The role of product and market information in an online marketplace

INTRODUCTION

The rise of the Internet has created a spurt for online marketplaces, with 97% of U.S. consumers who shop online do so in a marketplace as of 2017 (Ali, 2018). An online marketplace is a website or a mobile application where potential buyers have access to buy products offered by many different sellers. The operator of a marketplace typically operates on a consignment basis, meaning that it does not own the inventory. Rather, the operator provides a platform for sellers and buyers to list and browse products, respectively, and for the two sides to carry out secure transactions. Leading online marketplaces include Alibaba (Taobao), Amazon Marketplace, eBay, and JD.com, but there are many others such as Buy.com, Etsy, Newegg, Rakuten, Shopify, Swappa, just to name a few. To put things in perspective, half of all online sales in 2016 occurred in online marketplaces (Howland, 2017), with this number only expected to grow each year.

Typically, an online marketplace makes money by charging sellers a commission that is proportional to the total amount of the sale of a product. For example, eBay's commission is between 5% and 15% of the total sale depending on the product category while Amazon's is 8%–17%.1 As a result, revenue of an online marketplace typically increases with total sales of the platform (i.e., total dollar amount of all transactions). It is thus no surprise that sales are being used as a standard metric to measure an online marketplace's financial success. To attract sellers and buyers to visit its platform and complete transactions, an online marketplace can leverage different information structures on its platform to increase sales. We focus on informational strategies in this paper by distinguishing two types of information that can be influenced or provided by the online marketplace on its platform, namely, product information and market information.

Product information, in this paper, refers to detailed description of a product in addition to basic textual information. It can include detailed product description and technical specification illuminated by graphics and videos, as well as Q&As and customer reviews that will allow customers to better understand and evaluate the product according to their individual needs. Although some online marketplaces allow individual sellers to post product information on their own, we focus in this paper on the ones like Amazon where it is the platform that determines the amount and type of product information to be released. Without product information, the buyers may not be able to accurately infer whether the product can satisfy their individual needs, which ultimately affects the buyers' willingness‐to‐pay for the product. For example, while Amazon provides the product information (textual, graphics, videos, Q&As, and customer reviews) for the Bose QuietComfort 35 Series II Wireless Headphones to customers in the United States, Submarino.com.br (the leading online marketplace in Brazil) and Real.de (one of the top online marketplaces in Germany) provide little or no information for the same product to their customers.2

Market information, in this paper, refers to the actual demand and supply of a product in the online marketplace. This information can be obtained by the platform through real‐time data collection (i.e., tracking website visitors and product listings) and analysis (i.e., deploying machine learning algorithms). Note that the market information is not available to the sellers or the buyers unless the platform, who owns its website, chooses to disclose it. However, whether disclosing the information is a delicate decision of the platform because the sellers can use the information to better estimate the product's selling probability and optimize their individual selling prices. Consequently, the sellers in an online marketplace could alter their pricing strategies when the platform does provide the market information and that may end up hurting the platform financially.

Intriguingly, despite the unprecedented boom in the online marketplaces and the proliferation of information in contemporary life, not much research has been conducted in the existing literature on the role of product and market information in an online marketplace and the resulting decisions made by buyers and sellers that are involved. To this extent, we take an important first step in this paper to understand the following questions: (Q1) How do sellers make their optimal pricing decisions under different product‐ and market‐information structures in an online marketplace? (Q2) What are the impacts of market parameters and information structures on sales of the platform? (Q3) When should an online marketplace provide its buyers and sellers with product and/or market information on its platform?

To address these questions, we develop a stylized model to capture four different information structures of an online marketplace: (i) In the no‐information case, the platform does not provide its buyers and sellers with the product or market information; (ii) in the product‐information case, only the product information is provided; (iii) in the market‐information case, only the market information is provided; and finally, (iv) in the product‐and‐market‐information case, both the product and market information is provided. Furthermore, the number of buyers and sellers who join the platform are randomly determined from a buyers' pool and a sellers' pool (consisting of potential buyers and sellers in the market), respectively. The sellers make pricing decisions for their products by considering not only buyers' product valuations but also other sellers' strategies, necessitating an equilibrium analysis. While the market information directly changes sellers' pricing decisions in equilibrium, the product information directly changes buyers' product valuations and, therefore, indirectly affects the equilibrium pricing strategies of the sellers and the ultimate sales of the platform.

We analytically identify the Pareto‐dominant equilibrium for the sellers' pricing decisions under all of the different information structures (i.e., no information, product information, market information, and product‐and‐market information). We find that sales of the platform increase with the size of potential buyers but exhibit a nonmonotonic pattern with the increase in the size of potential sellers. This is because increasing the number of sellers in the market, at first, increases the product availability, which raises the expected sales volume and sales. Yet, eventually, when the number of sellers outnumbers that of buyers by so much, the competition among the sellers will drive down the listing prices and hurt the expected sales. This finding contradicts the conventional wisdom that more traffic attracted to an online marketplace is always more beneficial for the platform operator and suggests that there is a “sweet spot” for online marketplaces in terms of the number of sellers.

By comparing expected sales under the different information structures, we establish the platform's optimal information strategy, which is proven to depend on specific market conditions. In particular, providing market information to sellers always benefits the platform, as it allows sellers to make informed pricing decisions based on the realized market condition. However, providing the product information could backfire. Specifically, the provision of product information widens the spread/variation of consumers' valuations, which increases the number of high‐valuation buyers. Hence, in a seller's market (i.e., high ratio of potential buyers to sellers), increasing the number of high‐valuation buyers encourages more sales at higher prices, boosting the overall sales. By contrast, in a buyer's market (i.e., low ratio of potential buyers to sellers), concealing the product information drives up the overall sales as it reduces the number of low‐valuation buyers allowing sellers to strike better deals with buyers at higher prices. In sum, we conclude that it is optimal for the platform to provide both the product and market information in a seller's market and only the market information in a buyer's market.

The remainder of the paper is organized as follows. Section 2 reviews the related literature. Section 3 introduces our model framework. Section 4 sets up the no‐information case as a benchmark and derives the platform's performance metrics. Section 5 studies three informational cases. Section 6 identifies the optimal information strategy for the platform. Section 7 considers several extensions to establish robustness of our results. And finally, Section 8 concludes the paper. All the technical details and proofs are relegated to the Supporting Information of the paper.

LITERATURE REVIEW

First and foremost, our research is related to the literature on information control strategy, and we study two types of information in this paper, namely, product information and market information.

Provision of the product information can influence buyers' product valuations. Lewis & Sappington (1991, 1994) extended the principal–agent model to study the incentives of a seller to release product information to potential buyers, concluding that the optimal product‐information decision for the seller is an all‐or‐nothing strategy: Either release all of the product information or do not release any. Johnson & Myatt (2006) further justified the all‐or‐nothing product‐information revelation strategy by a U‐shaped function of dispersion for buyers' valuations. In contrast to static models in which the seller and buyers interact only once (as in Lewis & Sappington, 1991, 1994, and Johnson & Myatt, 2006), Chu & Zhang (2011) developed a dynamic two‐period model to study the joint impact of the optimal product‐information strategy and the optimal pricing strategy under a preorder setting, and found that the seller should release some product information or none, but should never release full information. Boleslavsky et al. (2017) investigated the influence of using offline product demonstration methods, such as in‐store interaction and public exhibition, to signal product information to consumers and found that revealing product information via demonstrations helps alleviate price competition and support high prices. Yet, both Chu & Zhang (2011) and Boleslavsky et al. (2017) considered the product‐information revelation from the seller's/manufacturer's perspective. In contrast, in our paper, we consider an online marketplace's optimal product (and market) information revelation strategy. Hence, different from the above‐mentioned papers, the information in our case is possessed by a third‐party online market operator as opposed to a seller.

On the other side, provision of the market information can directly influence sellers' decisions. Research related to the market information in the operations management literature typically targets the demand‐side market information (i.e., the market information regarding the number of end customers). Information sharing decisions are then studied under vertical supply chain settings, where the downstream firm has the demand information and could potentially release it to the upstream firm. There is an extensive literature on assessing the value of demand information (see, e.g., Cachon & Fisher, 2000; Gavirneni et al., 1999; Lee et al., 2000; Li & Zhang, 2013; Zhao & Simchi‐Levi, 2002), and various mechanisms have been proposed to encourage downstream firms to truthfully reveal and share demand information (e.g., Cachon & Lariviere, 2001; Özer & Wei, 2006). Our research considers the market‐information sharing strategy for online platform. In this line of research, Liu et al. (2021) studied how market demand information influences the quantity decision of sellers and whether the platform has an incentive to share the market demand information to sellers. Li et al. (2021) (resp., Zha et al., 2022) investigated whether an online platform is willing to share demand information with an upstream manufacturer and a reseller (resp., sellers). Ha et al. (2022) considered whether a platform should share information with a manufacturer who decides whether to sell through an agency channel at the platform in addition to an existing reselling channel. Different from these papers, the platform considered in our paper faces a two‐sided market and possesses both demand‐side and supply‐side market information, and may rely on revelation of the information afterwards to influence the product listing prices in the marketplace. Most recently, Bimpikis and Mantegazza (2022) also studied the platform's demand information disclosure strategy in a two‐sided market but the platform determines and announces the policy before it observes demand signal.

Next, our research is also broadly related to the literature of online marketplaces and two‐sided market. The platform can provide information to participating buyers and sellers to facilitate the exchange of products, creating economic value for buyers, sellers, and society at large (Bakos, 1991). In particular, the role and influential factors of a platform (such as market size, prices, commission model, product design) has been an active research topic in the economics, operations, and information system literatures (see, e.g., Chen et al., 2016, 2020; Cui et al., 2019; Hagiu, 2009; Hu & Zhou, 2019; Jiang et al., 2011; Lai et al., 2022; Li & Netessine, 2020; Parker & Van Alstyne, 2005; Tadelis, 2016; Tian et al., 2018).

There is also an increasing interest in studying the influence of a marketplace under various supply chain strategies (see Grieger, 2003, and Wang et al., 2008, for detailed reviews). For example, Ryan et al. (2012) considered a single retailer contemplating selling through a new marketplace channel, in addition to a traditional direct channel. The retailer either pays a flat monthly fee or proportional commission to the platform in the dual‐channel setting, and the authors characterized the optimal pricing decisions for both the retailer and the platform. Jiang et al. (2017) considered a retailer who orders products from a manufacturer and sells to customers through an online marketplace platform where the customers can then resell products later on. Different from these works, our paper focuses on a platform's information revelation strategies.

