Can an E-commerce Platform and its Third-Party Sellers Benefit From Each Other’s Market Entry?

Abstract

E-commerce platforms have an informational advantage over their third-party sellers, leading to the common belief that a platform's market entry would harm sellers with similar products. However, unlike traditional retail competition, the platform and its sellers have aligned incentives: the platform's commission depends on the seller's revenue, and sellers rely on the platform to strengthen their online presence.  Hence, the platform has no incentive to enter the market to harm the seller's revenue severely.  This paper introduces a duopoly model where the seller is the "incumbent" and the platform is the "potential entrant".  Our model captures two salient features: (a) the "reputation effect" that enables the platform to obtain a higher consumer valuation than the seller, and (b) the "spillover effect" that expands the market size when an additional entity (e.g., the platform) enters the market.  Our equilibrium analysis debunks the prevailing belief about platform's entry, showing that platform's entry can enable both the platform and the seller to obtain a higher profit when the unit cost is sufficiently low and the spillover effect is sufficiently high. For robustness checks, we consider three different extensions: an alternative duopoly model with reversed roles where the platform is the incumbent and the seller is the potential entrant, a scenario with an endogenously determined spillover effect, and a simultaneous market entry/exit decision-making process. We find a consistent result across all three extensions that both seller and platform entries can mutually benefit under similar market conditions, fostering a symbiotic relationship.

Introduction

Many traditional online retailers such as Amazon and JD.com transformed their online business models from retailers that sell their own products (books for Amazon or electronics for JD.com) to platforms that enable third-party sellers to sell their products online. Online E-commerce platforms (“platforms” or “online platforms” for short hereafter) such as Amazon, Alibaba, JD.com have fueled economic growth by generating value for the sellers, consumers, and the platform (Chen et al., 2020). First, online platforms can sell a vast selection of products to consumers as a marketplace for many sellers without owning inventory. By doing so, these platforms can earn commissions as a certain percentage of the seller revenues. Second, these platforms can enable sellers to establish their online sales channels, and yet they maintain control of their pricing and inventory decisions. Third, by shopping on these platforms, consumers can search for products with good quality or low prices more easily.

Online platforms like Amazon and JD.com can use the market information that they observe directly from the online sales generated by third-party sellers to analyze the market potentials of different products. By using this market intelligence and their unique positions, these platforms have the option to expand their operations as “hybrid” platforms.

Specifically, hybrid platforms can choose to sell certain products on their own platforms as sellers. In many instances, their selected products may be similar or identical to those of existing sellers. In doing so, these hybrid platforms are competing directly with those sellers who sell similar products. This hybrid model has been successful, enabling Amazon’s U.S. sales to surge to $316 billion in 2022 (Dai and Tang, 2020). ¹ Besides Amazon, JD.com along with Alibaba have transformed their modus operandi as hybrid platforms over the years.

Hybrid platforms certainly offer more purchasing options for consumers, but this hybrid model has raised various fairness concerns. Because an online platform serves as an online marketplace for independent sellers, it can leverage its direct observations of all online consumer behavior to develop search algorithms to promote their own products, creating unfair competition against other sellers (Khan 2019; Zhu 2019). The U.S. Senate alleged that Amazon’s hybrid model is hurting its third-party sellers (Holland, 2021), which motivated Senator Klobuchar to propose the “American Innovation and Choice Online Act” that is pending approval (Edgerton and Birnbaum, 2022). Across the Atlantic, the European Union has raised concerns about Amazon’s hybrid model, and examined whether it has violated the European competition law by using nonpublic data it gathers from third-party complementors to unfairly compete against them (Pop and Schechner, 2020).

It is a common belief that the hybrid platform model is harmful to independent sellers. Therefore, it was intriguing to observe that some independent sellers came forward to defend the platform’s hybrid model. Indeed, some third-party sellers actually support Amazon’s hybrid model because of the “spillover effect”—they believe that the platform’s entry can enlarge the market size that can benefit third-party sellers and that “the examples of Amazon unfairly using seller information are few and far between” (Lewis, 2021).

As diverging public views over the hybrid model continue, mixed research results ensued. Currently, empirical findings are mixed: Zhu and Liu (2018) find that third-party sellers in the United States tend to decrease the number of products they offer on a platform when it enters the market; however, Dryden et al. (2020) find an opposite result using data collected in France and Germany. More recently, Deng et al. (2023) analyze data provided by JD.com and find that third-party sellers tend to adjust their price higher and even sell more after the platform’s entry. Crawford et al. (2022) find Amazon’s entry into Germany’s Marketplace’s Home & Kitchen department to be more aligned with market expansion than business stealing. Unlike traditional retailing, there is a symbiotic relationship between the platform and sellers especially when the platform’s earnings are primarily based on the commissions they obtain from the sellers. Specifically, the incentives of the platform and the seller are aligned: the platform’s commission depends on the seller’s revenue, which in turn affects the seller’s profit. As such, when a platform decides on its market entry strategy and entry price, it must take the seller’s revenue (which affects the platform’s commission) into consideration. Because of the aligned incentive, the platform is unlikely to enter the market to force the seller to exit the market. These observations cast a doubt over the belief that a platform’s entry is always detrimental to third-party sellers.

As such, the aforementioned common belief and the limited empirical research motivate us to investigate the impact of a platform’s entry on independent sellers’ pricing decisions and their resulting profits. Also, we are interested in examining if and when a platform’s entry can benefit both the platform and the sellers. To do so, we first present our main model in which the seller is the “incumbent” who has been selling a product through the platform. At the same time, the platform is the “potential entrant” who needs to decide if she should enter the market to sell the same product to compete with the seller.

To model a platform’s entry by selling a similar product, our model captures two salient features. First, because the platform has its own physical infrastructure to support its logistics services, it has a stronger brand reputation compared to other independent sellers (Shen et al., 2020). ² We capture this “reputation effect” by assuming that the platform enjoys a higher consumer valuation than the seller.

Second, when the platform and the seller sell the same (or similar) product, the platform’s entry will enhance the visibility and create awareness of the product and the seller (Handarkho, 2020). The increased visibility generated by the platform’s entry can draw more consumers to examine the product. Consequently, it can expand the market size, which can benefit both the platform and the seller (Kang, 2017; Deng et al., 2023). To account for this “spillover effect,” we assume that the market size will increases when an additional entity (e.g., the platform) enters the market.

By examining and comparing the platform’s and the seller’s optimal price and profit in equilibrium, that correspond to the case when the platform enters the market and the case when the platform chooses not to enter, we find the following results for our main model that debunk the common belief. Specifically, we find that, when the unit cost is sufficiently low and when the spillover effect is sufficiently high, the platform’s entry is mutually beneficial. Interestingly, the platform’s entry can also enable the seller to sell more upon the platform’s entry. ³

For robustness checks about our key results obtained from our main model, we consider three different extensions. We first examine a variant of our main model by reversing the roles so that the platform is the incumbent whereas the seller is the potential entrant. Then we extend our main model to the case when the spillover effect can be endogenously determined by the platform (by exerting costly promotion efforts to enlarge the market size). Finally, we extend our main model to the case when the platform’s market entry decision and the seller’s market exit decision are made simultaneously.

By incorporating the same reputation and spillover effects, we find that the same structural results obtained from the main model continued to hold across all three extensions. Specifically, the seller’s entry in the first extension and the platform’s entry in the second and third extensions can be mutually beneficial when the cost is sufficiently low and the spillover effect is sufficiently high. Essentially, these favorable conditions foster a symbiotic relationship so that both the platform and sellers can benefit from each other’s entry.

Ultimately, our paper contributes to the platform entry literature by demonstrating the mutual benefits created by the entry. Contrary to the preconceived belief, our findings demonstrate that the platform’s entry can create value for the incumbent seller. Similarly, the seller’s entry can create value for the incumbent platform. As a result, these entries create mutual benefits without necessitating the exit of the incumbent from the market.

The structure of this article is organized as follows. The Section 2 examines the related literature and highlights our contributions. We present our model preliminaries in the Section 3. In Section 4, we analyze our main model in which the seller is the incumbent. Then we examine three extensions, including an alternative model in which the platform is the incumbent Section 5, a model that endogenizes the spillover effect Section 6, and a model when the platform and seller make simultaneous decisions Section 7. We conclude in the Section 8.

2 Literature Review

We review the recent research literature that examines various issues arising from retail platforms as summarized in Table 1.

Table 1.

Related literature.

