Peer‐to‐peer sharing platforms with quality differentiation: Manufacturer's strategic decision under sharing economy

Abstract

As peer‐to‐peer sharing platforms emerge in the downstream market, upstream product manufacturers may build their exclusive sharing platform, seeking benefits from the sharing market. To study the profit and welfare implications of the emergence of sharing economy and manufacturer's platform‐building strategy, we employ a vertically differentiated duopoly setting and consider three scenarios: no‐sharing benchmark, a single third‐party platform emerged, and manufacturer‐built platform co‐existing with the third‐party platform. Formulating and solving the game in each scenario, we compare the equilibrium outcomes, including manufacturers' profits, consumer surplus and social welfare, before and after scenario transitions. For the manufacturers' profits, no matter which manufacturer builds the platform in presence of the third‐party platform, that manufacturer will be better off, whereas the opponent manufacturer may also benefit, depending on the quality differentiation perceived by consumers in the product selling market and in the sharing market. Moreover, when comparing against the no‐sharing benchmark, the manufacturers benefit from the sharing only when the quality differentiation is large enough and the production cost is not small. For the welfare implication, if the renters derive the same usage utility as the owners in the sharing market, the consumer surplus and the social welfare will always increase as the third‐party platform emerges or a manufacturer builds its platform. Otherwise, either platform could hurt the consumer surplus and the social welfare, especially when the quality differentiation is large. Our research highlights the innovative platform‐building strategy in the presence of peer‐to‐peer sharing economy and offers important insights to all market participants.

INTRODUCTION

The recent proliferation of Internet‐based platforms has significantly fueled the growth of the peer‐to‐peer sharing market across a wide range of sectors, such as hospitality (Airbnb, CouchSurfing), retailing (SnapGoods, Tradesy), and transportation (Uber/Lyft, Turo). Using these platforms, individuals can monetize their under‐utilized resources, and therefore, enhance their utility. Similarly, people may have access to products that they do not necessarily own, which improves product utilization. As a result, such sharing economy has been very well received and has the potential of disrupting many traditional industries. Indeed, a PWC report (PwC, 2015) shows that 44% of US consumers are familiar with sharing economy and 72% of those who have tried it believe that they will keep using it in the near future; moreover, the report estimates the global revenue of sharing economy to increase over 20 times in less than 10 years.

For certain industries, product‐sharing among consumers facilitated by sharing platforms has become so prevalent that new economic implications are developed to understand the changes in consumer behavior and offer guidance to platform managers (Benjaafar et al., 2019). Moreover, even upstream firms such as product manufacturers, who on the surface do not interface with the downstream sharing platforms, must now factor in the impact of peer‐to‐peer sharing when making strategic decisions (Jiang & Tian, 2018; Tian & Jiang, 2018). Take the auto industry, for example, there are many platforms that enable peer‐to‐peer car‐sharing or ride‐hailing ¹ . Compared to before, consumer behavior is largely reshaped as people re‐consider the value of owning a car. Specifically, on one hand, they are comparing it with just having access to mobility and thus may simply become platform users rather than product buyers; on the other hand, they are also aware of the additional value of ownership from sharing with other peers and may be more willing to purchase. As a consequence, this paradigm shift in consumer preference has a profound influence on the upstream car manufacturers, as their products are redefined and their traditional buyer markets are restructured.

Facing both challenges and opportunities brought by the peer‐to‐peer sharing platforms, manufacturers have attempted to adapt to and even thrive in the new environment by using different strategies. Among these strategies, we are particularly interested in the platform‐building strategy, where manufacturers build their own platform to facilitate peer‐to‐peer car‐sharing service featuring their products exclusively. Two examples are notable in this regard. In 2018, the BMW Group launched a trial platform called MINI Sharing in Madrid, which enables consumers to share their MINI with others; since then, the premium manufacturer has been expanding the peer‐to‐peer sharing program in European cities as well as South Africa, and the trend is expected to continue. ² In his 2016 blog, Elon Musk proposed a “Master Plan” to create a shared fleet of customer‐owned Tesla. The manufacturer has been actively converting this plan into reality, launching its new sharing network that will compete directly against Uber/Lfyt. ³

The manufacturer‐built peer‐to‐peer sharing platforms mentioned above, be it already in operation or part of a business plan, do showcase firms' vision of proactively interacting with the sharing economy. However, little research has been done to study the effect of the platform‐building strategy. In a market of vertically differentiated products (such as cars with different brand names), it is not a priori clear whether one of the manufacturers building an exclusive sharing platform would benefit that manufacturer; neither is it clear whether other manufacturers could be hurt. Moreover, as the manufacturer's strategic move, along with the growing popularity of sharing economy, will affect the prices consumers pay for either owning or using the products and their behavior, the impact of the platform‐building strategy on the consumer surplus and the social welfare is also an interesting question to investigate.

The primary objective of our paper, therefore, is to examine the profit and welfare implications of the platform‐building strategy. Taking the economic and operational perspective, we aim to offer assessment on, and provide relevant managerial insights into, how the manufacturer‐built sharing platform could affect the equilibrium outcomes regarding the manufacturers and the consumers alike. As such, our paper could offer practical values to all parties involved in either the product selling market or the peer‐to‐peer sharing market.

To see the impact of sharing economy and the platform‐building strategy, we consider a series of scenarios which represents the development of sharing economy. First, we start with a benchmark setting where two quality differentiated manufacturers engage in price competition for the consumer market. This scenario is simply the classic vertically differentiated duopoly competition with no sharing economy. Then, we consider a scenario where the peer‐to‐peer sharing economy emerged and is operated by a third‐party platform. Such a scenario captures the changes brought by the emergence of sharing economy. Finally, the high‐quality manufacturer decides to deploy the platform‐building strategy and launches its own sharing platform, leading to the third scenario where two sharing platforms co‐exist. In each scenario, we formulate a Stackelberg game where the two manufacturers first set selling prices and then the consumers and the platform(s), if there is any, make decisions. Establishing the existence and uniqueness of the sub‐game perfect Nash equilibrium for every scenario, we mainly focus on the comparison in equilibrium outcomes between scenarios. Specifically, as the third‐party platform and/or the manufacturer‐built platform appears, we have a scenario transition from one to another; then, we investigate the changes in the manufacturers' profits and the consumer surplus/social welfare. In this way, we can characterize the impacts of the sharing economy and the platform‐building strategy.

Our analytical results pivot on the quality differentiation between the two manufacturers. On the one hand, different quality levels of the products give rise to different ownership utility, leading to the competition in the product selling market. On the other hand, the renters in the sharing market, who use the product without ownership, may not derive the same usage utility as the owners. As a result of this utility discount, the product quality differentiation can affect the constitution of the sharing market. Hence, our findings can be summarized according to the following two cases. First, suppose that the renters derive the same usage utility as the owners in the sharing market. Then, the emergence of the sharing economy may or may not benefit the manufacturers, depending on the production cost; moreover, given that a third‐party platform already exists, the platform‐building manufacturer will benefit from the strategy, whereas the opponent will be hurt. Furthermore, the consumer surplus and the social welfare both increase as sharing platforms become available. It is noteworthy that the threshold of the production cost obtained in this case is independent of the quality differentiation. Thus, when all consumers have the same perception of quality, either owning or renting the product, the emergence of sharing platforms will not change the ratio of the market size for each product.

In the second case, the renters of the high‐quality product can only derive a discounted usage utility compared to owning it. In this case, the emergence of the sharing economy will benefit the manufacturers if the quality differentiation is large. In addition, the low‐quality manufacturer may even benefit from its opponent's platform‐building strategy if, again, the quality is sufficiently differentiated. On the contrary, with large quality differentiation, the consumer surplus and the social welfare may both decrease as sharing platforms become available. The main logic behind this finding is that, with discounted usage utility, the high‐quality product on the sharing platform essentially becomes a new product in the renters' eyes. Hence, the more differentiated market is advantageous for manufacturers but harmful to consumers.

Finally, although our main model assumes that the high‐quality manufacturer builds the exclusive platform, which is consistent with our motivating example, we also examine the case where the low‐quality manufacturer deploys the platform‐building strategy. After all, relative to its opponent, the platform‐building manufacturer may have a lower quality. Under the new assumption, we repeat our analysis and focus on the similarities and differences in the comparison results for scenario transitions. Findings show that the impact of the platform‐building strategy with respect to the benchmark scenario is qualitatively the same as in the main model. However, when considering the effect of the platform‐building strategy given that a third‐party sharing platform already exists, the results are considerably different.

The rest of this paper is organized as follows. Section 2 reviews the related works. Section 3 lays out the basic elements of the model. Then, we formulate the problem in different scenarios and analyze the games in Section 4. The main results are presented in Section 5. Section 6 studies the paralleled results when the exclusive sharing platform is built by the low‐quality manufacturer. Finally, Section 7 summarizes our results. All proofs are provided in the Supporting Information.