Finally, another stream of the existing literature explores the determination of prices in marketplaces (see, e.g., Birge et al., 2021; Campbell et al., 2005; Kuruzovich et al., 2010) and the design of efficient trading mechanisms to match buyers and sellers (see, e.g., Chen & Hu, 2020; Chu & Shen, 2006; Wilson, 1985). In particular, McAfee (1992) examined the efficiency of the double auction mechanism among buyers and sellers, and Su (2010) proposed a matching mechanism in an online marketplace, which can be interpreted as a posted‐price mechanism with efficient rationing and retains similar matching outcome as the double auction. The matching mechanism of the online marketplace adopted in our paper directly follows this stream of research. We also contribute to the literature by the underlying technical analysis that identifies the Pareto‐dominant equilibrium of the sellers' pricing decisions under various informational structures. To the best of our knowledge, this is the first time an equilibrium for the sellers' pricing game is fully characterized in a two‐sided market with multiple buyers and sellers due to the complex nature of the problem (Chen et al., 2016, p. 591).

MODEL FRAMEWORK

We consider an online marketplace (hereafter referred to as the “platform”). The platform orchestrates a two‐sided market where a number of sellers try to sell the same new product to a number of buyers. For simplicity, we assume that each seller has one unit of the product in stock, and each buyer is interested in one unit of the product. Sellers and buyers make fully rational pricing and purchasing decisions, respectively, in order to maximize their individual utilities. The platform on the other hand can influence the decisions of both sides by providing (or not providing) product and/or market information. Details on the information structure will be given shortly.

The number of sellers to join the platform is described by a random variable

D s $D_s$

D s ∼ U [ 0 , s ] $D_s\sim U[0,s]$

v s $v_s$

v s $v_s$

v s $v_s$

F s ( · ) $F_s(\cdot )$

Formally, consider an arbitrary seller with reservation value

v s $v_s$

max p { p · P ( p ) } subject to p ≥ v s , $$\begin{equation} \max _p\lbrace p\cdot P(p)\rbrace \text{ subject to } p\ge v_s, \end{equation}$$

1

P ( p ) $P(p)$

P ( p ) $P(p)$

P ( p ) $P(p)$

OPEN IN VIEWER

TABLE 1

Notations.

Symbol	Description
D s ∼ U [ 0 , s ] $D_s\sim U[0,s]$	Random number of sellers where s is the size of potential sellers
p	Product listing price
v s $v_s$	Sellers' reservation value with cumulative distribution function (CDF) F s ( · ) $F_s(\cdot )$
P ( p ) $P(p)$	Probability of successfully selling the product at price p
F ∼ s ( · ) , f ∼ s ( · ) $\tilde{F}_s(\cdot ),\ \tilde{f}_s(\cdot )$	CDF and probability density function (PDF) of the sellers' equilibrium listing price distribution
I M ∈ { 0 , 1 } $I_M\in \lbrace 0,1\rbrace$	Whether market information is provided by the platform
D b ∼ U [ 0 , b ] $D_b\sim U[0,b]$	Random number of buyers where b is the size of potential buyers
v b $v_b$	Buyers' valuation for the product with CDF F b ( · ) $F_b(\cdot )$
p m a x ( d b , d s ) $p_{max}(d_b,d_s)$	Highest or maximum transaction price given market size realizations d b , d s $d_b,d_s$
I P ∈ { 0 , 1 } $I_P\in \lbrace 0,1\rbrace$	Whether product information is provided by the platform
T	Expected sales
Q	Expected sales volume
Model N $\mathcal {N}$	No‐information model, i.e., I P = 0 $I_P=0$ and I M = 0 $I_M=0$
Model P $\mathcal {P}$	Product‐information(‐only) model, i.e., I P = 1 $I_P=1$ and I M = 0 $I_M=0$
Model M $\mathcal {M}$	Market‐information(‐only) model, i.e., I P = 0 $I_P=0$ and I M = 1 $I_M=1$
Model B $\mathcal {B}$	(Both‐)product‐and‐market‐information model, i.e., I P = 1 $I_P=1$ and I M = 1 $I_M=1$

For the demand side, the number of buyers that will join the platform is determined by a random variable

D b ∼ U [ 0 , b ] $D_b\sim U[0,b]$

, where b is referred to as the size of potential buyers. Buyers are heterogeneous in their valuations

v b $v_b$

for the product. As there are multiple buyers and sellers in the marketplace, we follow the matching mechanism developed in Su (2010) to determine the outcome of the transactions: The product offered with the lowest price p (with ties broken randomly) will be acquired by the buyer with the highest valuation

v b $v_b$

(with ties broken randomly) as long as

p ≤ v b $p\le v_b$

, and then the second lowest priced unit will be acquired by the buyer who has the second‐highest valuation, and so on and so forth, until there are no more available products, or no more available buyers, or the prices of the remaining products are all higher than product valuations by the remaining buyers.3 The rationale of this matching mechanism lies in the principle that the higher valuation buyers are typically more self‐motivated to purchase the product, so they are more likely to arrive earlier in the market and/or insert more efforts to search for the product, which typically leads to a better price deal.

Next, we describe the platform, which can provide or withhold two different types of information on its website, namely, the (detailed) product information and the market information.

Product information refers to detailed product descriptions and technical specification, Q&As about the product, and consumer reviews, all of which can facilitate the decision‐making process of the buyers. We use the indicator parameter

I P ∈ { 1 , 0 } $I_P\in \lbrace 1, 0\rbrace$

to denote whether the product information is provided by the platform.4 When buyers are better informed of the product, they will form more accurate individual valuations of the product, that is, the provision of product information to the buyers leads to a larger spread of product valuations among them (Chu & Zhang, 2011). In particular, when

I P = 1 $I_P=1$

, through the detailed product information provided, the buyers can deduce their exact valuations of the product, and we set

v b ∼ U [ 0 , 1 ] $v_b\sim U[0,1]$

to model the buyers' differing valuation preferences of the product.5 In contrast, if the detailed product information is not provided by the platform, that is,

I P = 0 $I_P=0$

, the buyers cannot accurately assess whether the product will fulfill their individual needs. As a result, we assume for simplicity that all the buyers will evaluate the product at the expected value of all possible valuations, that is,

v b ≡ E ( U [ 0 , 1 ] ) = 1 2 $v_b\equiv \mathbb {E}(U[0,1])=\frac{1}{2}$

for all buyers.6 We denote the CDF of buyers' product valuation distribution, regardless of its exact distribution (whether

v b ∼ U [ 0 , 1 ] $v_b\sim U[0,1]$

or

v b ≡ 1 2 $v_b\equiv \frac{1}{2}$

), as

F b ( · ) $F_b(\cdot )$

.

Thanks to the development of data collection methods such as the visitor tracking technology, the platform is able to observe how many sellers and buyers are in the market, that is, the realized market sizes of

D s $D_s$

and

D b $D_b$

, which will be denoted by

d s $d_s$

and

d b $d_b$

, respectively, and referred to collectively as the market information. Provision of the market information will have an impact on the sellers' pricing decisions, because the sellers are optimizing their strategies by taking into account the selling probability function

P ( · ) $P(\cdot )$

, see (1), and

P ( · ) $P(\cdot )$

depends on the platform's information structure. We will use the indicator parameter

I M ∈ { 1 , 0 } $I_M\in \lbrace 1, 0\rbrace$

to denote whether the platform reveals the market information to the sellers (and buyers). In particular, if

I M = 1 $I_M=1$

, the sellers possess the information of the values of

d s $d_s$

and

d b $d_b$

when calculating

P ( · ) $P(\cdot )$

and pricing their products accordingly. By contrast, if

I M = 0 $I_M=0$

, then what the sellers know is only the distributional information, that is, they only know

D s $D_s$

(resp.,

D b $D_b$

) is uniformly distributed between 0 and s (resp., between 0 and b).

While each seller acts to maximize their expected revenue, so does the platform in our model. We assume the platform charges a commission that is a percentage of the transaction amount (Geng et al., 2018; Jiang et al., 2011; Ryan et al., 2012; Tian et al., 2018). Hence, the platform's total commission/revenue increases proportionally with the total transaction value (i.e., total sales). The commission rates are typically exogenously determined by the industry tradition (Liu et al., 2021), so we consider predetermined commission rates in our model. It is clear that for any predetermined commission rate, the platform can maximize revenue by maximizing sales. Therefore, we assume that the platform's goal is to equivalently maximize sales for the rest of the paper.

We now describe the sequence of events for our model, which is also summarized in Figure 1. First, the online marketplace determines whether it should provide product information and/or market information on its platform. Based on the availability of the product information, buyers form their valuations for the product (

v b $v_b$

). Then, random numbers of sellers and buyers (

d s $d_s$

and

d b $d_b$

) are realized. Next, the sellers make pricing decisions based on

v b $v_b$

and the availability of the market information, subject to their individual reservation value (

v s $v_s$

). In particular, all sellers can see if product information is being offered by the platform to the buyers, so the sellers can infer whether

v b ∼ U [ 0 , 1 ] $v_b\sim U[0,1]$

or

v b ≡ 1 2 $v_b\equiv \frac{1}{2}$

. Each seller makes a rational and optimal pricing decision by taking into account the other sellers' strategies. We model such competitive interaction among the sellers using the Nash equilibrium concept and refer to it as the sellers' game. The CDF of the sellers' listing price distribution in equilibrium is of our interest and will be denoted as

F ∼ s ( · ) $\tilde{F}_s(\cdot )$

. Finally, matchings/sales occur between the buyers and sellers based on the mechanism described earlier.

OPEN IN VIEWER

FIGURE 1

Sequence of events.

In what follows, we present four models to study the role of product and/or market information. Specifically, Section 4 focuses on the no‐information model as a benchmark, that is,

I P = 0 $I_P=0$

and

I M = 0 $I_M=0$

, and Section 5 examines the other three (informational) models where

I P = 1 $I_P=1$

or/and

I M = 1 $I_M=1$

.

