Blockchain Adoption to Fight Counterfeiting at the Source in a Vertically Differentiated Competition

Abstract

The proliferation of counterfeit products poses a substantial threat to numerous industries. Blockchain technology (BCT) offers an effective solution for product traceability, providing a means to combat counterfeiting. However, BCT can verify the authenticity of the information but cannot confirm the veracity of the product itself, a problem known as counterfeiting at the source. To our knowledge, this issue has yet to be studied. The security level of BCT traceability is used to indicate its ability to combat counterfeiting. We establish game-theoretical models to investigate BCT adoption strategies for a typically authentic firm and a premium firm to fight counterfeiting in a vertically differentiated competition. This study demonstrates that BCT reduces deceptive counterfeiters’ incentive to pool with the branded firm and mitigates the negative impact of asymmetric information on the prices, market share, and profits of authentic products in a monopoly. In instances where the proportion of counterfeits is substantial, premium products will lose market share, a phenomenon often referred to as “bad money driving out good money.” In a vertically differentiated competition, if the quality of the premium product is below a certain threshold, it is recommended that the premium firm be the first to adopt BCT, while the typically authentic firm should not follow (Scenario NB). That is, Scenario NB is a win-win situation for both firms in the competition. The premium firm that has adopted BCT can offer a “free ride” to the typically authentic firm.

1. Introduction

1.1. Background and Motivation

In the contemporary era, the proliferation of counterfeit products emerged as a significant challenge for numerous industries, including pharmaceuticals, food, jewelry, fashion, and electronics [1]. Examples of such products include fake toys with toxic paint, winter coats without padding, and contaminated cosmetics. The global economy loses over $500 billion a year as a result of counterfeiting (U.S. Chamber of Commerce’s Global Innovation Policy Center Information 2022). These unregulated products do not meet legal or safety standards and may pose a serious threat to the health and safety of consumers.

There are two distinct forms of counterfeiting: (a) non-deceptive counterfeiting, which occurs when customers can distinguish between authentic and counterfeit products, and (b) deceptive counterfeiting, which occurs when customers are unable to distinguish between the two types of products [2]. For example, many counterfeit imitations of designer bags or shoes have distinct external features that can be identified. Nevertheless, deceptive counterfeiting occurs when the counterfeit product appears to be identical to the authentic product and customers are unable to distinguish between the two types of products. This can be observed in the case of many counterfeit foods (e.g., baby formula) and medicines that have the same outer packaging as the authentic product.

The fight against counterfeits is a matter of the utmost importance, necessitating not only the establishment of a collaborative framework between the business community, government, and consumers but also the implementation of efficacious technologies. Conventional technologies include barcodes, RFID tags, and OACTs [3]. However, they can also be copied and printed on copycat products. Compared with traditional technologies, BCT represents a novel information technology, exhibiting distinctive features such as decentralization, transparency, traceability, immutability, data security, and the self-establishment of credit. To combat counterfeit goods, numerous firms adopt BCT for product traceability, such as Walmart, Amazon, JD, and Alibaba in China [4]. For example, the blockchain traceability and authentication system developed by the Ali Group to assist Moutai (a Chinese liquor) can effectively enhance product traceability, authenticity verification, transaction payment, and other services.

Using BCT for traceability guarantees that the information about the product is true, effective, and free from errors before uploading. However, this does not imply that the products are authentic. In other words, BCT cannot guarantee that all the data on the blockchain is from authentic products, i.e., BCT cannot prevent counterfeiting at the source or before uploading the blockchain. To illustrate, the data about Moutai that is incorporated into the BCT traceability system can be authentic and unaltered; however, BCT is unable to guarantee the veracity of the liqueur within the bottle. As a case in point, the valuable herb, Matsutake, is produced in Tibet, China. Initially, it is harvested by farmers and then traced through JD Blockchain. It is important to note that Matsutake inventory entering BCT traceability may contain counterfeit and inferior herbs if they do not undergo strict testing and screening before moving into blockchain traceability. This phenomenon is commonly known as ‘Garbage in, and garbage out.’ Consequently, BCT is unable to entirely prevent counterfeiting at the source. The ability of BCT traceability to resist counterfeits is referred to as the security level of BCT traceability in this paper.