Paper	Context	Key findings and underlying mechanisms
Analytical work
Mantin et al. (2014)	Reseller model, hybrid model	The hybrid model can increase the platform’s bargaining power in negotiations with the manufacturer. When the power of individual sellers is not too high, the hybrid model has the potential to enhance consumer utility.
Abhishek et al. (2016)	Pure platform model, reseller model	The choice between the two models depends on the effect of the online channel on sales in the traditional channel, competition between e-tailers, and sales externalities.
Hagiu and Wright (2015)	Pure platform model, reseller model	The choice between the two models depends on various factors such as information, spillovers, network effects, cost, etc.
Tian et al. (2018)	Pure platform model, reseller model, and hybrid model	The choice between the three models depends on the upstream supplier competition and order-fulfillment costs.
Hagiu et al. (2022)	Pure platform model, reseller model, and dual model	In equilibrium, the presence of a platform offering similar products exerts competitive pressure that drives down the price of the third-party seller.
Hagiu and Spulber (2013)	Platform’s incentive to invest in first-party content	Investment in first-party content can help the platform alleviate the coordination problem in user participation.
Jiang et al. (2011)	Platform’s entry when facing two types (high demand and low demand) of sellers	When a platform enters the market, a seller may lower its service level to disguise the high demand for its product. The option of a platform’s entry may initially decrease consumer surplus but increase consumer surplus later on.
Etro (2021)	Platform’s entry with private label in the context of competitive sellers	Platform’s entry tends to be constrained with competitive sellers. Sellers’ market power tends to lead to underprovision of private label.
Empirical work
Li and Agarwal (2017)	Facebook’s integration of Instagram	Facebook’s integration of Instagram positively affects big third-party photo-sharing apps, but negatively affects small third-party apps.
Wen and Zhu (2019)	Google’s entry into different app categories	Google’s entry threat reduces innovation and increases price for affected apps. Google’s entry leads to further reduction in innovation and price increase.
Foerderer et al. (2018)	Google’s entry into photo apps	The entry of Google into the market for photo apps resulted in an increase in demand for third-party photo apps and provided incentives for developers to update their apps.
Zhu and Liu (2018)	Amazon’s entry into third-party sellers’ product spaces	Amazon tends to enter third-party product spaces that have a track record of strong sales and positive reviews. Third-party sellers may reduce their efforts to grow on the platform upon Amazon’s entry.
He et al. (2020)	Platform entry in online and offline retail channels	Three potential mechanisms: competition effect, spillover effect, and disintermediation effect.
Deng et al. (2023)	JD.com’s entry into third-party sellers’ product spaces	Third-party sellers tend to charge more and sell more after JD.com entered the market.
Crawford et al. (2022)	Amazon’s entry in Home & Kitchen categories	Amazon’s entry is more consistent with market expansion than business stealing.
Pauwels and Srinivasan (2004)	Private label introduction	Private label entry typically benefits the retailer and consumers as well as premium-brand manufacturers, but it often harms manufacturers of second-tier brands.
Chintagunta et al. (2002)	Private label introduction (oats and frozen pasta)	Private label introduction coincides with the national brand’s retailer margin increase, but it does not tend to affect preferences for the national brand.
Geyskens et al. (2010)	Private label introduction (corn flakes and canned soup)	The introduction of both economy and premium private labels cannibalize incumbent store brands. However, the introduction of economy private label benefits mainstream-quality national brands.
Meza and Sudhir (2010)	Private label introduction (cereal)	Private labels can increase a retailer’s bargaining power. Retailers set retail prices to gain market share for private labels.

First, we build upon existing research that examines the underlying business models of different retail platforms. Researchers have studied three types of business models empowered by retail platforms: (i) a retailer model (or reseller model) in which the platform sells directly online, (ii) a pure platform model in which the platform earns sales commissions based on a percentage of the revenue obtained by third-party sellers, and (iii) a hybrid model in which the platform sells directly and collects sales commissions from third-party sellers.

Separate research studies have analyzed the underlying trade-offs between two (or three) types of business models, and considered the effects of different factors, such as supplier competition, spillover effect, information advantage, network effects, and cost advantage. For example, Hagiu and Wright (2015) and Abhishek et al. (2016) examined the trade-offs between types (i) and (ii), that is, the online retailing model (by selling directly online) and the online (pure) platform model (by earning sales commissions based on the seller’s revenue). Mantin et al. (2014) compared (i) and (iii), that is, the online retailing model and the hybrid model (by further collecting commission from third-party sellers). Tian et al. (2018) and Hagiu et al. (2022) examined the strategic choice between (i), (ii), and (iii).

Unlike this stream of research literature, we examine the implications when a platform transitions from type (ii) to type (iii); that is, from a pure platform model in which the platform relies solely on sales commission collected from a seller to a hybrid model in which the platform generates two revenue streams by selling directly and by collecting commission from a third-party seller. We explore the strategic interactions between the seller and the platform before and after such a transition, and identify the conditions under which such a transition is mutually beneficial.

By examining the implications of platform entry, we also contribute to existing literature on platform entry. For a comprehensive review, see Zhu (2019). In this research stream, research studies consider different issues arising from different contexts such as Google’s entry into photo apps (Foerderer et al., 2018) and other app categories (Wen and Zhu, 2019), Facebook’s integration of Instagram (Li and Agarwal, 2017), and the e-commerce platform’s entry into product spaces of third-party sellers (e.g., Zhu and Liu, 2018; He et al., 2020; Deng et al., 2023; Crawford et al., 2022). To some extent, the digital platform’s entry decision is similar to the traditional retailer’s decision to introduce private labels, and thus our paper also relates to existing literature on the effects of private label introduction (e.g., Pauwels and Srinivasan, 2004; Chintagunta et al., 2002; Geyskens et al., 2010; Meza and Sudhir, 2010).

By examining the data provided by JD.com, Deng et al. (2023) find that, upon JD.com’s entry, the sales prices and the sales quantities of those sellers who sell similar products tend to increase on average. We find this empirical result to be surprising and yet it gives a plausible reason to justify why many sellers continue to co-exist after the platform’s entry. This observation motivated us to develop a parsimonious analytical model that captures the rational behavior of all parties (consumers, the seller, and the platform) as well as the underlying strategic interactions. Our goal is to identify market conditions under which the platform’s entry can benefit the seller.

Our work complements the analytical research that deals with platform entry (e.g., Jiang et al., 2011; Hagiu and Spulber, 2013; Etro, 2021). Specifically, we examine the platform’s market entry conditions and the impact of a platform’s entry on the incumbent seller’s price and profit. Also, we identify market conditions that favor the platform’s market entry as well as those that result in mutual benefits for both parties. We further consider three different extensions. In the first extension, we consider an alternative model in which the platform is the incumbent (i.e., the reseller model) and the seller may enter the market by selling on the platform. In the second extension, we consider the case when the spillover effect can be endogenously determined by the platform. Finally, in the third extension, we investigate the case when the platform’s market entry decision and the seller’s market exit decision are made simultaneously. Overall, our study offers insights into the impact of a platform’s market entry and provides plausible explanations on why and how the platform’s entry can enable the seller to increase its sales quantity.

3 Model Preliminaries

In this article, we examine two models (see Figure 1). Our main model (top panel of Figure 1) considers the case when the seller is the “incumbent.” Our alternative model (bottom panel of Figure 1) deals with the case when the platform is the “incumbent.” The main model is commonly observed in recent years. However, the alternative model can occur when the platform (such as Amazon.com or JD.com) sells its own products (books or electronics) first before other sellers begin selling similar products on the platform.

Figure 1.

Two models: (a) main model—seller as the incumbent (top panel), and (b) alternative model—platform as the incumbent (bottom panel).

3.1 Main Model: Seller as the “Incumbent”

Observe from the top panel of Figure 1 that our main model is based on the case when the seller is the “incumbent” who has been selling a product on the platform for some time. Upon observing the consumer’s behavior and the success of the seller over time, the platform is the “potential entrant” who needs to decide on whether to enter the market by selling the same product to compete with the incumbent seller. ⁴

Given this backdrop, we consider two settings: (N) no entry by the platform; and (E) with entry by the platform.

Setting (N). In the absence of the platform’s entry in setting (N), the seller is essentially operating as a monopoly. By considering the seller as the monopoly, we can determine the seller’s optimal selling price $p_s^N$ that maximizes his expected profit ${\pi }_s^N$ . In setting (N), the platform is “passive” and collects her commission ${\pi }_p^N$ that is based on a proportion of the seller’s revenue.

Setting (E). In setting (E), the platform’s entry will enable her to earn extra profit generated from her direct sales (in addition to the commission to be collected from the seller). To capture the underlying dynamics, we model the underlying dynamics as a sequential game that can be described as follows. (We shall extend our analysis when both parties make their decisions simultaneously in Section 7) First, in setting (E), the platform sets her entry price $p_p^E$ upon entry. By using the observed platform entry price $p_p^E$ , the seller then selects his selling price $p_s^E$ . Then the game ends. ⁵

In Section 4, we shall analyze our “main model” as depicted in the top panel of Figure 1 via backward induction. Specifically, we will use backward induction to determine the equilibrium payoffs $({\pi }_s^E,{\pi }_p^E)$ for both parties. As a rational player, the platform will only choose to enter the market if ${\pi }_p^E>{\pi }_p^N$ , and we shall aim to identify the conditions that will yield ${\pi }_p^E>{\pi }_p^N$ . These conditions will also help us specify the market environment (“reputation effect” and “spillover effect” which we will define later) in which the platform’s entry can afford the seller to earn a higher profit in equilibrium.