NO‐INFORMATION MODEL

We first consider the no‐information model, or Model

N $\mathcal {N}$

, that is, when

I P = 0 $I_P=0$

and

I M = 0 $I_M=0$

. Recall that when the platform does not provide the product information, the buyers cannot accurately assess their individual utility of the product. Hence, they evaluate the product at its expected value, that is,

v b ≡ E ( U [ 0 , 1 ] ) = 1 2 $v_b\equiv \mathbb {E}(U[0,1])=\frac{1}{2}$

. On the other hand, without the market information, sellers only know the distributional information of

D b $D_b$

and

D s $D_s$

, but not the realized market size

d b $d_b$

and

d s $d_s$

. The goal of this section is to characterize the equilibrium for the sellers' pricing game, identify the matchings/transactions between the buyers and the sellers, and evaluate the corresponding performance metrics, all under the no‐information setting. First, we proceed to characterize the sellers' pricing decisions in equilibrium.

Let

F ∼ s N ( · ) $\tilde{F}_s^{\mathcal {N}}(\cdot )$

denote the CDF of the equilibrium listing price distribution of the sellers in Model

N $\mathcal {N}$

(we use the superscript

N $\mathcal {N}$

to denote quantities under the no‐information setting). The selling probability function can be expressed as follows:

2

where

1 { · } $\mathbb {1}\lbrace \cdot \rbrace$

is the standard indicator function. Because

v b ≡ 1 2 $v_b\equiv \frac{1}{2}$

, no buyer is willing to acquire the product for a price higher than

1 2 $\frac{1}{2}$

, thus the selling probability is zero when

p > 1 2 $p>\frac{1}{2}$

, which is reflected by the second line of Equation (2). If the listing price p is equal to or below

1 2 $\frac{1}{2}$

, then whether a unit gets sold or not depends on how many buyers and sellers join the platform. Based on the matching mechanism described earlier, a unit will be sold at a price

p ≤ 1 2 $p\le \frac{1}{2}$

if the number of buyers exceed the number of sellers who list the product for p or less, that is,

d b ≥ d s · F ∼ s N ( p ) $d_b\ge d_s\cdot \tilde{F}_s^{\mathcal {N}}(p)$

. Because the realizations of

D b $D_b$

and

D s $D_s$

are unknown to the sellers in the no‐information model, the selling probability

P N ( p ) $P^{\mathcal {N}}(p)$

is given by the expected value of the corresponding indication function over

D b $D_b$

and

D s $D_s$

, hence the first line in Equation (2). Note that in our model, we ignore the impact of shipping cost and speed on customers' purchasing decisions by implicitly assuming that each seller offers the same menu on shipping methods and costs determined by the platform (USPS first‐class service, priority service, UPS/Fedex ground service, overnight service, etc.) and that buyers can self‐select the service they want. Such practice is applicable to platforms such as Amazon Marketplace.

Recall from (1) that any individual seller with reservation price

v s $v_s$

rationally chooses a price p to maximize her expected revenue

p · P N ( p ) $p\cdot P^{\mathcal {N}}(p)$

subject to

p ≥ v s $p\ge v_s$

. Thus, the selling probability function

P N ( · ) $P^{\mathcal {N}}(\cdot )$

, given by (2), influences individual sellers' pricing decisions. In the meantime, the pricing decisions of all of the sellers, characterized by CDF

F ∼ s N ( · ) $\tilde{F}_s^{\mathcal {N}}(\cdot )$

, in turn determine the selling probability function

P N ( · ) $P^{\mathcal {N}}(\cdot )$

. This necessitates an equilibrium analysis. An equilibrium of the sellers' game is reached when no individual seller can improve her expected revenue by unilaterally changing her listing price, that is, in equilibrium, Equations (1) and (2) must hold simultaneously.

Note that in Model

N $\mathcal {N}$

, the pricing decisions of the sellers whose reservation value

v s > 1 2 $v_s>\frac{1}{2}$

are irrelevant—because they are not willing to sell the product for a price of

1 2 $\frac{1}{2}$

or less and the buyers are not willing to pay for anything more than

1 2 $\frac{1}{2}$

, leading to no successful transactions. Without loss of generality (WLOG), we assume that these sellers will list and price their products at their reservation values. There may exist a continuum of equilibria for the sellers' game (see the proof of Theorems 1 and 2), and in the following theorem, we capture the unique equilibrium that maximizes the sum of all sellers' expected revenues, defined as the Pareto‐dominant equilibrium.7 Theorem 1

When

b ≤ s 2 $b\le \frac{s}{2}$

, the sellers' listing price distribution and the selling probability function of the unique Pareto‐dominant equilibrium are given as follows:

When

b ≥ s 2 $b\ge \frac{s}{2}$

, they are given as follows:

There are a few important observations from the above theorem that we will now detail. An illustration of the results is provided in Figure 2.

OPEN IN VIEWER

FIGURE 2

Illustration of

F ∼ s N ( p ) $\tilde{F}_s^{\mathcal {N}}(p)$

,

P N ( p ) $P^{\mathcal {N}}(p)$

, and

p · P N ( p ) $p\cdot P^{\mathcal {N}}(p)$

as functions of p in panels (a), (b), and (c), respectively. Note: In each panel, we plot three functions/market conditions based on

b = 1 $b=1$

and

s ∈ { 1 , 2 , 3 } $s\in \lbrace 1,2,3\rbrace$

.

First, there exists a threshold

v s ̲ ( = b 2 s $\underline{v_s}(=\frac{b}{2s}$

or

1 2 − s 8 b ) $\frac{1}{2}-\frac{s}{8b})$

in both the

b ≤ s 2 $b\le \frac{s}{2}$

case and the

b ≥ s 2 $b\ge \frac{s}{2}$

case such that sellers with reservation values less than

v s ̲ $\underline{v_s}$

impose a strictly higher listing price (i.e., no less than

v s ̲ $\underline{v_s}$

) in equilibrium to achieve revenue maximization. In Figure 2a,

v s ̲ $\underline{v_s}$

corresponds to the largest p such that

F ∼ s N ( p ) = 0 $\tilde{F}^{\mathcal {N}}_s(p)=0$

. Note that

P N ( p ) = 1 $P^{\mathcal {N}}(p)=1$

for all

p ≤ v s ̲ $p\le \underline{v_s}$

meaning that in equilibrium any product offered at price

v s ̲ $\underline{v_s}$

or below will surely get sold to a buyer. However, no seller, even if their reservation value is sufficiently low, has an incentive to lower the listing price to

v s ̲ − ε 1 $\underline{v_s}-\epsilon _1$

where

0 < ε 1 ≤ v s ̲ $0<\epsilon _1\le \underline{v_s}$

, because the expected revenue at

v s ̲ − ε 1 $\underline{v_s}-\epsilon _1$

(i.e.,

( v s ̲ − ε 1 ) · P N ( v s ̲ − ε 1 ) = v s ̲ − ε 1 $(\underline{v_s}-\epsilon _1)\cdot P^{\mathcal {N}}(\underline{v_s}-\epsilon _1)=\underline{v_s}-\epsilon _1$

), is strictly dominated by the expected revenue at

v s ̲ $\underline{v_s}$

(i.e.,

v s ̲ · P N ( v s ̲ ) = v s ̲ $\underline{v_s}\cdot P^{\mathcal {N}}(\underline{v_s})=\underline{v_s}$

). In addition, there exists a second threshold

v s ¯ ( = 1 2 $\overline{v_s}(=\frac{1}{2}$

in Model

N $\mathcal {N}$

) such that all sellers with a reservation value

v s ≤ v s ¯ $v_s\le \overline{v_s}$

list the product for a price no higher than

v s ¯ $\overline{v_s}$

. This implies that any seller with a reservation value

v s ≤ v s ¯ $v_s\le \overline{v_s}$

cannot improve her expected revenue by unilaterally choosing a price

v s ¯ + ε 2 $\overline{v_s}+\epsilon _2$

for

0 < ε 2 ≤ 1 − v s ¯ $0<\epsilon _2\le 1-\overline{v_s}$

, that is,

( v s ¯ + ε 2 ) · P N ( v s ¯ + ε 2 ) ≤ v s ¯ · P N ( v s ¯ ) $(\overline{v_s}+\epsilon _2)\cdot P^{\mathcal {N}}(\overline{v_s}+\epsilon _2)\le \overline{v_s}\cdot P^{\mathcal {N}}(\overline{v_s})$

. In particular, for Model

N $\mathcal {N}$

, because

P N ( v s ¯ + ε 2 ) = 0 $P^{\mathcal {N}}(\overline{v_s}+\epsilon _2)=0$

for

0 < ε 2 ≤ 1 − v s ¯ $0<\epsilon _2\le 1-\overline{v_s}$

, we have

( v s ¯ + ε 2 ) · P N ( v s ¯ + ε 2 ) = 0 $(\overline{v_s}+\epsilon _2)\cdot P^{\mathcal {N}}(\overline{v_s}+\epsilon _2)=0$

, that is, a seller's expected revenue for a product is zero when it is listed for anything more than

1 2 $\frac{1}{2}$

, which is the maximum price that the buyers are willing to pay for the product.

Second, we observe that the selling probability function

P N ( p ) $P^{\mathcal {N}}(p)$

, although discontinuous at

p = 1 2 $p=\frac{1}{2}$

(because anything more expensive than

1 2 $\frac{1}{2}$

has a zero selling probability), is nonincreasing in price; see Figure 2b. This is intuitive as a higher listing price for the (same) product corresponds to a lower selling probability. However, the expected revenue,

p · P N ( p ) $p\cdot P^{\mathcal {N}}(p)$

, as a function of p exhibits the shape of almost a trapezoid (with the right leg truncated), see Figure 2c, because p increases while

P N ( p ) $P^{\mathcal {N}}(p)$

weakly decreases in p. The highest expected revenue occurs at the top base of the trapezoid in Figure 2c, which coincides with the interval

[ v s ̲ , v s ¯ ] $[\underline{v_s}, \overline{v_s}]$

of sellers' pricing decisions.