1.2. Research Questions and Innovations

This study examines the adoption strategy of BCT by authentic firms in two markets where deceptive counterfeits exist: a monopoly and a vertically differentiated competitive duopoly. In particular, we address the following research questions (RQs):

RQ 1: In a monopoly, what is the impact of BCT on the pricing, market share, and profits of the authentic firm? Additionally, what is the effect of information asymmetry and the counterfeiter?

RQ 2: In a vertically differentiated competitive duopoly, what are the BCT adoption strategies for authentic and premium firms in the presence of deceptive counterfeits? Is it possible to identify a win-win scenario for them?

RQ 3: What is the impact of BCT on consumer surplus and social welfare? Which scenario benefits consumers?

To answer these questions, we develop analytical models in a monopoly and a vertically differentiated competitive duopoly in the presence of deceptive counterfeits. In a monopoly, we obtain the perfect Bayesian equilibrium of an authentic firm and a deceptive counterfeiter. In a competitive duopoly, we build upon a vertical differentiation model for a typically authentic firm and a premium firm in the presence of deceptive counterfeits. The quality of products produced by a premium firm is higher than that of products produced by a typically authentic firm. The strategies of two authentic firms adopting BCT and the win-win scenario are identified.

Following the identification of the equilibrium decisions in two markets, we obtain the following anti-counterfeiting and BCT adoption strategies: (i) BCT serves to mitigate the adverse impact of asymmetric information on prices, market share, and profits of authentic products; (ii) If the proportion of counterfeit products in a duopoly is considerable, premium products will experience a loss of market share, which leads to the phenomenon of ‘bad money drives out good money’; (iii) In a vertically differentiated competition, when the quality of the premium product is below a threshold, Scenario NB is a win-win situation for both firms, that is, the premium firm adopts BCT, while the typically authentic firm does not. At this point, the premium firm that has adopted BCT can offer a “free ride” to the typically authentic firm.

To summarize, the contribution of this paper is twofold. From a practical perspective, this paper offers a novel perspective on the practical challenges posed by blockchain technology in addressing the issue of counterfeiting. To the best of our knowledge, this is the first study to consider strategies for adopting blockchain technology to combat counterfeiting in a vertically differentiated competition when BCT is not able to completely counteract counterfeits. This study offers managerial insights into the impact of BCT on an authentic firm and a counterfeiter, as well as the BCT adoption strategies of two competing authentic firms, i.e., a typically authentic firm and a premium firm. From an academic perspective, in contradistinction to the paucity of extant studies on the utilization of blockchain technology to combat counterfeiting (Shen et al. [1]), our study considers the adoption strategies for blockchain of two competing firms in the context of deceptive counterfeits being simultaneously mixed into two authentic channels. We obtain perfect Bayesian equilibrium results by analytical analysis. The optimal blockchain adoption strategy for vertically differentiated competitive firms is obtained when blockchain technology is unable to fully counteract counterfeits. Furthermore, this paper presents an innovative examination of the security level of blockchain technology.

We also clarify the scope and boundary conditions up front and provide a roadmap of implementation, equilibrium selection, mechanism explanations, cost thresholds, and policy implications developed in Section 2.4, Section 3.1, Section 3.2, Section 3.3, Section 4, Section 5, Section 6 and Section 6.3.

1.3. Paper Organization

The rest of the paper is organized as follows. Section 2 reviews the related literature. Section 3 presents the model descriptions of markets, products, and consumers. Section 4 analyzes the effect of BCT on a monopoly with deceptive counterfeits. Section 5 provides BCT adoption strategies of two competing authentic firms in a vertically differentiated competition. Section 6 extends the base model in two aspects. Section 7 concludes this paper.

2. Literature Review

We examine the BCT adoption strategies to combat counterfeiting in a monopoly and vertically differentiated competition. Based on the research focus of this paper, we present three related streams of literature as follows.

