p^{Ae1*}$	${\displaystyle \frac{r(2n\theta +(2+n){\theta }^2-4(1+n){)}^2}{4(4(1+n)-(2+n(3-r)){\theta }^2{)}^2}}$
${\pi }_i^{Ae1*}$	${\displaystyle \frac{(2-{\theta }^2)(2-(2-r)\theta {)}^2}{2(4(1+n)-(2+n(3-r)){\theta }^2{)}^2}}$

In Figure 5, we use the same parameters as in Figure 2 to demonstrate that when the supplier sells through the platform’s agency channel, regardless of whether she chooses her quantity at the same time or after the traditional resellers choose their quantities, there is a wide range of commission rates for which both the total quantity sold through the platform and the quantity sold through the traditional resellers exceed the first-best quantities. In fact, the range expands when the supplier postpones her quantity decision until after receiving the orders from the traditional resellers.

Figure 5.

Equilibrium quantities when the supplier sells through the platform’s agency channel and chooses her quantity after receiving the orders from traditional resellers. (a) $\theta =$ 0.9, $n=5$ ; (b) $\theta =$ 0.9, $n=100$ .

As discussed, when the supplier uses the platform’s reselling channel, the platform would not be able to observe the orders placed by the traditional resellers, so for this case the quantity decisions would be exactly as described in Section 4.2. Consequently, neither Lemma 2 nor Lemma 3 are affected by the assumptions about what happens when the supplier sells through the platform’s agency channel. For Lemmas 4 and 5 and Proposition 2, the basic structure remains the same, but the specific values of $r^{sp}$ , $r^s$ , $\overline{r}$ , ${\overline{w}}_p(r)$ , $F^{R*}$ all need to be modified. Denote by $r^{spe1}$ , $r^{se1}$ , ${\overline{r}}^{e1}$ , ${\overline{w}}_p^{e1}(r)$ , $F^{Re1*}$ the modified values after adjusting for the sequential quantity setting subgame for the case where the supplier sells through the platform’s agency channel. In Figure 6, using same parameters as in Figure 3 we show the combinations of $(\theta ,r)$ for which there exists a two-part contract to which they both agree to interact through the platform’s reselling channel.

Figure 6.

Parameters where supplier sells through platform’s reselling channel when selling through the agency channel allows postponement of the supplier’s quantity decision. (a) $n=5$ ; (b) $n=100$ .

By comparing Figures 3 and 6, it is apparent that allowing the supplier to postpone her ordering decision, when she sells through the platform’s agency channel, does not alter the overall structure of when the supplier and platform will agree to interact through the platform’s reselling channel. When the competition among the traditional resellers is weak, that is, $n=5$ , the postponement of the ordering decision somewhat reduces the range of parameters for which the two firms will agree to use the platform’s reselling channel. This is because of the fact that the sequential quantity setting subgame allows the supplier to more effectively use the platform’s agency channel to discipline the traditional resellers.

5.2. Supplier Can Credibly Commit Not to Sell Through the Platform’s Agency Channel

In our base model, we assume that unless the supplier reaches an arrangement with the platform to sell through its reselling channel, she has no way to credibly commit that she will not sell through its agency channel. Note that, when the commission rate, the inter-channel substitutability, and competition among traditional resellers are all high, the supplier’s ability to sell through the on-line platform’s agency channel can result in her earning less profit than she would if the platform did not exist. As long as the traditional resellers choose their quantities in anticipation that the supplier will determine the quantity that it should sell as a best response to their decisions, the supplier will end up selling a positive quantity through the platform’s agency channel in equilibrium. The fact that Amazon has 1.5–2.5 million active third-party sellers in its agency channel, and very few branded products are not available in either Amazon’s agency or reselling channel, suggests that it may be difficult for a supplier to credibly commit to not selling her product through the agency channel.

Nevertheless, it is worth exploring how our results would be affected if the supplier could make a credible commitment to not sell through the platform’s agency channel when it is in her interest to do so. In contrast to our base model, we now assume that, in the absence of an agreement between the platform and the supplier to interact through the platform’s reselling channel, the supplier has the ability to make a credible commitment to sell nothing through the platform’s agency channel. With such a commitment in place, the traditional resellers would anticipate that $y=0$ regardless of how much they order or the commission rate. Given a wholesale price of $w_r$ , each traditional reseller would order:

$$q_i^{Ae3}(w_r,r)=\frac{1-w_r}{1+n},i=1,\dots ,n$$

In anticipation of this, the supplier would optimally set her wholesale price to $w_r^{NA}=\frac{1}{2}$ . By substituting $w_r^{NA}$ , $q_i^{Ae3}(\frac{1}{2},r)$ for $i=1,\dots ,n$ , and $y=0$ into (5), we can confirm that, in the absence of a reselling agreement with the platform, by credibly committing to $y=0$ in the platform’s agency channel, the supplier’s profits would be:

$${\pi }_s^{Ay0}=\frac{n}{4(1+n)}$$

(24)

Of course, the platform would earn nothing, that is, ${\pi }_p^{Ay0}=0$ . By comparing the supplier’s profits from this commitment to what she would earn without it, we can now identify the condition for her to benefit from such a commitment.

