Using Blockchain Technology to Combat Counterfeits: The Optimal Pricing Scheme of Two Competitive Platforms

Abstract

This paper investigates using blockchain technology to fight deceptive counterfeits in an electronic commerce environment. Thereby, a two-period pricing model is built under two competitive platforms: a blockchain-based platform which ensures product authentication and provides a higher value to customers but increases customers’ privacy concerns, and its rival (i.e., the traditional platform) in the absence of blockchain implementation which is perceived as having a lower value due to the existence of deceptive counterfeits and thus faces more government enforcement. Customers on both platforms are influenced by the electronic word-of-mouth (eWOM) effect, and customers value a platform more if the platform has more online sales. The two platforms either adopt the fixed pricing scheme or the modifiable pricing scheme and so four possible cases may occur. By deriving the equilibrium of each possible case, we analytically find that the attenuation of consumer privacy concerns, increases in government enforcement efforts, and eWOM can benefit the platform’s adoption of blockchain technology to combat counterfeits, and a strong eWOM effect is conducive to consumers but deteriorates price competition and thus harms both platforms. Whether the pricing schemes enhance the competitiveness of the blockchain-based platform over its rivals depends on the eWOM effect and the advantage gained from adopting blockchain technology.

1. Introduction

The e-commerce boom has caused traditional stores to seek out an online presence, in the form of entering platforms or developing mobile applications, to respond quickly to market needs. Nevertheless, counterfeits on e-commerce platforms are a serious problem and receive more attention from consumers and the government. According to a recent study by Ali Research, platform counterfeits and fake commodities climbed dramatically during the period of 2010–2020. The annual economic loss from copycatting products is estimated to be approximately CNY 55 million (abbreviation of Chinese Yuan) [1]. Counterfeiting can occur in two different settings, i.e., a customer can distinguish that a product is counterfeit and yet they decide to buy it (non-deceptive counterfeit), and a customer cannot distinguish between a genuine and a counterfeit product ex ante (deceptive counterfeit). A deceptive counterfeit, the focus of this paper, usually causes more harm to consumers as it may even involve health and safety risks. For example, fake medicines, which are deliberately and fraudulently mislabeled with respect to their identity or source, may cause therapeutic failure or even adverse effects in patients as they include wrong or insufficient active ingredients [2]. Additionally, on platforms where e-retailers have utilized technology such as RFID (Radio Frequency Identification) and hologram tags, there are still cases of deceptive counterfeits.

Technologies such as RFID or holograms have been widely applied to address the issue of fakes [3]. However, those techniques have had two main obstacles. First, it is likely that counterfeiters will imitate the genuine product’s tag. Second, once a product has been purchased, product authenticity can no longer be guaranteed since the tags are removed or replaced. Therefore, second-hand purchases are difficult to verify. But blockchain technology has been deemed as an ideal solution to anti-counterfeit operational challenges including the control of counterfeiting and providing deal transparency [4,5], and several blockchain-based applications have been carried out in recent years. For example, JD.COM partnered with the Australian startup InterAgri to develop a blockchain platform to track beef imports from overseas suppliers. The platform can record information about the breeding of cattle, processing, and transportation to final consumers. Bumble Bee Foods uses blockchain technology to track fresh fish from ocean to table: customers can scan a QR code on the product package to view the information about the fish-to-market journey, including the point of capture and the fishing community that caught it. In these typical cases, the use of a private key from a customer along with a public key and complex cryptography allows blockchain to provide an immutable, irreversible, and permanent record of transactions associated with a product [6]. In this way, a blockchain-based solution provides better transparency for customers and more easily and accurately verifies the authenticity of the product compared to previous technologies.

However, in addition to the additive costs associated, customer privacy concerns are also a major roadblock to blockchain implementation [4], because, in the blockchain scenario, customers must disclose their personal information by registering themselves as an owner to obtain a private key; such data, for example, in healthcare and the medicine industry, contain patients’ medical history which may have privacy implications for patients [6]. Similarly, the luxury industry giant LVMH requires customers to download its mobile apps and digital hot wallets in order to access the blockchain information, which leaves their personal information and funds exposed to hackers and potential security threats; meanwhile, some firms may use this information to carry out personalized marketing promotion to customers, but customers may regard such marketing activities as invasive to their privacy.

In particular, online e-commerce platforms, different from conventional physical stores, are prone to leak private information but also yield an electronic word-of-mouth effect (i.e., consumers’ comments, ratings, and online sales volumes), greatly influencing the consumers’ purchase behaviors. In this regard, e-retailers are more sensitive to platform dynamics, including rival pricing, marketing promotion, blockchain technology adoption, etc. A direct and simple way to counteract rivals’ dynamics is to capitalize on dynamic pricing schemes, which are frequently used to enhance their competitiveness.

Though the utilization of blockchain technology against deceptive counterfeits and pricing schemes is present in practice, some issues still remain ambiguous in this field of operations management. Motivated by the above practice, this paper will try to answer the following questions: (1) Compared to the traditional platform, does the blockchain-based platform help to generate more benefit for e-retailers, and do the fixed and modifiable pricing schemes yield different results? (2) With the support of blockchain technology, do the pricing schemes also aid in preventing counterfeits, and do enforcement efforts increase the chances of seizing the fakes to help the blockchain-based platform combat counterfeits? (3) Under the combating of counterfeits, which critical factors (e.g., electronic word-of-mouth (eWOM), unit blockchain-based cost, and consumers’ sensitive degree of privacy concern) impact both the platforms’ performance and the pricing scheme selection? (4) Under what conditions does the traditional platform like its rival also adopt the blockchain technology to compete with the blockchain-based platform?

To address the above four major questions, this paper conducts a two-period pricing game between two competitive platforms under the eWOM effect. To be specific, the blockchain-based platform provides a higher value for consumers due to blockchain technology against counterfeits, and yet some consumers are sensitive to privacy concerns of blockchain applications, whereas the other platform is a traditional one that is more likely to face government enforcement to monitor pirated goods in the absence of blockchain implementation. Two platforms may adopt the fixed pricing or the modifiable pricing scheme, and we analyze the equilibrium outcomes in four possible cases: case (F, F), where both platforms implement the fixed pricing; case (F, M), where the blockchain-based platform utilizes the fixed pricing and the traditional platform leverages the modifiable pricing; case (M, F), where the blockchain-based platform uses the modifiable pricing and the traditional platform leverages the fixed pricing; and case (M, M), where both platforms implement the modifiable pricing. The optimal decisions of the pricing scheme can be obtained by comparing the outcomes of four cases.

The novelties of this paper are threefold. (1) We are one of the first studies providing insights into the optimal decisions under blockchain technology and the pricing scheme for combating counterfeits. Although prior studies in the literature examine the impact of blockchain technology on firms’ anti-fake operations, it is rarely studied in a two-period competition setting combined with government enforcement efforts. (2) Adopting blockchain technology can help consumers identify products’ authenticity, yet it raises consumers’ privacy concerns and increases operation costs, thereby both key factors are taken into account in this research. Specifically, to characterize the consumer’s privacy concern, we use the fraction to quantify two groups of consumers, i.e., sensitive and insensitive consumers, which were seldom considered in anti-fake works before. (3) This paper utilizes the factor of government enforcement effort to link the relation between the counterfeit-existing possibility and the being-caught probability, which is consistent with the real world, because consumers care about the counterfeit-existing possibility, while e-retailers using traditional platforms may worry about the being-caught probability in the setting of two competitive platforms.

The rest of this paper is organized as follows: Section 2 reviews the relevant literature. Section 3 formulates our model. In Section 4, we analyze four possible cases to see how they are affected by adopting blockchain technology. Then, the optimal scheme selection and the related conditions are examined in Section 5. In Section 6, the extension is conducted to investigate under what conditions the traditional platform may also choose to adopt the blockchain technology. Section 7 summarizes the managerial insights and concludes with suggestions for future research. All proofs are provided in Appendix A.

2. Literature Review

2.1. Anti-Measures for Deceptive Counterfeit

The analytical research on counterfeiting mainly focuses on non-deceptive counterfeits. Grossman and Shapiro [7] discuss government policies towards non-deceptive counterfeiters and show that the policies that discourage foreign counterfeiting may reduce the home country’s welfare since non-deceptive counterfeits positively contribute to consumers’ welfare due to their low prices. Qian [8] finds that counterfeit entry induces incumbent brands to introduce an innovation strategy. And the pricing scheme will be adopted only if the counterfeit quality is lower than a threshold level. Scandizzo [9] takes consumers’ income level and two possible quality levels into the model and studies a competing market where firms who do not invest in quality improvement will become counterfeiters. Zhang et al. [10] compare the different fighting strategies in a market with one brand product and non-deceptive counterfeit. Similarly, Gao et al. [11] examine the impacts of different attributes and consumers’ utilities of the copycat on luxury branded products by using quality as a deterrence scheme and demonstrate that a higher branded product quality can deter a copycat’s entrance. More comprehensively, Pun and DeYong [12] suggest that product quality, legal enforcement, and customers’ forward-looking behaviors are effective deterrence strategies.

To the best of our knowledge, there are only several papers addressing deceptive counterfeiting. Liu et al. [13] investigate a multi-item newsvendor problem in the market where a retailer sells authentic and deceptive counterfeiting products under uncertain demand and analyze the effectiveness of the government’s monitoring scheme for the retailer’s cheating activities. Qian [14] assumes that only a fraction of consumers will be deceived and studies the effects of both price and non-price signaling under a Stackelberg game setting and finds that a brand name company will raise the price after a counterfeit’s entry. Cho et al. [15] investigate the impact of product characteristics on a counterfeiter’s decision in terms of deceptive and non-deceptive quality and price. Zhang and Zhang [16] and Qian et al. [17] further extend these results to multiple symmetric deceptive counterfeiters and introduce two dimensions of quality: searchable quality and experiential quality.

Under all the anti-measures studied in the existing literature, counterfeiters always had the possibility of manipulating fake products to look genuine to fool customers. However, blockchain strategy is fundamentally different from the conventional anti-counterfeiting ones. Products with a unique blockchain identifier cannot be duplicated because of their immutable, irreversible, and permanent characteristics. All customers can identify whether a product is authentic or fake during the deployment of a blockchain, so the problem where customers buy a fake unknowingly is completely eliminated. More importantly, apart from considering the adoption of blockchain technology as a countermeasure, our paper also contributes two new features to the literature. First, we take into account customers’ psychological factor of privacy concerns from blockchain adoption, which was seldom addressed before. Second, we consider the government enforcement efforts to monitor the market cheat behaviors.