2.1. Relevant Research on Counterfeits

The issue of counterfeiting has been the subject of academic research since the 1980s. Grossman and Shapiro [5] classify counterfeit products into two categories: non-deceptive and deceptive counterfeits. Non-deceptive counterfeits are those that consumers can distinguish from brand-name products. Deceptive counterfeits exhibit physical characteristics that are nearly indistinguishable from those of authentic products, rendering it impossible for consumers to ascertain whether a product is authentic or counterfeit. The literature on counterfeit goods encompasses a multitude of disciplines, including parallel imports [6], intellectual property rights [7], inventory management [8], and consumers’ behavior [9,10].

To illustrate, Cho et al. [2] compares deceptive and non-deceptive counterfeiters and provide insights into the impact of anti-counterfeiting strategies on a brand-name company, a counterfeiter, and consumers. Furthermore, Qian et al. [11] examine the searchable and experiential dimensions of quality responses to entry by counterfeiters and analyze market equilibria under competition from counterfeiting as well as under monopoly branding. In the context of counterfeit drugs, Gao [3] considers a model in which an authentic firm sells its drug at a reliable source, while counterfeiters sell their drugs at a dubious source, and shows there may be an inverted U-shaped relationship between the complexity of the OACT and the volume of counterfeit drug purchases. In the context of luxury products, Gao et al. [12] develop a game-theoretic model to examine the entry of copycats and its implications and find that copycats with a high physical resemblance, but low product quality are more likely to successfully enter the market.

In summary, the existing literature discusses two main types of counterfeits, non-deceptive and deceptive counterfeits, and describes the characteristics of counterfeits. Based on the existing literature, our work mainly considers deceptive counterfeits and uses the characteristics of counterfeits of existing studies. We also categorize the quality attributes of a product into searchable characteristics and experiential characteristics. Differently, we consider the strategy of genuine companies adopting blockchain technology when deceptive counterfeits are mixed into two genuine channels with quality differences.

2.2. Using Blockchain to Combat Counterfeiting

Blockchain is a decentralized, traceable, multi-party distributed database that has the potential to significantly enhance the security of supply chains [13,14,15,16,17]. The potential of blockchain technology to transform supply chain functions is immense, encompassing supply chain provenance, business process reengineering, consumer demand, and security enhancement [18,19,20,21,22]. For example, Choi et al. [22] believe that blockchain technology helps the firm accurately assess the proportion of risk-seeking, risk-neutral and risk-averse customers; Lu et al. [23] explore the ways in which firms can profit from blockchain traceability with regard to convenience preference products and trust preference products; Choi [24] proposes the implementation of blockchain with cryptocurrency engenders a mutually beneficial scenario for all supply chain agents and consumers; Zhao et al. [25] indicate that prominent e-commerce platforms use blockchain to enhance consumer confidence in product quality; Gupta et al. [26] find that blockchain technology is more effective in facilitating the financial resilience of a supply chain under the moderating influence of environmental dynamism, in comparison with artificial intelligence; Choi et al. [27] investigate the blockchain technology would potentially improve the use of social media analytics for supply chain operations management.

At present, blockchain technology is the focus of extensive research in the field of product traceability. Furthermore, the use of BCT for product traceability can guarantee the veracity of products, thereby deterring the proliferation of counterfeit goods. Specifically, Choi, T. M. [28] proposes that a significant application of blockchain technology lies in the realm of diamond authentication and certification, delves into various consumer-driven operations models, and underscores the merits of blockchain-empowered platforms in facilitating diamond authentication and certification. Subsequently, Shen et al. [1] examine the efficacy of permissioned blockchain technology in combating copycats in the supply chain and show that PBT increases the BNC profit, consumer surplus, and social welfare and reduces the copycat’s profit. Pun et al. [29] examine the effectiveness of blockchain as a solution to combat deceptive counterfeits and find that blockchain should be used when customers have intermediate distrust about products in the market. Furthermore, Zhu et al. [30] focus on whether the powerful brand owner in a dual-channel supply chain should adopt BCT and indicate that the adoption of BCT is always beneficial to the retailer, which creates a “free-rider” issue. Choi and Ouyang [31] propose that blockchain-based product provenance authentication (BPPA) platforms have been developed to assist in the authentication of products such as diamonds and reveal the analytical conditions governing when it is beneficial to use the BPPA platform. In addition, Li et al. [32] explores the interplay between blockchain technology adoption and channel selection in combating counterfeits and examine the impact of this interaction on consumer surplus and social welfare.