LITERATURE REVIEW

As the focus of the sharing economy is on the peer‐to‐peer sharing platform along with the two‐sided market it services, much research has been devoted to understanding the economic incentives of the platform managers and the consumers who use the service, as well as in addressing the marketing and operations issues they face. For example, Benjaafar et al. (2019) propose an innovative model formulation to understand how a peer‐to‐peer sharing platform matches supply with demand in the two‐sided market. Fraiberger and Sundararajan (2017) analyze the segmentation of the sharing market and identify the target customers who tend to use the platform. These papers provide some fundamental economic implications of the peer‐to‐peer sharing market. Several other papers focus on the platform's pricing issues, which include setting prices for the renters (demand) and setting wages for the owners (supply). Taylor (2018) and Bai et al. (2019) consider the price and wage decisions based on several operational factors in the on‐demand service setting. Adopting a similar modeling framework, Benjaafar et al. (2022) address important issues related to labor welfare. Banerjee et al. (2016) show that static pricing outperforms dynamic pricing, but is less robust to the system parameters. Moreover, Cachon et al. (2017) and Hu and Zhou (2020) also study the pricing problem of the platform in order to understand the matching mechanism in more specific settings. Finally, Gurvich et al. (2019) tackle a similar problem but focus on the self‐scheduling issue that may arise in the car‐sharing context.

Our paper contributes to the nascent, yet, growing literature on sharing economy, and adopts the modeling techniques based on customer utility, following the basic analytical approaches laid out by the above works. However, our focus is on analyzing the competitive strategy of an upstream manufacturer who supplies products that are shared in the downstream market. Therefore, our paper is more related to the stream of literature that studies the impact of sharing economy on channel partners. Using different model formulations, Jiang and Tian (2018) and Weber (2016) show that although peer‐to‐peer sharing intuitively reduces the incentive for the consumers to own a product, it can benefit the firm who sells to the sharing market if the production cost is relatively high. Moreover, Razeghian and Weber (2019) focus on product durability and show that the presence of a peer‐to‐peer sharing platform never decreases firm's incentive to provide durability and that the optimal durability may even increase in production cost. Finally, in a two‐tier supply chain setting, Tian and Jiang (2018) explore the upstream manufacturer's capacity and wholesale price decisions when its buyer is selling to a sharing market.

The peer‐to‐peer sharing platform studied in the papers above belong to a third party. To the best of our knowledge, there is limited literature that looks at manufacturer‐built peer‐to‐peer sharing platforms. One is by Weber (2017), who studies how to set retail price and the sharing tariff for a firm's “smart” product. The platform is firm‐run in the sense that peer‐to‐peer sharing may be done under the supervision of the firm. In another paper, Abhishek et al. (2021) study and compare different business models for the manufacturer in the presence of a downstream sharing market. They find that the manufacturer and consumers can both benefit from the peer‐to‐peer sharing for intermediate ranges of consumer heterogeneity in usage level. In addition, they find that it is optimal for the firm to operate a frictionless platform in order to match supply with demand. Finally, Tian et al. (2021) study a manufacturer's entry strategy in the product‐sharing market and find that the optimal strategy will depend on the marginal production cost. Our paper also treats production cost as a moderating variable, but is quite different from the above works, because we explicitly focus on a duopoly setting and the product quality level, which plays an important part in affecting consumers' preference. In fact, our results show that product quality differentiation would be a key factor that decides the effect of the platform‐building strategy on equilibrium outcomes.

Finally, our paper is among the few first ones to analyze the case where multiple peer‐to‐peer sharing platforms co‐exist and interplay with each other. Recent relevant works include Bernstein et al. (2021), Nikzad (2017), and Cohen and Zhang (2022). However, in those papers, the scope and the model formulation are quite different from ours. More importantly, none of them takes the perspective of an upstream manufacturer like we do. In this regard, our paper contributes to this stream of literature with a novel standpoint.

MODEL SETUP

In this section, we describe the major components of our model framework. For ease of reference, the key notations used in this paper are listed in EC.1 of the Supporting Information.

Manufacturers Consider two manufacturers whose products are vertically differentiated in their quality levels, denoted by $q_i>0$ ( $i=L,H$ ), with $q_L<q_H$ . They both sell to a common consumer market, and are therefore engaged in a price competition. Assume that, for $i=L,H$ , manufacturer i charges a unit selling price $w_i$ and incurs a unit production cost, $k{q}_i$ , which is proportionate to its quality. The coefficient $k>0$ , which is assumed to be an exogenous constant, represents the common cost contributors in the production processes for both manufacturers.

Platforms We consider two peer‐to‐peer sharing platforms. First, there is a third‐party platform, ${\mathbf{P}}_1$ , which is not manufacturer‐specific. Hence, products from both manufacturers may be shared on this platform and the consumers who rent a product know the product quality ex ante. Let $p_{i1}$ be the rental price (per unit time) for product i, and α₁ be the commission rate on platform ${\mathbf{P}}_1$ . Thus, the consumers who rent product i on ${\mathbf{P}}_1$ are charged $p_{i1}$ and those whose products are shared receive $(1-{\alpha }_1)p_{i1}$ ; the rest is collected by the platform. As the third‐party platform is not the focus of our research, we consider α₁ as an exogenous parameter, which is an assumption commonly made in prior related research (see, e.g., Benjaafar et al., 2019; Jiang & Tian, 2018). Besides, this assumption is also in line with reality; indeed, a survey of major peer‐to‐peer sharing platforms reveals that commission rates fall mostly within a relatively narrow range from 30% to 40% and do not typically vary (Benjaafar et al., 2019, p. 9). Hence, based on its practical meaning, we further assume $0<{\alpha }_1<1/2$ .

To derive the equilibrium rental price on the platform, we assume that ${\mathbf{P}}_1$ follows the market clearing mechanism: The pricing decision is made such that supply, which is from the owners sharing their products in the nonutilizing time, and demand, which is from the renters in need of utilizing the products, are equal at equilibrium. This assumption is appropriate when the third‐party platform does not dictate the rental price but instead lets consumers to decide it; Turo, for example, is such a platform. As each owner wants to pair with a renter and vice versa, the equilibrium outcome would be a matching between the total supply and the total demand. Note that the market clearing mechanism is also frequently assumed in the peer‐to‐peer literature (see, e.g., Abhishek et al., 2021; Jiang & Tian, 2018; Tian & Jiang, 2018).

Second, facing the emergence of the sharing economy and the existence of the third‐party sharing platform, a manufacturer may build its own sharing platform, ${\mathbf{P}}_2$ , which is exclusive to its own product and thus the opponent's product is not eligible to appear on it. Thus, the platform‐building manufacturer may leverage the potential benefit presented by the sharing market. In our main model (Sections 4 and 5), we consider the case where the high‐quality manufacturer H (“the manufacturer” for short, in the main model) builds its own platform. Although this case fits in our motivating examples, the platform‐building manufacturer may be L as well. In Section 6, we show that similar study can be done when the low‐quality manufacturer L builds the exclusive platform. Like the third‐party platform, the unit time rental price is denoted by $p_{H2}$ and the commission rate is α₂. Having the full control over the platform, the platform‐building manufacturer can decide the rental price and the commission rate to maximize profit. As both platforms are promoting access to the product usage rather than ownership, they are competing with each other.

Consumers Let all the targeted consumers form a market of size 1. Suppose that the product usage level of consumers is $x\in [0,1]$ , which represents the fraction of time they plan to use the product. We remark that the usage level may be any random variable that has continuous distribution over [0,1], in which case our model remains the same if we treat x as the expectation of this random variable. In EC.2 of the Supporting Information, we provide the proof and justify the rationality of this model assumption. Consumers are heterogeneous in the derived value from their use of the product. We assume that the unit‐time usage value, $v\sim U[0,1]$ , is a uniformly distributed random variable. With the emergence of the sharing economy, consumers may either purchase the product and become owners or use the product by renting on the platform and become renters. In the following, we specify the utility functions for owners and renters, respectively, and characterize the consumer behaviors.

Owners utility. Let $u_o^{(ij)}$ be the utility of a product $i\in \{L,H\}$ owner on platform $j\in \{1,2\}$ ( $i\ne L$ whenever $j=2$ , due to exclusiveness of ${\mathbf{P}}_2$ ). Then, we have $$u_o^{(ij)}(v)=x{q}_{i}v+(1-x)(1-{\alpha }_j)p_{ij}-w_i.$$ 1

The first term in the above owners utility function is the valuation on usage, $x{q}_{i}v$ ( $i=L,H$ ), which is proportionate to the quality of the product. Thus, vertical differentiation has an impact on market segmentation. The second term ⁴ in (1) represents the income from sharing the product on the platform. The rental price is therefore a key factor that influences the consumers' propensity to purchase the products and become owners. Finally, we assume that all components in the utility function have the same unit (e.g., on an hourly basis). Thus, x is the fraction of an hour that the owner plans to use the product, the rental price is an average hourly rate, and the selling price $w_i$ is calculated as an hourly, rather than lifetime, ownership cost.