2.2. Platform Service Operations

Platform operations play a critical role in e-commerce [18,19,20,21], and a body of platform-related OM studies have been published. For example, Bhargava et al. [22] study the optimal establishment timing for the platform technology. Anderson et al. [1] examine the platform operation decisions with the consideration of network externalities. Choi and He [19] study the platform operations in the setting of P2P. Zhang et al. [23] investigate the interaction between the e-retail platform’s contract selection and the manufacturer’s product quality decision. Meanwhile, more research further extends to different specific settings [24], such as crowdsourcing platforms [25], car-sharing platforms [26], fresh product platforms [18,19,27], and rental platforms [28].

Some studies focus on exploring the pricing decisions for platform services, which are related to our paper. For instance, Banerjee et al. [29] explore the optimal pricing decisions in the platform for ride-sharing services. Wang et al. [30] study the optimal pricing decisions for a service platform for calling taxis. Cachon et al. [31] look into the surge pricing policies on a platform when the service capacity is under self-scheduling control. Kung and Zhong [32] investigate the pricing decisions of a two-side platform with the delivery service considerations. Taylor [33] studies the optimal supply–demand matching in on-demand service platforms with independent service agents and considers the optimal service pricing decision. Most recently, Barenji et al. [34] explore smart platform pricing for e-commerce-based logistics services. The authors propose two types of communication schemes to better integrate data for the platform operations. Bai et al. [35] explore the optimal pricing problem for the on-demand service platform with impatient consumers.

Different from the aforementioned work focusing on one single platform [36], our study addresses two competitive platforms except for Bai and Tang [37], Zhang et al. [38], and Liu et al. [38]. Bai and Tang [37] study the case when two on-demand service platforms compete. They highlight the situations when both platforms can be profitable under such a duopoly competitive setting. Zhang et al. [38] study whether and when two competitive platforms should launch mobile applications simultaneously and sequentially. In addition, Chen et al. [39] examine two differentiated Cournot competitions on auction platforms with respect to quantity. Zhang et al. [40] use Bertrand competition to delineate the nexus of consumption network externalities and corporate social responsibility issues by setting prices until they reach the marginal cost. Although we also examine two competitive platforms, this paper concentrates on the optimal pricing decision for using blockchain against deceptive counterfeits, combined with the eWOM effect, which has been addressed less in prior studies in the platform OM literature.

2.3. Blockchain Technologies

Blockchain technologies have emerged as a crucial technological advance in recent years [41,42,43]. In operations management, Azzi et al. [44] believe that adopting blockchain technology will bring many benefits, such as increasing the trust level between producers and consumers, reducing or eliminating counterfeit products, and creating more transparent and accurate point-to-point tracking. Babich and Hilary [4] and Chod et al. [45] examine how blockchain can help improve operations in different topical areas, which include information and data sharing, risk management, automated smart contracting, etc. Shi and Choi [46] analytically explore how blockchain can be used to enhance food safety in supply chains and information visibility for facilitating the recall of poor quality or contaminated food products. Most recently, Rahmanzadeh et al. [47] presented a tactical supply chain planning model to integrate the designing process in the form of open innovation with consideration of intellectual property issues based on a blockchain platform. Zhang et al. [48] consider the two-period pricing on blockchain-based platforms, and customers are influenced by the network effect, revealing the ‘Matthew effect’ on platforms.

Additionally, some scholars have conducted other related research such as privacy [49], traceability [50], and counterfeiting [18]. Tian et al. [51] propose a secure digital evidence framework based on blockchain, which can ensure the integrity and effectiveness of data, so as to better balance privacy and traceability. Xu et al. [52] reconstruct the traceability system by replacing the central database with blockchain. They believe that the new system can provide transparent, efficient, and tamper-proof tracking data. For combating counterfeits, Choi [18] explores the values of blockchain technology against counterfeits in the diamond industry, considers three models, namely, the traditional retail operations, and the blockchain technology-supported selling platform and the blockchain technology-supported certification platform, and derives the condition of the values of blockchain technology-supported platforms for diamond authentication and certification. Pun et al. [53] consider a market with a manufacturer and a deceptive counterfeiter. The manufacturer can either use blockchain technology or signal authenticity through pricing and show that blockchain should only be used when the counterfeit quality is intermediate or when customers have intermediate distrust about products in the market. When customers have serious distrust about products, the pricing scheme is more effective than blockchain adoption, and it is found that blockchain can be more effective than a pricing strategy in eliminating post-purchase regret.

Although our paper also focuses on the blockchain-based platform operations for combating counterfeits, to the best of our knowledge, it is rare that the studies consider a two-periodic model with the consumers’ psychological factor of privacy concerns from blockchain adoption, and the government enforcement on two competitive platforms; thus, our work tries to fill this gap.

3. Model

Consider that a traditional platform T competes with a blockchain-based platform B. It is assumed that there are no existing counterfeits on platform B due to the blockchain technology ensuring product authentication. However, there may be some fakes on platform T with the counterfeit-existing possibility $e^{-\lambda },$ $e^{-\lambda }\in (0,1)$, and the platform T will be penalized by the amount $\Phi$. It is assumed that $\Phi =1$ to simplify the model and not impact the main results. If counterfeits are found by government enforcement, the being-caught probability $\omega (\lambda )$, $\omega (\lambda )\in (0,1)$, and both the possibility functions are monotonic with respect to the enforcement effort $\lambda$. Without loss of generality, $\omega (\lambda )=k\lambda (0<k<1)$ is set, where $\lambda$ is not higher than $1/k$, and $1/k$ represents the highest level of the government’s enforcement efforts. If each platform sells one type of product to consumers over two periods, the individual consumer has one unit demand. Considering that platform B uses blockchain to combat deceptive counterfeits, customers have to leave their own information owing to their use of blockchain-based hot wallets and registration of the platform as owners to obtain a private key, and some consumers may be sensitive to privacy information and worry about leaking their digital footprint, while other consumers do not care about it. To this end, we posit that the fraction of privacy-information-sensitive consumers is $\beta$, while the fraction for the privacy-information-insensitive consumers is $1-\beta$. The consumer’s perceived product’s base value on platform B and platform T is denoted by $v_B$ and $v_T$, respectively, and $v_T>0$ and $v_B>0$ are assumed, thus ensuring that consumers at the market buy either product on platform B or platform T.

Additionally, considering that platform B adopts blockchain technology, consumers will perceive a higher base value of products on platform B than that on platform T due to the fact that the authentication and quality of products on platform B are well monitored; thus, we have $v_B>v_T$. $\Delta =v_B-v_T$ denotes the gains from blockchain implementation. However, the blockchain implementation incurs extra costs, assuming that the cost per unit for blockchain implementation c includes the cost of cloud-based service and the cost for the tag; the tag is a type of digital technology called a non-fungible token (NFT) that represents a unique digital proof of ownership over product and identity and is stored and protected on a shared public exchange. To avoid trivial calculations, the fixed cost of adopting blockchain technology and other platform costs are normalized to zero.

We use the Hotelling model to describe the platform differentiation. Platform B and platform T are located at $x=0$ and $x=1$, respectively. The customers are uniformly distributed along the Hotelling line from 0 to 1, with a total number normalized to 1. A customer located at $x$ has to pay a disutility $\mu x$ of buying the product on platform B and a disutility $\mu (1-x)$ of buying the product on platform T, where $\mu$ characterizes the degree of product differentiation on two platforms. We assume that consumers patronize two platforms and buy products on one platform in one period.

In period 1, the eWOM effect is not present due to the fact that the platforms have no prior data on product sales. Two kinds of consumers have different utilities on two platforms.

(i)

For the privacy-information-sensitive consumers ($\beta$), the basic utility obtained by purchasing the product on platform B is given by $U_1=v_B-\mu x-p_B^{(1)}-\sigma$, where $p_B^{(1)}$ denotes the price of platform B in period 1, and $\sigma$ represents the consumer’s perceived privacy-information leakage degree due to blockchain adoption, whereas the utility function of purchasing the product on platform T is $U_T^{(1)}=v_T-\mu (1-x)-p_T^{(1)}-\epsilon e^{-\lambda }$, where $\epsilon$ represents the consumer’s sensitivity degree to counterfeits.

(ii)

For the privacy-information-insensitive consumers ($1-\beta$), the basic utility obtained by purchasing the product on platform B is given by $U_2=v_B-\mu x-p_B^{(1)}$, whereas the utility function of purchasing the product on platform T is $U_T^{(1)}=v_T-\mu (1-x)-p_T^{(1)}-\epsilon e^{-\lambda }$.

According to the work by the authors of [54], the privacy-information-sensitive consumers ($\beta$) will purchase products on platform B only if $U_1>U_T^{(1)}$, or will purchase products on platform T only if $U_1<U_T^{(1)}$. Thus, we can infer a decoupling point $(x_1)$ between purchasing products on platform B or products on platform T based on $U_1=U_T^{(1)}$, i.e., $v_B-\mu x-p_B^{\left(1\right)}-\sigma =v_T-\mu \left(1-x\right)-p_T^{(1)}-\epsilon e^{-\lambda }$; thus, we have $x_1={\displaystyle \frac{\mu +\Delta +p_T^{(1)}-p_B^{(1)}+\epsilon e^{-\lambda }-\sigma }{2\mu }}$. Thereby, the first-periodic demand of the privacy-information-sensitive consumers ($\beta$) on platform B is presented as $\beta {\displaystyle {\int }_0^{x_1}dx}$=$\beta {\displaystyle \frac{\mu +\Delta +p_T^{(1)}-p_B^{(1)}+\epsilon e^{-\lambda }-\sigma }{2\mu }}$, and the first-periodic demand of privacy-information-sensitive consumers ($\beta$) on platform T is presented as $\beta {\displaystyle {\int }_{x_1}^{1}dx}$ = $\beta (1-{\displaystyle \frac{\mu +\Delta +p_T^{(1)}-p_B^{(1)}+\epsilon e^{-\lambda }-\sigma }{2\mu }}$).