To summarize, extant research on the utilization of blockchain technology in the context of counterfeiting reaches a core finding that this technology is capable of guaranteeing the authenticity and verifiability of products, thereby providing a complete counteraction to counterfeiting. Nevertheless, there are instances in current practice where products with blockchain traceability information are found to be counterfeits, highlighting the necessity for further research into the newly emerging issues in commerce. This constitutes a significant research gap in the field.

Our study posits that blockchain can guarantee the authenticity of the data and information of the products on the chain. However, it should be noted that blockchain does not provide any assurance regarding the authenticity of the products entering the channel, which is referred to as “counterfeiting at the source”. This paper presents an innovative examination of the security level of blockchain technology in light of the aforementioned problem. In contrast to existing studies, we focus on combating counterfeits and analyzing strategic options for using blockchain technology to combat counterfeiting in a vertically differentiated competition.

2.3. Vertically Differentiated Competition

This paper is also related to the literature on vertically differentiated competition. Vertically differentiated competition refers to the competition between products or services that vary in quality (Vandenbosch and Weinberg [33]; Kuksov and Lin [34]). This type of competition is prevalent in markets where consumers have different preferences for product quality (Tian et al. [35]). The literature on vertically differentiated competition focuses on various aspects, such as pricing strategies, channel competition, consumer behavior, and the impact of strategic interactions between firms.

Specifically, the extant literature mainly focuses on pricing (Xu et al. [36]; Jing [37]; Tang et al. [38]; Nire and Matsubayashi [39]), product quality (Zhou and Choudhary [40]; Zhao et al. [41]; Guan et al. [42]), channel competition (Lu and Menezes [43]), and service market (Zhou et al. [44]). For example, Li et al. [45] investigates pricing strategies in a competition in which two platforms offer dependent products and identify the impact of message dissemination on pricing strategies. Kwark et al. [46] examine the effect of managerial optimism on firms’ performance in competition and find that managerial optimism about the demand of only one firm can increase both firms’ profits. Xu et al. [47] consider a duopoly supply chain and identify the impact of the horizontal and vertical fairness concerns on the three-party supply chain coordination.

In the research conducted on the adoption of blockchain technology by competing firms, Ye et al. [48] seek to answer whether and under what conditions two competing agri-food supply chains can benefit from the adoption of blockchain technology (BT). The results suggest that the Nash equilibrium outcome for the BT adoption strategy is strongly influenced by key parameters such as the intensity of competition, the growth rate of market size and investment costs with BT adoption, and the planting costs of the agri-food industry. Liu et al. [49] demonstrate that the application of blockchain technology in the certification of the green level of products has the potential to transform the competitive landscape between green and non-green products. Niu et al. [50] find that a brand’s efficient image investment encourages e-tailers to connect to the blockchain system, increasing the genuine product’s market share through enhanced competition with copycats. E-tailers are also more likely to participate if their commission from copycat sales is low and their reselling channel advantage is limited.

In conclusion, scholars examine strategies for the adoption of blockchain technology in different competing scenarios of practical problems. We also study blockchain adoption strategies in competitive scenarios, but our research questions are different from the current research. We focus on how a typically authentic firm, and a premium firm should decide on a blockchain selection strategy when there is a source counterfeiting problem in vertically differentiated competition, i.e., when the blockchain is not able to fully counteract counterfeiting. Our research can provide strategic support for branding companies in current practice.