In Section 5, we will examine the “alternative model” as depicted in the bottom panel of Figure 1 as a robustness check. Relative to the main model, the role of the seller and the platform is “reversed” in the sense that the platform is now the “incumbent” whereas the seller is the “potential entrant.” Akin to the main model, we consider two settings: (N) no entry by the seller; and (E) with entry by the seller. We analyze the impact of the seller’s entry by solving the corresponding sequential game via backward induction.

3.2 Main Model: Consumer Utility, Demand, and Profit Functions

At the beginning, the seller (i.e., the incumbent in the main model) sells in a heterogeneous consumer market of size $1$ (normalized to $1$ as a “baseline” to ease our exposition).

3.1.1 Setting (N): No platform entry

We begin with setting (N) in which the platform (denoted by subscript $p$ ) chooses not to enter so that the seller operates as a monopoly. In this case, we assume that the consumer utility for purchasing from seller (denoted by subscript $s$ ) is:

$$U_s^N=V-p_s,$$

(1)

where $V\sim U[0,1]$ is the heterogeneous consumer valuation of purchasing the product from the seller at price $p_s$ . Knowing that consumers will purchase from the seller when $U_s^N>0$ and that $V\sim U[0,1]$ , the demand for the seller in setting (N) is:

$$d_s^N=1-p_s.$$

(2)

Given the price $p_s$ and demand $d_s^N$ , the seller’s and the platform’s profits are:

$$\begin{array}{rl}{\pi }_s^N& =((1-\varphi )p_s-c)d_s^N,\end{array}$$

(3)

$$\begin{array}{rl}{\pi }_p^N& =\varphi p_s{d}_s^N,\end{array}$$

(4)

where $\varphi$ is the commission rate that has been established in advance. ⁶ As commonly observed in practice, the rate $\varphi$ is established well in advance and remains constant regardless of the platform’s entry. Therefore, the commission rate $\varphi$ is treated as a parameter rather than a decision variable.

3.1.2 Setting (E): With platform entry

When the platform enters the market to compete with the incumbent seller in setting (E), the size of the market increases from $1$ to $m>1$ due to the “spillover effect” (Handarkho, 2020) as explained in Section 1 the platform’s entry enhances the visibility and awareness of the product (Lewis, 2021). Also, in view of the platform’s “reputation effect” due to better service quality (Shen et al., 2020), the consumer utility in setting (E) for both selling parties are given as:

$$\begin{array}{rl}{U}_s^E& =V-p_s,\end{array}$$

(5)

$$\begin{array}{rl}{U}_p^E& =\alpha V-p_p,\end{array}$$

(6)

where the parameter $\alpha >1$ represents the reputation effect and $p_p$ is the selling price associated with the platform.

Given the enlarged market size $m(>1)$ , the seller and the platform compete for market share in setting (E) endogenously as follows. Specifically, a utility-maximizing consumer will purchase from the seller if $U_s^E>max\{0,U_p^E\}$ , purchase from the platform is $U_p^E>max\{0,U_s^E\}$ , and make no purchase otherwise. By applying (5) and (6) and the fact that $V\sim U[0,1]$ , it can be shown that the demands for both parties satisfy ⁷ :

$$\begin{array}{rl}{d}_s^E& =m(\frac{p_p-p_s}{(\alpha -1)}-p_s)=m\left(\frac{p_p-\alpha p_s}{(\alpha -1)}\right),\end{array}$$

(7)

$$\begin{array}{rl}{d}_p^E& =m(1-\frac{p_p-p_s}{(\alpha -1)})=m\left(\frac{(\alpha -1)-(p_p-p_s)}{(\alpha -1)}\right).\end{array}$$

(8)

For any given commission rate $\varphi$ , we can express the profits for the seller and the platform as:

$$\begin{array}{rl}{\pi }_s^E& =((1-\varphi )p_s-c)d_s^E,\end{array}$$

(9)

$$\begin{array}{rl}{\pi }_p^E& =\varphi p_s{d}_s^E+(p_p-c)d_p^E.\end{array}$$

(10)

Here, the second term $(p_p-c)d_p^E$ in (10) corresponds to the platform’s profit generated from her direct sales after entering the market (in addition to the commission $\varphi p_s{d}_s^E$ collected from the seller).

3.2 Main Model: Analysis

Given the demand and profit functions for settings (N) and (E) as defined in Section 3.2, we analyze our main model by using the following approach. First, for setting (N) in which the platform chooses not to enter, the seller operates as a monopoly. We determine the optimal price for the seller $p_s^N$ and retrieve the profits for both parties (i.e., $({\pi }_s^N,{\pi }_p^N)$ ).

Second, for setting (E) that involves the platform’s entry, we examine the sequential game as explained in Section 3.1 via backward induction. First, given the platform entry price $p_p$ , we determine the seller’s best response price $p_s^E(p_p)$ that maximizes his profit ${\pi }_s^E(p_s,p_p)$ by taking the demand functions (i.e., $(d_s^E,d_p^E)$ ) into consideration. Second, anticipating the seller’s best response price $p_s^E(p_p)$ , the platform determines her optimal entry price $p_p^E$ that maximizes her total profit ${\pi }_p^E(p_p)$ . Once we determine the seller’s optimal equilibrium price $p_p^E$ , we can retrieve all other equilibrium outcomes (i.e., the platform’s price and the profits for both parties) through direct substitution.

Finally, by comparing these equilibrium outcomes, we determine the market conditions under which the platform will enter without causing the seller to exit (i.e., ${\pi }_p^E>{\pi }_p^N$ and ${\pi }_s^E>0$ ). Also, we specify conditions under which the platform entry can benefit both parties (i.e., ${\pi }_p^E>{\pi }_p^N$ and ${\pi }_s^E>{\pi }_s^N$ ). (We shall use the same approach in Section 5 to analyze the alternative model in which the platform is the incumbent, as depicted in the bottom panel in Figure 1.)

4 Main Model Analysis: When the Seller is the Incumbent

In this section, we analyze the main model in which the seller is the incumbent as depicted in the top panel of Figure 1. We proceed by following the approach as explained in Section 3.3.

4.1 Setting (N): No Platform Entry

In setting (N), the platform chooses not to enter, and yet the seller operates as a monopoly by selling through the platform. In this case, the seller aims to select his optimal price $p_s^N$ that maximizes his profit ${\pi }_s^N$ as stated in (3). By letting $y\equiv c/2(1-\varphi )$ and by considering the first-order condition, we get:

Proposition 1: Monopoly Price and Profits

When the platform chooses not to enter in setting (N), the seller’s optimal price $p_S^N$ , demand $d_s^N$ , and profit ${\pi }_S^N$ , and the platform’s income ${\pi }_P^N$ satisfy:

$$\begin{array}{rl}{p}_s^N& =\frac{(1-\varphi )+c}{2(1-\varphi )}=\frac{1}{2}+y,d_s^N=\frac{(1-\varphi )-c}{2(1-\varphi )}=\frac{1}{2}-y,\end{array}$$

(11)

$$\begin{array}{rl}{\pi }_s^N& =(1-\varphi ){\left(\frac{(1-\varphi )-c}{2(1-\varphi )}\right)}^2=(1-\varphi ){(\frac{1}{2}-y)}^2,\end{array}$$

(12)

$$\begin{array}{rl}{\pi }_p^N& =\frac{\varphi }{4}(1-{\left(\frac{c}{1-\varphi }\right)}^2)=\varphi ({\left(\frac{1}{2}\right)}^2-y^2).\end{array}$$

(13)

All proofs are provided in the Appendix. To ensure that the seller’s demand $d_s^N>0$ , we assume: ⁸

Assumption 1: Commission Rate and Marginal Cost

The unit cost $c$ is sufficiently low so that: $1-\varphi >c$ , which implies $y\equiv c/2(1-\varphi )<\frac{1}{2}$ .

Observe from Proposition 1 that, when the unit cost $c$ increases, the seller’s profit and the platform’s earning will both decrease. This is because the platform’s commission is based on the seller’s revenue, and this observation will become useful for us to specify the conditions under which the platform will enter the market.

4.2 Setting (E): With Platform Entry

We now examine the case when the platform chooses to enter as in setting (E).