Similar to the derivation of the demand of the privacy-information-sensitive consumers ($\beta$), we also can derive the demand of the privacy-information-insensitive consumers (1 − $\beta$), the decoupling point $\left(x_2={\displaystyle \frac{\mu +\Delta +p_T^{(1)}-p_B^{(1)}+\epsilon e^{-\lambda }}{2\mu }}\right)$, and the privacy-information-insensitive consumers (1 − $\beta$) will purchase $(1-\beta ){\displaystyle {\int }_0^{x_2}dx}$ products on platform B (i.e., $(1-\beta ){\displaystyle \frac{\mu +\Delta +p_T^{(1)}-p_B^{(1)}+\epsilon e^{-\lambda }}{2\mu }}$)) and purchase $(1-\beta ){\displaystyle {\int }_{x_2}^{1}dx}$ products on platform T (i.e., $(1-\beta )(1-{\displaystyle \frac{\mu +\Delta +p_T^{(1)}-p_B^{(1)}+\epsilon e^{-\lambda }}{2\mu }}$)).

Thus, product demands of platform B and platform T in period 1 from the privacy-information-sensitive and -insensitive consumers are as follows:

$$\begin{array}{ll}\hfill q_B^{(1)}& =\beta \cdot {\displaystyle \frac{\mu +\Delta +p_T^{(1)}-p_B^{(1)}+\epsilon e^{-\lambda }-\sigma }{2\mu }}+(1-\beta )\cdot {\displaystyle \frac{\mu +\Delta +p_T^{(1)}-p_B^{(1)}+\epsilon e^{-\lambda }}{2\mu }}\hfill \\ & ={\displaystyle \frac{\mu +\Delta +p_T^{(1)}-p_B^{(1)}+\epsilon e^{-\lambda }-\beta \sigma }{2\mu }}\hfill \end{array}$$

(1)

$$\begin{array}{ll}{q}_T^{(1)}& =\beta \cdot (1-{\displaystyle \frac{\mu +\Delta +p_T^{(1)}-p_B^{(1)}+\epsilon e^{-\lambda }-\sigma }{2\mu }})+(1-\beta )\cdot (1-{\displaystyle \frac{\mu +\Delta +p_T^{(1)}-p_B^{(1)}+\epsilon e^{-\lambda }}{2\mu }})\\ & ={\displaystyle \frac{\mu -\Delta +p_B^{(1)}-p_T^{(1)}+\beta \sigma -\epsilon e^{-\lambda }}{2\mu }}\end{array}$$

(2)

In period 2, the utility of purchasing the products on platforms is impacted by the eWOM effect, which is positively related to the previous sales. Similarly, two kinds of consumers have different utilities on two platforms.

(i)

For the privacy-information-sensitive consumers ($\beta$), the basic utility obtained by purchasing the product on platform B is given by $U_3=v_B-\mu x-p_B^{(2)}-\sigma +\eta q_B^{(1)}$, where $\eta$ measures the impact degree of the first period of online sales on the consumer’s utility in period 2, i.e., the power of the eWOM effect, while the utility function of purchasing the product on platform T is $U_T^{(2)}=v_T-\mu (1-x)-p_T^{(2)}-\epsilon e^{-\lambda }+\eta q_T^{(1)}$. Owning to the fact that both platforms serve the same market consumers, we reasonably suppose that the power of the eWOM effect is the same for both platforms.

(ii)

For the privacy-information-insensitive consumers ($1-\beta$), the basic utility obtained by purchasing the product on platform B is $U_4=v_B-\mu x-p_B^{(2)}+\eta q_B^{(1)}$, while the basic utility on platform T is $U_T^{(2)}=v_T-\mu (1-x)-p_T^{(2)}-\epsilon e^{-\lambda }+\eta q_T^{(1)}$.

Using the same logic, only if $U_3>U_T^{(2)}$ and $U_4>U_T^{(2)}$, the privacy-information-sensitive and -insensitive consumers will purchase the products on platform B. Otherwise, they will purchase products on platform T. Thereby, we can calculate the product demands of platform B and platform T in period 2 as follows:

$$\begin{array}{ll}{q}_B^{(2)}& =\beta \cdot {\displaystyle \frac{{\rm M}-\sigma \mu }{2{\mu }^2}}+(1-\beta )\cdot {\displaystyle \frac{M}{2{\mu }^2}}\\ & ={\displaystyle \frac{{\mu }^2+(\mu +\eta )(\Delta +\epsilon e^{-\lambda }-\beta \sigma )+[p_T^{(2)}-p_B^{(2)}]\mu +[p_T^{(1)}-p_B^{(1)}]\eta }{2{\mu }^2}}\end{array}$$

(3)

$$\begin{array}{ll}{q}_T^{(2)}& =\beta \cdot (1-{\displaystyle \frac{{\rm M}-\sigma \mu }{2{\mu }^2}})+(1-\beta )\cdot (1-{\displaystyle \frac{M}{2{\mu }^2}})\\ & ={\displaystyle \frac{{\mu }^2-(\mu +\eta )(\Delta +\epsilon e^{-\lambda }-\beta \sigma )-[p_T^{(2)}-p_B^{(2)}]\mu -[p_T^{(1)}-p_B^{(1)}]\eta }{2{\mu }^2}}\end{array}$$

(4)

where $M={\mu }^2+(\mu +\eta )(\Delta +\epsilon e^{-\lambda })-\beta \eta \sigma +[p_T^{(2)}-p_B^{(2)}]\mu +[p_T^{(1)}-p_B^{(1)}]\eta$.

Both platforms have two pricing scheme options: the fixed pricing (F) or the modifiable pricing (M). We characterize the change in prices over two periods. If one platform’s prices over two periods remain unchanged, we refer to it as the fixed pricing scheme; if one platform’s prices over two periods are different, we define it as the modifiable pricing scheme. Both pricing schemes have different pricing mechanisms.

For the fixed pricing mechanism, this is when platform $i$ decides to have the same price over the two periods, i.e., $p_i^{(1)}=p_i^{(2)}=p_i$. Specifically, with platform B, it determines $p_B$ via maximizing the following two-periodic profit function:

$${\pi }_B(p_B)=(p_B-c)[q_B^{(1)}+q_B^{(2)}]$$

(5)

And, with platform T, it decides $p_T$ via maximizing the following two-periodic profit function:

$${\pi }_T(p_T)=p_T[q_T^{(1)}+q_T^{(2)}]-k\lambda e^{-\lambda }$$

(6)

It should be noted that without the adoption of blockchain technology, counterfeits may sneak into platform T and could be caught by government enforcement, and with the possibility of $k\lambda$, $k\lambda \in (0,1)$, it is definitely fined the amount $\Phi$ (assuming that $\Phi =1$, for the model simplification, but this does not impact the main results), as well as with the possibility of $k\lambda e^{-\lambda }$, because the counterfeit-existing possibility is $e^{-\lambda }$ and the being-caught possibility is $k\lambda$.

For the modifiable pricing mechanism, this is when platform $i$ (B or T) decides the prices $p_i^{(1)}$ and $p_i^{(2)}$ by optimizing the profit. Specifically, with platform B, it decides $p_B^{(1)}$ by maximizing the total profit:

$${\pi }_B(p_B^{(1)})=(p_B^{(1)}-c)q_B^{(1)}+(p_B^{(2)}-c)q_B^{(2)}$$

(7)

Then, it determines $p_B^{(2)}$ by maximizing the second-period profit:

$${\pi }_B^{(2)}(p_B^{(2)})=(p_B^{(2)}-c)q_B^{(2)}$$

(8)

And with platform T, it determines $p_T^{(1)}$ by maximizing the total profit:

$${\pi }_T(p_T^{(1)})=p_T^{(1)}{q}_T^{(1)}+p_T^{(2)}{q}_T^{(2)}-k\lambda e^{-\lambda }$$

(9)

Then, it determines $p_T^{(2)}$ by maximizing the second-period profit:

$${\pi }_T^{(2)}(p_T^{(2)})=p_T^{(2)}{q}_T^{(2)}$$

(10)

Similar to the work by the authors of [23], for two platforms, there may be four possible cases that could happen. Specifically, in the process of competition, if two platforms’ prices remain unchanged over two periods, we say that two platforms adopt the fixed pricing scheme, and it is refered to as case (F, F). If both platforms’ prices are changed over two periods, we say that both platforms adopt the modifiable pricing scheme, that is, case (M, M). If one platform’s price remains stable over two periods while the other’s price is altered, we say the former utilizes the fixed pricing scheme while the latter leverages the modifiable pricing scheme, and this is described as two cases, i.e., case (F, M) and case (M, F).

To concentrate on the setting of two platform competitions, we deposit the inequality $\max \{-{\displaystyle \frac{3{\mu }^2}{\mu +\eta }},{\displaystyle \frac{{\eta }^3+4\mu {\eta }^2-\eta {\mu }^2-18{\mu }^3}{{\eta }^2+5\mu \eta +6{\mu }^2}}\}\le h\le \min \{{\displaystyle \frac{3{\mu }^2}{\mu +\eta }},{\displaystyle \frac{18{\mu }^3+\eta {\mu }^2-{\eta }^3-4\mu {\eta }^2}{{\eta }^2+5\eta \mu +6{\mu }^2}}\}$, where $h=\Delta -(\beta \sigma -\epsilon e^{-\lambda }+c)$, which indicates that the net advantage of purchasing the product on platform B over platform T (i.e., $\Delta$) or the net disadvantage of purchasing the product on platform B over platform T (i.e., $\beta \sigma -\epsilon e^{-\lambda }+c$) is not large enough. We prove that $\max \{-{\displaystyle \frac{3{\mu }^2}{\mu +\eta }},{\displaystyle \frac{{\eta }^3+4\mu {\eta }^2-\eta {\mu }^2-18{\mu }^3}{{\eta }^2+5\mu \eta +6{\mu }^2}}\}\le h\le \min \{{\displaystyle \frac{3{\mu }^2}{\mu +\eta }},{\displaystyle \frac{18{\mu }^3+\eta {\mu }^2-{\eta }^3-4\mu {\eta }^2}{{\eta }^2+5\eta \mu +6{\mu }^2}}\}$ can guarantee that a platform will not price another platform out of the market in Appendix A.