Renters utility. Let $u_r^{(ij)}$ be the utility of a renter on platform $j\in \{1,2\}$ renting product $i\in \{L,H\}$ ( $i\ne L$ whenever $j=2$ , due to exclusiveness of ${\mathbf{P}}_2$ ). We write this renter's utility as $$u_r^{(ij)}(v)=x({\mu }_i{q}_{i}v-p_{ij}).$$ 2

One distinguishing feature of the renters utility in our paper is that we assume consumers renting product i may only derive a fraction, ${\mu }_i\in (0,1]$ , of the usage valuation compared to owning the product. This fraction of the quality pertains to the mere usage of the product, and the rest, $(1-{\mu }_i)q_i$ , is associated with ownership possession. Indeed, it is plausible that just using a product without ownership transfer may only amount to a discounted value compared to using it as an owner. Usually, the notion of “social comparison” can generate certain social status utility to the products owners, whereas it would be absent for the renters. Moreover, this difference is more noticeable when the product becomes more premium; therefore, for simplicity ⁵ , we assume $0<{\mu }_H\le {\mu }_L=1$ . In addition, we further assume ${\mu }_H{q}_H>q_L$ to reflect the fact that renting high‐quality product is more attractive than owning low‐quality product. Finally, it is noteworthy that the renters are able to perceive the quality of the to‐be‐shared product along with the corresponding rental price before sharing transpires.

Consumer behaviors. Based on the utility functions (1) and (2), the consumers behave in a utility‐maximizing manner. Let $O_{ij}$ be the size of potential owners of product i on ${\mathbf{P}}_j$ and $R_{ij}$ be the size of product i renters on ${\mathbf{P}}_j$ . These sizes can be determined when consumers compare the utility derived from each feasible option, that is, being an owner, being a renter, or taking the outside option (zero utility). Specifically, given the usage valuation v for a consumer, the maximum utility of being an owner is $U_o(v)=\max \{u_o^{(H1)},u_o^{(L1)},u_o^{(H2)}\}$ and the maximum utility of being a renter is $U_r(v)=\max \{u_r^{(H1)},u_r^{(L1)},u_r^{(H2)}\}$ . Hence, for $i\in \{L,H\}$ and $j\in \{1,2\}$ ( $i\ne L$ if $j=2$ ), we have $$O_{ij}=\mathbf{Prob}\left(u_o^{(ij)}(v)\ge \max \{U_o(v),U_r(v),0\}\right);$$ 3 $$R_{ij}=\mathbf{Prob}\left(u_r^{(ij)}(v)\ge \max \{U_o(v),U_r(v),0\}\right).$$ 4

Therefore, from the utility functions (1) and (2), we may deduce that the platform can control the owner and renter sizes by adjusting the rental price. Higher rental price will encourage consumers to be owners, whereas lower price induces larger renter size. Moreover, the platform‐building manufacturer can affect the owner and renter size via the product selling price. In general, expensive product ownership would incentivize consumers to become renters. Using the above owner and renter sizes, we can directly derive the platform supply and demand in terms of the amount of usage time.

PROBLEM FORMULATION AND ANALYSIS

Along the development of peer‐to‐peer sharing economy, we have the benchmark scenario where no sharing platform exists, the scenario where a single third‐party platform emerges, and the scenario where the manufacturer builds its own sharing platform to co‐exist with the third‐party platform. We formulate the problem as a Stackelberg game in each of the three scenarios and establish the existence and uniqueness of Nash equilibrium under sufficient conditions.

Scenario B: Benchmark

To study the impact of the sharing economy, we first analyze the benchmark case (scenario B) where no peer‐to‐peer sharing platform exists. In this scenario, our problem degenerates to the classic duopoly price competition with vertical differentiation. Specifically, the game can be formulated as follows.

• (1)

The two manufacturers simultaneous determine the selling prices, $w_i$ ( $i=L,H$ ), to maximize their respective profits, which equal to the margin, $w_i-k{q}_i$ , multiply the sales volume.

(2)

The consumers choose to purchase product L or product H by comparing utility (1) (with $p_{ij}=0$ in the function), after which the sales are realized.

In this benchmark scenario, the consumers will either purchase the ownership of a product or leave for outside options. We will see more complex market structures regarding consumers segmentation in other scenarios.

Scenario S: Single existing platform

Now, as the sharing economy emerges, we consider scenario S, where a single third‐party sharing platform exists. Here, the manufacturers still compete in price for the traditional product selling market as a vertically differentiated duopoly. However, the consumers face more options in terms of using the products. As such, the problem is formulated based on the following multiple stages.

• (1)

Anticipating the ensuing consumer behavior and platform activities, which decide the owner size $O_{i1}$ of product i on the platform ${\mathbf{P}}_1$ , the two manufacturers simultaneously set the selling prices to maximize the profit, $${\pi }_i=(w_i-k{q}_i)O_{i1},i\in \{L,H\}.$$ 5

(2)

Given the selling prices of the products, consumers maximize their utility on the one hand and the platform ${\mathbf{P}}_1$ sets rental price $p_{i1}$ for product i to clear market on the other; that is, the following is achieved for the sharing market: $$(1-x)O_{i1}=x{R}_{i1},i=L,H.$$ 6

The above owner size $O_{i1}$ and renter size $R_{i1}$ for $i\in \{L,H\}$ are given by Equations (3) and (4), with the understanding that $u_o^{(H2)}$ and $u_r^{(H2)}$ are removed because there is only one platform, ${\mathbf{P}}_1$ .

As previously mentioned, we assume that the commission rate α₁ is exogenous, and the rental price is derived via the market clearing mechanism, which is to match supply with demand. This approach is commonly seen in this stream of research (Abhishek et al., 2021; Jiang & Tian, 2018; Tian & Jiang, 2018).

Scenario M: Manufacturer builds its platform

When the manufacturer decides to deploy the platform‐building strategy, scenario M occurs, where the manufacturer‐built platform ${\mathbf{P}}_2$ and the third‐party platform ${\mathbf{P}}_1$ co‐exist. In this scenario, the two manufacturers still compete in price in a vertical differentiated setting, but manufacturer H will also operate a self‐built exclusive platform ${\mathbf{P}}_2$ to compete in the sharing market. Again, we formulate a multi‐stage game that proceeds as follows:

• (1)

Manufacturer L and manufacturer H simultaneously sets the selling price $w_L$ and $w_H$ , respectively. Both firms make decisions to maximize their respective profits: 7

(2)

Entering the second stage, consumers will maximize their utility, manufacturer H decides commission rate α₂ and rental price $p_{H2}$ to maximize the profit ${\pi }_H$ , and platform ${\mathbf{P}}_1$ sets rental price $p_{i1}$ for product i to match the supply and the demand in terms of usage time, that is, $$(1-x)O_{i1}=x{R}_{i1},i=L,H.$$ 8

Similar to the previous scenario, the above owner and renter sizes are given by Equations (3) and (4). While choosing which platform to reside, an owner of product H will consider the income from the platform that rents out the product. We assume ⁶ that in case of a tie in the rental income, the owner consumer will choose ${\mathbf{P}}_2$ over ${\mathbf{P}}_1$ .

The next lemma shows some structural properties of the manufacturer's problem that could be helpful to our analysis. Lemma 1

Consider scenario M, where the manufacturer‐build platform co‐exists with the third‐party sharing platform. Then, the profit‐maximizing rental price must agree with the market clearing rental price. Moreover, any commission rate ${\alpha }_2\ne {\alpha }_1$ will not be in the equilibrium.

Lemma 1 identifies an important structural property, which allows us to use the market clearing mechanism for the manufacturer‐built platform. Indeed, although the manufacturer aims at maximizing the profit, the third‐party platform will always match the usage supply with demand. Thus, any mismatch from ${\mathbf{P}}_2$ will be absorbed and corrected by ${\mathbf{P}}_1$ , which will inflict harm on the platform‐building manufacturer's profit.

Moreover, Lemma 1 rules out certain off‐equilibrium decisions. In particular, due to the tie breaking rule, setting ${\alpha }_2>{\alpha }_1$ makes ${\mathbf{P}}_2$ lose all the owners, whereas setting ${\alpha }_2<{\alpha }_1$ is sub‐optimal in maximizing profit. Thus, ${\alpha }_2={\alpha }_1$ is the only outcome and platform ${\mathbf{P}}_2$ will attract all the owners of product H, resulting in $O_{H1}=0$ .

Analysis

Based on the above problem formulation in each of the three scenarios, we solve the Stackelberg game using backward induction for the sub‐game perfect Nash equilibrium. Four equilibrium outcomes in particular will be our focus in this paper; namely, the manufacturers' profits, ${\pi }_L$ and ${\pi }_H$ , the consumer surplus $CS$ , which is the integration of all consumers' utilities, and the social welfare $SW$ , which is the sum of every party's welfare, including the platforms if there is any. Lemma 2

Consider scenario $n\in \{B,S,M\}$ . Fix $q_L>0$ and let $t:=q_H/q_L$ . There exists a unique sub‐game perfect Nash equilibrium, in which the manufacturers' profits $({\pi }_L^n,{\pi }_H^n)$ , the consumer surplus $C{S}^n$ , and the social welfare, $S{W}^n$ , are all positive if the parameters satisfy $$\begin{array}{c}\hfill \{0<x<1,0<{\alpha }_1<1/2,0<{\mu }_H\le 1,0<k<x,t>t^n\}.\end{array}$$ 9The equilibrium outcomes, $({\pi }_L^n,{\pi }_H^n,C{S}^n,S{W}^n)$ , and the threshold, $t^n$ , are specified in EC.5 of the Supporting Information.