Third, recall that b and s capture the sizes of potential buyers and sellers, respectively. As the number of buyers and sellers at the platform are determined by

D b ∼ U [ 0 , b ] $D_b\sim U[0,b]$

and

D s ∼ U [ 0 , s ] $D_s\sim U[0,s]$

, we can use b and s to mirror the relationship between supply and demand. When

b ≤ s 2 $b\le \frac{s}{2}$

, because supply far exceeds demand, the sellers have no choice but to list their products at lower prices relative to the other case when

b ≥ s 2 $b\ge \frac{s}{2}$

(see Figure 2a where

F ∼ s N ( · ) $\tilde{F}_s^{\mathcal {N}}(\cdot )$

for the

b ≤ s 2 $b\le \frac{s}{2}$

case is stochastically dominated by that for the

b ≥ s 2 $b\ge \frac{s}{2}$

case). This is due to a fierce competition among the sellers. By contrast, when

b ≥ s 2 $b\ge \frac{s}{2}$

, because there is relatively more demand, the sellers are able to list their products for higher prices, and a portion of the sellers even charge a price that is equivalent to the willingness‐to‐pay of the buyers (i.e.,

1 2 $\frac{1}{2}$

). These results can further generalize to the following Corollary 1 on the usual stochastic order of

F ∼ s N ( · ) $\tilde{F}_s^{\mathcal {N}}(\cdot )$

in b and s. Correspondingly, the selling probability function

P N ( · ) $P^{\mathcal {N}}(\cdot )$

increases from the case

b ≤ s 2 $b\le \frac{s}{2}$

to the case

b ≥ s 2 $b\ge \frac{s}{2}$

, see Figure 2b, and so does the expected revenue for the sellers (whose

v s ≤ v s ¯ $v_s\le \overline{v_s}$

), see Figure 2c. All of these are driven by the market forces governed by supply and demand, that is, b and s. Corollary 1

Equilibrium listing prices (stochastically) increase in b and decrease in s, that is,

P r ( p > x ) = 1 − F ∼ s N ( x ) $Pr(p>x)=1-\tilde{F}_s^{\mathcal {N}}(x)$

weakly increases in b and decreases in s for all

x ∈ [ 0 , 1 ] $x\in [0,1]$

.

Finally, we point out that the proof of Theorem 1 is by no means straightforward and the explicit characterization of the Pareto‐dominant equilibrium for the sellers' pricing game is one of the major theoretical contributions of our paper. The complete proof of Theorem 1 and other proofs are contained in the Supporting Information of the paper (see EC.1).

Performance metrics

In this subsection, we derive performance metrics of the platform. While we focus on total sales (i.e., the total dollar amount of all transactions) in the paper, we also provide the derivation of sales volume (i.e., the total number of transactions), which will help explain some properties of the sales in Proposition 1.

In equilibrium, the sellers list their products according to prices determined by

F ∼ s N ( · ) $\tilde{F}^{\mathcal {N}}_s(\cdot )$

, and the transactions between the sellers and the buyers occur in the increasing order of the listing prices (from the lowest listing price to the highest). Let us denote

p m a x N ( d b , d s ) $p^{\mathcal {N}}_{max}(d_b,d_s)$

as the maximum transaction price given

d b $d_b$

and

d s $d_s$

, ithat is, the highest listing price at which a successful transaction occurs. For notational convenience, we write

p m a x ( · ) ( d b , d s ) $p^{(\cdot )}_{max}(d_b,d_s)$

simply as

p m a x ( · ) $p^{(\cdot )}_{max}$

in the remaining paper when doing so is not causing confusion. Under the no‐information setting, two scenarios need to be discussed: (i) If buyers are outnumbered by sellers whose listing price is no higher than the buyers' product valuation

1 2 $\frac{1}{2}$

(i.e., if

d b ≤ d s · F ∼ s N ( 1 2 ) $d_b\le d_s\cdot \tilde{F}^{\mathcal {N}}_s(\frac{1}{2})$

), then

p m a x N ( ≤ 1 2 ) $p_{max}^{\mathcal {N}}(\le \frac{1}{2})$

can be determined uniquely by solving

d b = d s · F ∼ s N ( p m a x N ) $d_b= d_s\cdot \tilde{F}^{\mathcal {N}}_s(p_{max}^{\mathcal {N}})$

; (ii) otherwise (i.e., if

d b ≥ d s · F ∼ s N ( 1 2 ) $d_b\ge d_s\cdot \tilde{F}^{\mathcal {N}}_s(\frac{1}{2})$

), there are sufficient buyers to acquire all products that are listed for

1 2 $\frac{1}{2}$

or below, and hence

p m a x N = 1 2 $p_{max}^{\mathcal {N}}=\frac{1}{2}$

.

From Theorem 1, it can be verified that

F ∼ s N ( · ) $\tilde{F}_s^{\mathcal {N}}(\cdot )$

is differentiable everywhere except at

v s ̲ $\underline{v_s}$

and

v s ¯ $\overline{v_s}$

. Let

f ∼ s N ( · ) $\tilde{f}_s^{\mathcal {N}}(\cdot )$

denote the corresponding probability density function (PDF). Then, the expected sales volume in equilibrium, denoted by Q, is given by

And the expected sales in equilibrium, denoted by T, can be characterized by

In the next result, we establish the impact of the sizes of the potential buyers (b) and potential sellers (s) on

Q N $Q^{\mathcal {N}}$

and

T N $T^{\mathcal {N}}$

. Proposition 1

Under the no‐information model, (i)

the expected sales volume

Q N $Q^{\mathcal {N}}$

increases in b and s;

(ii)

the expected sales

T N $T^{\mathcal {N}}$

increase in b and are unimodal in s.

Proposition 1(i) is in line with expectations, because when there is either more demand or more supply to the platform, which is a two‐sided market, more transactions will occur leading to a higher sales volume.

The more interesting result is Proposition 1(ii), which states that sales are monotonic in the size of potential buyers but not in the size of potential sellers. Intuitively, when there are more buyers in the market (i.e., an increased b), equilibrium prices (Corollary 1) as well as the sales volume go up (Proposition 1(i)), thus higher sales are expected as sales can be viewed roughly as the multiplication of price and sales volume. Yet, when there are more sellers in the market (i.e., an increased s), there are two competing forces, which now affect the sales. On the one hand, equilibrium prices go down (Corollary 1) due to increased competition among the sellers, and on the other hand, sales volume picks up (Proposition 1(i)). These two opposing effects lead to the nonmonotonic behavior of the sales with respect to the size of potential sellers s, which first increases then decreases. It may also be helpful to think of the limiting cases: When

s → 0 $s\rightarrow 0$

, there are no sellers in the platform so no sales would occur. And when

s → ∞ $s\rightarrow \infty$

, excessive sellers drive the listing/sales prices down toward zero, again yielding near‐zero total sales for the platform despite a significant sales volume.

The important managerial implication here is that while attracting more buyers is always ideal for a sales‐maximizing platform, the number of sellers has a “sweet spot.” Having more sellers is good at first because it can help boost sales by increasing the transaction volume, but eventually when the sellers greatly outnumber the buyers, the competition among the sellers will drive down prices despite driving up sales volume and start to negatively impact the sales of the platform. This is an important message for platform operators because it suggests at some point they may need to restrict the number of sellers, which runs counter to the conventional wisdom that more traffic in an online marketplace is always better for the platform. This also suggests that the platform operators should wisely allocate their resources to attract buyers and (the right number of) sellers.

INFORMATIONAL MODELS

In this section, we will investigate how product information and/or market information influence the sellers' pricing decisions in equilibrium. To this end, we will propose and analyze three informational models (when

I P = 1 $I_P=1$

or/and

I M = 1 $I_M=1$

): the production‐information model in Section 5.1, the market‐information model in Section 5.2, and the product‐and‐market‐information model in Section 5.3.

Product‐information model

We start with the product‐information(‐only) model, or Model

P $\mathcal {P}$

, where the platform provides the product information but not the market information (i.e.,

I P = 1 $I_P=1$

and

I M = 0 $I_M=0$

). Specifically, with the product information being provided, the buyers are able to accurately assess the product and formulate an individual‐specific product valuation. Therefore, different from Model

N $\mathcal {N}$

in Section 4 where all buyers evaluated the product with the expected value

1 2 $\frac{1}{2}$

, the buyers under Model

P $\mathcal {P}$

exhibit heterogeneous product valuations, ranging uniformly from 0 to 1.

Let

F ∼ s P ( · ) $\tilde{F}_s^{\mathcal {P}}(\cdot )$

denote the CDF of the equilibrium listing price distribution of the sellers in Model

P $\mathcal {P}$

(superscript

P $\mathcal {P}$

represents the product‐information setting). The selling probability function, given earlier in (2) for Model

N $\mathcal {N}$

, needs to be updated to the following general expression for Model

P $\mathcal {P}$

:

P P ( p ) = ̇ E D s , D b 1 D b ( 1 − F b ( p ) ) ≥ D s · F ∼ s P ( p ) . $$\begin{equation} P^{\mathcal {P}}(p)\ \dot{=}\ \mathop {\mathbb {E}}\limits _{D_s,D_b}{\left[\mathbb {1}{\left\lbrace D_b(1-F_b(p))\ge D_s\cdot \tilde{F}_s^{\mathcal {P}}(p) \right\rbrace} \right]}. \end{equation}$$

3

Equation (3) reflects the notion that a product at price p gets sold, upon the realization of

D b = d b $D_b=d_b$

and

D s = d s $D_s=d_s$

, if and only if the number of buyers whose valuation for the product exceeds p is greater than or equal to the number of sellers who list the product for p or less, that is,

d b ( 1 − F b ( p ) ) ≥ d s · F ∼ s P ( p ) $d_b(1-F_b(p))\ge d_s\cdot \tilde{F}_s^{\mathcal {P}}(p)$

.

Following similar techniques used in the proof of Theorem 1, we can obtain the equilibrium listing price distribution and the corresponding selling probability function for Model

P $\mathcal {P}$

. Theorem 2

Under Model

P $\mathcal {P}$

, the sellers' listing price distribution and the selling probability function of the unique Pareto‐dominant equilibrium, which maximizes the aggregate expected revenue for all sellers, are given as follows:

and

The results of Theorem 2 are illustrated in Figure 3. Similar to Model

N $\mathcal {N}$

, we observe that the sellers charge higher prices in equilibrium when the size of potential buyers (b) increases or the size of potential sellers (s) decreases; see Figure 3a. This result is formalized as in the following remark. Note that any remark in the paper states a proven result that is exactly analogous to an earlier result.8 Remark 1

Corollary 1 is preserved under Model

P $\mathcal {P}$

, that is, equilibrium listing prices under Model

P $\mathcal {P}$

(stochastically) increase in b and decrease in s.

OPEN IN VIEWER

FIGURE 3

Illustration of

F ∼ s P ( p ) $\tilde{F}_s^{\mathcal {P}}(p)$

,

P P ( p ) $P^{\mathcal {P}}(p)$

, and

p · P P ( p ) $p\cdot P^{\mathcal {P}}(p)$

as functions of p in panels (a), (b), and (c), respectively. Note. In each panel, we plot three functions/market conditions based on

b = 1 $b=1$

and

s ∈ { 1 , 2 , 3 } $s\in \lbrace 1,2,3\rbrace$

.