Table 1. Main notation.

Notation	Definition
$p_i^{(j)}$	The price of platform $i$ in period $j$ under modifiable pricing
$p_i$	The price of platform $i$ under fixed pricing
$\lambda$	The government enforcement efforts for combating counterfeits
$\omega (\lambda )$	The being-caught probability
$\epsilon$	The consumer’s sensitivity degree to counterfeits
$\beta$	The fraction of consumers who are sensitive to privacy concerns
$\sigma$	The consumer’s perceived privacy-information leakage degree
$\Delta$	The net advantage of purchasing the product on platform B over platform T
$c$	The unit cost of blockchain implementation
$v_B$, $v_T$	The consumer’s perceived product’s base value on platform B and platform T, respectively
$\mu$	The degree of product differentiation on two platforms
$x$	The customer location
$\eta$	The power of the eWOM effect, $\eta \ge 0$
$U_i^{(j)}$	The utility of using platform $i$ in period $j$
$q_i^{(j)}$	The product demand of platform $i$ in period $j$
${\pi }_i^{(j)}$	The profit of platform $i$ in period $j$
${\pi }_i$	The total profit of platform $i$

Note $i=$ B or T and $j=1$ or 2.

illustrates the main notation of this research.

4. Equilibrium Analysis in Different Cases

Next, we proceed to calculate the equilibrium outcomes in four cases: (F, F), (F, M), (M, F), and (M, M).

4.1. Case (F, F)

In case (F, F), both platforms implement the fixed pricing scheme. That is to say, they set their own prices $p_B$ and $p_T$, and they remain unchanged over two periods. The equilibrium is displayed in Theorem 1.

Theorem 1.

In case (F, F), the equilibrium outcomes of platform B and platform T are shown in

Table 2. The equilibrium outcomes in case (F, F).

Outcome	Platform B	Platform T
Price	$p_B^{FF}={\displaystyle \frac{6{\mu }^2+(3c+h)(2\mu +\eta )}{3\eta +6\mu }}$	$p_T^{FF}={\displaystyle \frac{6{\mu }^2-h(2\mu +\eta )}{3\eta +6\mu }}$
First-period product demand	$q_B^{FF(1)}={\displaystyle \frac{3\mu +h}{6\mu }}$	$q_T^{FF(1)}={\displaystyle \frac{3\mu -h}{6\mu }}$
Second-period product demand	$q_B^{FF(2)}={\displaystyle \frac{3{\mu }^2+h(\mu +\eta )}{6{\mu }^2}}$	$q_T^{FF(2)}={\displaystyle \frac{3{\mu }^2-h(\mu +\eta )}{6{\mu }^2}}$
Profit	${\pi }_B^{FF}={\displaystyle \frac{{[h(2\mu +\eta )+6{\mu }^2]}^2}{18{\mu }^2(\eta +2\mu )}}$	${\pi }_T^{FF}={\displaystyle \frac{{[h(2\mu +\eta )-6{\mu }^2]}^2}{18{\mu }^2(\eta +2\mu )}}-k\lambda e^{-\lambda }$

.

Theorem 1 shows that platform B has more product sales than platform T in two periods due to the fact that some customers shift from platform T to platform B, especially in period 2; the incremental demand on platform B over two periods will increase with consumer’s sensitivity degree to counterfeits but decrease with the unit cost of blockchain adoption, and the government enforcement effort for combating counterfeits as well (the proofs are shown in Appendix A).

4.2. Case (F, M)

In case (F, M), platform B utilizes the fixed pricing scheme, and platform T adopts the modifiable pricing scheme. This means that Platform B’s prices remain stable, while platform T’s prices fluctuate over two periods. Using the backward induction method via the pricing mechanism, the equilibrium results are demonstrated in Theorem 2.

Theorem 2.

In case (F, M), the equilibrium outcomes of platform B and platform T are shown in

Table 3. The equilibrium outcomes in case (F, M).

Outcome	Platform B	Platform T
First-period price	$p_B^{FM}={\displaystyle \frac{\begin{array}{l}12{\mu }^3-c\eta (\mu +\eta )\\ +{\mu }^2(10c-6\eta +4h)\end{array}}{-{\eta }^2-\mu \eta +10{\mu }^2}}$	$p_T^{FM(1)}={\displaystyle \frac{\begin{array}{l}22{\mu }^4-7\eta {\mu }^2(\eta +\mu )\\ +({\eta }^3+4{\eta }^2\mu +\eta {\mu }^2-6{\mu }^3)h\end{array}}{-N_1}}$
Second-period price		$p_T^{FM(2)}={\displaystyle \frac{-22{\mu }^4+{\mu }^2\eta (\eta -5\mu )+N_2\mu h}{N_1}}$
First-period product demand	$q_B^{FM(1)}={\displaystyle \frac{\begin{array}{l}18{\mu }^3+N_{2}h\\ +\eta ({\mu }^2-{\eta }^2-4\mu \eta )\end{array}}{-2N_1}}$	$q_T^{FM(1)}={\displaystyle \frac{-22{\mu }^3+\eta ({\eta }^2+2\mu \eta -15{\mu }^2)+N_{2}h}{2N_1}}$
Second-period product demand	$q_B^{FM(2)}={\displaystyle \frac{\begin{array}{l}18{\mu }^3+\eta (11{\mu }^2\\ -2{\eta }^2-5\mu \eta )+N_{2}h\end{array}}{-2N_1}}$	$q_T^{FM(2)}={\displaystyle \frac{-22{\mu }^3+\mu \eta (\eta -5\mu )+N_{2}h}{2N_1}}$
Profit	${\pi }_B^{FM}={\displaystyle \frac{{\mu }^2(3\mu +\eta ){(6\mu -3\eta +2h)}^2}{{({\eta }^2+\mu \eta -10{\mu }^2)}^2}}$	${\pi }_T^{FM}={\displaystyle \frac{484{\mu }^6+\eta {\mu }^2{N}_5+N_3{h}^2+N_{4}h}{2(2\mu +\eta ){({\eta }^2+\eta \mu -10{\mu }^2)}^2}}-k\lambda e^{-\lambda }$

Note: $N_1={\eta }^3+3{\eta }^2\mu -8\eta {\mu }^2-20{\mu }^3$, $N_2={\eta }^2+5\mu \eta +6{\mu }^2$, $N_3=36{\mu }^4+24\eta {\mu }^3-{\eta }^4-6\mu {\eta }^3-5{\mu }^2{\eta }^2$, $N_4=23{\eta }^3{\mu }^2-{\eta }^5-4{\eta }^4\mu +82{\eta }^2{\mu }^3-76\eta {\mu }^4-264{\mu }^5$, and $N_5=7{\eta }^3+8{\eta }^2\mu -139\eta {\mu }^2-44{\mu }^3$.

.

Theorem 2 shows that, under case (F, M), some customers shift from platform T to platform B in period 2. The difference between the second-period price of platform T and the first-period price of platform B increases with the proportion of consumers having privacy concern $\beta$ as well as enforcement efforts $\lambda$ but decreases with consumers’ sensitivity degree to counterfeits $\epsilon$.

4.3. Case (M, F)

In case (M, F), platform B utilizes the modifiable pricing scheme, and platform T implements the fixed pricing scheme. This means that platform B’s price is altered over two periods while platform T’s price remains stable. Using the backward induction method via the pricing mechanism, the equilibrium outcomes are demonstrated in Theorem 3.

Theorem 3.

In case (M, F), the equilibrium outcomes of the two platforms are given in

Table 4. The equilibrium outcomes in case (M, F).

Outcome	Platform B	Platform T
First-period price	$p_B^{MF(1)}={\displaystyle \frac{\begin{array}{l}-22{\mu }^4+7{\mu }^3(\eta -2c)+{\eta }^2\mu (7\mu -c)\\ -9c\eta {\mu }^2+N_6(h+c)\end{array}}{N_1}}$	$p_T^{MF}={\displaystyle \frac{2{\mu }^2(3\eta -6\mu )+4{\mu }^{2}h}{{\eta }^2+\eta \mu -10{\mu }^2}}$
Second-period price	$p_B^{MF(2)}={\displaystyle \frac{\begin{array}{l}22{\mu }^4+\eta {\mu }^2(3c-\eta )+{\mu }^3(14c+5\eta )\\ +\mu N_2(h+c)-c{\eta }^2(\eta +4\mu )\end{array}}{-N_1}}$
First-period product demand	$q_B^{MF(1)}={\displaystyle \frac{22{\mu }^3+15\eta {\mu }^2-{\eta }^2(\eta +2\mu )+N_{2}h}{-2N_1}}$	$q_T^{MF(1)}={\displaystyle \frac{\begin{array}{l}-18{\mu }^3-\eta {\mu }^2\\ +{\eta }^2(\eta +4\mu )+N_{2}h\end{array}}{\begin{array}{l}2{\eta }^3+6{\eta }^2\mu \\ -16\eta {\mu }^2-40{\mu }^3\end{array}}}$
Second-period product demand	$q_B^{MF(2)}={\displaystyle \frac{22{\mu }^3+(5\mu -\eta )\eta \mu +N_{2}h}{-2N_1}}$	$q_T^{FM(2)}={\displaystyle \frac{\begin{array}{l}-22{\mu }^3+\\ \mu \eta (\eta -5\mu )+N_{2}h\end{array}}{2N_1}}$
Profit	${\pi }_B^{MF}={\displaystyle \frac{N_9{\mu }^2+N_7{h}^2+N_{8}h}{2N_1^2}}$	$\begin{array}{ll}\hfill {\pi }_T^{MF}& ={\displaystyle \frac{{\mu }^2(\eta +3\mu ){(3\eta -6\mu +2h)}^2}{{({\eta }^2+\eta \mu -10{\mu }^2)}^2}}\hfill \\ & -k\lambda e^{-\lambda }\hfill \end{array}$

Note: $N_6={\eta }^3+4{\eta }^2\mu +\eta {\mu }^2-6{\mu }^3$, $N_7=72{\mu }^5+84\eta {\mu }^4+14{\eta }^2{\mu }^3-{\eta }^5-8{\eta }^4\mu -17{\eta }^3{\mu }^2$, $N_8={\eta }^6+6{\eta }^5\mu -15{\eta }^4{\mu }^2-128{\eta }^3{\mu }^3-88{\eta }^2{\mu }^4+416\eta {\mu }^5+528{\mu }^6$, $N_9=7{\eta }^5+22\mu {\eta }^4-123{\eta }^3{\mu }^2-322{\eta }^2{\mu }^3+396\eta {\mu }^4+968{\mu }^5$.