2.4. Comparison to Closely Related Models

Relative to Shen et al. [1], who study permissioned blockchain to deter copycats in a supply chain, we focus on deceptive counterfeits that can still enter the channel before data capture (“source counterfeiting”) and on vertical quality differentiation between two authentic firms. Pun et al. [29] highlights that blockchain is useful under intermediate distrust; our analysis complements theirs by endogenizing adoption timing in duopoly and showing when NB (premium adopts; standard does not) dominates NN and BB under quality and fee thresholds. Zhu et al. [30] examines dual-channel dominance by a brand owner and document free-rider issues; we obtain a distinct free-ride spillover where the standard firm benefits when the premium rival adopts first (Proposition 6). Finally, Li et al. [32] connect channel selection with blockchain; we hold channels fixed and instead explore source-counterfeit security $\mu$ as a lever shaping prices, demands, and welfare across scenarios. Together, these differences clarify the niche our model fills.

3. Model Setup

This section begins by describing the types of markets, the individual market players and products, and consumer utility.

3.1. Markets

This study examines two market structures: a monopoly and a competitive duopoly. There is only one authentic firm $a$ in the monopoly. In the context of a vertically differentiated competitive duopoly, two authentic firms compete for market share. Each firm specializes in the production of either typically authentic products or premium products, which are imperfect substitutes. In the following, these two firms are referred to as a typically authentic firm $a_1$ and a premium firm $a_2$, respectively. Deceptive counterfeit products are present within both markets. These counterfeit products are often designed to match the external characteristics and price points of their authentic counterparts, with the intent of deceiving consumers. However, such products are often of substandard quality, lacking in durability, and sometimes posing health and safety concerns for consumers. Examples of such products include precious Chinese herbs such as Ginseng and Matsutake, wine, tea, and designer bags. The present study focuses exclusively on the issue of deceptive counterfeiting, with relevant examples and references provided herein.

Branded firms can utilize BCT to combat the counterfeiting of products. Given that BCT is unable to eradicate counterfeiting at its source, the present study proposes a novel methodology for evaluating the blockchain’s capacity to resist such illicit activities. The following definition is proposed for the security level of BCT.

Definition 1 

(Security level). The security level of blockchain traceability, $\mu \in [0, 1]$, is the fraction of source counterfeits blocked from entering the authentic sales channel by the end-to-end traceability and auditing process.

$\mu =0$ means no protection; $\mu =1$ means full protection. Implementation-wise, $\mu$ increases with the intensity and coverage of upstream inspections, tamper-evident devices, cryptographic anchoring, and smart-contract enforcement. We assume a one-off service fee $F\left(\mu \right)$ that is increasing (and possibly convex) in $\mu$; the baseline linear form $F\left(\mu \right)=\varphi \mu$ is used in Section 4 and Section 5 for tractability without affecting the qualitative comparative statics.

In the context of Bitcoin transactions, the security level of blockchain technology is characterized by its capacity to prevent the occurrence of “double spending,” which refers to the process of attempting to spend the same Bitcoin more than once. The achievement of this security level is facilitated by the utilization of smart contracts within the blockchain. This value is taken as given or exogenous by producers and consumers. In practice, the authentic firm employs a third-party blockchain traceability service, such as JD Blockchain in China.

The security level is contingent upon the capacity of the smart contract protocol to establish a “trusted execution environment.” The automated rules embedded within the protocol are of crucial importance. The incentives for the parties involved are modified, which results in a significant increase in the risk and cost of detection for fraudulent activities. This, in turn, serves to deter counterfeiting at its source. Security does not arise automatically; it is the outcome of a meticulously designed protocol that transforms technical trust (immutability) into commercial trust (transparent processes, clear rewards and penalties). A robust protocol is one which, by virtue of its very nature, significantly reduces the potential for counterfeiting.

3.2. Products

As posited by Qian et al. [11], we also consider that a product incorporates two dimensions of quality: that which is searchable and that which is experiential. Searchable quality is defined as the observable characteristics of a product that are actively sought out at the time of purchase. In contrast, experiential quality encompasses unobservable characteristics such as the comfort, friction, and cushioning effects of shoes, which are unobserved at the time of purchase. Customers can infer experiential quality based on word of mouth, past experiences, searchable quality, and price.