On the other hand, the selling probability function

P P ( p ) $P^{\mathcal {P}}(p)$

is now positive for all

p ∈ [ 0 , 1 ) $p\in [0,1)$

under Model

P $\mathcal {P}$

, compared to Model

N $\mathcal {N}$

where the selling probability is zero for

p > 1 2 $p>\frac{1}{2}$

; see Figure 3b, cf. Figure 2b. Correspondingly, the expected revenue,

p · P P ( p ) $p\cdot P^{\mathcal {P}}(p)$

, as a function of p exhibits the shape of a full trapezoid, see Figure 3c. This implies that sellers with reservation values

v s > 1 2 $v_s>\frac{1}{2}$

receive a higher expected revenue under Model

P $\mathcal {P}$

(positive amount) compared to under Model

N $\mathcal {N}$

(zero). Therefore, provision of the product information benefits the sellers with high reservation values because now there are high‐valuation buyers who can afford the listing prices of these sellers.

Finally, given the sellers' pricing decisions characterized by CDF

F ∼ s P ( · ) $\tilde{F}_s^{\mathcal {P}}(\cdot )$

and the buyers' product valuation

v b ∼ U [ 0 , 1 ] $v_b\sim U[0,1]$

, let

p m a x P ( d b , d s ) $p^{\mathcal {P}}_{max}(d_b,d_s)$

denote the maximum transaction price between the two sides when

D b = d b $D_b=d_b$

and

D s = d s $D_s=d_s$

. Then,

p m a x P ( d b , d s ) $p^{\mathcal {P}}_{max}(d_b,d_s)$

can be uniquely determined by solving

d b [ 1 − F b ( p m a x P ) ] = d s · F ∼ s P ( p m a x P ) $d_b[1-F_b(p_{max}^{\mathcal {P}})]= d_s\cdot \tilde{F}^{\mathcal {P}}_s(p_{max}^{\mathcal {P}})$

. The total expected sales volume and sales for the platform under Model

P $\mathcal {P}$

can be derived as follows:

Furthermore, we find that the impact of b and s on the platform's expected sales and sales volume under Model

P $\mathcal {P}$

remains qualitatively the same as in Model

N $\mathcal {N}$

. Remark 2

Proposition 1 is preserved under Model

P $\mathcal {P}$

.

As the primary purpose for this section is to establish the sellers' pricing decisions in equilibrium, we will postpone the comparison of the expected sales between Model

P $\mathcal {P}$

and Model

N $\mathcal {N}$

(or between any two models) to Section 6 where we discuss the impact of different information structures on the profitability of the platform.

Market‐information model

In this section, we introduce the third model, the market‐information(‐only) model, or Model

M $\mathcal {M}$

, in which the platform provides the market information but not the product information (i.e.,

I P = 0 $I_P=0$

and

I M = 1 $I_M=1$

). Under Model

M $\mathcal {M}$

, the sellers know the realized market size

D b = d b $D_b=d_b$

and

D s = d s $D_s=d_s$

when making pricing decisions. Yet, without the product information, all buyers will valuate the product at its mean value, that is,

v b = E ( U [ 0 , 1 ] ) = 1 2 $v_b=\mathbb {E}(U[0,1])=\frac{1}{2}$

.

Such an information structure will significantly simplify the seller's game. In particular, denote

p m a x M ( d b , d s ) $p^{\mathcal {M}}_{max}(d_b,d_s)$

as the maximum transaction price between the sellers and buyers for given

d b $d_b$

and

d s $d_s$

(clearly,

p m a x M ( d b , d s ) ≤ 1 2 $p^{\mathcal {M}}_{max}(d_b,d_s)\le \frac{1}{2}$

). Then, in equilibrium, all the sellers whose reservation value

v s ≤ p m a x M $v_s\le p^{\mathcal {M}}_{max}$

should list their products at the price

p m a x M $p^{\mathcal {M}}_{max}$

in order to maximize their expected revenue, and the corresponding products will be sold to the buyers with valuation

v b ≥ p m a x M $v_b\ge p^{\mathcal {M}}_{max}$

. Moreover, the number of sellers who successfully sell a product must be equal to the number of buyers who successfully purchase a product, that is,

d b · [ 1 − F b ( p m a x M ) ] = d s · F ∼ s ( p m a x M ) = d s · F s ( p m a x M ) . $$\begin{equation} d_b \cdot \big[1-F_b\big(p^{\mathcal {M}}_{max}\big)\big]=d_s\cdot \tilde{F}_s\big(p^{\mathcal {M}}_{max}\big)=d_s\cdot F_s\big(p^{\mathcal {M}}_{max}\big). \end{equation}$$

4

Therefore, we can directly characterize the sellers' listing price distribution and selling probability function of the unique (Pareto‐dominant) equilibrium in the following theorem. Note that the pricing decisions of the sellers with a reservation value

v s > p m a x M $v_s>p^{\mathcal {M}}_{max}$

are irrelevant, so WLOG we assume that their listing prices are the same as their reservation values. Theorem 3

Under Model

M $\mathcal {M}$

, given the market information

( d b , d s ) $(d_b,d_s)$

, the sellers' listing price distribution and the selling probability function in equilibrium are given as follows:

where by (4),

5

It is clear from (5) that

p m a x M ( d b , d s ) $p^{\mathcal {M}}_{max}(d_b,d_s)$

weakly increases in

d b $d_b$

and decreases in

d s $d_s$

. Therefore, we can immediately deduce the following result: Corollary 2

Equilibrium listing prices (stochastically) increase in

d b $d_b$

and decrease in

d s $d_s$

, that is,

P r ( p > x | d b , d s ) = 1 − F ∼ s M ( x | d b , d s ) $Pr(p>x|d_b,d_s)=1-\tilde{F}^{\mathcal {M}}_s(x|d_b,d_s)$

weakly increases in

d b $d_b$

and decreases in

d s $d_s$

for all

x ∈ [ 0 , 1 ] $x\in [0,1]$

.

Essentially, Corollary 2 for Model

M $\mathcal {M}$

is analogous to Corollary 1 for Model

N $\mathcal {N}$

, both of which state the notion that the product prices in equilibrium increases in demand but decreases in supply, due to the market forces. However, in Model

M $\mathcal {M}$

, because the market information is provided to the buyers and sellers, the monotonic result is based on realized market size

d b $d_b$

and

d s $d_s$

, instead of market parameters b and s as in Model

N $\mathcal {N}$

when no market information is provided by the platform.

From Theorem 3, we can further derive the sales volume and the sales for the platform for any given market size

d b $d_b$

and

d s $d_s$

, denoted by

q M ( d b , d s ) $q^{\mathcal {M}}(d_b,d_s)$

and

t M ( d b , d s ) $t^{\mathcal {M}}(d_b,d_s)$

, respectively. Hence, we can characterize the expected sales volume

Q M $Q^{\mathcal {M}}$

and expected sales

T M $T^{\mathcal {M}}$

as follows:

Finally, we can verify that the impacts of the sizes of potential buyers (b) and potential sellers (s) on the platform's expected sales and sales volume remain unchanged from previous models. Remark 3

Proposition 1 is preserved under Model

M $\mathcal {M}$

.

Product‐and‐market‐information model

In the last model, we will analyze the scenario where the online marketplace provides both the product and the market information on its platform (i.e.,

I P = 1 $I_P=1$

,

I M = 1 $I_M=1$

), which we will refer to as Model

B $\mathcal {B}$

. The thought process of the equilibrium analysis is analogous to that of Model

M $\mathcal {M}$

. In particular, if we use

p m a x B ( d b , d s ) $p^{\mathcal {B}}_{max}(d_b,d_s)$

to denote the maximum transaction price between the sellers and buyers given

d b $d_b$

and

d s $d_s$

, then in equilibrium, all sellers with a reservation value

v s ≤ p m a x B $v_s\le p^{\mathcal {B}}_{max}$

will list their products at the price

p m a x B $p^{\mathcal {B}}_{max}$

, and the corresponding products will be sold to buyers with valuation

v b ≥ p m a x B $v_b\ge p^{\mathcal {B}}_{max}$

. Similar to Equation (4), we have

d b · [ 1 − F b ( p m a x B ) ] = d s · F ∼ s ( p m a x B ) = d s · F s ( p m a x B ) . $$\begin{equation} d_b \cdot \big[1-F_b\big(p^{\mathcal {B}}_{max}\big)\big]=d_s\cdot \tilde{F}_s\big(p^{\mathcal {B}}_{max}\big)=d_s\cdot F_s\big(p^{\mathcal {B}}_{max}\big). \end{equation}$$

6

The sellers' listing price distribution and selling probability function of the unique (Pareto‐dominant) equilibrium under Model

B $\mathcal {B}$

can be formally characterized in the following theorem. Theorem 4

Under Model

B $\mathcal {B}$

, given the market information

( d b , d s ) $(d_b,d_s)$

, the sellers' listing price distribution and the selling probability function in equilibrium are given as follows:

where by (6),

p m a x B ( d b , d s ) = ̇ d b / ( d b + d s ) $p^{\mathcal {B}}_{max}(d_b,d_s)\ \dot{=}\ d_b/(d_b+d_s)$

.

As

p m a x B ( d b , d s ) $p^{\mathcal {B}}_{max}(d_b,d_s)$

increases in

d b $d_b$

and decreases in

d s $d_s$

, we can directly verify that the sellers' equilibrium listing prices given in Theorem 4 (stochastically) increase in

d b $d_b$

and decrease in

d s $d_s$

, that is, Remark 4

Corollary 2 is preserved under Model

B $\mathcal {B}$

.

Finally, from Theorem 4, we can obtain expressions for the platform's expected sales volume and expected sales under Model

B $\mathcal {B}$

as follows:

We can verify that the impact of b and s on the platform's expected sales and sales volume remains unchanged from before. Remark 5

Proposition 1 is preserved under Model

B $\mathcal {B}$

.