.

Theorem 3 indicates that the gap between the second-period price and the first-period price of platform B decreases with the proportion of consumers having privacy concern $\beta$, the unit cost of blockchain adoption (c), and the enforcement efforts $\lambda$, but increase with consumers’ sensitivity degree to counterfeits $\epsilon$.

4.4. Case (M, M)

In case (M, M), both platforms implement the modifiable pricing scheme simultaneously. We obtain the equilibrium outcomes in Theorem 4.

Theorem 4.

In case (M, M), the equilibrium outcomes of the platforms are shown in

Table 5. The equilibrium outcomes in case (M, M).

Outcome	Platform B	Platform T
First-period price	$p_B^{MM(1)}={\displaystyle \frac{\begin{array}{l}-8{\eta }^3+6\eta (c\eta -c\mu +2\eta \mu )\\ +27{\mu }^2(2\eta -2c-3\mu )\\ +3(2{\eta }^2+2\eta \mu -9{\mu }^2)(h+c)\end{array}}{12{\eta }^2-81{\mu }^2}}$	$p_T^{MM(1)}={\displaystyle \frac{\begin{array}{l}8{\eta }^3+3\mu (27{\mu }^2-4{\eta }^2-18\eta \mu )\\ +(6{\eta }^2+6\eta \mu -27{\mu }^2)h\end{array}}{81{\mu }^2-12{\eta }^2}}$
Second-period price	$p_B^{MM(2)}={\displaystyle \frac{\begin{array}{l}27{\mu }^3+(3\eta \mu +9{\mu }^2)(h+c)\\ -4{\eta }^2(c+\mu )+3c\mu (6\mu -\eta )\end{array}}{27{\mu }^2-4{\eta }^2}}$	$p_T^{MM(2)}={\displaystyle \frac{-27{\mu }^3+4{\eta }^2\mu +3\mu (\eta +3\mu )h}{4{\eta }^2-27{\mu }^2}}$
First-period product demand	$q_B^{MM(1)}={\displaystyle \frac{27{\mu }^2-4{\eta }^2+(9\mu +4\eta )h}{54{\mu }^2-8{\eta }^2}}$	$q_T^{MM(1)}={\displaystyle \frac{-27{\mu }^2+4{\eta }^2+(9\mu +4\eta )h}{8{\eta }^2-54{\mu }^2}}$
Second-period product demand	$q_B^{MM(2)}={\displaystyle \frac{27{\mu }^2-4{\eta }^2+3(\eta +3\mu )h}{54{\mu }^2-8{\eta }^2}}$	$q_T^{MM(2)}={\displaystyle \frac{-27{\mu }^2+4{\eta }^2+3(\eta +3\mu )h}{8{\eta }^2-54{\mu }^2}}$
Profit	${\pi }_B^{MM}={\displaystyle \frac{\begin{array}{l}3M_1{h}^2+2M_{2}h+6\eta \mu M_3\\ +4374{\mu }^5-32{\eta }^5\end{array}}{6(4{\eta }^2-27{\mu }^2{)}^2}}$	$\begin{array}{l}{\pi }_T^{MM}={\displaystyle \frac{\begin{array}{l}3M_1{h}^2-2M_{2}h+6\eta \mu M_3\\ +4374{\mu }^5-32{\eta }^5\end{array}}{6{(4{\eta }^2-27{\mu }^2)}^2}}\\ -k\lambda e^{-\lambda }\end{array}$

Note: $M_1=162{\mu }^3+72\eta {\mu }^2-17{\eta }^2\mu -8{\eta }^3$, $M_2=28{\eta }^4-12{\eta }^3\mu +81\eta {\mu }^3-405{\mu }^2{\eta }^2+1458{\mu }^4$, $M_3=16{\eta }^3+72{\eta }^2\mu -216\eta {\mu }^2-243{\mu }^3$.

.

In case (M, M), we find that the price change in platform B from period 1 to period 2 is larger than that of platform T. As a result, some first-period consumers of platform B shifted to buy the product on platform T in period 2. The increased demand for platform T or the decreased demand for platform B decreases with the proportion of consumers having privacy concerns and enforcement efforts but increases with consumers’ sensitivity degree to counterfeits.

Corollary 1.

In four cases, the effects of the government’s enforcement effort $\lambda$ on platform B ’s and platform T ’s profits.

a. 

For platform B, $\partial {\pi }_B^{FF}/\partial \lambda <0$, $\partial {\pi }_B^{FM}/\partial \lambda <0$, $\partial {\pi }_B^{MF}/\partial \lambda <0$, and $\partial {\pi }_B^{MM}/\partial \lambda <0$.

b. 

For platform T, in case (F, F), when $\lambda >{\lambda }_1$, then $\partial {\pi }_T^{FF}/\partial \lambda >0$. (ii) In case (F, M), when $\lambda >{\lambda }_2$, then $\partial {\pi }_T^{FM}/\partial \lambda >0$. (iii) In case (M, F), when $\lambda >{\lambda }_3$, then $\partial {\pi }_T^{MF}/\partial \lambda >0$. (iv) In case (M, M), when $\lambda >{\lambda }_4$, then $\partial {\pi }_T^{MM}/\partial \lambda >0$, where

$${\lambda }_1={\displaystyle \frac{(\eta h-6{\mu }^2+2\mu h)\epsilon +9k{\mu }^2}{9k{\mu }^2}}$$

$${\lambda }_2=1-{\displaystyle \frac{-(\eta -2\mu )(\eta +3\mu )\epsilon [-2(\eta +3\mu )h-{\eta }^2-\mu \eta +22{\mu }^2]}{2k{({\eta }^2+\mu \eta -10{\mu }^2)}^2}}$$

$${\lambda }_3=1-{\displaystyle \frac{4{\mu }^2(\eta +3\mu )(6\mu -2h-3\eta )\epsilon }{k{(10{\mu }^2-{\eta }^2-\mu \eta )}^2}}$$

$${\lambda }_4=1-{\displaystyle \frac{\epsilon [(7\eta +18\mu )(\eta -3\mu )(4{\eta }^2-27{\mu }^2)-3(-8{\eta }^3-17{\eta }^2\mu +72\eta {\mu }^2+162{\mu }^3)h]}{3k{(4{\eta }^2-27{\mu }^2)}^2}}$$

From Corollary 1a, we can see that platform B’s profits decrease with the government’s enforcement efforts $\lambda$ in four cases. The reason is that, with the higher enforcement efforts, platform T has fewer counterfeits, so platform T’s competitiveness is relatively improved, thus explaining the phenomenon that intensifying enforcement efforts will benefit platform T’s profits in the long run, but has a negative impact on platform B in the setting of competitive environment. Therefore, platform B’s profits decrease with the government’s enforcement effort $\lambda$ in four cases. Corollary 1b indicates that when $\lambda$ exceeds a certain threshold, platform T’s profit increases with $\lambda$ in four cases; this result is consistent with reality. It implies that an effective way to combat counterfeits is either intensifying government enforcement or adopting blockchain technology.

4.5. Summary of Equilibrium in Four Cases

In this subsection, we summarize demand changes over the two periods in

Table 6. Changes in product demands over two periods.

Outcome		(F, F)	(F, M)	(M, F)	(M, M)
Product demand	Platform B	↑$(h>0$) ↓$(h<0$)	↑	↓	↓$(h>0$) ↑$(h<0$)
	Platform T	↓$(h>0$) ↑$(h<0$)	↓	↑	↑$(h>0$) ↓$(h<0$)

Note: ‘↑’ means that the product demand in the second period exceeds that in the first period, and ‘↓’ means that the product demand in the first period exceeds that in the second period.

, followed by examining the effects of the gap between advantage over disadvantage (h), the unit cost of blockchain implementation ($c$), the consumer’s sensitivity degree to counterfeits ($\epsilon$), and the government enforcement efforts ($\lambda$) on the equilibrium in the four cases. The results are presented in

Table 7. Effects of $h$ on the equilibrium results in four cases.

Outcome		(F, F)	(F, M)	(M, F)	(M, M)
Platform B	First-period price	↑	↑	↑	↑
	Second-period price			↑	↑
	First-period product demand	↑	↑	↑	↑
	Second-period product demand	↑	↑	↑	↑
	Profit	↑	↑	↑	↑
Platform T	First-period price	↓	↓	↓	↓
	Second-period price		↓		↓
	First-period product demand	↓	↓	↓	↓
	Second-period product demand	↓	↓	↓	↓
	Profit	↓	↓	↓	↓

Note: ‘↓’ means that the variable decreases in $h$ and ‘↑’ means that the variable increases in $h$.

,

Table 8. Effects of $c$ on the equilibrium results in four cases.

Outcome		(F, F)	(F, M)	(M, F)	(M, M)
Platform B	First-period price	↑	↑	↑	↑
	Second-period price			↑	↑
	First-period product demand	↓	↓	↓	↓
	Second-period product demand	↓	↓	↓	↓
	Profit	↓	↓	↓	↓
Platform T	First-period price	↑	↑	↑	↑
	Second-period price		↑		↑
	First-period product demand	↑	↑	↑	↑
	Second-period product demand	↑	↑	↑	↑
	Profit	↑	↑	↑	↑

Note: ‘↓’ means that the variable decreases in $c$ and ‘↑’ means that the variable increases in $c$.

,

Table 9. Effects of $\epsilon$ on the equilibrium results in four cases.

Outcome		(F, F)	(F, M)	(M, F)	(M, M)
Platform B	First-period price	↑	↑	↑	↑
	Second-period price				↑
	First-period product demand	↑	↑	↑	↑
	Second-period product demand	↑	↑	↑	↑
	Profit	↑	↑	↑	↑
Platform T	First-period price	↓	↓	↓	↓
	Second-period price		↓		↓
	First-period product demand	↓	↓	↓	↓
	Second-period product demand	↓	↓	↓	↓
	Profit	↓	↓	↓	↓

Note: ‘↓’ means that the variable decreases in $\epsilon$ and ‘↑’ means that the variable increases in $\epsilon$.

and

Table 10. Effects of $\lambda$ on the equilibrium results in four cases.