We let product quality be $q={\omega }_s{q}_s+{\omega }_e{q}_e$ with ${\omega }_s,{\omega }_e>0$ and ${\omega }_s+{\omega }_e=1$. Deceptive counterfeits perfectly mimic the searchable component but suffer an experiential discount, $q^c={\omega }_s{q}_s+{\omega }_e\delta q_e$, $\delta \in (0, 1)$. All results in Section 4 and Section 5 carry over with a re-scaling of coefficients; in particular, price and demand monotonicities and the ranking NN vs. NB vs. BB remain unchanged (proof sketch in Appendix A and Appendix B).

The quality of an authentic product in a monopoly is expressed as $q_a$. In a competitive duopoly, we denote the quality of an authentic product as $q_{a_1}$ and that of a premium product as $q_{a_2}$, and $q_{a_1}<q_{a_2}$. The quality of a deceptive counterfeit is presented as $q_d$.

The quality of an authentic product incorporates a searchable quality $s$ and an experiential quality $h$, i.e., $q_a=s+h$. The quality of the authentic product is taken as given in the model. As a deceptive counterfeit imitates the authentic product, its quality is $q_d=s+{\delta }_{d}h$, where $0<{\delta }_d<1$. It has the same searchable quality as the authentic product to confuse consumers. However, a deceptive counterfeit is typically characterized by a lack of perfect experiential quality. Moreover, we exclusively consider marginal costs and do not take into account sunk costs, which do not alter the qualitative implications of the results. We assume physical products have marginal production cost, and the marginal cost is linear with respect to quality, $c{q}_i$, where $0<c<{\displaystyle \frac{1}{2}}$, which applies to all the results in the paper.

3.3. Consumers

A unit mass of consumers is in the market. Each consumer purchases at most one product. Consumers’ preference for the quality of the product is denoted by $\theta$. Denote the cumulative distribution function of consumers’ taste for the quality as $F\left(\theta \right)$, and the probability density function as $f\left(\theta \right)$. Without loss of generality, assume $\theta$ follows a uniform distribution of $\left[0, 1\right]$. Relaxing this assumption does not change the results qualitatively but only complicates calculations (Qian et al. [11]). In the model extensions, we further discuss the nonuniform distribution of consumer preference to verify the robustness of the basic model. The utility that a customer consumes one unit of product $i$ is $U\left(\theta \right)=\theta q_i-p_i$, where $i\in \left\{a,a_1,a_2,d\right\}$ and $p_i$ is the price of the product $i$.

Table 1. Notations.

Notation	Description
$i$	Subscript for firms (or products), $i\in \left\{a,a_1,a_2,d\right\}$
$a$	Authentic firm (or authentic product) in a monopoly
$a_1$	Authentic firm (or authentic product) in a competition
$a_2$	Premium firm (or premium product) in a competition
$d$	Deceptive counterfeiter (or deceptive counterfeit product)
$j$	Superscript for scenarios in two markets, $j\in \left\{N,B,NN,NB,BB\right\}$
$N$	No use of BCT in a monopoly
$B$	Use of BCT in a monopoly
$NN$	No use of BCT in both firms in a competition
$NB$	$a_1$ adopts BCT and $a_2$ does not adopt BCT in a competition
$BB$	Both firms adopt BCT in a competition
$\theta$	Consumers’ taste for the quality of the product
$\lambda$	Probability of deceptive counterfeits in the market
$s$	Searchable quality of an authentic product
$h$	Experiential quality of an authentic product
$h^{\prime }$	Experiential quality of a premium product
${\delta }_d$	Discount factor of the experiential quality of a deceptive counterfeit
$\mu$	Security level of BCT traceability, $\mu \in \left[0, 1\right]$
$q_i$	Quality of a product $i$, $i\in \left\{a,a_1,a_2,d\right\}$
$p_i^j$	Retail price of a product $i$ in Scenario $j$
$D_i^j$	Demand for a product $i$ in Scenario $j$
${\Pi }_i^j$	Profits of the firm $i$ in Scenario $j$
$c$	Sensitivity of marginal cost to quality ($0<c<{\displaystyle \frac{1}{2}}$)

summarizes all the notations.