OPTIMAL INFORMATION STRUCTURE FOR THE PLATFORM

Having characterized the Pareto‐dominant equilibrium for each of the four information structures in Sections 4 and 5 (i.e., Model

N $\mathcal {N}$

, Model

P $\mathcal {P}$

, Model

M , $\mathcal {M,}$

and Model

B $\mathcal {B}$

), we are now ready to seek an answer to the fundamental question of the paper: Should the platform provide the buyers and sellers with the product and/or market information? By comparing the expected total sales under different information structures, we obtain the following result: Theorem 5

The expected sales satisfy the following relations: (i)

T M ≥ T N $T^{\mathcal {M}}\ge T^{\mathcal {N}}$

; (ii)

T B ≥ T M $T^{\mathcal {B}}\ge T^{\mathcal {M}}$

if and only if

b / s ≥ ψ 1 = ̇ 0.9190 $b/s\ge \psi _1\ \dot{=}\ 0.9190$

; (iii)

T B ≥ T N $T^{\mathcal {B}}\ge T^{\mathcal {N}}$

if and only if

b / s ≤ ψ 2 = ̇ 0.3230 $b/s\le \psi _2\ \dot{=}\ 0.3230$

or

b / s ≥ ψ 3 = ̇ 0.7304 $b/s\ge \psi _3\ \dot{=}\ 0.7304$

.

The comparison results in Theorem 5 are contingent exclusively on the demand‐to‐supply ratio

b / s $b/s$

. As b and s correspond to the sizes of potential buyers and potential sellers, respectively, and the realized market size of the buyers and the sellers are uniformly distributed, we will address the ratio of

b / s $b/s$

simply as the demand‐to‐supply ratio. Borrowing a term from the real estate industry, we will categorize a market with high (resp., low) demand‐to‐supply ratio as a seller's market (resp., a buyer's market) in the remaining paper. In what follows, we elaborate on the findings of Theorem 5.

First, Theorem 5(i) reveals that in the absence of the product information (i.e.,

I P = 0 $I_P=0$

), provision of the market information always improves the total sales of the platform. Recall that without the product information, the buyers cannot accurately assess whether the product will meet their individual needs and, therefore, evaluate the product with an expected value. As a result, based on the realized market size of the buyers and sellers (

d b $d_b$

and

d s $d_s$

), either all of the

d b $d_b$

buyers are able to acquire the product or all of the

d s · F s ( 1 2 ) $d_s\cdot F_s(\frac{1}{2})$

sellers whose reservation value is no higher than the buyers' mean valuation

1 2 $\frac{1}{2}$

are able to sell their products, that is,

q M = q N = min { d b , d s · F s ( 1 2 ) } $q^{\mathcal {M}}=q^{\mathcal {N}}=\min \lbrace d_b, d_s\cdot F_s(\frac{1}{2})\rbrace$

. In other words, the lesser of the two quantities, which are both independent of the market‐information revelation, determines the sales volume of the platform. However, even if the same number of transactions occur between the sellers and buyers with or without market information, provision of the market information can facilitate the sellers in making target pricing decisions based on the realized market size. Thus, market information boosts the transaction prices, and this will lead to improved sales (revenue) for the platform. Furthermore, Theorem 5(i) suggests that revealing at least some information to market participants is preferable to the platform, as the no‐information case is (weakly) dominated by an information revelation strategy (i.e., announcing only market information).

Second, if the platform releases the market information (i.e.,

I M $I_M$

=1), Theorem 5(ii) suggests that it can improve its expected total sales by releasing the product information if and only if the demand‐to‐supply ratio is sufficiently high (i.e.,

b / s ≥ ψ 1 = 0.9190 $b/s\ge \psi _1=0.9190$

). To intuit this result, let us first consider a seller's market (i.e., the market is under a high demand‐to‐supply ratio and there are abundant buyers). If there were no product information, all the buyers are willing to pay no more than the mean valuation

1 2 $\frac{1}{2}$

. Hence, the total sales of the platform are limited by the sellers who have high reservation values and cannot successfully sell their product to available buyers because their listing prices for the product are higher than

1 2 $\frac{1}{2}$

. Under this scenario, it is optimal for the platform to reveal the product information, as doing so increases the spread of product valuations for the buyers. The buyers with high product valuations are now willing to pay for a high price to acquire the product. Therefore, product information helps facilitate high‐price trades and boosts the total sales of the platform as a result. On the other hand, in a buyer's market (i.e., the market is under a low demand‐to‐supply ratio), there are more sellers than buyers. If the platform provides the product information, buyers with median or high product valuations can always acquire the product, but buyers with low product valuations may not always be able to find a trade because they are the last ones to be matched with the sellers in the marketplace and prices of the remaining sellers may be too high due to their high reservation values. In this case, the platform can benefit from not providing the product information to avoid such lost sales.

Finally, Theorem 5(iii) states that providing both product and market information leads to higher total sales for the platform compared to the strategy of withholding both types of information, if and only if the demand‐to‐supply ratio is either sufficiently low or sufficiently high but not when it is at an intermediate level (i.e., if and only if

b / s ≤ ψ 2 $b/s\le \psi _2$

or

b / s ≥ ψ 3 $b/s\ge \psi _3$

). To explain the result, we can first consider the effect of product information and that of market information on the sales of the platform in isolation. On the one hand, provision of product information reduces (resp., increases) sales when the demand‐to‐supply ratio is under (resp., above) some threshold, see the explanation for Theorem 5(ii). On the other hand, provision of market information always increases sales, see the explanation for Theorem 5(i). When the demand‐to‐supply ratio is sufficiently low (i.e.,

b / s ≤ ψ 2 $b/s\le \psi _2$

), the negative effect on sales by providing product information is outweighed by the positive effect on sales by providing market information, making announcing both types of information a better strategy compared to withholding them. However, when the demand‐to‐supply ratio is at an intermediate level (i.e.,

b / s ∈ ( ψ 2 , ψ 3 ) $b/s\in (\psi _2,\psi _3)$

), the negative effect on sales by providing product information can no longer be offset by the positive effect on sales by providing market information, making announcing both types of information a worse strategy than not announcing them. Lastly, when the demand‐to‐supply ratio becomes sufficiently high (i.e.,

b / s ≥ ψ 3 $b/s\ge \psi _3$

), the provision of either product information or market information has a positive effect on sales. Combining both positive effects, the platform is certainly better off with providing both types of information compared to not providing any information.

Based on Theorem 5, we can summarize the platform's optimal information strategy in the following proposition: Proposition 2

Consider Model

N $\mathcal {N}$

, Model

M $\mathcal {M}$

, and Model

B $\mathcal {B}$

. It is optimal for the platform to provide both the product and market information when

b / s ≥ ψ 1 $b/s\ge \psi _1$

. Otherwise, it is optimal for the platform to provide only the market information.

It is necessary to note that Theorem 5 and Proposition 2 do not present any comparison results under Model

P $\mathcal {P}$

, because the total sales under Model

P $\mathcal {P}$

(

T P $T^{\mathcal {P}}$

) cannot be explicitly characterized and analytically compared to other models. Nevertheless, through extensive numerical experiments, we find that Model

B $\mathcal {B}$

always dominates Model

P $\mathcal {P}$

, that is,

T B ≥ T P $T^{\mathcal {B}}\ge T^{\mathcal {P}}$

. This is because when product information is provided, there will be more high‐valuation buyers. At this point, providing market information can facilitate sellers to make target price decisions based on the actual number of buyers and sellers on the platform. In particular, it softens the price competition between the sellers caused by the high‐valuation buyers. As a result, the products are sold to them at higher prices, boosting the total sales of the platform. Accordingly, we can infer that the platform's optimal information strategy remains the same as given by Proposition 2 even when Model

P $\mathcal {P}$

is considered.

Based on Proposition 2, we also know that it is always optimal for the platform to provide some information to the customers (this is true even without being able to analytically compare Model

P $\mathcal {P}$

because providing market information only always dominates providing no information). However, the platform should be strategic about how much information to reveal when faced with different market conditions, because the optimal decision can be different in different circumstances. In particular, providing market information always seems wise because it allows sellers to make informed pricing decisions based on the realized market condition. However, providing product information in addition to the market information can backfire at times.

We plot the optimal information revelation strategies based on market conditions in Figure 4. Specifically, it is optimal for the platform to provide customers with both the product and market information only in a seller's market (high ratio of potential buyers to sellers). Provision of the product information can increase the number of high‐valuation buyers, which encourage more deals to be closed at higher prices in a seller's market. By contrast, when facing a buyer's market (low ratio of potential buyers to sellers), the platform will find it wise to conceal the product information so the buyers' valuations for the product are less dispersed. In this case, more buyers can strike deals with sellers without the detailed product information.

OPEN IN VIEWER

FIGURE 4

Optimal information structure for the platform as the demand‐to‐supply ratio changes.

ROBUSTNESS OF FINDINGS

In this section, we present several extensions to the main model for robustness check. Specifically, Section 7.1 considers general distributions concerning how sellers value the product. Section 7.2 examines the scenario when the platform can provide partial product information. Section 7.3 addresses the case that customers may have heterogeneous product valuations even without product information provided by the platform. Section 7.4 explores the impact of outside options. Section 7.5 studies continuous product‐information provision. Section 7.6 considers partial market information. And finally, Section 7.7 examines an alternative matching mechanism. For tractability purpose, we will modify one assumption/feature of the main model in each extension while keeping all the others unchanged.

General distribution for sellers' reservation value

In the main model, we assumed that sellers' reservation value of the product, when no market information released, follows a standard uniform distribution for closed‐form expressions. However, our insights are not driven by this assumption. To establish robustness of our results, we consider the beta distributions, whose density function can capture various curvatures depending on the two shape parameters, including horizontal lines (i.e., uniform distributions), bell‐shaped curves, or U‐shaped curves. Note that, under the beta distribution, the functional form of the unique Pareto‐dominant equilibrium for the sellers' game can still be explicitly characterized. However, numerical analyses are needed to compare the platform's sales in equilibrium across different information structures.

We find that our insights remain qualitatively unchanged. Specifically, Figure 5a illustrates the optimal information structure under beta distribution B(2, 4), B(2, 2), and B(4, 2), which exhibits a bell‐shaped density‐function curve, with mean 1/3, 1/2, and 2/3, respectively. Bell‐shaped density‐function curves imply that sellers' reservation value of the product tend to cluster around the mean, and the further from the mean, the less likely they are to occur. We observe that Figure 5a bears a close resemblance to Figure 4 under the uniform distribution. As such, our main insights regarding the optimal information structure continue to hold.

OPEN IN VIEWER

FIGURE 5

Optimal information structure for the platform when (a)

v s $v_s$

follows various beta distributions and when (b)

v b ∼ U [ 1 2 − γ , 1 2 + γ ] $v_b\sim U[\frac{1}{2}-\gamma ,\frac{1}{2}+\gamma ]$

if

I P = 1 $I_P=1$

.