Lemma 2 above gives the feasible region of the parameters, within which all our subsequent discussions are restricted, and establishes the existence and uniqueness of the equilibrium. From the proof we can see that the equilibrium outcome $Z\in \{{\pi }_L,{\pi }_H,CS,SW\}$ in scenario $n\in \{B,S,M\}$ can be written as homogeneous functions in $q_L$ and $q_H$ . Therefore, we can simply assume $q_L>0$ is fixed and factor it out, leaving $t=q_H/q_L$ , which represents quality differentiation between products, as the primary variable in our study. Furthermore, the production cost coefficient k is a critical moderating variable because the production investment may affect the proportion of the production volume that contributes to the sharing market. Hence, every equilibrium outcome is a function of $(t,k)$ along with other exogenous parameters.

Naturally, we will constrain our focus within a feasible region where the manufacturers' product sales, and therefore the equilibrium outcomes, are nonnegative. In the feasible set (9), $k<x$ and $t>t^n$ together represent a sufficient condition to ensure that the manufacturers' sales are positive. Recall that in our model setup, we assume ${\mu }_H{q}_H>q_L$ . Hence, the lower bound of t in the lemma satisfies $t^n\ge 1/{\mu }_H$ . These results lay out the technical foundations for our subsequent analysis.

RESULTS

The main objective of our analysis is to characterize the changes of the equilibrium outcomes caused by the emergence of sharing economy and the deployment of the platform‐building strategy. Define $Z^{nl}=Z^l-Z^n$ as the difference between the equilibrium outcome $Z\in \{{\pi }_L,{\pi }_H,CS,SW\}$ when the scenario transits from n to l ( $n,l\in \{B,S,M\}$ ).

Although our problem formulation in each scenario admits closed form solution in the general form (see Lemma 2), the analysis can easily get intractable when comparing the equilibrium outcomes between scenarios, rendering difficulties in deriving meaningful insights. Hence, to clearly illustrate the comparison between the equilibrium results in different scenarios, we will adopt the following analysis roadmap.

First, we divide our study into two groups: profit impact and welfare implication. The former refers to the changes in manufacturers' profits ( $Z={\pi }_L,{\pi }_H$ ), which will be investigated in Subsection 5.1. The latter includes the comparison of consumer surplus and social welfare ( $Z=CS,SW$ ) between scenarios, which will be shown in Subsection 5.2.

Then, for each group, the equilibrium comparison will separately consider two cases: (1) ${\mu }_H=1$ , and (2) ${\mu }_H=1/2$ . Recall that ${\mu }_H\le {\mu }_L=1$ , capturing the fact that the ownership utility is practically no less than the usage utility and the gap is usually larger when the product has a more premium brand name. Hence, the two cases correspond to situations where renters of product H derive full and partial utility, respectively.

Finally, in each case, we analyze the direction of change in three comparable scenario pairs, namely, from scenario B to scenario S, from scenario S to scenario M, and from scenario B to scenario M. Thus, we examine the properties of the difference functions $Z^{BS}$ , $Z^{SM}$ , and $Z^{BM}$ .

Comparing manufacturers' profits

At the beginning, the two manufacturers compete in the classic vertically differentiated duopoly setting. With the emergence of a third‐party sharing platform, some consumers are incentivized to forgo the ownership and simply pay for the usage of the products owned by peers. Then, the manufacturer builds its own platform, seeking benefits from the sharing economy, even though some of its product owners may convert to renters. In this subsection, we scrutinize the differences between the manufacturers' profits when the scenario develops from one to another.

Case 1: ${\mu }_H=1$ .

We first conduct the study under the assumption ${\mu }_H=1$ . Along with our basic premise ${\mu }_L=1$ , this case means that all renters have exactly the same quality perception as the owners. In other words, the ownership of the products generate the same utility as the mere usage of the products. Hence, a natural conjecture is that quality differentiation will be relatively independent with the impact of sharing platforms in terms of dictating the consumer behaviors. We give more details under different scenario transitions in the following.

From scenario B to scenario S. First, we focus on $Z^{BS}$ , for $Z={\pi }_L,{\pi }_H$ . The comparison reveals how the emergence of sharing economy affects the manufacturers. Will either manufacturer be better off due to the sharing market operated by the third‐party platform? We answer this question below. Proposition 1

Suppose ${\mu }_H=1$ . There exists a threshold $k_0^{BS}\in (0,x)$ such that the equilibrium profit change for manufacturer i ( $i=L,H$ ) from scenario B to scenario S, ${\pi }_i^{BS}$ , satisfies the following: ${\pi }_i^{BS}\le 0$ if $0<k\le k_0^{BS}$ and ${\pi }_i^{BS}>0$ if $k_0^{BS}<k<x$ . Moreover, the threshold $k_0^{BS}$ is increasing in x and α₁.

Proposition 1 compares the manufacturers' equilibrium profits between scenario B and scenario S. Several observations are interesting. First, the emergence of sharing economy may or may not benefit the manufacturers, depending on the production cost coefficient k. The manufacturers will be better off if and only if k is larger than a threshold $k_0^{BS}$ . Note that the related literature (e.g., Jiang & Tian, 2018) found that the unit production cost has the same effect on a monopoly firm's profit facing sharing economy, because the sharing market will make the costly production process more efficient in meeting consumers' need. Here, we extend that rationale to a duopoly setting where ${\mu }_H=1$ . Indeed, a smaller k means that the manufacturers could produce more if there were no sharing platform that discourages consumers from purchasing the products.

Second, quality differentiation plays no role in determining the manufacturers' profit change. Moreover, the threshold $k_0^{BS}$ is the same for both manufacturers. This observation can be understood as follows. When ${\mu }_H=1$ , all consumers are facing the same product quality differentiation, large or small, and therefore the quality becomes a common factor to consumers, leading to the same consumer behavior for either manufacturer before and after the emerging of the third‐party platform. As a result, its impact will prevail in the profit performance of the manufacturers.

Third, the threshold $k_0^{BS}$ is shown to increase in x and α₁. This means that the sharing economy is more likely to benefit the manufacturers when the consumers' usage of the products is lower or the commission rate of the third‐party platform is smaller. To understand this result, note that the manufacturers can benefit from the sharing market when the owners size is boosted (because more consumers will purchase the products). Hence, lower usage level or smaller commission rate sends incentives to consumers to become owners and share their products on the platform. As a result, the manufacturers can charge higher selling prices to gain more profits.

From scenario S to scenario M. Next, suppose that manufacturer H, seeing the third‐party sharing platform ${\mathbf{P}}_1$ and the potential of the sharing market, decides to build its own platform ${\mathbf{P}}_2$ . Intuitively, the existence of ${\mathbf{P}}_2$ poses a direct competition against ${\mathbf{P}}_1$ . However, as some consumers will become renters, it is not clear whether the sharing market could compensate the product selling market for the manufacturer. To find the answer, we will examine ${\pi }_L^{SM}$ and ${\pi }_H^{SM}$ . Proposition 2

Suppose ${\mu }_H=1$ . From scenario S to scenario M, manufacturer L is always worse off and manufacturer H is always better off; that is, ${\pi }_L^{SM}<0$ and ${\pi }_H^{SM}>0$ .

Proposition 2 shows that the manufacturer's platform‐building strategy has completely opposite effects on the two manufacturers' profits. For manufacturer H, the foremost advantage brought by the self‐built platform is the flexibility in leveraging profits from two sources, that is, profit from selling to the owners and commission from operating platform ${\mathbf{P}}_2$ . It is worth noting that manufacturer H will decrease its selling price from scenario S to scenario M, and the profit from product selling actually drops in spite of increased sales volume.

However, larger sales of product H will increase its accessibility in the sharing market, which boosts the usage of the high‐quality product and diminishes the usage of the low‐quality product in the sharing market. Hence, the gain from the sharing market via building ${\mathbf{P}}_2$ is larger than the loss from the product selling market (due to conversion from owners to renters) for the manufacturer.

On the other hand, from scenario S to scenario M, the low‐quality manufacturer suffers from profit loss regardless of the system parameters. Indeed, the effect of platform ${\mathbf{P}}_2$ , while mostly positive for manufacturer H, is completely negative for manufacturer L. As the two manufacturers are engaged in a price competition for the product selling market, building platform ${\mathbf{P}}_2$ effectively enhances manufacturer H's competitive advantage, as it yields additional profit from the sharing market. As a consequence, manufacturer H becomes more aggressive in the product selling market and is able to set lower selling price to compete with manufacturer L. Facing a more intensified price competition, manufacturer L has no other means to combat against it but to also lower the selling price and bear the harm.