4.2.1 Seller’s Best Response

Using the backward induction steps as described in Section 3.3, we begin our analysis by examining the seller’s best response for any given platform’s entry price $p_p$ . Specifically, given the platform’s entry price $p_p$ , the seller solves: $\underset{p_s}{max}{\pi }_s^E(p_s,p_p)$ , where the seller’s profit ${\pi }_s^E$ is given in (9) and the seller’s demand $d_s^E$ is given in (7). By examining the first-order condition and by using (7), (9), (8), and (10) to retrieve all relevant quantities, we get:

Proposition 2: Seller’s Best Response

When the platform enters the market in setting (E) and sells her product at a given price $p_p$ , the seller’s best response price $p_s^E(p_p)$ , demand $d_s^E(p_p)$ , and profit ${\pi }_s^E(p_p)$ , and the platform’s corresponding demand $d_p^E(p_p)$ and profit ${\pi }_p^E(p_p)$ satisfy:

$$\begin{array}{rl}{p}_s^E(p_p)& =(\frac{p_p}{2\alpha }+\frac{c}{2(1-\varphi )}),\\ d_s^E(p_p)& =m\frac{\alpha }{(\alpha -1)}(\frac{p_p}{2\alpha }-\frac{c}{2(1-\varphi )}),\end{array}$$

(14)

$$\begin{array}{rl}{\pi }_s^E(p_p)& =m\frac{\alpha (1-\varphi )}{(\alpha -1)}{(\frac{p_p}{2\alpha }-\frac{c}{2(1-\varphi )})}^2,\end{array}$$

(15)

$$\begin{array}{rl}{d}_p^E(p_p)& =m(1-\frac{(2\alpha -1)}{(\alpha -1)}\cdot \frac{p_p}{2\alpha }+\frac{1}{(\alpha -1)}\cdot \frac{c}{2(1-\varphi )}),\end{array}$$

(16)

$$\begin{array}{rl}{\pi }_p^E(p_p)& =\varphi \cdot p_s^E(p_p)\cdot d_s^E(p_p)+(p_p-c)\cdot d_p^E(p_p).\end{array}$$

(17)

Proposition 2 reveals that the seller’s best response price $p_s^E(p_p)$ , demand $d_s^E(p_p)$ , and profit ${\pi }_s^E(p_p)$ are increasing in the platform’s price $p_p$ , whereas the platform’s corresponding demand $d_p^E(p_p)$ is decreasing in $p_p$ . However, the platform’s profit ${\pi }_p^E(p_p)$ given in (17) is concave in $p_p$ .

4.2.2 Auxiliary Variable: $x=p_p/2\alpha$

Armed with Proposition 2, we now proceed to determine the platform’s optimal price $p_p^E$ by anticipating the seller’s best response. Specifically, the platform solves: $\underset{p_p}{max}{\pi }_p^E(p_p)$ as given in (17). However, the analysis can become unwieldy because of the complex expression of the platform’s profit function ${\pi }_p^E(p_p)$ as given in (17). Fortunately, we can simplify our analysis tremendously if we transform our analysis by considering an auxiliary variable:

$$x\equiv \frac{p_p}{2\alpha },$$

where $x$ depends on $\alpha$ , whereas $y\equiv c/2(1-\varphi )$ is independent of $\alpha$ .

Through substitution, we can simplify the expressions stated in Proposition 2 by considering $x$ and $y$ instead of $p_p$ (which equals $2\alpha x$ ) and $c$ (which equals $2(1-\varphi )y$ ) as follows:

$$\begin{array}{rl}{p}_s^E(x)& =x+y,d_s^E(x)=m\frac{\alpha }{(\alpha -1)}(x-y),\end{array}$$

(18)

$$\begin{array}{rl}{\pi }_s^E(x)& =m(1-\varphi )\frac{\alpha }{(\alpha -1)}(x-y{)}^2,\end{array}$$

(19)

$$\begin{array}{rl}{d}_p^E(x)& =m((1-2x)-\frac{1}{(\alpha -1)}(x-y)),\end{array}$$

(20)

$$\begin{array}{rl}{\pi }_p^E(x)& =m(\varphi \frac{\alpha }{(\alpha -1)}(x^2-y^2)+(2\alpha x-2(1-\varphi )y)\\ & \times ((1-2x)-\frac{1}{(\alpha -1)}(x-y))).\end{array}$$

(21)

4.2.3 Platform’s Optimal Entry Price

By using the auxiliary variables $x$ and $y$ as defined above, we can simplify the platform’s profit ${\pi }_p^E(x)$ given in (21), which is concave in $x$ . By considering the first-order condition, we can determine the optimal $x^{*}$ that maximizes ${\pi }_p^E(x)$ . Once we determine $x^{*}$ , we can obtain the optimal platform price $p_p^E=2\alpha x^{*}$ as stated below:

Proposition 3: Platform’s Optimal Auxiliary Price $x^{*}$ and Retail Price $p_p^E$

Upon platform’s entry in setting (E), her optimal auxiliary price $x^{*}$ and retail price $p_p^E$ satisfy:

$$\begin{array}{rl}{x}^{*}& =\frac{\alpha (\alpha -1)+\alpha y+(2\alpha -1)(1-\varphi )y}{2\alpha (2\alpha -1)-\alpha \varphi },\text{where}\\ y& =\frac{c}{2(1-\varphi )},\end{array}$$

(22)

$$\begin{array}{rl}{p}_p^E& =2\alpha x^{*}=\frac{2\alpha (\alpha -1)+((2\alpha -1)+\frac{\alpha }{(1-\varphi )})c}{2(2\alpha -1)-\varphi }.\end{array}$$

(23)

By using $x^{*}$ given in (22) and by noting that $y=c/2(1-\varphi )$ , we can retrieve the corresponding equilibrium outcomes; that is, the seller’s price $p_s^E=p_s^E(x^{*})$ , the seller’s profit ${\pi }_s^E={\pi }_s^E(x^{*})$ , and the platform’s profit ${\pi }_p^E={\pi }_p^E(x^{*})$ by substituting $x^{*}$ into (18), (19), and (21), respectively.

By comparing these equilibrium outcomes in setting (E) with the platform’s entry against the platform’s profit in setting (N) for the case without the platform’s entry, we can identify conditions under which the platform will enter the market without forcing the seller to exit; that is, when ${\pi }_p^E>{\pi }_p^N$ and ${\pi }_s^E>0$ , where ${\pi }_p^N$ and ${\pi }_s^E$ are given in (13) and (19), respectively. However, direct comparisons of these quantities are complex. Therefore, we opt to compare these quantities indirectly through the reputation effect captured by $\alpha$ and the spillover effect captured by $m$ . In preparation, let us examine the comparative statics of $x^{*}$ and $p_p^E$ with respect to $\alpha$ in the following lemma.

Lemma 1:

In setting (E), when the unit cost $c<\frac{(2-\varphi )(1-\varphi )}{6-4\varphi }(<1-\varphi )$ , the optimal $x^{*}$ given in (22) and the platform’s optimal price $p_p^E$ given in (23) possess the following properties:

$x^{*}$ is increasing in $\alpha$ for any $\alpha >1$ .

$\frac{1}{4}>x^{*}>y$ for any $\alpha >1$ .

$p_p^E$ is increasing in $\alpha$ for any $\alpha >1$ , and $p_p^E>c$ .

Lemma 1 reveals that, when the unit cost is sufficiently low, the associated auxiliary price $x^{*}$ and the platform’s optimal price $p_p^E$ are increasing in the reputation effect $\alpha$ . By focusing on the case when $c<\frac{(2-\varphi )(1-\varphi )}{6-4\varphi }$ , we can apply Lemma 1 to get:

Corollary 1:

Suppose the unit cost $c<\frac{(2-\varphi )(1-\varphi )}{6-4\varphi }$ . Then, in setting (E), upon the platform’s entry, the seller’s price $p_s^E(x^{*})$ and demand $d_s^E(x^{*})$ given in (18) as well as the seller’s profit ${\pi }_s^E(x^{*})$ given in (19) satisfy:

$p_s^E(x^{*})$ is increasing in $\alpha$ ;

$0<p_s^E(x^{*})<p_s^N$ ; and

$d_s^E(x^{*})>0$ and ${\pi }_s^E(x^{*})>0$ .

To understand Corollary 1, let us first recall from Lemma 1 that, as the platform’s reputation effect $\alpha$ becomes stronger, the platform is able to charge a higher price $p_p^E$ upon entry. However, even when both the platform and the seller charge higher prices as the platform’s reputation effect $\alpha$ becomes stronger (as shown in statement 3 of Lemma 1 and statement 1 of Corollary 1, respectively), statement 2 of Corollary 1 reveals that the seller’s optimal price $p_s^E(x^{*})$ upon the platform’s entry is still lower than his monopoly price $p_s^N$ due to the underlying competition upon the platform’s entry.

Despite competition, the platform’s commission depends on the seller’s revenue, so the interests of the platform and the seller are somewhat aligned. As such, Lemma 1 reveals that the platform has a strong incentive to set her price $p_p^E$ to “soften competition” that will enable the seller to also increase his price (along with the platform) as stated in statement 1 of Corollary 1. Additionally, because of the platform’s interest is aligned with the seller, the platform will set the price $p_p^E$ so that, upon the platform’s entry, the seller can survive as shown in statement 3 of Corollary 1. This observation offers a hint about how these aligned interests can enable the platform to facilitate a mutually beneficial entry under certain market conditions. We explore this issue next.

4.3 Platform Entry Decision and its Impact

We now show how we can use Corollary 1 to identify the “co-existent” platform entry conditions; that is, ${\pi }_p^E>{\pi }_p^N$ and ${\pi }_s^E>0$ . Also, we shall derive the conditions under which the platform entry will create value for both parties; that is, ${\pi }_p^E>{\pi }_p^N$ and ${\pi }_s^E>{\pi }_s^N$ . To begin, let us explore the platform’s co-existence entry conditions. In preparation, let us consider the following properties:

Lemma 2: The Platform’s Entry

Suppose $c<\frac{(2-\varphi )(1-\varphi )}{6-4\varphi }$ . Then, upon her entry in setting (E), the platform’s demand $d_p^E>0$ and her profit ${\pi }_p^E>0$ .