Outcome		(F, F)	(F, M)	(M, F)	(M, M)
Platform B	First-period price	↓	↓	↓	↓
	Second-period price			↓	↓
	First-period product demand	↓	↓	↓	↓
	Second-period product demand	↓	↓	↓	↓
Platform T	First-period price	↑	↑	↑	↑
	Second-period price		↑		↑
	First-period product demand	↑	↑	↑	↑
	Second-period product demand	↑	↑	↑	↑

Note: ‘↓’ means that the variable decreases in $\lambda$ and ‘↑’ means that the variable increases in $\lambda$.

, respectively.

From Table 6, we observe that in case (F, F), when the net advantage of platform B over platform T is higher than the net disadvantage of platform T over platform B (i.e., $h>0$), customers on Platform B will increase in period 2, whereas customers on platform T will decrease accordingly, and vice versa. In case (M, M), when the net advantage of Platform B over platform T is higher than the net disadvantage of platform over platform B (i.e., $h>0$), the result is the opposite; some customers shift from platform B to platform T in period 2, and vice versa.

In case (F, M) or case (M, F), it does not matter that the net advantage of platform T over platform B is higher or lower than the net disadvantage because the platform with fixed pricing can always attract customers from its rival—the platform that adopts the modifiable pricing in period 2—which indicates that fixed pricing is more desirable than the modifiable pricing for platforms’ expanding market in case (F, M) and case (M, F).

Table 7 reveals that in four cases, the price on Platform B increases with $h$ in two periods, while that on Platform T decreases with it. These findings are intuitive because the growth of platform B’s advantages given by blockchain makes platform B more competitive, and thus platform B will charge higher prices while platform T will charge lower prices to attract consumers accordingly. Table 7 also displays that, in four cases, the demand and profit on platform B increased with $h$ in two periods, while those on Platform T decreased with it. It should be noted that, due to the equation $h=\Delta -(\beta \sigma -\epsilon e^{-\lambda }+c)$, h increases with $\Delta$, $\epsilon$, and $\lambda$ but decreases with $c$, $\sigma$, and $\beta$. This means that the increases in $\Delta$, $\epsilon$, and $\lambda$, and the decreases in $c$, $\sigma$, and $\beta$, will make h larger; thus, Platform B (T) is better (worse) off.

Table 8 displays that, in four cases, the prices of both platforms increase with the unit cost of blockchain implementation ($c$) in two periods. However, the demand on platform T increases with $c$ in two periods, while that on platform B decreases with it. The rationale of this fact is that the growth of unit cost of blockchain implementation ($c$) will definitely push platform B’s price upward, thus eliciting its corresponding demand shrinkage, which in turn is conductive to its rival platform T, that is, platform T’s profit rises while platform B’s profit drops accordingly.

Table 9 demonstrates that, in four cases, platform T’s demand decreases with the consumer’s sensitivity degree to counterfeits ($\epsilon$) in two periods; its rival’s demand shows the reverse result. In this regard, platform T has to lower its price, while its rival will increase its own price in response to an increase in consumer’s sensitivity degree to counterfeits ($\epsilon$). To this end, platform T will suffer more loss but platform B will benefit from it.

We can see from Table 10 that, in four cases, platform T’s demand will increase with the government enforcement efforts for combating counterfeits ($\lambda$) in two periods, but this has a negative effect on platform B’s demand. On the other hand, intensifying government enforcement is also conducive to an increase in platform T’s price and forces platform B to lower its price accordingly. It is worth noting that the optimum schemes could be found by considering more combined influencing factors; thereby, we further analyze the optimal scheme and the related conditions.

5. Optimal Pricing Scheme Selection

The platforms’ inclination to the fixed pricing scheme and the modifiable pricing scheme can be deduced by comparing the profits. $\Delta {\pi }_B^{FF-MF}={\pi }_B^{FF}-{\pi }_B^{MF}$, $\Delta {\pi }_B^{FM-MM}={\pi }_B^{FM}-{\pi }_B^{MM}$, $\Delta {\pi }_T^{FF-FM}={\pi }_T^{FF}-{\pi }_T^{FM}$, and $\Delta {\pi }_T^{MF-MM}={\pi }_T^{MF}-{\pi }_T^{MM}$ are set. A positive value implies that the platform has the motivation to transfer from modifiable pricing to fixed pricing, a negative value implies that the platform has the motivation to transfer from fixed pricing to modifiable pricing, and a zero value implies that the platform is indiscriminate between adopting fixed pricing and modifiable pricing.

Lemma 1.

If $\eta =0$, the inequations $\Delta {\pi }_B^{FF-MF}<0,$$\Delta {\pi }_B^{FM-MM}>0,$$\Delta {\pi }_T^{FF-FM}<0,$ and $\Delta {\pi }_T^{MF-MM}>0$ hold.

Lemma 1 examines the situation in the absence of the eWOM effect, where the platforms are apt to choose a different pricing scheme from their rivals. Thus, the optimal scheme for platforms is case (M, F) or case (F, M), namely, one platform launches the fixed pricing scheme and the other implements the modifiable pricing scheme, due to $\Delta {\pi }_B^{FF-MF}<0$, $\Delta {\pi }_T^{FF-FM}<0$ and $\Delta {\pi }_B^{FM-MM}>0$, $\Delta {\pi }_T^{MF-MM}>0$; this also verifies that neither case (F, F) nor case (M, M) occurs without the eWOM effect. The rationale of this fact is that the absence of the eWOM effect indicates that previous sales fail to enlarge the next periodic demand, thus weakening the positive impact of the eWOM effect on profit. To this end, the platforms turn to a pricing scheme rather than eWOM, with an aim to enhance its performance. Meanwhile, there is an apparent discrepancy between the two platforms in consumers’ perceived value due to adopting blockchain technology; the platforms are more inclined to select a different pricing scheme from their rivals, enhancing consumers’ purchase intention.

Next, we investigate the optimal pricing schemes in the presence of the eWOM effect ($\eta >0$). When the conditions $\Delta {\pi }_B^{FF-MF}<0$ and $\Delta {\pi }_T^{FF-FM}<0$ are satisfied, it means that a platform decides to adopt the fixed pricing scheme while another platform adopts the modifiable pricing scheme (see Appendix A). But when a platform decides to adopt the modifiable pricing scheme, we cannot exactly identify another platform’s scheme selection. Thus, we need to further analyze two other conditions (i.e., $\Delta {\pi }_B^{FM-MM}$ and $\Delta {\pi }_T^{MF-MM}$), and hence, both platforms’ optimal scheme selection can be obtained. Due to the computational complexity, we conduct numerical studies to observe them and deduce the two following observations.

Observation 1.

When the eWOM effect $\eta$ is strong,

(i) 

if $\left|h\right|$ is smaller, case (M, M) is the optimal equilibrium, where both platforms adopt the modifiable pricing.

(ii) 

if $\left|h\right|$ is larger, when $h>0$, case (F, M) is the optimal equilibrium, where the blockchain-based platform B adopts fixed pricing and the traditional platform T adopts modifiable pricing, while when $h<0$, case (M, F) is the optimal equilibrium, where the blockchain-based platform B adopts modifiable pricing and the traditional platform T adopts fixed pricing.

(iii) 

there will only exist case (M, M) in equilibrium when $\eta =\mu$.

Observation 1(i) and Figure 1a display that one platform does not apparently outperform the other platform, which means that when the eWOM effect $\eta$ is strong, and $\left|h\right|$ is smaller, both platforms will adopt the modifiable pricing schemes due to $\Delta {\pi }_B^{FM-MM}<0$ and $\Delta {\pi }_T^{MF-MM}<0$; two platforms compete in price to attract consumers via the eWOM effect $\eta$, instead of being dependent on adopting a blockchain, because $\left|h\right|$ is smaller.

Observation 1(ii) and Figure 1a show that when $\left|h\right|$ is larger (i.e., larger than 0.5), and the increase in $h$ leads to platform B’s choosing of fixed pricing and its rival for modifiable pricing, because platform B adopts blockchain technology, this can dramatically enhance its advantage over its rival Platform T, i.e., $h>0$. In contrast, if platform B adopts blockchain technology with its disadvantage over its rival platform T, i.e., $h<0$, platform B will select modifiable pricing and its rival will select fixed pricing. This reveals that the platform with more advantages than the other one always prefers fixed pricing. The reason is consistent with reality because the platform with more advantages wants to maintain the status quo, and is unwilling to make too many changes, including prices, whereas the rival platform with the disadvantage hopes to reverse the outcome and eagerly and actively adjusts the corresponding policies (for example, price policy) in response to such a passive situation.

Observation 1(iii) and Figure 1b characterize that both platforms will adopt the modifiable pricing scheme when the eWOM effect is equal to the degree of product differentiation on the two platforms, namely, $\eta =\mu$. Under this circumstance, both platforms will choose the modifiable pricing scheme because the demand in period 2 will be dramatically affected by the demand in period 1, and platforms will set low prices to stimulate early demands, and then change late prices, combined with the eWOM effect, to increase its profit.

Observation 2.

When the eWOM effect $\eta$ is weak,

(i) 

if $\left|h\right|$ is small, case (F, M) or case (M, F) is the optimal equilibrium, where one platform adopts fixed pricing and another platform adopts modifiable pricing.

(ii) 

if $\left|h\right|$ is larger, when $h>0$, case (F, M) is the optimal equilibrium, where the blockchain-based platform B adopts fixed pricing and the traditional platform T adopts modifiable pricing, while when $h<0$, case (M, F) is the optimal equilibrium, where the blockchain-based platform B adopts modifiable pricing and the traditional platform T adopts fixed pricing.