From scenario B to scenario M. The previous two scenario transitions allow us to see how manufacturers' profits are affected by the development of sharing economy, that is, from no sharing to a single third‐party sharing platform, and to the launching of the manufacturer‐built platform. However, although $Z^{BM}=Z^{BS}+Z^{SM}$ , for $Z={\pi }_L,{\pi }_H$ , we still cannot have definite comparison results between scenarios B and M. Note that the comparison results can shed lights into the impact of the manufacturer's platform‐building strategy on the traditional duopoly in the absence of sharing economy. The following proposition states our findings in this regard. Proposition 3

Suppose ${\mu }_H=1$ . From scenario B to scenario M, manufacturer H is always better off. For manufacturer L, there exists a threshold $k_0^{BM}$ for k such that ${\pi }_L^{BM}\le 0$ if $0\le k\le k_0^{BM}$ ; when $k_0^{BM}<k<x$ , there exists a decreasing function of k, $t_0^{BM}(k)$ , as a threshold for t, such that ${\pi }_L^{BM}>0$ if $t>t_0^{BM}(k)$ and ${\pi }_L^{BM}\le 0$ otherwise. Moreover, $k_0^{BM}$ increases in x and α₁, and $k_0^{BM}>k_0^{BS}$ .

For the platform‐building manufacturer, the benefit of this strategy prevails in scenario M despite the fact that the third‐party sharing platform may hurt the manufacturer from scenario B to scenario S. That is, ${\pi }_H^{SM}>0$ is the dominating term for ${\pi }_H^{BM}={\pi }_H^{BS}+{\pi }_H^{SM}$ even though ${\pi }_H^{BS}$ may be negative when k is small (see Proposition 1). This means that it is beneficial for the manufacturer to actively enter the sharing market when peer‐to‐peer sharing economy emerges, especially when the production is not costly.

For manufacturer L, on the other hand, the effect of platform ${\mathbf{P}}_2$ on its profit compared to scenario B is similar to the effect of platform ${\mathbf{P}}_1$ . In particular, there is a threshold $k_0^{BM}$ for the production cost coefficient k, such that the profit decreases when $k\le k_0^{BM}$ . Note that the threshold $k_0^{BM}$ is independent of t. Hence, like Proposition 1, small production cost coefficient will make manufacturer L worse off after a sharing platform comes into the picture, no matter it is a third‐party platform or a platform built by manufacturer H. However, for large production cost coefficient, unlike Proposition 1, the quality ratio t starts to become a deciding factor. Specifically, Proposition 3 states that, when the production cost is large ( $k_0^{BM}<k<x$ ), manufacturer L can be better off if the quality differentiation is larger than a k‐dependent threshold $t_0^{BM}(k)$ . This situation corresponds to the case where the duopoly competition in the product selling market is relatively soft and scenario B is not very profitable. Hence, benefited by the platform‐building strategy, manufacturer H will not intensify the price competition for the largely differentiated opponent, leading to a favorable outcome for manufacturer L.

Finally, it is worth mentioning that, compared to the threshold $k_0^{BS}$ , the threshold $k_0^{BM}$ here has the same monotonicity property with respect to x and α₁. Thus, the effect of the third‐party sharing platform ${\mathbf{P}}_1$ and the manufacturer‐built platform ${\mathbf{P}}_2$ on manufacturer L's profit depends on the consumers' usage level and the commission rate in the same way: lower x or smaller α₁ alleviates the harm of the sharing platform. Furthermore, as we have $k_0^{BM}>k_0^{BS}$ , platform ${\mathbf{P}}_1$ is more likely to bring benefit to manufacturer L compared to ${\mathbf{P}}_2$ .

Case 2: ${\mu }_H=1/2$

Next, we repeat our study under the assumption ${\mu }_H=1/2$ . The foremost difference this assumption brings to the equilibrium comparison is that, unlike the previous case, quality differentiation will influence the segmentation of the sharing market in a more complicated way. Specifically, the renters of product H on the sharing platform are effectively facing a new product with quality $q_H/2$ , which is in between $q_L$ and $q_H$ . Thus, consumer behavior will be determined by their valuation toward owning/renting a product L, owning a product H, and renting a product H. This will lead to significant differences in our findings.

From scenario B to scenario S/M. First, we examine how the manufacturers' profits would change from scenario B to the scenario where either a third‐party platform ${\mathbf{P}}_1$ exists alone (scenario S) or the manufacturer‐built platform ${\mathbf{P}}_2$ co‐exists with ${\mathbf{P}}_1$ (scenario M). We investigate these two scenarios together because, as we shall see, they share the same structural properties and can be explained side‐by‐side. In addition, the paralleled results can provide insights into the differences between the effects of the two sharing platforms. The following proposition summarizes the findings about the equilibrium comparison. Proposition 4

Suppose ${\mu }_H=1/2$ . Consider the change of manufacturers' equilibrium profits from scenario B to scenario n ( $n=S,M$ ). For manufacturer i ( $i=L,H$ ), there exist two thresholds $0<k_i^{Bn}<K_i^{Bn}<x$ such that ${\pi }_i^{Bn}\ge 0$ if $k\ge K_i^{Bn}$ , and ${\pi }_i^{Bn}\le 0$ if $k\le k_i^{Bn}$ . When $k_i^{Bn}<k<K_i^{Bn}$ , there exists a decreasing function of k, $t_i^{Bn}(k)$ , as a threshold of t, such that ${\pi }_i^{Bn}>0$ if $t>t_i^{Bn}(k)$ and ${\pi }_i^{Bn}\le 0$  otherwise.

Proposition 4 reveals a couple of interesting implications of the effect of peer‐to‐peer sharing platform on a classic vertically differentiated duopoly. Moreover, these implications are in contrast with those from Propositions 1 and 3. First, under the assumption ${\mu }_H=1/2$ , even the platform‐building manufacturer may be hurt from scenario B to scenario M. Specifically, this happens when either production cost k is small or, if k is intermediate, t is smaller than a k‐dependent threshold. If the latter case happens, the quality levels $q_H$ and $q_L$ are close to each other, and therefore the renters of product H perceive the quality level $q_H/2$ that is even closer to product L quality $q_L$ . This would hurt the sharing market for manufacturer H, leading to less benefit from building platform ${\mathbf{P}}_2$ .

Second, Proposition 4 highlights the key role of quality differentiation in several ways. To illustrate this point, it is helpful to provide some technical details about the thresholds mentioned in the results. As the threshold $t_i^{Bn}(k)$ decreases in k, we can find its inverse function, ${\kappa }_i^n(t)$ , which decreases in t; then, ${\kappa }_i^n(t)$ serves as the threshold for k in the sense that ${\pi }_i^{Bn}\ge 0$ if $k\ge {\kappa }_i^n(t)$ for $i=L,H$ and $n=S,M$ . Moreover, define $k_i^{Bn}={inf}_t{\kappa }_i^n(t)$ and $K_i^{Bn}={sup}_t{\kappa }_i^n(t)$ , which are the two thresholds in the proposition and are independent of t. Therefore, similar to the rationale discussed following Proposition 1, smaller production cost makes manufacturers worse off facing sharing economy, whereas larger production cost makes them better off. However, here the threshold of production cost coefficient depends on the quality ratio. Therefore, our finding extends the results in monopoly setting from the related literature to the vertical differentiation duopoly setting.

To understand the dependence on t of the threshold result, note that, with small t, the manufacturers will engage in an intense competition and set low selling prices. Worse still, when there is a sharing platform, another product of quality $q_H/2$ appears in the sharing market, which again induces intense competition. Hence, the sharing market will not be profitable as expected, and both manufacturers may be hurt by the lowered prices. By contrast, when t is large, product quality levels are sufficiently differentiated and therefore the competition (in product selling market as well as in sharing market) is soft; as a result, both manufacturers may benefit from the sharing platform, which enhances the ownership value and boosts the sales.

From scenario S to scenario M. Next, we study the manufacturers' profits change from scenario S to scenario M. The comparison between these two scenarios sheds light into the effect of manufacturer H building its own sharing platform to compete for the sharing market. Hence, some of the results are comparable to Proposition 2. However, the assumption ${\mu }_H=1/2$ may twist other results to reflect the consequences of product H renters having lower usage utility than ownership utility. We give the main findings in the next proposition. Proposition 5

Suppose ${\mu }_H=1/2$ . From scenario S to scenario M, manufacturer H is always better off, that is, ${\pi }_H^{SM}>0$ . For manufacturer L, its profit ${\pi }_L^{SM}\le 0$ if $k\ge x(1-x)/2$ ; otherwise, there exists an increasing function of k, $t_0^{SM}(k)$ , as a threshold for t such that ${\pi }_L^{SM}>0$ if $t>t_0^{SM}(k)$ and ${\pi }_L^{SM}\le 0$  otherwise.

First of all, the platform‐building manufacturer is always better off from scenario S to scenario M, which is the same result as Proposition 2 where ${\mu }_H=1$ . That is, regardless of whether the renters of product H have discounted usage utility or not, manufacturer H can always benefit from building its own platform. Recall that the benefits include having two sources of profits, namely, product selling profit and platform operating profit. However, as the platform is essentially encouraging consumers who would purchase the product in the absence of sharing economy to become renters, there is a cannibalization effect from building the platform. In the case ${\mu }_H=1$ , we mentioned that the product selling profit indeed drops after the manufacturer builds platform ${\mathbf{P}}_2$ . By contrast, when ${\mu }_H=1/2$ , we find that the product selling profit of manufacturer H can still increase, especially when t is small. Thus, offering the renters on ${\mathbf{P}}_2$ a product with quality $q_H/2<q_H$ can also protect the platform‐building manufacturer's profit in product selling.