Lemma 2 reveals that, as long as the unit cost is below a threshold, the platform entry is plausible (but not necessarily optimal). However, when the reputation effect $\alpha$ is very low, say, $\alpha \to 1$ , it is easy to check from (22), (19), and (21) that, as $x^{*}\to y$ , the seller’s profit ${\pi }_s^E(x^{*})\to 0$ , and yet the platform’s meager profit ${\pi }_p^E(x^{*})\to 2\varphi y(1-2y)$ . This is because, when the platform has a very weak reputation effect (say, $\alpha \to 1$ ), the platform has virtually no differentiating value relative to the seller. However, because of the commission that the seller has to pay to the platform, the seller’s “effective” cost structure is higher than that of the platform. Consequently, the seller earns nothing and exits, and the platform earns a meager profit. Hence, it is only conceivable for the platform to enter the market when her reputation effect is above a threshold, say, $\alpha >1$ as assumed.

4.3.1 Co-existent Entry Conditions

Lemma 2 provides the prerequisite condition (i.e., $c<(2-\varphi )(1-\varphi )/6-4\varphi$ ) for the platform’s entry. We now identify the platform’s “co-existent entry conditions” that ensure that ${\pi }_p^E>{\pi }_p^N$ and ${\pi }_s^E>0$ . Using the expressions given in Proposition 1 for setting (N) and given in Proposition 3 for setting (E), we obtain the following sufficient co-existent platform entry conditions:

Proposition 4: Platform Co-existent Entry Condition

Suppose $c<\frac{(2-\varphi )(1-\varphi )}{6-4\varphi }$ . Then, if the spillover effect $m>{\gamma }_1$ , where ${\gamma }_1\equiv \frac{\frac{\varphi }{4}(1-(\frac{c}{1-\varphi }{)}^2)}{(\varphi \frac{\alpha }{(\alpha -1)}((x^{*}{)}^2-y^2)+(2\alpha x^{*}-2(1-\varphi )y)(1-\frac{(2\alpha -1)}{(\alpha -1)}{x}^{*}+\frac{1}{(\alpha -1)}y))},$ the platform can afford to enter without causing the seller to exit; that is, ${\pi }_p^E>{\pi }_p^N$ and ${\pi }_s^E>0$ .

Proposition 4 reveals that, in the presence of spillover effect $m$ caused by the platform entry, it is optimal for the platform to enter and allow the seller to stay so that both parties can coexist in equilibrium. This result provides the conditions under which the seller can afford to continue to sell alongside the platform.

Also, Proposition 4 leads us to explore our next question: when will the platform’s entry be mutually beneficial so that both parties can attain a higher profit? (In other words, when will ${\pi }_p^E>{\pi }_p^N$ and ${\pi }_s^E>{\pi }_s^N$ ?) Before we identify such market conditions, the following corollary offers additional insights. First, by considering the platform entry conditions (i.e., $c<(2-\varphi )(1-\varphi )/6-4\varphi$ and $m>{\gamma }_1$ ), we obtain the following result.

Corollary 2: Impact of Platform Entry

Suppose $c<\frac{(2-\varphi )(1-\varphi )}{6-4\varphi }$ . Then seller can sell more (i.e., $d_s^E>d_s^N$ ) upon the platform’s entry if $m>{\gamma }_2$ , where ${\gamma }_2\equiv \frac{(\alpha -1)(\frac{1}{2}-y)}{\alpha (x^{*}-y)}$ .

The result of Corollary 2 has been observed in a recent empirical study (Deng et al., 2023). Corollary 2 specifies the conditions for the seller to sell more upon the platform’s entry by charging a lower price as shown in statement 2 of Corollary 1. By considering these results, we get:

Corollary 3: Mutually Beneficial Platform Entry Condition

Suppose $c<\frac{(2-\varphi )(1-\varphi )}{6-4\varphi }$ . Then, if the spillover effect $m>{\gamma }^{*}$ , the platform’s entry is mutually beneficial: ${\pi }_p^E>{\pi }_p^N$ and ${\pi }_s^E>{\pi }_s^N$ , where ${\gamma }^{*}=max\{{\gamma }_1,{\gamma }_3\}$ and ${\gamma }_3\equiv \frac{(\alpha -1)(\frac{1}{2}-y{)}^2}{\alpha (x^{*}-y{)}^2}$ .

Corollary 3 reveals that, when the unit cost is low (i.e., $c<(2-\varphi )(1-\varphi )/6-4\varphi$ ) and the spillover effect is sufficiently strong (i.e., $m>{\gamma }^{*}$ ), both the seller and the platform can obtain a higher profit upon the platform’s entry. The underlying reason is as follows. When the cost is low and the reputation effect is high, the platform can generate some demand $d_p^E>0$ upon entry as shown in Lemma 2 without forcing the seller to exit (so that the platform can continue to earn the commission from the seller). Therefore, when the spillover effect is strong enough, the platform is better off by entering the market. At the same time, the seller can piggyback on this spillover effect to obtain a higher demand $d_s^E(x^{*})$ as stated in Corollary 2 despite a lower price $p_s^E(x^{*})$ as shown in Corollary 1. This way, the seller can leverage the spillover effect and benefit from the platform’s entry by earning a higher profit as shown in Corollary 3.

In summary, Corollary 3 presents the market conditions that can foster a mutually beneficial platform entry: both parties will earn a higher profit upon the platform’s entry. Because these market conditions are reasonable, our results offer a plausible explanation about the empirical result obtained by Deng et al. (2023) as explained in Section 1. Also, our results debunk a common belief that a platform’s entry is always detrimental to the seller.

5 Extension 1: When the Platform is the Incumbent

To examine the robustness of our results as shown in Corollary 3, we now extend our base model by considering an alternative model as illustrated in the bottom panel of Figure 1. In this extension, we reverse the roles of the platform and the seller, such that the platform is now the incumbent and the seller is the potential entrant. As explained in Section 3, this alternative scenario arises when the platform has been selling her own products prior to any seller entering the market. (For example, Amazon was selling books and JD.com was selling electronics directly to consumers before transitioning into platforms to allow third-party sellers to sell products to consumers.)

Like before, our intent is to identify the seller’s entry conditions so that the seller’s entry is mutually beneficial, and examine whether these conditions possess a similar structure as stated in Corollary 3 for the main model. In preparation, we modify the demand and profit functions established in Section 3.2 to capture a different dynamic arising from the reversed role of both parties.

5.1 Model: Consumer Utility, Demand, and Profit Functions

Before the seller’s entry, the platform is the incumbent who sells in a market of size $1$ (normalized to $1$ as a baseline). Analogously, we consider two settings (N) and (E).

Setting (N). Without the seller’s entry in setting (N), the platform operates as a monopoly and the consumer utility is:

$$U_p^N=\alpha V-p_p,$$

(24)

where $V\sim U[0,1]$ is the consumer valuation of purchasing the product from the platform at price $p_p$ and $\alpha >1$ is the platform’s reputation effect as explained in Section 3.2.2. Knowing that consumers will purchase from the platform when $U_p^N>0$ , the platform’s demand and profit in setting (N) are:

$$\begin{array}{rl}{d}_p^N& =1-p_p/\alpha ,\end{array}$$

(25)

$$\begin{array}{rl}{\pi }_p^N& =(p_p-c)d_p^N=(p_p-c)(1-p_p/\alpha ).\end{array}$$

(26)

Without entering the market, the seller earns nothing in setting (N) so that ${\pi }_s^N=0$ .

Setting (E). In setting (E), the seller enters the market at price $p_s^E$ by paying a commission to the platform. Hence, the consumer utility for purchasing from the platform and the seller are:

$$\begin{array}{rl}{U}_p^E& =\alpha V-p_p,\end{array}$$

(27)

$$\begin{array}{rl}{U}_s^E& =V-p_s.\end{array}$$

(28)

Observe that the above utility functions are identical to (6) and (5), respectively. However, because the platform is the incumbent who has already established a market of size $1$ , the spillover effect brought by the seller’s entry can be different from that of the main model. Instead of $m$ , we shall use $k>1$ to denote the spillover effect associated with the seller’s entry.