Observation 2(i) and Figure 2 show that given that one platform does not have particularly more competitiveness than another platform (i.e., $\left|h\right|$ is small), both platforms tend to choose different pricing schemes. Because the network effect is weak and $\left|h\right|$ is small, if both platforms adopt the same pricing schemes, instead of different pricing schemes, to attract more consumers, which will cause fierce competition, such a situation makes it impossible for this condition to last longer. As a result, both are ultimately inclined to choose different pricing schemes from the other, namely case (F, M) or case (M, F) is the optimal equilibrium. But which one is the best between case (F, M) and case (M, F)? The optimal outcomes are closely related to the factors such as consumers’ privacy concern ($\beta$,$\sigma$), enforcement effort ($\lambda$,$\omega$), consumer’s sensitivity degree to counterfeits ($\epsilon$), unit cost (c), and the degree of differentiation ($\mu$) on two platforms.

Observation 2(ii) shows that when $\left|h\right|$ is larger, and the positive value $h$ increases, two equilibrium schemes are reduced to an equilibrium scheme (F, M). Because the positive value $h$ increases, $\Delta {\pi }_B^{FM-MM}$ rises dramatically and $\Delta {\pi }_T^{MF-MM}$ is close to zero. For both platforms, scheme (F, M) is the only unique and optimal solution. Under this circumstance, platform B has more competitiveness than platform T. In order to survive the fierce market competition, platform T must adopt the modifiable pricing scheme and use price advantage to attract more consumers. The advantage of platform B is obvious, as it does not need to rely on price competition to attract consumers, but on blockchain technology, it is different. To this end, platform B has a stronger willingness to adhere to the fixed pricing scheme without deviating from it. Following the same logic, when $\left|h\right|$ is larger, and the negative value $h$ decreases, two equilibrium schemes are reduced to an equilibrium scheme (M, F). Because the positive value $h$ increases, $\Delta {\pi }_T^{MF-MM}$ rises considerably and $\Delta {\pi }_B^{FM-MM}$ is close to zero. For both platforms, scheme (M, F) is the only unique and optimal solution.

Then, in the following part, the effect of several key pair parameters ($\beta$,$\lambda$), ($\sigma$, $\epsilon$), and ($c$,$\omega$) on the optimal pricing scheme is examined.

We first examine the impact of the fraction of consumers having privacy concerns ($\beta$) and the government enforcement efforts ($\lambda$) on the platform’s optimal pricing scheme selection. For convenience of analysis, $\mu$ = 1, $c=0.1$, and $\epsilon =0.5$ are set, and $\Delta =2.4$ and 0.7, $\sigma =5$ and 3, and $\eta =0.1$ and 0.6. Figure 3a indicates that when the strength of the eWOM effect $\eta$(0.1) is weaker, to some degree, no matter the amount of government enforcement effort for combating counterfeits ($\lambda$) that is made, if the fraction of consumers having privacy concerns ($\beta$) is at a low (high) level, platform B will choose the fixed (modifiable) pricing scheme as its optimal one, while platform T will choose the modifiable (fixed) pricing scheme; if the fraction of the consumer having privacy concerns ($\beta$) is at a mediate level, platform B or platform T will prefer to select a different pricing scheme from its rivals due to the fact that case (F, M) is the same as case (M, F) for both platforms. Interestingly, from the perspective of the colored area size, we also find that in the setting of the weaker eWOM effect, the greater likelihood of selecting a pricing scheme for both platforms is to choose a different pricing scheme from its rivals.

Figure 3b demonstrates the different results when the strength of the eWOM effect $\eta$ (0.6) is stronger. In this case, the government enforcement effort for combating counterfeits ($\lambda$) will play a role in the platforms’ selection of a pricing scheme. With an increase in the fraction of the consumers having privacy concerns ($\beta$), the optimal scheme for platform B switches from fixed pricing to modifiable pricing, while platform T switches from modifiable to fixed pricing. Particularly, when the fraction of consumers having privacy concerns ($\beta$) is at a relatively low level, if the efforts for combating counterfeits ($\lambda$) are intensified during exertion, platform B will choose modifiable pricing, otherwise, it will select a fixed one. By contrast, When the proportion of consumers having privacy concerns ($\beta$) is at a relatively high level, the more efforts for combating counterfeits ($\lambda$) will cause platform T to choose the fixed pricing, otherwise, it will select the modifiable one. Additionally, although case (M, M) is the most likely case for the platforms’ preference, the gap between it and two other cases, i.e., case (F, M) and (M, F), becomes narrow.

Figure 4 shows the effects of the degree of privacy concern ($\sigma$) and the consumer’s sensitivity degree to counterfeits ($\epsilon$) on the platform’s optimal pricing scheme selection. We specify that $c=0.1$ and $\lambda =-\ln (3/10)$, and that $\Delta =2.4$ and 0.6, $\beta =0.8$ and 0.2, and $\eta =0.1$ and 0.6. Figure 4a demonstrates that when the strength of the eWOM effect is weaker, the degree of privacy concern ($\sigma$) is a greater critical influencing factor than the consumer’s sensitivity degree to counterfeits ($\epsilon$) in the impact on platforms’ pricing choice. In detail, except for the case of the extremely lower and higher level of the degree of privacy concern ($\sigma$), platform B or platform T will normally prefer to select a different pricing scheme from its rivals. When consumers have an extremely lower level of the degree of privacy concern ($\sigma$), the increase in the consumer’s sensitivity degree to counterfeits ($\epsilon$) will facilitate platform T’s adoption of modifiable pricing while platform B adopts fixed pricing. In contrast, when consumers have a higher level of the degree of privacy concern ($\sigma$), the decrease in the consumer’s sensitivity degree to counterfeits ($\epsilon$) will evoke platform T to adopt fixed pricing while platform B adopts modifiable pricing.

Figure 4b demonstrates the case of when the strength of the eWOM effect $\eta$ (0.6) is stronger. It is obvious that the strength of the eWOM effect will improve the role of the consumer’s sensitivity degree to counterfeits ($\epsilon$) in platforms’ pricing scheme decision-making; meanwhile, the strong strength of the eWOM effect leads to two platforms clearly choosing their pricing scheme in comparison with the weak case. With an increase in the degree of privacy concerns ($\sigma$), the optimal scheme for platform B switches from fixed pricing to modifiable pricing, while platform T switches from modifiable to fixed pricing.

Figure 5 shows the effects of the unit cost of blockchain implementation (c) and being-caught probability ($\omega$) on the platform’s optimal pricing scheme selection. We specify that $\epsilon =0.5$, $\beta =0.2$, $\sigma =1.5$, $\Delta =2.5$, and $k=0.5$. We can see that, given the different values of the strength of the eWOM effect, the role between the unit cost of blockchain implementation (c) and the being-caught probability ($\omega$) proceeds in two different extremes when choosing a pricing scheme for both platforms. Specifically, when the strength of the eWOM effect is weaker ($\eta$ = 0.1), the unit cost of blockchain implementation (c) is a key factor for platforms to decide the pricing schemes, whereas the factor of the being-caught probability ($\omega$) is almost negligible (Figure 5a). By contrast, when the strength of the eWOM effect is stronger ($\eta$ = 0.6), it shows that the being-caught probability ($\omega$), and the unit cost of blockchain implementation (c) are the same indispensable determinants impacting platforms’ selection (Figure 5b).

Additionally, when the strength of the eWOM effect is weaker, it is most likely that platform B or platform T will prefer to select a different pricing scheme from its rivals when the strength of the eWOM effect is stronger; if the value of the being-caught probability ($\omega$) falls on the lower area, platform B will choose fixed pricing and platform T will prefer to select the modifiable pricing scheme; if the value of the being-caught probability ($\omega$) falls on the higher area, platform B will choose modifiable pricing and platform T will choose fixed pricing; if the value of the being-caught probability ($\omega$) falls on the mediate area, both platforms select the modifiable pricing; interestingly, it is most likely that both platforms will select modifiable pricing when compared with the higher and lower areas where the value of the being-caught probability ($\omega$) falls on.

6. Extension

In this section, we consider the condition of the traditional platform T also choosing to adopt the blockchain technology to compete with the blockchain-supported platform B under four different pricing schemes, and then we take some other factors into account including the platform brand and product quality to examine the possible impact on the outcomes.

6.1. Both Platforms’ Adoption of Blockchain Technology

When the traditional platform T decides to adopt blockchain technology, the first-periodic utility of the privacy-information-(in)sensitive consumers for both platforms is presented as follows. For privacy-information-sensitive consumers in period 1,

$${\widehat{U}}_1=v_B-\mu x-p_B^{(1)}-\sigma =v-\mu x-p_B^{(1)}-\sigma$$

$${\widehat{U}}_T^{(1)}=v_T-\mu (1-x)-p_T^{(1)}-\sigma =v-\mu (1-x)-p_T^{(1)}-\sigma$$

where $v_T=v_B=v$ due to both platforms adopting blockchain technology.

For privacy-information-insensitive consumers in period 1,

$${\widehat{U}}_2=v-\mu x-p_B^{(1)}, {\widehat{U}}_T^{(1)}=v-\mu (1-x)-p_T^{(1)}$$

Using the same reasoning as before, we can derive the product demands of both platforms in period 1.

$${\widehat{q}}_B^{(1)}=\beta \cdot {\displaystyle \frac{\mu +p_T^{(1)}-p_B^{(1)}}{2\mu }}+(1-\beta )\cdot {\displaystyle \frac{\mu +p_T^{(1)}-p_B^{(1)}}{2\mu }}={\displaystyle \frac{\mu +p_T^{(1)}-p_B^{(1)}}{2\mu }}$$

(11)

$${\widehat{q}}_T^{(1)}=\beta \cdot (1-{\displaystyle \frac{\mu +p_T^{(1)}-p_B^{(1)}}{2\mu }})+(1-\beta )\cdot (1-{\displaystyle \frac{\mu +p_T^{(1)}-p_B^{(1)}}{2\mu }})={\displaystyle \frac{\mu +p_B^{(1)}-p_T^{(1)}}{2\mu }}$$

(12)

In the same way, we can also calculate the product demands of two platforms in period 2 as follows:

$${\widehat{q}}_B^{(2)}=\beta \cdot {\displaystyle \frac{K}{2{\mu }^2}}+(1-\beta )\cdot {\displaystyle \frac{K}{2{\mu }^2}}={\displaystyle \frac{{\mu }^2+[p_T^{(2)}-p_B^{(2)}]\mu +[p_T^{(1)}-p_B^{(1)}]\eta }{2{\mu }^2}}$$

(13)

$${\widehat{q}}_T^{(2)}=\beta \cdot (1-{\displaystyle \frac{K}{2{\mu }^2}})+(1-\beta )\cdot (1-{\displaystyle \frac{K}{2{\mu }^2}})={\displaystyle \frac{{\mu }^2-[p_T^{(2)}-p_B^{(2)}]\mu -[p_T^{(1)}-p_B^{(1)}]\eta }{2{\mu }^2}}$$

(14)

where ${\rm K}={\mu }^2+[p_T^{(2)}-p_B^{(2)}]\mu +[p_T^{(1)}-p_B^{(1)}]\eta$.