Lemma 6

There exists a threshold commission rate, $r^{Ay0}$ , such that ${\pi }_s^{Ay0}\ge {\pi }_s^{A*}$ if and only if $r\ge r^{Ay0}$ , where:

$$r^{Ay0}:=\frac{4+n(8+4n{(1-\theta )}^2-(8-\theta )\theta )}{{(2+n(2-\theta ))}^2}$$

(25)

and $r^{Ay0}<r^s$ .

It is easy to confirm that $r^{Ay0}$ is decreasing in both $n$ and $\theta$ , which implies that when the platform is a close substitute for the traditional resale channel, and the competition in the traditional channel is high, there will be lower and lower commission rates for which the platform could benefit from credibly committing that she will not sell through the agency channel. The fact that $r^{Ay0}<r^s$ has important implications for a possible reselling arrangement with the platform. Recall from Proposition 2 that, in our base model, for $r\ge Max\{r^s,r^{sp}\}$ supplier and platform in our base model would agree to a reselling contract with a positive slotting fee. However, this was based on the assumption that the supplier would necessarily have the ability to sell through the platform’s agency channel which would imply a reservation profit of ${\pi }_s^{A*}$ . But if the supplier could credibly commit to not selling through the platform’s agency channel whenever $r\ge r^{Ay0}$ , this would increase her reservation profits from ${\pi }_s^{A*}$ to ${\pi }_s^{Ay0}$ .

Proposition 4

If the supplier can credibly commit to not sell through its agency channel whenever ${\pi }_s^{Ay0}\ge {\pi }_s^{A*}$ and she lacks a reselling arrangement with the platform, then: (i) for any $r\ge r^{Ay0}$ , there exists an optimal solution platform’s two-part contract design problem in which:

$$\begin{array}{rl}{w}_p^{Re3*}& =w^{S\mathrm{\&}P}\ge {\overline{w}}_p\left(r\right)\\ F^{Re3*}& ={\pi }_s^{RCO}(0,w_p^{S\mathrm{\&}P})-{\pi }_s^{Ay0}\end{array}$$

(ii) If $r^{sp}<r^{Ay0}$ , then there exists a threshold on the commission rate, $\overline{r}\in (r^{sp},r^{Ay0})$ such that, for $r\in [\overline{r},r^{Ay0}]$ , there exists an optimal solution to (17), (18), and (19) in which, $w_p^{Re3*}={\overline{w}}_p(r)\ge w^{S\mathrm{\&}P}$ , and $F^{Re3*}=0$ .

(iii) For all other values of commission rate, there does not exist a two-part contract with $F\ge 0$ for which both the supplier and the platform can earn at least as much by interacting through the platform’s reselling channel as they can by interacting through its agency channel.

In Figure 7, we show the pairs of $(\theta ,r)$ for which the supplier and the platform could both benefit from a reselling arrangement. For $r\ge r^{Ay0}$ the ability to credibly commit that she will not sell through the platform’s agency channel increases the supplier’s reservation profit and decreases the platform’s reservation profit. By comparing Figures 7 and 3, we can see that the supplier’s ability credibly commit to not sell through the platform’s agency channel increases the range of parameters for which they could both benefit from a reselling arrangement. First, because $r^{Ay0}<r^s$ , a sliver of the region in which there exists a reselling contract with $F=0$ in our base model now becomes part of the region where the platform can charge a positive slotting fee. Second, because the supplier’s ability to commit to $y=0$ in the absence of a reselling contract reduces the platform’s reservation profit, this expands the region in which a two-part contract exists in the lower-right corner, that is, high values of substitutability and low values of commission rate.

Figure 7.

Parameters where supplier sells through the platform’s reselling channel when the supplier can credibly commit to not sell through the agency channel. (a) $n=5$ ; (b) $n=100$ .

While the ability to credibly commit not to sell through the platform’s agency channel would benefit the supplier at the expense of the platform, it would not alter the overall structure of our results. The platform and the supplier would still be able to agree for the supplier to sell through the reselling channel so that they both earn at least as much as they could without such an agreement when competition among the traditional resellers and the inter-channel substitutability are both high, and the commission rate is not toosmall.