By using the same approach as explained in Section 3.2.2, the demand functions are:

$$\begin{array}{rl}{d}_p^E& =k\cdot (1-\frac{p_p-p_s}{(\alpha -1)})=k\cdot \left(\frac{(\alpha -1)-(p_p-p_s)}{(\alpha -1)}\right),\end{array}$$

(29)

$$\begin{array}{rl}{d}_s^E& =k\cdot (\frac{p_p-p_s}{(\alpha -1)}-p_s)=k\cdot \left(\frac{p_p-\alpha p_s}{(\alpha -1)}\right).\end{array}$$

(30)

Hence, we can express the profits of the platform and the seller as follows:

$$\begin{array}{rl}{\pi }_p^E& =\varphi p_s{d}_s^E+(p_p-c)d_p^E,\end{array}$$

(31)

$$\begin{array}{rl}{\pi }_s^E& =((1-\varphi )p_s-c)d_s^E.\end{array}$$

(32)

5.2 Analysis: When the Platform is the Incumbent

Given the demand and profit functions of both parties in settings (N) and (E), we determine the monopoly price for the platform in setting (N). For setting (E) that involves the seller’s entry, we shall use the backward induction steps as explained in the “Main Model: Analysis” to solve the corresponding sequential game. Specifically, we first determine the platform’s best response price $p_p(p_s)$ for any given seller’s entry price $p_s$ . Then, anticipating the platform’s best response price, the seller sets his optimal entry price $p_s^E$ . By comparing the equilibrium outcomes, we can specify the conditions for the case when the seller entry can create values for both parties; that is, ${\pi }_s^E>{\pi }_s^N$ and ${\pi }_p^E>{\pi }_p^N$ .

5.3 Setting (N): No Seller Entry

When the seller chooses not to enter, the monopoly platform solves: $\underset{p_p}{max}\{{\pi }_p^N\}$ , where ${\pi }_p^N$ is given in (26). We obtain the following result that resembles Proposition 1.

Proposition 5:

When the seller chooses not to enter in setting (N), the platform’s optimal price $p_p^N$ , demand $d_p^N$ , and profit ${\pi }_p^N$ , and the seller’s profit ${\pi }_s^N$ satisfy:

$$\begin{array}{rl}{p}_p^N& =\frac{\alpha +c}{2},d_p^N=\frac{\alpha -c}{2\alpha },\end{array}$$

(33)

$$\begin{array}{rl}{\pi }_p^N& =\frac{(\alpha -c{)}^2}{4\alpha },\end{array}$$

(34)

$$\begin{array}{rl}{\pi }_s^N& =0.\end{array}$$

(35)

As we shall see later, our market conditions for facilitating a mutually beneficial seller’s entry hinge upon the following assumption that is more stringent than Assumption 1:

Assumption 2: Commission Rate and Marginal Cost

The unit cost $c$ is sufficiently low so that: $c<\frac{1-\varphi }{2}$ .

5.4 Setting (E): With Seller Entry

We examine setting (E) that entails the seller entry as depicted in the bottom panel of Figure 1.

5.4.1 Platform’s Best Response Price

Given seller entry price $p_s$ , the platform solves: $\underset{p_p}{max}{\pi }_p^E(p_s,p_p)$ , where the platform’s profit ${\pi }_p^E$ is given in (31) and the platform’s demand $d_p^E$ is given in (29). By using the same approach as described in Section 4.2, we get:

Proposition 6: Platform’s Best Response

When the seller chooses to enter at a given price $p_s$ , the platform’s best response price $p_p^E(p_s)$ and demand $d_p^E(p_s)$ , as well as the seller’s corresponding demand $d_s^E(p_s)$ and profit ${\pi }_s^E(p_s)$ satisfy:

$$\begin{array}{rl}{p}_p^E(p_s)& =\frac{(\alpha -1)+c+(1+\varphi )p_s}{2},\end{array}$$

(36)

$$\begin{array}{rl}{d}_p^E(p_s)& =k\cdot \left(\frac{(\alpha -1)-(p_p^E(p_s)-p_s)}{(\alpha -1)}\right),\end{array}$$

(37)

$$\begin{array}{rl}{d}_s^E(p_s)& =k\cdot \left(\frac{p_p^E(p_s)-\alpha p_s}{(\alpha -1)}\right)\\ & =k\cdot \frac{(\alpha -1)+c+((1+\varphi )-2\alpha )p_s}{2(\alpha -1)},\end{array}$$

(38)

$$\begin{array}{rl}{\pi }_s^E(p_s)& =((1-\varphi )p_s-c)\cdot d_s^E(p_s)=((1-\varphi )p_s-c)\\ & \cdot k\cdot \frac{(\alpha -1)+c+((1+\varphi )-2\alpha )p_s}{2(\alpha -1)}.\end{array}$$

(39)

Proposition 6 reveals that the platform’s best response price $p_p^E(p_s)$ given in (36) is increasing in the seller entry price $p_s$ as well as the platform’s reputation effect $\alpha$ . As expected, the seller’s demand $d_s^E(p_s)$ given in (38) is decreasing in $p_s$ (because $\alpha >1>\varphi$ ), and the seller’s profit ${\pi }_s^E(p_s)$ given in (39) is concave in $p_s$ .

5.4.2 Seller’s Optimal Entry Price

Anticipating the platform’s best response price $p_p^E(p_s)$ given in (36), the seller determines his optimal entry price by solving: $\underset{p_s}{max}\{{\pi }_s^E(p_s)\}$ , where ${\pi }_s^E(p_s)$ is given in (39). By considering the first-order conditions and by rearranging the terms, we get:

Proposition 7: Seller’s Optimal Price $p_s^E$

Suppose that the cost $c<(1-\varphi )/2$ . Then the seller’s optimal price $p_s^E$ , demand $d_s^E$ , and profit ${\pi }_s^E$ upon his entry in setting (E) satisfy:

$$\begin{array}{rl}{p}_s^E& =\frac{(1-\varphi )(\alpha -1)+2(\alpha -\varphi )c}{2(1-\varphi )(2\alpha -(1+\varphi ))},\end{array}$$

(40)

$$\begin{array}{rl}{d}_s^E& =k\cdot \frac{(1-\varphi )-2c}{4(1-\varphi )},\end{array}$$

(41)

$$\begin{array}{rl}{\pi }_s^E& =k\cdot \frac{(\alpha -1)}{2\alpha -(1+\varphi )}\cdot \frac{1}{8(1-\varphi )}\cdot ((1-\varphi )-2c{)}^2.\end{array}$$

(42)

In addition, both $p_s^E$ and ${\pi }_s^E$ are increasing in $\alpha$ even though $d_s^E$ is independent of $\alpha$ .

Under Assumption 2 which has $c<(1-\varphi )/2$ , the seller’s profit margin $((1-\varphi )p_s^E-c)>0$ . Also, Assumption 2 ensures that the seller’s demand $d_s^E>0$ and profit ${\pi }_s^E>0$ . Moreover, Proposition 7 reveals an interesting observation. When the platform has a strong reputation effect $\alpha$ , it is natural to observe that her optimal response price $p_p^E(p_s)$ given in (36) is increasing in $\alpha$ . This behavior implies that a higher reputation effect $\alpha$ will soften competition, enabling the seller to charge a higher price even when the platform’s reputation effect is strong.

5.4.3 Seller Entry Decision and its Impact

To avoid repetition, we shall skip the seller’s co-existence entry conditions. Instead, we establish the market conditions in the following corollary that can ensure that the seller’s entry benefits both parties, creating a win-win situation (i.e., ${\pi }_s^E>{\pi }_s^N=0$ and ${\pi }_p^E>{\pi }_p^N$ .)

Corollary 4: Mutually Beneficial Seller Co-existent Entry Conditions

Suppose that the cost $c<(1-\varphi )/2$ and the spillover effect $k>\hat{\gamma }$ , where $\hat{\gamma }\equiv \frac{(\alpha -c{)}^2}{4\alpha \left((\varphi p_s^E\frac{(1-\varphi )-2c}{4(1-\varphi )}+(p_p^E(p_s^E)-c)\left(\frac{(\alpha -1)-(p_p^E(p_s^E)-p_s^E)}{(\alpha -1)}\right)\right)}$ (with various quantities in the denominator as stated in Propositions 6 and 7). Then the seller’s entry is mutually beneficial so that ${\pi }_s^E>{\pi }_s^N=0$ and ${\pi }_p^E>{\pi }_p^N$ .

Considering the results obtained from both the base model and this extension, we can draw the following conclusions. First, besides the fact that the platform provides a channel for many small sellers to enter the market, the spillover effect can create value for both parties upon the platform entry. This is because the platform’s entry creates additional awareness (Handarkho, 2020), which can increase product demand for both parties (Li and Agarwal, 2017). Hence, even when the seller is the incumbent, allowing the platform to enter the market can be mutually beneficial when the market conditions are favorable as shown in Corollary 3.

Second, even with a stronger reputation effect $a$ , we show in our extension presented in Section 5 that there is a room for the seller to enter the market to create mutual benefits when the platform is the incumbent. Specifically, even when the platform is the incumbent, allowing the seller to enter the market can be mutually beneficial when the market conditions are favorable as shown in Corollary 4.

To conclude, we have identified favorable market conditions under which both the platform and the seller can benefit from their co-existence by allowing for entrance. These findings debunk the common belief as explained in Section 1. More importantly, our results deepen our understanding about how platform entry can create value for the incumbent seller, and vice versa. Ultimately, incumbents and entrants can be friends, and not foes.