Second, manufacturer L's profit could increase due to its opponent's building an exclusive sharing platform, which is not seen in Proposition 2. Interestingly, manufacturer L's profit is more likely to increase if the production cost coefficient k is relatively small. This is contrary to the condition for ${\pi }_L^{BS}>0$ , which requires k to be large.

To understand this result, note that the quality differentiation is not the same for renters of product H and the rest of the consumers. Hence, for the platform‐building manufacturer, its product selling market and sharing market face different quality gaps against the competitor. This results in some interplay of manufacturer H's pricing strategy in different market. For example, when k is small, as ${\mu }_H<1$ , the renters of product H perceive less quality than product H owners. Then, the renters size will decrease on ${\mathbf{P}}_2$ . As a response, manufacturer H has to raise selling price $w_H$ to match supply and demand for the sharing market. This will happen because the vertical differentiation is sufficiently large relative to k; that is, $t>t_0^{SM}(k)$ . Therefore, manufacturer L can also increase its selling price and benefit from the relaxed competition. Note that when k is large, the increase of selling price will be very limited to keep the product sales positive, which may not let manufacturer L enjoy a profit increase.

Comparing consumer surplus and social welfare

Aside from the manufacturers' profits, we are also interested in how the consumer surplus and the social welfare change across scenarios. Indeed, the peer‐to‐peer sharing platforms can provide the consumers with more options: they can use the product with or without ownership transfer. Hence, with product renting becomes available, consumers will consider and compare the owners utility and the renters utility. This may result in different consumer behaviors and consumer surplus may change. Moreover, we also study the social welfare change due to the emergence of sharing economy and the deployment of the platform‐building strategy. Note that, in our setting, the social welfare is mostly determined by the total number of consumers that has access to the products usage. We follow the same logic as the previous subsection and divide our analysis into two cases based on the value of ${\mu }_H$ .

Case 1: ${\mu }_H=1$

In this case, the renting products on the sharing platform is perceived as having the same quality as purchasing the ownership of the products. Hence, the sharing market and the product selling market will have structurally similar consumer segmentation, as the quality differentiation is the same to owners as to renters. In particular, we have the following proposition for all three cases of scenario transit. Proposition 6

Suppose ${\mu }_H=1$ . We have $Z^{nl}>0$ for $Z=\{CS,SW\}$ and $nl=\{BS,SM,BM\}$ .

Proposition 6 shows that both the consumer surplus and the social welfare in equilibrium increases from scenario B to scenario S, from scenario S to scenario M, and from scenario B to scenario M. In these scenario transitions, consumers could benefit from more options and the social welfare increases due to the extension of product selling market to sharing market. Moreover, this result is independent of the product cost information and the quality differentiation.

From scenario B to scenario S/M, the peer‐to‐peer sharing market emerges. The foremost effect of the sharing platform is that the ownership value is enhanced, that is, the products owners could monetize the unused time. In fact, as shown in the equilibrium analysis in EC.5 of the Supporting Information, compared to scenario B, scenario S/M results in the same consumers' optimization problem except that the quality $q_i$ is multiplied by a constant ratio for $i=L,H$ (an important condition that makes this statement true is ${\mu }_H=1$ ). As a result, even though the selling price is higher in scenario S/M than in scenario B, the access to products with effectively higher quality makes the consumers better off. Similarly, as the sharing market allows more consumers to derive higher utility either as owners or as renters, the social welfare increases from scenario B to scenario S/M.

From scenario S to scenario M, as mentioned, the manufacturers will engage in a more intense competition and lower the selling prices. A direct consequence is that the consumers become better off. Moreover, based on our proof, the product sales will decrease for manufacturer L but increase for manufacturer H. This is because the competition favors the high‐quality manufacturer when it gets more intense. Note that the social welfare ignores the internal frictions between parties, which include the transactions from consumers to the manufacturers and the platforms. Therefore, the social welfare mainly depend on the production costs (fixed across scenarios) and the total usage utility derived by all consumers. Hence, more consumers have access to higher quality product in scenario M compared to scenario S, leading to a higher social welfare.

Case 2: ${\mu }_H=1/2$

Now, assuming ${\mu }_H=1/2$ , we compare the consumer surplus and the social welfare in different scenarios again. In this case, product H on the sharing platform in effect becomes a new product with quality $q_H/2$ , which is lower than owning product H but higher than owning product L. As a result, the consumer behavior in the sharing market will be different from that in the product selling market. Furthermore, the competition between the vertically differentiated duopoly can affect the sharing market in some ways, causing different changing directions for the consumer surplus and the social welfare. Proposition 7

Suppose ${\mu }_H=1/2$ . For $Z=\{CS,SW\}$ and $nl=\{BS,SM,BM\}$ , there exists a threshold ${\widehat{k}}_Z^{nl}$ such that the difference $Z^{nl}\ge 0$ if ${\widehat{k}}_Z^{nl}\le k<x$ . When $0<k<{\widehat{k}}_Z^{nl}$ , there exists an increasing function of k, ${\widehat{t}}_Z^{nl}(k)$ , as a threshold for t, such that $Z^{nl}<0$ if $t>{\widehat{t}}_Z^{nl}(k)$ and $Z^{nl}\ge 0$  otherwise.

In contrast with Proposition 6, Proposition 7 here indicates the potential decrease of consumer surplus/social welfare as scenario transits. In addition, the $(t,k)$ ‐region in which they decrease is similar in each case. Specifically, from scenario B to scenario S, from scenario S to scenario M, and from scenario B to scenario M, the consumer surplus and the social welfare increase for large production cost coefficient k, but decrease when k is small and t is large. This difference is due to the assumption ${\mu }_H=1/2<1$ , which can be explained as follows.

From scenario B to scenario S/M, unlike the case ${\mu }_H=1$ , the quality levels of the products in the market will not increase by the same factor anymore. In fact, there is an effectively new product with quality $q_H/2$ in the sharing market, which is product H for renting. Hence, the consumers' optimization problem will be completely different. Our analysis (see proof in EC.5 of the Supporting Information) shows the following. When k is small, the product selling prices will increase when t is no less than the threshold given in the proposition, because the duopoly competition is not intense. Besides, the sales of both products will decrease. Therefore, in this case, the consumer surplus and the social welfare will both decrease. By contrast, when k is large, the production is costly. Nevertheless, few products could still be used by many consumers due to sharing among peers. Thus, the consumers are happier and the social welfare also rises.

Similarly, from scenario S to scenario M, our finding in Proposition 7 may be understood by a close look at the changes in products selling prices and sales. When the production cost coefficient k is small and the quality ratio t is larger than the threshold, the selling prices will increase due to larger differentiation and more relaxed competition. As the production is not costly, there is much room for selling price to increase (while keeping sales positive). Hence, the consumers will be hurt. In addition, we find that the low‐quality product's sales will increase, whereas the high‐quality product will sell less. This further hurts the social welfare.

On the other hand, when k is large, the low‐quality product sells less, whereas the high‐quality product sells more. Besides, the selling prices will decrease by a small amount. Hence, the benefit from more access to products at lower prices renders higher consumer surplus. Similarly, the social welfare increases because of larger market coverage of product H, both in the product selling market and the sharing market.

Discussions

In this subsection, we provide a couple of additional discussions based on our findings presented in the previous subsections. We first discuss the impact of ${\mu }_H$ by highlighting several notable differences between the results in the two cases ${\mu }_H=1$ and ${\mu }_H=1/2$ . Then, we discuss the effect of the platform‐building strategy from the angle of the evolution of the sharing economy ecosystem.

Impact of ${\mu }_H$

Subsections 5.1 and 5.2 have illustrated the comparison regarding the equilibrium outcomes in different scenarios. There are several interesting differences in the results under the two cases ${\mu }_H=1$ and ${\mu }_H=1/2$ . Basically, the first case would lead to less involved comparisons, whereas the second case may contain complicated changes across scenarios. Indeed, the core difference between the two cases lies in the quality differentiation perceived by the owners and the renters. When ${\mu }_H=1$ , the product renters feel the same impact of quality on their usage values as the product owners. As such, the partition of owners and renters will not be affected by the quality differentiation but only by the matching of the sharing market. However, when ${\mu }_H=1/2$ , consumer behavior on the sharing platform (either third‐party or manufacturer‐built) starts to depend on the product quality differentiation. In the following, therefore, we discuss the impact of ${\mu }_H$ by noting three relevant insights brought by the assumption ${\mu }_H=1/2$ and use them to explain some of the contrasting points in our analytical findings.