Remark 1 

(Existence and Uniqueness of the Price Nash Equilibrium). With standard vertically differentiated demand and downward-sloping best responses, the product of best-response slopes below unity yields a contraction mapping, ensuring a unique price Nash equilibrium. Increasing $\mu$ does not break contraction: it shifts demand and affects slopes only through second-order terms, so uniqueness and the direction of comparative statics are preserved.

4. Monopoly in the Presence of Counterfeiting

In this study, we examine two scenarios: one in which a branded producer does not adopt BCT traceability and another in which the same producer adopts BCT. Use superscript $N$ to denote no BCT adoption, and $B$ to denote BCT adoption. Given that our principal focus is on deceptive counterfeits, the issue can be conceptualized as a pooling equilibrium. This is because deceptive counterfeits make it difficult for consumers to differentiate between genuine and counterfeit products. Our analysis yields optimal Bayesian equilibrium solutions within the context of a pooling equilibrium.

4.1. No Use of Blockchain

We initially examine the scenario in which the authentic firm does not utilize BCT. In light of the superior quality of the authentic product, the counterfeiter opts for a deceptive strategy, leading to the emergence of pooling equilibrium solutions. For tractability, we assume $s=h={\displaystyle \frac{1}{2}}$ henceforth in the paper.

The sale of deceptive counterfeits presents a significant challenge for consumers attempting to differentiate between authentic and counterfeit products. This is due to the fact that the searchable qualities and price of the counterfeit products are identical to those of the authentic products, making it difficult for consumers to ascertain whether they are purchasing an authentic product or a counterfeit. This creates an information asymmetry between sellers and consumers. This ultimately leads to uncertainty among consumers regarding the products in question. Similarly to the findings of Qian et al. [11], consumers possess a prior understanding of the likelihood of a product being authentic or counterfeit. We denote the prior probability belief of a counterfeit as $\lambda$, and that of the authentic product as $1-\lambda$. Hence, customers have the probability $\lambda$ of being deceived into purchasing counterfeits and the utility is $U\left(\theta \right)=\left(1-\lambda \right)\left(\theta q_a-p_a^N\right)+\lambda \left(\theta q_d^N-p_a^N\right)$. The marginal consumer who is indifferent between purchasing a product and not purchasing is denoted by ${\theta }^{N*}$.

$${\theta }^{N*}={\displaystyle \frac{p_a^N}{s+\left(1-\lambda +\lambda \cdot {\delta }_d\right)}}.$$

(1)

An authentic firm’s payoff function is

$$\underset{p_a^N}{max}{\Pi }_a^N=\left(p_a^N-c\cdot q_a\right)\left(1-\lambda \right)\left(1-{\theta }^{N*}\right).$$

(2)

A deceptive counterfeiter’s payoff function is

$${\Pi }_d^N=\left(p_a^N-c\cdot q_d\right)\lambda \left(1-{\theta }^{N*}\right).$$

(3)

The equilibrium results are $p_a^{N*}={\displaystyle \frac{1}{4}}\left(2+2c-\lambda +\lambda {\delta }_d\right)$ and ${\Pi }_a^{N*}={\displaystyle \frac{\left(1-\lambda \right){\left(-2+2c+\lambda -\lambda {\delta }_d\right)}^2}{8\left[2+\lambda \left(-1+{\delta }_d\right)\right]}}$.

Lemma 1.

In the absence of BCT, the profit of a deceptive counterfeiter is a concave function of the proportion of counterfeits $\lambda$.

If the proportion of counterfeits is small, the positive effect on the demand for counterfeits is greater than the negative effect on the price of genuine goods and total demand, and the counterfeiter’s profit increases. If it is large, its negative impact on price and total demand will outweigh its positive impact on the demand for counterfeits, and hence the profit will decrease. Thus, it is not the case that a higher proportion of counterfeits leads to a higher profit for the counterfeiter.

4.2. Use of Blockchain

Welfare is defined as consumer surplus plus firms’ profits net of $F\left(\mu \right)$; counterfeiters’ profits are excluded.