6 Extension 2: When the Spillover Effect $m$ is Endogenously Determined

As articulated in Section 3.2.2, there is empirical evidence (Handarkho, 2020) and anecdotal evidence (Lewis, 2021) supporting the existence of the spillover effect, whereby the market size increases from $1$ to $m>1$ upon the platform’s entry. Also, when the exogenously given spillover effect $m>{\gamma }^{*}(>1)$ , Corollary 3 reveals that the platform’s entry leads to a mutually beneficial outcome where both the platform and the seller enjoy higher profits. This result raises an interesting question: would this result hold if the spillover effect $m$ were endogenously determined?

To answer this question, we now extend our base model presented in Section 3 to the case when the spillover effect can be controlled by the platform. ⁹ In preparation, let us examine the mechanism by which the spillover effect is created, so that we can incorporate this mechanism in our model. In our context, spillover is a form of “externality,” where the action of one party (e.g., the platform’s entry) can impact a third party (e.g., through the total market size) even without directly participating. As explained in Section 1, a platform’s entry can “increase awareness” of the products sold by the platform and the seller, so that the market size expands upon the platform’s entry (Handarkho, 2020).

The spillover effect generated by the increased awareness has been examined in the context of advertising and promotion, predating the notion of platform entry. First, in a natural experiment conducted on Yahoo! homepage, Lewis and Nguyen (2015) find empirical evidence of spillover: display ads can lead to a 30%–45% increase in searches for the advertised brand, as well as a potential increase of up to 23% in searches for competitors’ brands. Hence, when one firm advertises its own product, it increases consumer awareness that may benefit its competitors. Similar spillover effects have been found in different contexts (e.g., restaurant-search websites (Sahni, 2016); search advertising on Google (Chiou and Tucker, 2012). Second, in the context of platform entry, Foerderer et al. (2018) find that, upon Google’s entry into the photo category (i.e., Google Photos), consumer demand increased for all providers who offer similar services on the Google’s Android platform. This spillover effect is due to the heightened awareness of this particular product space driven by Google’s entry, which has expanded the overall market (Li and Agarwal, 2017). Likewise, releases of Apple Health and Google Fit can potentially provide positive spillovers to health and fitness mobile apps because they educate consumers on why this category matters, which enlarges the market size (Kang and Suarez, 2023).

While empirical evidence has been established in the research literature, we are not aware of analytical models that endogenize the spillover effect associated with the platform entry. However, we can leverage this empirical evidence to examine how a platform can control the spillover effect $m$ by utilizing costly advertising and promotional efforts to increase consumer awareness. In the remainder of this section, we extend our base model to the case when $m$ is endogenously determined, and establish the conditions under which our results stated in the Section 4 would continue to hold.

Upon the platform’s entry, we assume that the platform can choose her promotional effort $a\ge 0$ by incurring a cost $r{a}^2$ , which can increase the total market size from $1$ to $m=1+a$ . ¹⁰ (For ease of exposition, we rewrite the corresponding effort $a\equiv (m-1)$ with a requisite cost $r{a}^2\equiv r\cdot (m-1{)}^2$ .) Hence, by assuming that the platform can exert costly effort to increase consumer awareness, ¹¹ we now extend our base model to endogenize the spillover effect $m$ by allowing the platform to set her effort level $a\equiv (m-1)$ in addition to her price $p_p^E$ upon entry.

For any given market size $m\ge 1$ , the platform can determine her entry price as examined in Section 4.2. Specifically, we can apply Proposition 3 stated in Section 4.2.3 so that the platform’s optimal price $p_p^E=2\alpha x^{*}$ , where $x^{*}$ is given in (22). Also, for any given $m\ge 1$ we can retrieve the platform’s optimal profit via (21) as:

$$\begin{array}{rl}{\pi }_p^E(m)& =m\cdot {\pi }_p,\text{where}\\ {\pi }_p& =\varphi \frac{\alpha }{(\alpha -1)}((x^{*}{)}^2-y^2)+(2\alpha x^{*}-2(1-\varphi )y)\\ & \times ((1-2x^{*})-\frac{1}{(\alpha -1)}(x^{*}-y)).\end{array}$$

(43)

Observe that ${\pi }_p$ is independent of the market size $m$ . Hence, by considering (43) along with the requisite promotion cost $r{a}^2\equiv r\cdot (m-1{)}^2$ to create a market of size $m$ , we can determine the platform’s optimal promotional effort $a^{*}$ (via the optimal market size $m^{*}$ ) by solving the platform’s problem:

$$\underset{m\ge 1}{max}(-r\cdot (m-1{)}^2+m\cdot {\pi }_p).$$

(44)

By noting that ${\pi }_p$ is independent of $m$ , it is easy to check that the optimal market size $m^{*}=1+{\pi }_p/2r$ .

Combining the fact that $m^{*}=1+{\pi }_p/2r$ and Corollary 3, it is easy to check that $m^{*}>{\gamma }^{*}$ if $r<{\pi }_p/2({\gamma }^{*}-1)$ . More formally, we have:

Corollary 5:

Suppose $c<\frac{(2-\varphi )(1-\varphi )}{6-4\varphi }$ . Then, if the platform’s promotion cost factor $r<\frac{{\pi }_p}{2({\gamma }^{*}-1)}$ , the platform’s entry is mutually beneficial: ${\pi }_p^E>{\pi }_p^N$ and ${\pi }_s^E>{\pi }_s^N$ .

Hence, when the spillover effect $m$ can be controlled (i.e., endogenously determined) by the platform through costly promotional effort $a$ , Corollary 5 reveals that the platform’s entry can be mutually beneficial when the promotion cost factor $r$ is sufficiently low.

7 Extension 3: When Platform and Seller Make Simultaneous Decisions

Recall from the top panel of Figure 1 in Section 3.1 that our main model and the analysis presented in Section 4 are based on the assumption that the seller sets his price $p_s^E$ “after” observing the platform’s entry price $p_p^E$ upon her entry in setting (E). We now consider an alternative scenario in which the seller and the platform set their prices simultaneously upon the platform entry in setting (E). In addition, we also consider the case when both parties choose their strategies simultaneously: the platform decides whether or not to enter. At the same time, the seller chooses whether or not to stay in the market. Essentially, these two parties engage in a $2\times 2$ simultaneous moves game, resulting in the following payoff matrix:

First, observe from the above table that the payoff $({\pi }_s^N,{\pi }_p^N)$ corresponds to the case when the platform chooses not to enter and the seller stays in the market. This case corresponds to our setting (N) in the main model so that the expressions for ${\pi }_s^N>0$ and ${\pi }_p^N>0$ are as stated in Proposition 1. Second, consider the case when the platform enters and the seller exits the market. As the platform operates as a monopoly, we can use the consumer utility function given in (6) and the fact that $V\sim U[0,1]$ to determine the platform’s monopolistic profit ${\pi }_p^M$ , where ${\pi }_p^M=\underset{p_p}{max}(p_p-c)(1-\frac{p_p}{\alpha })=\frac{(\alpha -c{)}^2}{4\alpha }>0$ . ¹² To fully specify the expressions for the payoffs in Table 2, we shall determine the payoff $({\pi }_s^E,{\pi }_p^E)$ for the case when the platform chooses to enter and the seller chooses to stay in the Section 7.1.

Table 2.

Payoff matrix of the entry game.

Platform $\mathrm{\setminus }$ Seller	Do not enter	Enter
Stay	$({\pi }_s^N,{\pi }_p^N)$	$({\pi }_s^E,{\pi }_p^E)$
Exit	$(0,0)$	$(0,{\pi }_p^M)$

Our objective is to identify the conditions under which (stay, enter) is the only Nash equilibrium, where neither firm can benefit from making a unilateral move. By comparing the payoffs associated with different pairs of strategies in Table 2, we observe that (stay, enter) is the unique Nash equilibrium when the following three requirements are satisfied: (a) ${\pi }_s^E>0$ , (b) ${\pi }_p^M>0$ , and (c) ${\pi }_p^E>{\pi }_p^N$ . Because condition (b) has already been shown to hold, it remains to find the conditions that support requirements (a) and (c).

In the remainder of section, we first determine the expressions for the payoff $({\pi }_s^E,{\pi }_p^E)$ in Section 7.1. Then we identify the conditions for requirements (a) and (c) to hold in Section 7.2.