Considering that platform T is a late blockchain technology adopter, at the start of period 1, it will bear the related preparation cost (for example, familiarity with blockchain devices, staff training, etc.), denoted by I, while platform B does not bear such expenditure at this time due to its early bird of implementing blockchain technology against counterfeits; thus, the two-periodic profits of platforms B and T are

$${\pi }_B(p_B)=(p_B-c)[{\widehat{q}}_B^{(1)}+{\widehat{q}}_B^{(2)}], {\pi }_T(p_T)=(p_T-c)[{\widehat{q}}_T^{(1)}+{\widehat{q}}_T^{(2)}]-I$$

Utilizing the same method as in Section 3, we can derive both platforms’ profits under four different circumstances. Then, by comparing platform T’s profits between not adopting and adopting blockchain technology against counterfeits, the conditions of the traditional platform T choosing to adopt blockchain technology are yielded as below.

Theorem 5.

(1) In case (F, F), platform T will adopt blockchain technology when $k\lambda e^{-\lambda }>I+{\displaystyle \frac{[h(2\mu +\eta )-12{\mu }^2]h}{18{\mu }^2}}$; (2) in case (F, M), platform T will adopt blockchain technology when $k\lambda e^{-\lambda }>I+{\displaystyle \frac{(\eta +3\mu )(2\mu -\eta )({\eta }^2+\eta \mu +\eta h-22{\mu }^2+3h\mu )h}{2{({\eta }^2+\eta \mu -10{\mu }^2)}^2}}$; (3) in case (M, F), platform T will adopt blockchain technology when $k\lambda e^{-\lambda }>I+{\displaystyle \frac{4{\mu }^{2}h(\eta +3\mu )(3\eta -6\mu +h)}{{({\eta }^2+\eta \mu -10{\mu }^2)}^2}}$; and (4) in case (M, M), platform T will adopt blockchain technology when $k\lambda e^{-\lambda }>I+{\displaystyle \frac{\begin{array}{l}h(-56{\eta }^4+24{\eta }^3\mu -24{\eta }^{3}h+810{\eta }^2{\mu }^2-51{\eta }^2\mu h\\ -162\eta {\mu }^3+216\eta {\mu }^{2}h-2916{\mu }^4+486{\mu }^{3}h)\end{array}}{6{(4{\eta }^2-27{\mu }^2)}^2}}$.

Theorem 5 obviously shows that when the government’s anti-fake penalty amount ($k\lambda e^{-\lambda }$) exceeds a certain threshold, platform T will also turn to adopt blockchain technology against counterfeits as its rival; otherwise, platform T has no motivation to implement it. Thus, from the perspective of the government, setting an appropriate amount of fines can drive platforms to adopt blockchain technology to combat counterfeiting.

6.2. Impact of Other Factors on Blockchain Adoption and Combating Counterfeits

We take the factors of the platform brand and the product quality into account to examine the possible impact on the outcomes. It is assumed that platform B has a brand reputation and high-quality products, inducing it to adopt blockchain technology. Therefore, in period 1, for the privacy-information-sensitive and -insensitive consumers, the basic utilities obtained by purchasing the product on platform B are given by

$${\overline{U}}_1=v_B-\mu x-p_B^{(1)}-\sigma +\tau (R+s),$$

$${\overline{U}}_2=v_B-\mu x-p_B^{(1)}+\tau (R+s)$$

where $R$ denotes the consumer’s perceived brand reputation of platform B, $s$ represents the consumer’s perceived product quality of platform B relative to platform T, and $\tau$ represents the consumer’s sensitive degree to platform B’s product quality and brand reputation.

In period 2, for the privacy-information-sensitive and -insensitive consumers, the basic utilities obtained by purchasing the product on platform B are

$${\overline{U}}_3=v_B-\mu x-p_B^{(2)}-\sigma +\eta q_B^{(1)}+\tau (R+s),$$

$${\overline{U}}_4=v_B-\mu x-p_B^{(2)}+\eta q_B^{(1)}+\tau (R+s)$$

For platform T, the utility function of purchasing products on platform T remains unchanged. In the same method as in Section 3, we can derive both platforms’ equilibrium outcomes under four cases and compare their impacts, the results are shown in

Table 11. Impacts of the other factors on the equilibrium results in four cases.

Outcome		(F, F)	(F, M)	(M, F)	(M, M)
Platform B	First-period price	↑♂	↑♂	↑♂	↑♂
	Second-period price			↓♀	↑♂
	First-period product demand	↑♂	↑♂	↑♂	↑♂
	Second-period product demand	↑♂	↑♂	↑♂ or ↓♀	↑♂
	Profit	↑♂	↑♂	↑♂	↑♂
Platform T	First-period price	↓♀	↓♀	↓♀	↓♀
	Second-period price		↑♂ or ↓♀		↑♂ or ↓♀
	First-period demand	↓♀	↓♀	↑♂	↓♀
	Second-period demand	↓♀	↑♂ or ↓♀	↑♂ or ↓♀	↑♂ or ↓♀
	Profit	↑♂	↑♂ or ↓♀	↓♀	↑♂ or ↓♀

Note: ‘↓’ and ‘↑’ mean that the variable increases with R, and ‘♀’ and ‘♂’ mean that the variable decreases or increases with S.

.

7. Conclusions

To investigate the effects of using blockchain technology for combating counterfeits, we examine a two-period model where a traditional platform and a blockchain-based platform compete via different pricing schemes, i.e., fixed pricing or modifiable pricing. The implementation of blockchain technology can enhance the perceived utility of purchasing products on the blockchain-based platform but it can bear the related costs and raise customers’ privacy concerns, while the traditional platform in the absence of blockchain implementation is perceived as having a lower value due to the existence of deceptive counterfeits, thus facing more government enforcement. Customers on both platforms are impacted by the eWOM effect. We analyze the results of the optimal decisions under four possible cases. The equilibrium pricing schemes are derived, and the main results and important managerial insights are presented as follows:

(1)

Compared to the traditional platform T, the blockchain-based platform B helps generate more benefits for e-retailers. Platform B had more product sales than Platform T in two periods due to the fact that some customers shifted from platform T to platform B, especially in period 2, which made the traditional platform T adopt fixed or modifiable pricing schemes in response to sale changes. Also, the gap between the second-period price of Platform T and the first-period price of platform B changes with the proportion of consumers having privacy concerns. This suggests that when adopting blockchain technology and different pricing schemes for anti-fakes, managements must also make efforts to mitigate consumers’ anxieties related to privacy concerns, for example, by strengthening data security, introducing reliable encryption technology, and enhancing mutual trust via propaganda.

(2)

With the support of blockchain technology, the pricing schemes do not directly help combat counterfeits, but they do indirectly facilitate anti-fakes. The reason is that regardless of whether the blockchain-based platform B adopts the fixed or the modifiable pricing scheme, its rival (platform T) may turn to different one, thus inevitably intensifying competition; as a result, platform T is forced to reduce counterfeits with an aim to improve eWOM. This implies that both blockchain technology (external factor) and eWOM (internal factor) play important roles in fighting copycats, and managements do not emphasize one and neglect the other because these two factors intertwine and transform with each other.

(3)

The enforcement efforts increase the chances of seizing the copycats on platform T, but Platform B’s profits decrease with the government’s enforcement efforts in four cases. The reason is that, with the higher enforcement efforts, platform T has less counterfeits, so platform T’s competitiveness is relatively enhanced. Meanwhile, when enforcement efforts exceed a certain threshold, platform T’s profit increases with it in four cases, and this result is consistent with reality. This implies that an effective way to combat counterfeits is either by intensifying government enforcement or adopting blockchain technology; strengthening government enforcement not only benefits consumers but also platform T in the long run.

(4)

For combating counterfeits, these critical factors, including eWOM, unit blockchain-based cost, and consumer’s sensitive degree of privacy concern, greatly impact both platforms’ performance and pricing scheme selection. We find that if the eWOM effect is strong or the competitor adopts the fixed pricing scheme, the positive effect of the modifiable pricing scheme dominates its negative effect, and the modifiable pricing scheme is more desirable; otherwise, the fixed pricing scheme is more favorable. When the eWOM effect is weak, one platform adopts the fixed pricing scheme and the other adopts the modifiable pricing scheme. This suggests that, in the setting of a weak eWOM effect, managements must focus on their rivals’ pricing schemes to select their own pricing schemes, while in the setting of a strong eWOM effect, managements should shift focus from their rivals to consumers, and then select the modifiable pricing scheme to directly benefit consumers.

(5)

The result also reveals that when the government anti-fake penalty amount exceeds a certain threshold, the traditional platform T will also turn to adopt blockchain technology against counterfeits; otherwise, the traditional platform T has no motivation to implement it. Thus, from the perspective of the government, setting an appropriate amount of fines can drive platforms to adopt blockchain technology to combat counterfeiting.

There are also some research limitations of this paper.

(1)

This paper concentrates on the impact of adopting blockchain technology on platform competition and merely accommodates two different platforms rather than two supply chains. Future research could extend its investigation to the sophisticated supply chain, including interactions with upstream suppliers and platforms.

(2)

This research examines one platform adopting blockchain technology but does not address the issue of how to allocate the blockchain construction costs (i.e., fixed costs) between members in the setting of a supply chain, which may be considered in the future.

(3)

We build parsimonious models to acquire tractable outcomes. Our findings may be subject to the specific model setting. For instance, we only consider deceptive counterfeits and a deterministic demand function. Future research can further take it into account by introducing non-deceptive counterfeits and random demand parts.