First, with ${\mu }_H=1/2$ , there are effectively three products available for consumers. In addition to products L and H, renting product H becomes the third choice, which renders the quality level $q_H/2$ . As we assume $q_H/2>q_L$ , product H as a rental can attract consumers who were originally using product L. Hence, overall there is more competition when ${\mu }_H$ is less than 1. More importantly, the intensity of the competition hinges on the quality differentiation. This explains the difference in Propositions 1 and 4 concerning changes from scenario B to scenario S. When ${\mu }_H=1$ , the partition of the sharing market is proportionate to the product selling market because all consumers have the same perception of quality differentiation. By contrast, when ${\mu }_H=1/2$ , the third product comes into play and its impact depends on the parameter that measures the quality differentiation, that is, t. Therefore, the threshold of k that determines the profit change of the manufacturers is a function of t in Proposition 4, but is independent of t in Proposition 1. Moreover, as the competition may be quite fierce when t is small, it is more likely that the manufacturers are worse off, which explains the monotonicity of $t_i^{BS}$ in Proposition 4.

Second, when ${\mu }_H=1/2$ , the matching of the sharing market and the sales in the product selling market are interdependent. This is especially the case in scenario M, where manufacturer H builds its own platform and thus can directly affect the sharing market by pricing. An illustrating example is the different result for manufacturer L's profit change from scenario S to scenario M. Recall that manufacturer L will always be hurt by the platform‐building strategy when ${\mu }_H=1$ (Proposition 2), but may be better off when ${\mu }_H=1/2$ (Proposition 5). In the latter case, after building ${\mathbf{P}}_2$ in scenario M, manufacturer H finds that renters view its product with a discounted quality and are thus less willing to participate on the platform; so, the owner size should not be too large so the sharing market can be matched. As a result, manufacturer H may raise selling price, which yields more profit from the product selling market, especially when the duopoly competition is soft (e.g., k is small and t is relatively large). Moreover, manufacturer L could follow manufacturer H to set higher selling price and gain more market, resulting in a better financial performance. Note this will not happen in scenario S, where the sharing platform belongs to the third party and manufacturers cannot effectively interact with the sharing market.

Third, assuming ${\mu }_H=1/2$ means that renters of product H cannot derive full utility compared to owners. This observation has direct implications on the changes of the consumer surplus and the social welfare. Indeed, the emergence of sharing platforms, third‐party or manufacturer‐built, may not be good for consumers. As indicated by Proposition 7, the consumer surplus and the social welfare can indeed decrease as scenario transits from one to another. Recall that renting product H could convert some product L owners/renters, but on the other hand some product H owners may become product H renters. The competition is fierce when t is small and the intense competition is unfavorable to manufacturer L, who may lose much of the market. As a result, more consumers switch from owning product L to renting product H, leading to better consumer surplus and social welfare. However, when t is large, the competition is relaxed and the consumers will be worse off. In addition, due to higher selling price, more product H owners are converted to product H renters, hurting the social welfare. Note that the above situation will not happen if ${\mu }_H=1$ , as shown in Proposition 6, showing the impact of the assumption ${\mu }_H=1/2$ .

Finally, we make a brief remark regarding general values of ${\mu }_H$ . First and foremost, although we capture the usage valuation discount for renters of the high‐quality product by assuming a specific value of ${\mu }_H=1/2$ , all our findings for ${\mu }_H=1/2$ will not change in nature if we use another $0<{\mu }_H<1$ . Indeed, by continuity of the functions Z ( $Z={\pi }_H,{\pi }_L,CS,SW$ ), the threshold results described in our propositions in the case of ${\mu }_H=1/2$ are still valid for ${\mu }_H$ in a neighborhood around 1/2. Then, the differences between the two cases ( ${\mu }_H=1$ and ${\mu }_H=1/2$ ) studied in the paper can be naturally generalized to comparison between ${\mu }_H=1$ and any other $0<{\mu }_H<1$ . As a result, the contrasting points due to ${\mu }_H$ changing from 1 to 1/2 will remain qualitatively the same. In fact, we conduct numerical studies in EC.3 of the Supporting Information to show that the impact of ${\mu }_H$ discussed above is essentially unchanged for any value of ${\mu }_H$ in a certain region determined by the quality ratio t and the production cost k.

Evolution of the sharing economy ecosystem

For a manufacturer, it is an active strategy to leverage the ever‐growing peer‐to‐peer product sharing market by building a sharing platform to facilitate matching the owners of its product with the renters. Our results in Subsections 5.1 and 5.2 show how this move affects the market equilibrium. Here, we further discuss the effectiveness of such a platform‐building strategy from the standpoint of the evolving business ecosystem for the manufacturer. Specifically, the scenario transitions from B to S and from S to M signify an evolution of the manufacturer's business ecosystem as the sharing economy becomes trending. The first transition captures the emergence of sharing economy and introduces a third‐party platform ${\mathbf{P}}_1$ to indirectly compete with the manufacturers for consumers' usage of the products. During this transit, the manufacturers passively adjust to the business environment changes. The second transition, from scenario S to scenario M, represents one possible response a manufacturer could have toward the sharing economy. That is, the manufacturer who builds its own exclusive platform embraces and actively interacts with the sharing market. Therefore, along the line of the changes in the sharing economy ecosystem, we discuss the impact of the platform‐building strategy from a new perspective.

First of all, we look at its impact on the platform‐building manufacturer's financial performance. According to our analytical findings, regardless of the value of ${\mu }_H$ , the platform‐building manufacturer is always better off compared to when only a third‐party platform exists; that is, ${\pi }_H^M>{\pi }_H^S$ . Hence, now that the sharing economy has emerged and the third‐party platform is already existing, it is a profitable move to build its own exclusive platform. Moreover, when the production cost coefficient k is relatively large, we have ${\pi }_H^M>{\pi }_H^S>{\pi }_H^B$ , which means that, for the platform‐building manufacturer, it has benefited from the emergence of sharing economy and it continues to benefit from its own sharing platform. On the other hand, when k is very small, we have ${\pi }_H^B>{\pi }_H^M>{\pi }_H^S$ , which implies that, although the peer‐to‐peer product sharing has made the manufacturer worse off, it can alleviate the loss by building the exclusive sharing platform. Finally, it is possible to have ${\pi }_H^M>{\pi }_H^B>{\pi }_H^S$ (see Propositions 1 and 4). In this situation, the manufacturer is initially hurt by the emergence of the peer‐to‐peer sharing platform; however, after building its own platform, the manufacturer can now benefit from the sharing economy. Here, the platform‐building strategy is the most effective for the manufacturer in terms of enhancing its profit.

Next, we investigate how everyone in the business ecosystem is affected by the scenario transitions. Different parties involved in the economy may experience different impact from the emergence of sharing platform, and they may also have different attitudes toward the platform‐building manufacturer's active strategy. Hence, one interesting question is, from scenario B to scenario S, and from scenario S to scenario M, whether there will be an “all‐win” situation. For the case ${\mu }_H=1$ , as $CS$ and $SW$ are always better off during the scenario transitions, it is just the manufacturers' profits that are concerned; therefore Propositions 1 and 2 have already answered above question. In the following, we use graphical illustration to investigate the case ${\mu }_H=1/2$ .

Figure 1 depicts the profits and welfare changes on the $(t,k)$ ‐plane from scenario B to scenario S and from scenario S to scenario M, respectively. The foremost observation is that, while the “all‐win” region exists when scenario transits from B to S, it is not the case from scenario S to scenario M. Hence, when the production cost coefficient or the quality differentiation is large, everyone will benefit from the emergence of the third‐party platform. However, after manufacturer H builds its own sharing platform, either manufacturer L or the consumer surplus/social welfare will be hurt. Note that the regions for ${\pi }_L^{SM}>0$ and $C{S}^{SM}>0$ (or $S{W}^{SM}>0$ ) share a boundary in the figure. Indeed, manufacturer L will benefit from manufacturer H's platform‐building strategy if the quality differentiation is large and production cost is small (so the competition is soft); this is exactly the condition under which the consumers are hurt.

FIGURE 1

Illustration for the profits and welfare changes as business ecosystem evolves. The figure is for the case ${\mu }_H=1/2$ and we set $x=0.5$ and ${\alpha }_1=0.2$ .

THE PLATFORM‐BUILDING MANUFACTURER IS L

The primary focus of our research is on the effect of platform‐building strategy taken by an upstream manufacturer facing a downstream peer‐to‐peer sharing market. The focal manufacturer builds a sharing platform exclusive to its product; but the opponent manufacturer does not build platform. In a vertically differentiated duopoly setting, the platform‐building manufacturer could have either high‐ or low‐quality relative to its opponent. In the main model, we consider the case where the high‐quality manufacturer, H, deploys the strategy of building its own sharing platform. To complete our analysis, we now study the case where the exclusive platform ${\mathbf{P}}_2$ is built by the (relative) low‐quality manufacturer, L.

To start, we first define a new scenario named M', which is the same as scenario M, except that the roles of the two manufacturers are swapped. Specifically, in this scenario, manufacturer H stays status quo, whereas manufacturer L builds its own platform ${\mathbf{P}}_2$ to co‐exist with the third‐party platform ${\mathbf{P}}_1$ . Using the same problem formulation and analysis approach as in Section 4, we can directly derive the equilibrium results for scenario M'. As the equilibrium analysis is simply to repeat that for scenario M, the details are relegated to EC.5 of the Supporting Information.