Note that, we can alternatively consider the possibility that the platform could threaten to deny a supplier admission to its agency channel if she declines an offer to participate in the reselling channel. If the platform were able to do this, it would effectively get to choose whether the right-hand-side of (12), which is subsequently re-stated in (18), should be replaced with ${\pi }_s^{Ay0}$ , that is, the profit that the supplier would earn from selling only through its traditional resellers. This could potentially benefit the platform only for $r<r^{Ay0}$ , which implies that ${\pi }_s^{A*}>{\pi }_s^{Ay0}$ . In this case, by refusing to allow the supplier access to its agency channel the platform could benefit from reducing the value of the supplier’s outside option. Because this would reduce the right-hand-side of the supplier’s participation constraint, it would also expand the set of parameters for which the supplier and platform would agree to a reselling arrangement.

6. Conclusions

Our work is motivated by the fact that while Amazon makes it very easy for a supplier to participate in its agency channel, participation in its reselling channel is by invitation only. Our goal is to understand when and why a reselling arrangement between a supplier and a platform can be Pareto improving relative to having the supplier sell through the platform’s agency channel. We contribute to the dual channels literature by specifically recognizing two important features of the interaction between suppliers and a powerful on-line platform like Amazon. First, we recognize that most suppliers who sell through on-line platforms also sell their products through traditional resellers. Second, we recognize that, while suppliers can often unilaterally choose a wholesale price for their traditional resellers, they typically do not have the power to do this for a powerful platform.

We find that, as long as the competition among the supplier’s traditional resellers is at least moderate, when the substitutability between the on-line platform and the traditional resale channel or the commission rate are sufficiently large, there exist reselling arrangements between the supplier and the platform that are Pareto improving relative to the supplier selling through the platform’s agency channel. This can be explained by the fact that, when a supplier sells through both a traditional resale channel and the platform’s agency channel, at large enough commission rates, the equilibrium quantities sold through both of these channels exceed the first-best quantities. In contrast, when a supplier sells through the platform’s reselling channel, either the quantity sold through traditional resale channel or the quantity sold through the platform exceeds the first-best, but they never both exceed the first-best simultaneously.

These results help to understand why branded products that are well-understood by consumers and are readily available in stores that are visited frequently are very often sold through Amazon’s reselling channel. For these products the on-line channel is a close substitute for the traditional resale channel and competition among resellers is also generally intense. On the other hand, many of the products that are available through the agency channel are products for which either there are fewer traditional resellers, or there is lower substitutability between the online and the traditional reselling channels, where lower substitutability could be caused either by greater variation among consumers’ need to “touch and feel” a product, or by geographic concentration of traditional resellers that results in variation among consumers’ ability to access the product in the traditional resale channel.

Two limitations of our study are that we have taken the platform’s commission rate as exogenous and have normalized to zero any fixed fees for participating in the agency channel. Allowing for a positive (exogenous) fixed fee for participating in the agency channel would complicate our results. But as long as the fixed fee is small enough that it does not discourage the supplier from selling through the agency channel, then adding a fixed fee for participating in the agency channel would only decrease (increase) the reservation profits of the supplier (platform). The main effect of this would be to reduce the threshold commission rate above which the supplier’s profit would be at least as large under a reselling arrangement, expanding the range of parameters for which there exists a Pareto improving reselling contract with a positive slotting fee. On the other hand, if the fixed fee in the agency channel were large enough to discourage the supplier from participating in the agency channel, then her reservation profit would be the profit that she would earn without the platform, while the platform’s reservation profit would be zero. This would be similar to what we discuss in Section 5.2 when the supplier can credibly commit to not participate in the platform’s agency channel. So, while allowing for a positive (exogenous) fixed fee for participating in the platform’s agency channel would add complexity to our results, it should not alter the main qualitative conclusions.

On the other hand, if we were to endogenize the platform’s parameters for its agency channel, either the commission rate or any fixed fees, this would raise an entirely new set of questions. As previously discussed, because the major on-line platform’s typically set their commission rates and fees for broad categories of products, it is reasonable to take these as exogenous when studying how and when there exists a Pareto improving reselling contract with a particular supplier. However, it would be of interest to investigate how a platform should choose these parameters in a setting where there are heterogeneous suppliers. Note that, changing the commission rate and or fixed fees for participating in the agency channel affect not only the profits that the platform earns from suppliers in the agency channel, but also its ability to attract suppliers to its reselling channel. Consequently, we conjecture that the platform’s choice of commission rate and any fixed fees for participating in its agency channel should depend upon the mixture of characteristics among the potential suppliers. This is beyond the scope of our study, but is worthy of future research.

Supplemental Material

sj-pdf-1-pao-10.1177_10591478241249478 - Supplemental material for Channel Choice via On-Line Platform

Supplemental material, sj-pdf-1-pao-10.1177_10591478241249478 for Channel Choice via On-Line Platform by Stephen M Gilbert, Parshuram Hotkar and Chuanjun Liu in Production and Operations Management