7.1 Equilibrium Payoff Under Strategy (Stay, Enter): $({\pi }_s^E,{\pi }_p^E)$

Suppose that the platform enters while the seller stays, and suppose that both parties set their prices simultaneously. Then the seller solves: $\underset{p_s}{max}{\pi }_s^E(p_s,p_p)$ , where the seller’s profit function ${\pi }_s^E$ is given in (9). At the same time, the platform solves: $\underset{p_p}{max}{\pi }_p^E(p_s,p_p)$ , where the platform’s profit function ${\pi }_p^E$ is given in (10). We can solve for the equilibrium prices and corresponding payoffs associated with the strategy (stay, enter) by considering the first-order conditions of both problems simultaneously. The equilibrium prices and corresponding payoffs are as follows:

Proposition 8: Subgame Equilibrium Outcomes Under Strategy (Stay, Enter)

Let $\tilde{x}\equiv \frac{\alpha -1+(3-\varphi )y}{4\alpha -(1+\varphi )}$ and $y\equiv \frac{c}{2(1-\varphi )}$ . Suppose the platform enters the market and the seller stays as in Setting (E). Then the seller’s equilibrium price $p_s^E(\tilde{x})$ , demand $d_s^E(\tilde{x})$ , and profit ${\pi }_s^E(\tilde{x})$ , and the platform’s equilibrium price $p_p^E(\tilde{x})$ , demand $d_p^E(\tilde{x})$ and profit ${\pi }_p^E(\tilde{x})$ satisfy:

$$\begin{array}{rl}{p}_s^E(\tilde{x})& =\tilde{x}+y,d_s^E(\tilde{x})=m\frac{\alpha }{(\alpha -1)}(\tilde{x}-y),\end{array}$$

(45)

$$\begin{array}{rl}{\pi }_s^E(\tilde{x})& =m(1-\varphi )\frac{\alpha }{(\alpha -1)}(\tilde{x}-y{)}^2,\end{array}$$

(46)

$$\begin{array}{rl}{p}_p^E(\tilde{x})& =2\alpha \tilde{x},\end{array}$$

(47)

$$\begin{array}{rl}{d}_p^E(\tilde{x})& =m((1-2\tilde{x})-\frac{1}{(\alpha -1)}(\tilde{x}-y)),\end{array}$$

(48)

$$\begin{array}{rl}{\pi }_p^E(\tilde{x})& =m(\varphi \frac{\alpha }{(\alpha -1)}((\tilde{x}{)}^2-y^2)+(2\alpha \tilde{x}-2(1-\varphi )y)\\ & \times ((1-2\tilde{x})-\frac{1}{(\alpha -1)}(\tilde{x}-y))).\end{array}$$

(49)

Except for the auxiliary price $x^{*}$ given in Proposition 3 stated in Section 4.2.3 being changed to $\tilde{x}$ as stated in Proposition 8, it is noteworthy that all equilibrium outcomes in the simultaneous pricing case of Proposition 8 are equivalent to those presented in Section 4.2.2 for the sequential pricing case, given by Equations (18)–(21).

7.2 Conditions for Strategy (Stay, Enter) as the Unique Equilibrium

Armed with the payoff $({\pi }_s^E,{\pi }_p^E)$ given in Proposition 8, we now identify conditions for requirements (a) ${\pi }_s^E>0$ , and $(c){\pi }_p^E>{\pi }_p^N$ to hold. In preparation, we establish the following lemmas that are analogous to Lemma 1 and Corollary 1 as stated in Section 4.2.3 (for the case when pricing decisions are made sequentially). To avoid repetition, we refer the reader to Section 4.2.3 for details.

Lemma 3:

Suppose the unit cost $c<\frac{(2-\varphi )(1-\varphi )}{6-4\varphi }(<(1-\varphi ))$ . Then, under strategy (stay, enter), $\tilde{x}$ given in Proposition 8 and the platform’s equilibrium price $p_p^E(\tilde{x})$ given in (47) possess the following properties:

$\tilde{x}$ is increasing in $\alpha$ for any $\alpha >1$ .

$\frac{1}{4}>\tilde{x}>y$ for any $\alpha >1$ .

$p_p^E(\tilde{x})$ is increasing in $\alpha$ for any $\alpha >1$ , and $p_p^E(\tilde{x})>c$ .

Corollary 6:

Suppose the unit cost $c<\frac{(2-\varphi )(1-\varphi )}{6-4\varphi }$ . Then, under strategy (stay, enter), the seller’s price $p_s^E(\tilde{x})$ and demand $d_s^E(\tilde{x})$ given in (45) as well as the seller’s profit ${\pi }_s^E(\tilde{x})$ given in (46) satisfy:

$p_s^E(\tilde{x})$ is increasing in $\alpha$ ;

$0<p_s^E(\tilde{x})<p_s^N$ ; and

$d_s^E(\tilde{x})>0$ and ${\pi }_s^E(\tilde{x})>0$ .

Statement 3 of Corollary 6 shows that requirement (a) ${\pi }_s^E>0$ holds when $c<\frac{(2-\varphi )(1-\varphi )}{6-4\varphi }$ . Hence, to show that (stay, enter) is the unique equilibrium, it remains to find the conditions for the requirement (c) ${\pi }_p^E>{\pi }_p^N$ to hold. These conditions are stated in the following proposition:

Proposition 9: Unique Equilibrium

Suppose $c<\frac{(2-\varphi )(1-\varphi )}{6-4\varphi }$ and the spillover effect $m>\widetilde{{\gamma }_1}$ , where $\widetilde{{\gamma }_1}\equiv \frac{\frac{\varphi }{4}(1-(\frac{c}{1-\varphi }{)}^2)}{(\varphi \frac{\alpha }{(\alpha -1)}((\tilde{x}{)}^2-y^2)+(2\alpha \tilde{x}-2(1-\varphi )y)(1-\frac{(2\alpha -1)}{(\alpha -1)}\tilde{x}+\frac{1}{(\alpha -1)}y))}$ . Then (stay, enter) is the unique equilibrium so that requirements (a), (b), and (c) hold.

Proposition 9 resembles Proposition 4 as stated in Section 4.3.1 (for the case when decisions are made sequentially): it reveals that, if the cost $c$ is sufficiently low and when the spillover effect $m>\widetilde{{\gamma }_1}$ , then (stay, enter) is the unique equilibrium strategy for both parties when the decisions are made simultaneously. While $c<(2-\varphi )(1-\varphi )/6-4\varphi$ and the spillover effect $m>\widetilde{{\gamma }_1}$ are the conditions for (stay, enter) to sustain as the unique equilibrium, the following corollary shows that, when the spillover effect is even higher (i.e., when $m>\tilde{\gamma }(\ge \widetilde{{\gamma }_1})$ ), this unique equilibrium is also a payoff dominant equilibrium.

Corollary 7: Payoff Dominant Equilibrium Conditions

Suppose $c<\frac{(2-\varphi )(1-\varphi )}{6-4\varphi }$ and the spillover effect $m>\tilde{\gamma }$ , where $\tilde{\gamma }=max\{\widetilde{{\gamma }_1},\widetilde{{\gamma }_3}\}$ with $\widetilde{{\gamma }_3}\equiv \left(\frac{\alpha -1}{\alpha }\right){\left(\frac{\frac{1}{2}-y}{\tilde{x}-y}\right)}^2$ . Then the unique equilibrium (stay, enter) is payoff dominant: ${\pi }_p^E>{\pi }_p^N$ and ${\pi }_s^E>{\pi }_s^N$ .

Corollary 7 resembles Corollary 3 with similar conditions. Hence, we can conclude that when the unit cost is sufficiently low and when the spillover effect $m$ is sufficiently high, the platform entry can create value to both parties regardless of whether the decisions are made sequentially (as presented in Section 4) or simultaneously (as presented in Section 7). Therefore, we can conclude that our results are robust.

8 Conclusion

It is common for online E-commerce platforms to enter the market to compete with third-party sellers operating within a particular product space. Due to their informational advantage, there is a widespread belief that the platform’s market entry will always wreck havoc on the sellers.

This article seeks to examine the impact of the platform’s entry on the sellers when the platform operates as a hybrid platform. By examining the main model (in which the seller is the incumbent) and the alternative model (in which the platform is the incumbent), we identify market conditions under which both parties can benefit from an additional entry by the platform (in the main model) or the seller (in the alternative model). These market conditions are determined by factors such as the underlying unit cost, the platform’s reputation effect, and the spillover effect created by an additional entry. These market conditions provide a plausible explanation for the empirical findings obtained by Deng et al. (2023). Our results are robust in extensions when the spillover effect can be endogenously determined by the platform, and when the platform’s market entry decision and the seller’s market exit decision are made simultaneously.

Overall, our results debunk the belief that additional entry (by the platform) is always detrimental to the seller. From this vantage point, our paper contributes to the ongoing debate on whether a platform’s entry is detrimental to the sellers. Contrary to the common belief as explained in Section 1, our findings suggest that provided that certain market conditions are met, the platform can actually be a “friend” rather than a “foe” when entering the market to compete with sellers. In addition to the context of the platform’s market entry, our model could also be relevant in other settings where one firm relies on a leading firm, and this leading firm garners a commission, which provides aligned interests between these firms.

To ensure tractability, we only consider one seller in our model. Future research can extend our main model to include asymmetric competing sellers who sell similar products on the platform. Another interesting area of study is the case where the platform enters the market by developing a private label product (e.g., Amazon Basics), which would have different valuation and cost structure and lead to different reputation and spillover effects. While private label products have been examined in the context of supermarkets (e.g., Alan et al., 2019; Nasser et al., 2013; Li et al., 2022; Zheng et al., 2022), this issue in the context of E-commerce platforms remains an opportunity to be explored in the future.