We also performed numerical analysis to explore the scenario when both the sellers' reservation value distribution and the buyers' valuation distribution (when product information is provided) follow beta distributions. The main insights from Figure 4 continued to hold.9 As such, we conclude that the results of our main model are not driven by the uniform‐distribution assumptions.

Providing partial product information

In the main model, we assumed that if the platform decides to release the product information (i.e., Model

P $\mathcal {P}$

and Model

B $\mathcal {B}$

), then full product information will be provided to the buyers. Yet, in practice, the platform may be able to provide partial product information, which could influence buyers' product valuation. Take a printer for example, a platform could merely publish the printer's key technical specifics (e.g., dimension, ink, and paper size) in a plain textual format, or it can supply a large amount of information with multimedia (e.g., texts, pictures, videos, and 3D interactions) and community forums (e.g., Q&As and review forum) to illustrate the detailed features of the printer (e.g., whether it supports borderless printing and Ethernet networking capability). With more information provided, each buyer can more accurately assess their individual needs, which leads to a larger spread of product valuations among them (Chu & Zhang, 2011).

To capture such an influence, we generalize the main model by allowing the buyers' product valuations, upon product‐information revelation, to follow a uniform distribution on the support of

[ 1 2 − γ , 1 2 + γ ] $[\frac{1}{2}-\gamma , \frac{1}{2}+\gamma ]$

, where the parameter

γ ∈ [ 0 , 1 2 ] $\gamma \in [0, \frac{1}{2}]$

represents the level of product information provided—a higher value of γ implies that more product information is provided by the platform.10 In particular, no product information corresponds to

γ = 0 $\gamma =0$

when customers' valuations of the product are all equal to

1 2 $\frac{1}{2}$

, which is the same as the main model when no product information is provided. In contrast, when all product information is provided, we have

γ = 1 2 $\gamma =\frac{1}{2}$

and customers' valuations will follow a standard uniform distribution, which is the same as the main model when product information is provided. Last but not least,

γ ∈ ( 0 , 1 2 ) $\gamma \in (0, \frac{1}{2})$

corresponds to the case where the platform provides partial product information.11

We will briefly summarize our findings in this section, and defer the technical details and proofs to EC.2 in the Supporting Information. Specifically, when the platform decides to provide product information (i.e., Model

P $\mathcal {P}$

and Model

B $\mathcal {B}$

), the analysis will depend critically on γ, which is the level of product information provided. For any given γ value, we are still able to fully characterize the unique Pareto‐dominant equilibrium for the sellers' game (e.g., see Theorem EC.2.1 and Theorem EC.2.2 in the Supporting Information). The sellers' pricing decisions and the selling probability function qualitatively resemble those from the main model (see Figure EC.2.1 in the Supporting Information, cf. Figure 3 in Section 5.1). Furthermore, we reproduce Figure 4 from the main model in Figure 5b using different values of γ and find that the optimal information structure for the platform carries over nearly identically. That is, it is optimal for the platform to provide both the product and market information in a seller's market (high ratio of potential buyers to sellers) and only the product information in a buyer's market (low ratio of potential buyers to sellers).

We can also observe from Figure 5b that the platform is more likely to provide product information to the buyers (i.e., the region for

I P = 1 $I_P=1$

expands) when more information is available (i.e., when γ is large).

Heterogeneous customer valuation when no product information is provided

In the main model, for simplicity, we assumed that when no product information is available (i.e., when

I P = 0 $I_P=0$

in Model

N $\mathcal {N}$

and Model

M $\mathcal {M}$

), buyers' valuations for the product will converge to its mean value at

1 2 $\frac{1}{2}$

, that is, the buyers would be homogeneous. In reality, however, customers may have heterogeneous product valuations even without product information provided by the platform. For example, they can obtain information of the product by searching on the Internet (we consider the information searching cost of the customers as a sunk cost by the time they make the purchase decision on the platform). To address this issue, we now assume that the buyers' valuations of the product are uniformly distributed on the support of

[ 1 2 − η , 1 2 + η ] $[\frac{1}{2}-\eta , \frac{1}{2}+\eta ]$

, when the platform does not provide the product information (i.e., in Model

N $\mathcal {N}$

and Model

M $\mathcal {M}$

), where

η ∈ [ 0 , 1 2 ] $\eta \in [0,\frac{1}{2}]$

. This captures the fact that customers can have access to different amount of product information when it is not provided by the platform. Finally, all other assumptions remain unchanged from the main model.

We can fully characterize the unique Pareto‐dominant equilibrium for the sellers' game (e.g., see Theorem EC.2.1 and Theorem EC.2.2 in the Supporting Information)—we provide technical details and proofs in Section EC.3 in the Supporting Information while briefly summarizing our findings in this section. The optimal information structure for the platform is reproduced in Figure 6a using

η = 0.2 $\eta =0.2$

as an example. Compared to Figure 4 in the main model, we observe that it qualitatively remains the same.

OPEN IN VIEWER

FIGURE 6

Optimal information structure for the platform when (a)

v b ∼ U [ 1 2 − η , 1 2 + η ] $v_b\sim U[\frac{1}{2}-\eta ,\frac{1}{2}+\eta ]$

if

I P = 0 $I_P=0$

and (b) there is an outside option.

The impact of outside options

In the main model, we considered a two‐sided online marketplace where individual buyers can only purchase a product from private sellers on the platform. In practice, however, buyers may also be able to purchase the product from an outside option, for example, an online retailer, or even from the platform itself (e.g., Amazon Marketplace and Amazon are integrated). In this section, we will examine the impact of outside options on the equilibrium of the sellers' game and the optimal information structure for the platform.

For simplicity, we posit that there exists a best outside option from which any potential buyers can purchase the product at a given price

p o $p_o$

. The price can be the listing price of the outside option or an effective price to the buyers taking into account both the listing price and service quality. Furthermore, we assume that the outside option possesses a large inventory so that it is able to satisfy all demand from potential buyers. Finally, all other assumptions remain unchanged from the main model.

Given the price of the outside option

p o $p_o$

, buyers will only consider purchasing the product from a seller from the online marketplace if the seller's price is lower than

p o $p_o$

. In the Supporting Information where we provide detailed technical analysis and proofs (see EC.4), we explicitly derive the unique Pareto‐dominant equilibrium for the sellers' game under all of our four models when the outside option is present (see Theorems EC.4.1–EC.4.4). We verify that the sellers' pricing decisions and the selling probability function under the equilibrium remain qualitatively the same as those in the main model (see Figures EC.4.1–EC.4.2).

In addition, we derive the optimal information structure for the platform in the presence of the outside option and present the results in Figure 6b. It is clear that Figure 6b bears a very reasonable qualitative resemblance to its counterpart of the main model (Figure 4), suggesting that our findings of the main model continue to hold even with the consideration of outside options. In other words, it is optimal for the platform to provide both the product and market information in a seller's market (high ratio of potential buyers to sellers) and only the product information in a buyer's market (low ratio of potential buyers to sellers), even when outside options are present. Figure 6b also contains multiple values of

p o $p_o$

so the impact of the outside option can be visualized. In particular, as the outside option gains attractiveness (i.e., as

p o $p_o$

decreases), the platform is less likely to provide information to the buyers (i.e., the region for

I P = 1 $I_P=1$

shrinks).

Continuous product‐information provision model

In the main paper, we have shown that providing market information (

I M = 1 $I_M=1$

) always benefits the platform, regardless of a seller's market or a buyer's market. Yet, providing all product information (

I P = 1 $I_P=1$

) may backfire, especially in a buyer's market. These observations prompt the question of whether it will be beneficial for the platform to provide partial product information compared to providing all or none of the product information. In other words, what is the optimal level of product information that maximizes the platform's revenue? To answer this question, in this section, we study a continuous product‐information provision model in which the platform can choose the amount of product information to be provided to the buyers and sellers. WLOG, we assume that the platform always provides the market information (i.e.,

I M = 1 $I_M=1$

).12 We demonstrate that providing either all or none of the product information continues to be optimal for the platform.

Similar to Section 7.2, the buyers' product valuations, upon product‐information revelation, follow a uniform distribution on the support of

[ 1 2 − γ , 1 2 + γ ] $[\frac{1}{2}-\gamma , \frac{1}{2}+\gamma ]$

, where the parameter

γ ∈ [ 0 , 1 2 ] $\gamma \in [0, \frac{1}{2}]$

represents the level of product information provided—a higher value of γ implies that more product information is provided by the platform. In the Supporting Information (see Section EC.5), we first analytically characterize the unique Pareto‐dominant equilibrium for the sellers' game in Theorem EC.5.1 for a given γ. The expression for the platform's expected sales is now substantially complicated by γ, see Equation EC.5.3. However, we are able to show that the platform's expected sales first decrease then increase in γ (see Proposition EC.5.2), which implies that the platform's expected sales are maximized at either

γ = 0 $\gamma =0$

(which is equivalent to

T M $T^{\mathcal {M}}$

in Model

M $\mathcal {M}$

) or

γ = 1 2 $\gamma =\frac{1}{2}$

(which is equivalent to

T B $T^{\mathcal {B}}$

in Model

B $\mathcal {B}$

), based on the demand‐to‐supply ratio. In other words, when the platform can choose the product‐information provision level to maximize its expected sales, it is always optimal to either reveal all or none of the product information that it has on hand.

Providing partial market information

In the main model, providing market information means providing both realized numbers of buyers and sellers (i.e.,

d b $d_b$

and

d s $d_s$

) to the users on the platform. One remaining question we intend to answer in this section is whether providing partial market information (i.e., releasing just the

d b $d_b$

information or just the

d s $d_s$

information) can benefit the platform. By studying the corresponding partial market‐information models (see details in Section EC.6), we demonstrate that disclosing all market information always generates higher expected sales for the platform compared to disclosing partial market information.

In particular, in Section EC.6.1 (resp., Section EC.6.2), we consider the scenario in which the platform discloses

d s $d_s$

(resp.,

d b $d_b$

) but not

d b $d_b$

(resp.,

d s $d_s$

). Within each information structure, we further derive the equilibrium listing price distributions and the corresponding selling probability functions analytically, when there is or is not product information. We show that when there is no product information, the platform's expected sales with partial market information is dominated by those with full market information (i.e., Model

M $\mathcal {M}$

), see Theorem EC.6.2 and Theorem EC.6.6(i). In addition, where there is product information, the platform's expected sales with partial market information is still dominated by those with full market information (i.e., Model

B $\mathcal {B}$

), see Theorem EC.6.6(ii).13 These observations, together with Theorem 5 and Proposition 2 in the main model, suggest that disclosing all market information (containing both

d b $d_b$

and

d s $d_s$

) remains the optimal strategy for the platform.