Based on the equilibrium results of scenario M', we mainly investigate the implications on profit and welfare due to scenario transitions. Clearly, the analysis about scenario B and scenario S will not be affected. Thus, we only examine the equilibrium changes during scenario transitions from B to M' and from S to M'. As before, we divide the study into two cases ${\mu }_H=1$ and ${\mu }_H=1/2$ , which allows us to have direct comparison results and derive relevant insights.

Scenario transition from B to M'

From the benchmark scenario where no peer‐to‐peer sharing platform exists, the impact of the platform‐building strategy is qualitatively independent of the relative quality of the manufacturer deploying it. In fact, the comparison results for scenario transition from B to M' have the same structure as described in Propositions 3, 4, and 7, except that the critical thresholds are different. An elaboration on this point is given in EC.4 of the Supporting Information.

When ${\mu }_H=1$ , it is noteworthy that whoever builds the platform can always enhance the competitive advantage and gain a higher profit by leveraging revenues from two sources. In addition, the consumers and the society overall can also benefit from the sharing platform, which enlarges the size of consumers who have access to products usage compared to scenario B. Therefore, our results confirm that the platform‐building manufacturer is always better off, regardless of its quality level, and its opponent may be better off when production cost and quality differentiation are both relatively large; moreover, the consumer surplus and the social welfare can always benefit from manufacturer's building platform ${\mathbf{P}}_2$ .

When ${\mu }_H=1/2$ , just as what would happen when scenario transits from B to M, the platform‐building strategy has qualitatively the same impact regardless of the relative quality of the manufacturer who deploys this strategy. However, naturally, the results here are not exactly the same as those in Section 5, because the thresholds for the signs of $Z^{B{M}^{\prime }}$ ( $Z=\{{\pi }_L,{\pi }_H,CS,SW\}$ ) are different; see a numerical illustration of this point in EC.4 of the Supporting Information. We observe two interesting distinctions for scenario transition from B to M'.

First, from scenario B to scenario M', either manufacturer may be hurt while the other is better off due to manufacturer L's building its own platform. In other words, by building its platform, manufacturer L may hurt itself while benefiting the opponent. However, when manufacturer H builds the platform, it will never be worse off if the opponent is better off.

Second, when manufacturer H builds the sharing platform, consumers are more likely to be worse off compared to when manufacturer L builds the platform. Indeed, if the platform‐building manufacturer is of high quality, it has more competitive advantage to squeeze the consumer surplus (such as charging higher price). By contrast, when manufacturer L builds the platform, its (quality‐wise) more advantageous opponent will compete aggressively, which may benefit the consumers.

Scenario transition from S to M'

Next, we study how the equilibrium results change from scenario S to scenario M'. The following proposition reveals interesting differences from our previous results in Section 5. Proposition 8

Consider the scenario transition from S to M'. For both cases of ${\mu }_H=1$ and ${\mu }_H=1/2$ , we have ${\pi }_L^{S{M}^{\prime }}>0$ and ${\pi }_H^{S{M}^{\prime }}<0$ ; moreover, the consumer surplus always increases, that is, $C{S}^{S{M}^{\prime }}>0$ . The change in social welfare can be summarized as follows:

• (i)

Suppose ${\mu }_H=1$ . Then, there exists a decreasing function of k, ${\widehat{t}}^{S{M}^{\prime }}(k)$ , as a threshold of t, such that $S{W}^{S{M}^{\prime }}<0$ if $t<{\widehat{t}}^{S{M}^{\prime }}(k)$ and $S{W}^{S{M}^{\prime }}\ge 0$ otherwise.

(ii)

Suppose ${\mu }_H=1/2$ . Then, there exists a nonmonotone function of t, ${\widehat{\kappa }}^{S{M}^{\prime }}(t)$ , as a threshold of k, such that $S{W}^{S{M}^{\prime }}<0$ if $k<{\widehat{\kappa }}^{S{M}^{\prime }}(t)$ and $S{W}^{S{M}^{\prime }}\ge 0$ otherwise.

Several observations from Proposition 8 are worth mentioning. First, in contrast to Proposition 5, now the manufacturer that does not build the platform can never benefit from ${\mathbf{P}}_2$ when comparing with scenario S. Hence, although the platform‐building manufacturer can still benefit from its own platform, there can hardly exist a “win‐win” situation. Recall that, when manufacturer H builds the platform and the quality differentiation is large, the opponent manufacturer, L, may also benefit due to a relaxed competition. This will not happen if the platform is built by manufacturer L. Indeed, as manufacturer L's position in the duopoly competition is weaker compared to its high‐quality opponent, it will not easily forgo the sales in the product selling market and the competition will not be relaxed. As a result, manufacturer H will have to bear a profit loss.

Regarding the consumer surplus and the social welfare, from scenario S to scenario M/M', they have different changes depending on which manufacturer deploys the platform‐building strategy. When manufacturer H builds the platform, Propositions 6 and 7 show that $CS$ and $SW$ will increase if ${\mu }_H=1$ but may both decrease if ${\mu }_H=1/2$ . However, when the platform‐building manufacturer is L, Proposition 8 states that, no matter ${\mu }_H=1$ or ${\mu }_H=1/2$ , $CS$ always increases but $SW$ could incur a loss.

To understand this result, note that the consumer surplus mainly depends on the prices they pay for either ownership or usage, whereas the social welfare is largely decided by the size of covered market and the quality of products that can be accessed. Based on this rationale, we further explain our findings in the following.

For the consumer surplus, $C{S}^{S{M}^{\prime }}>0$ because the selling prices of the products will be lower after the scenario transition. On the one hand, as the renters of product L perceive the same quality as the owners when manufacturer L builds the exclusive platform, the manufacturer does not have to increase the price to incentivize the renters. On the other hand, the duopoly competition in the product selling market will not be relaxed. Consequently, the consumers benefit from the intense competition and the resulting lower prices. As for the social welfare, $S{W}^{S{M}^{\prime }}$ could be negative when t is small ⁷ . Indeed, when the quality is not sufficiently differentiated, manufacturer L wants to gain more advantage from the exclusive sharing platform ${\mathbf{P}}_2$ , so it will set lower rental price to induce more renters of product L. As a result, no matter ${\mu }_H=1$ or ${\mu }_H=1/2$ , more consumers are using the lower quality product and the social welfare will decrease.

SUMMARY

Facing the emerging peer‐to‐peer sharing economy, a product manufacturer may choose to build its own exclusive sharing platform, seeking to benefit from the sharing market. This paper studies such platform‐building strategy from one of two competing manufacturers with different quality levels. As more attention from academic research is drawn to the effect of sharing economy, our paper distinguishes from the prior works by highlighting the following two features. First, we consider the impact of quality differentiation on how the sharing platforms affect the market participants. Second, we explicitly consider the co‐existence of two peer‐to‐peer sharing platforms, one of which is owned and operated by the upstream manufacturer. We compare the equilibrium outcomes, including profits and surplus/welfare, before and after scenario transitions to investigate the impact of sharing platform ${\mathbf{P}}_1$ (third‐party) or platforms ${\mathbf{P}}_1$ and ${\mathbf{P}}_2$ (manufacturer‐built). Findings show that the product quality differentiation is a key determinant.

The foremost profit implication is that, no matter which manufacturer builds the platform, that manufacturer will benefit from it compared to the scenario where only the third‐party platform exists. ⁸ The benefit comes from the advantage that the platform‐building manufacturer is able to leverage from two sources of revenue; hence it can flexibly adjust selling price and rental price on the two ends. The opponent manufacturer, on the other hand, may or may not be better off when scenario transits from S to M/M'. Interestingly, when the low‐quality manufacturer builds the platform, the high‐quality manufacturer can never benefit from it as scenario transits from S to M'. Finally, considering the effect of sharing economy (comparing either scenario S or M/M' to scenario B), we find that the manufacturers benefit from the sharing only when the quality differentiation is large enough and the production cost is not small.

Turning to the welfare implications of the sharing platforms, we find that, when the renters of the high‐quality product can only derive a discounted usage utility, either the third‐party platform or the manufacturer‐built platform could hurt the consumer surplus and the social welfare. This is true especially when the quality differentiation is large. The underlying reason is that with discounted usage utility, renting the high‐quality product essentially has a new differentiated quality in the renters' eyes. Hence, large quality differentiation creates a relaxed competitive environment for the manufacturers, hurting the consumers; moreover, with relaxed competition, more consumers are owning the low‐quality product or renting the high‐quality product, and thus the overall utility decreases, resulting in a lower social welfare. Our work is motivated by the platform‐building strategy that manufacturers like Tesla envision to deploy in order to engage with the peer‐to‐peer sharing economy. However, this is not the only strategy seen in practice. Other strategic moves such as establishing partnership with existing peer‐to‐peer sharing platforms are also observed in reality. For example, Toyota has made a strategic investment in Uber and has come up with flexible leasing programs for Uber's Toyota drivers (Bhuiyan, 2016). Apparently, the manufacturer's move is to counteract the consumers' shifted preferences (from buying/leasing cars to simply being riders) by offering attractive terms to those who intend to use the platform as owners. Such alliance‐forming strategies may serve as an interesting extension to the paper, which we leave for future research.