Alternative matching mechanism

In the main model, we assume that the product offered with the lowest price will be acquired by the buyer with the highest valuation, and so forth. In this subsection, we analyze an alternative/opposite matching mechanism where the product offered with the lowest price will be acquired by the buyer with the lowest valuation. More specifically, the lowest valuation buyer (whose valuation exceeds the listing price of the lowest price seller) will be matched with the lowest price seller with ties broken randomly, and they exit the market by completing the sale. If a buyer's valuation is lower than the listing price of the lowest price seller, then this buyer will not be able to obtain the product from this seller or any other sellers, and the buyer exits the market. Then the lowest valuation buyer among the remaining buyers (whose valuation exceeds the listing price of the lowest price seller among the remaining sellers) will be matched with the lowest price seller among the remaining sellers, and so on and so forth, until there are no more buyers and/or no more sellers in the market.

We can show that under the alternative matching mechanism, the analysis of Model

N $\mathcal {N}$

, Model

M $\mathcal {M}$

, and Model

B $\mathcal {B}$

remains the same as the main model. However, characterizing all equilibria for the sellers' game under Model

P $\mathcal {P}$

becomes prohibitively difficult. As a result, we analytically identify a representative equilibrium in Theorem EC.7.1 and Section EC.7. Comparison of the expected total sales between Model

N $\mathcal {N}$

, Model

M $\mathcal {M}$

, and Model

B $\mathcal {B}$

remains the same as in Theorem 5 and Proposition 2. The total sales under Model

P $\mathcal {P}$

cannot be explicitly characterized or analytically compared to the other three models. However, through extensive numerical experiments, we find that

T B > T P $T^{\mathcal {B}}>T^{\mathcal {P}}$

and

T M > T P $T^{\mathcal {M}}>T^{\mathcal {P}}$

for

b / s < 0.16 $b/s<0.16$

,

T B < T P $T^{\mathcal {B}}<T^{\mathcal {P}}$

and

T M > T P $T^{\mathcal {M}}>T^{\mathcal {P}}$

for

0.16 < b / s < 0.64 $0.16 < b/s<0.64$

, and

T B < T P $T^{\mathcal {B}}<T^{\mathcal {P}}$

and

T M < T P $T^{\mathcal {M}}<T^{\mathcal {P}}$

for

b / s > 0.64 $b/s> 0.64$

. As a result, it is optimal for the platform to provide only the product information when

b / s ≥ 0.64 $b/s \ge 0.64$

, otherwise, only the market information. In other words, providing only product (resp., market) information seems to benefit the platform in a seller's (resp., buyer's) market under the alternative matching mechanism studied in this subsection.

CONCLUDING REMARKS

In this paper, we study the role of information in an online marketplace. We find that information could be a double‐edged sword for the platform. On the one hand, the platform benefits from the revelation of (product and market) information in a seller's market (high ratio of potential buyers to sellers). On the other hand, it is less helpful or even harmful for the platform when all the information is revealed in a buyer's market (low ratio of potential buyers to sellers).

In particular, while market information should always be provided to reduce price competition and boost sales amount among the sellers, product information should be only provided in a seller's market and not in a buyer's market. This is because in a seller's market, there are more buyers than sellers. If all sellers can sell their products, the platform can maximize sales, especially if those sellers with high reservation values can sell their products. Provision of product information is a great strategy in this case as it allows the buyers to develop heterogeneous product valuations and buyers with high product valuations are willing to pay for a high price to acquire the product. In contrast, in a buyer's market, sellers outnumber buyers, and total sales of the platform can be improved when more buyers can successfully purchase the product, which happens when more buyers have sufficient willingness‐to‐pay. By not providing the product information, the platform can benefit from the less dispersed product valuation distribution of the customers, because fewer customers would have low willingness‐to‐pay for the product.

Our other contribution in this research is the underlying technical analysis that identifies the Pareto‐dominant equilibrium of the sellers' pricing decisions under various informational structures. As noted by Chen et al. (2016) on the seller competition for an online marketplace (see p. 591 of the paper), “it is difficult to make a comprehensive and rigorous analysis for the general seller competition case,” and we have sought to carry out the analysis under reasonable assumptions. Furthermore, we find that after taking into account sellers' strategic pricing decisions, the sales of the online marketplace increase in the size of potential buyers but are actually unimodal in the size of potential sellers. Having more sellers is good at first because it increases transaction volume, but eventually the sellers outnumber the buyers by so much that the competition among them drives down prices and starts to hurt the platform's sales revenue. This observation suggests that at some point an online marketplace may need to restrict the number of sellers on its platform, which runs counter to the conventional wisdom that more people on the platform is always more beneficial for the platform operator.

As the objective of our model framework is to capture the essential elements relevant to the information structure of an online marketplace while at the same time, keeping the analysis tractable, the model is certainly not without limitations. First, we have assumed in our model that each seller who participates in the platform only has one unit of the product in stock. In reality, when each seller represents a small business, they can carry multiple products in the inventory. However, we can extend our model without sacrificing any results to include the case where each seller has n units of the product for sale. Yet, when the market has limited number of sellers, leading to oligopoly, future work is needed to understand how limited competition among sellers influences the platform's information provision decisions. Second, products from different sellers in our model are perfectly substitutable as we focus on customers' buying and selling decisions of a particular product. In comparison, Chen et al. (2016) consider products that are not at all substitutable. Future work is needed to shed more light on the intermediate case where products from different sellers are substitutable to a certain extent.

Third, we have focused on the benefits of information to a platform, which is only half of the story—the costs of information need to be assessed to determine the overall optimal strategy for the platform. In fact, some online marketplaces do not currently provide information to customers exactly due to concerns regarding the costs of collecting information. We showed that this actually may not lead to an adverse outcome under certain situations (e.g., providing product information under a buyer's market). Fourth, we follow the matching mechanism developed in Su (2010), and future research is needed to understand whether the optimal information structure remains the same under alternative matching mechanism. Finally, we considered a monopolist platform in this paper as is typically done in the literature (see, e.g., Benjaafar et al., 2019; Cachon et al., 2017; Taylor, 2018). Under oligopoly settings, how competitive pressure influences online marketplaces' information decisions can be of an interesting yet difficult extension to this research.

Footnotes

ACKNOWLEDGMENTS

The authors are deeply grateful to the Department Editor Haresh Gurnani, the senior editor (SE), and the reviewers, for their detailed comments through the review process. This work was partially supported by the National Natural Science Foundation of China (Grant No. 71901197).

1

See https://www.ebay.com/help/selling/fees‐credits‐invoices/frais‐pour‐les‐vendeurs‐particuliers?id=4822 and https://sell.amazon.com/pricing#referral‐fees, respectively.

2

See https://www.amazon.com/Bose‐QuietComfort‐Wireless‐Headphones‐Cancelling/dp/B0756CYWWD, https://www.submarino.com.br/produto/1422013485, and https://www.real.de/product/326945939, respectively.

3

It is proven that the outcome of the matching mechanism can be achieved by either a double auction (McAfee, 1992; Wilson, 1985) or efficient rationing (Su, 2010). This matching mechanism has also been extensively used in experimental studies (see, e.g., Cason & Friedman, ; Plott & Gray, 1990; Smith et al., 1982). In particular, Cason & Friedman (1996) found that high‐surplus trades (between high‐value buyers and low‐cost sellers) tend to occur earlier within a trading period than low‐surplus trades.

4

While only binary product‐information decisions are considered here, we consider continuous product information in the Supporting Information (see EC.5) and show that the optimal product‐information revelation decision is still all or nothing.

5

For the sake of mathematical tractability, we use uniform distributions in our main model to glean clean analytical insights, but these results continue to hold under more general distributions such as the beta distribution (see Section ).

6

Note that our insights continue to hold when buyers' valuation, without the product information, is equal to a value

δ ∈ ( 0 , 1 ) $\delta \in (0,1)$

that is not

1 2 $\frac{1}{2}$

. Results and numerical illustrations are available from the authors.

7

The Pareto‐optimality maximizes the aggregate revenue for the sellers because the decisions are made by the sellers who may not be concerned about the welfare of the buyers. It can be shown that the Pareto‐dominant equilibrium actually maximizes any individual seller's expected revenue among all equilibria of the sellers' pricing game.

8

Proofs for any remarks are omitted from the Supporting Information to avoid duplication but available from the authors.

9

Numerical illustrations and results are available from the authors.

10

When modeling the impact of information revelation on consumers' valuations, the existing literature typically specifies that more information leads to higher consumer valuation dispersion/variance (see Chu & Zhang, ; Osborne, 2011). Chu & Zhang (2011) assume that consumers' valuations follow a normal distribution

N ( μ , λ κ 2 ) $N(\mu , \lambda \kappa ^2)$

where λ measures the amount of information provided—a higher λ value means that more information is provided. In section 3.3 of their paper, the authors also provide two examples as the underlying microfoundations. We adopt the uniform distribution

U [ 1 2 − γ , 1 2 + γ ] $U[\frac{1}{2}-\gamma ,\frac{1}{2}+\gamma ]$

to model consumer valuations, instead of the normal distribution, for tractability purposes. An alternative modeling approach could be that with some probability (the probability can depend on the level of product information provided), a consumer can fully resolve her valuation uncertainty, and otherwise the consumer maintains her prior valuation of 0.5. However, this alternative modeling approach is difficult to incorporate into our model framework.

11

We consider γ as an exogenously given parameter in this section (Section 7.2). We will study the optimal product‐information level in Section .

12

The sellers' game for the case when the platform provides no market information (

I M = 0 $I_M=0$

) and partial product information can be analyzed similarly to the model in Section . We can demonstrate that when providing the same amount of partial product information, the platform can always improve its total sales by offering market information.

13

Similar to the main model, the platform's expected sales when there is product information and partial market information on

d s $d_s$

can only be compared to other models by performing numerical experiments. It can be shown that the strategy is dominated by Model

B $\mathcal {B}$

.

ORCID

Mike Mingcheng Wei

Shiliang Cui

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