When the authentic firm uses BCT, he needs to pay the service fee. In practice, the service fee for the BCT traceability is a one-time payment. Hence, we assume the one-time BCT service fee is $\varphi \mu \left(\varphi >0\right)$, where $\varphi$ is a unit service fee and referred to as the payment rate for BCT. The BCT service fee is positively correlated to the security level.

While BCT guarantees the integrity of existing blockchain data, it does not prevent the introduction of counterfeit products at the source. To illustrate, in the context of tracing the provenance of marine fish in a specific marine area, BCT can’t guarantee that all the data on the blockchain originates from high-quality marine fish. Nevertheless, BCT can markedly diminish the incursion of counterfeit products into the supply chain, thereby facilitating the authentication of genuine merchandise.

BCT’s traceability service prevents some counterfeits from entering the blockchain. The proportion of counterfeits on the market is now reduced to $\lambda \left(1-\mu \right)$ from $\lambda$. Therefore, the probability of counterfeits on the market when using BCT is $\tilde{\lambda }={\displaystyle \frac{\lambda \left(1-\mu \right)}{1-\lambda \mu }}$, and that of authentic products is $1-\tilde{\lambda }={\displaystyle \frac{1-\lambda }{1-\lambda \mu }}$. After observing the use of BCT, consumers also update their prior beliefs about the type of product. Thus, a consumer’s utility for the product sold when using BCT is $U\left(\theta \right)=\left(1-\tilde{\lambda }\right)\left(\theta q_a-p_a^B\right)+\tilde{\lambda }\left(\theta q_d^B-p_a^B\right)$. The marginal consumer who is indifferent between purchasing a product and not purchasing is denoted by ${\theta }^{B*}$.

$$\underset{p_a^B}{max}{\Pi }_a^B=\left(p_a^B-c\cdot q_a\right)\cdot {\displaystyle \frac{1-\lambda }{1-\lambda \mu }}\cdot \left(1-{\theta }^{B*}\right)-\varphi \mu .$$

(4)

An authentic firm’s profits are as follows.

$$\underset{p_a^B}{max}{\Pi }_a^B=\left(p_a^B-c\cdot q_a\right)\cdot {\displaystyle \frac{1-\lambda }{1-\lambda \mu }}\cdot \left(1-{\theta }^{B*}\right)-\varphi \mu .$$

(5)

A deceptive counterfeiter’s payoff function is

$${\Pi }_d^B=\left(p_a^B-c\cdot q_d\right)\cdot {\displaystyle \frac{\lambda \left(1-\mu \right)}{1-\lambda \mu }}\cdot \left(1-{\theta }^{B*}\right)-\varphi \mu .$$

(6)

We derive the pooling equilibrium with blockchain use, following a backward approach.

Lemma 2.

With the use of BCT, the price, market share, profits, consumer surplus, and social welfare are as follows.

(a) Price of an authentic product:

$${p_a^B}^{*}={\displaystyle \frac{2-\lambda \left[1-{\delta }_d\left(1-\mu \right)+\mu \right]+2c\left(1-\lambda \mu \right)}{4-4\lambda \mu }}.$$

(7)

(b) Market share of an authentic firm:

$$D_a^{B*}={\displaystyle \frac{\left(1-\lambda \right)K+2c\left(1-\lambda \mu \right)}{2\left(1-\lambda \mu \right)K}}.$$

(8)

(c) Profits of an authentic firm:

$${\Pi }_a^{B*}={\displaystyle \frac{\left(1-\lambda \right){\left[2-2c-\lambda +\lambda {\delta }_d-\lambda \mu \left(1-2c+{\delta }_d^B\right)\right]}^2}{8{\left(1-\lambda \mu \right)}^{2}K}}-\varphi \mu .$$

(9)

(d) Consumer surplus:

$$C{S}^{B*}=\left(1-\tilde{\lambda }\right){\int }_{{\theta }^{*}}^1\left[\theta \left(s+h\right)-{p_a^B}^{*}\right]d\theta +\tilde{\lambda }{\int }_{{\theta }^{*}}^1\left[\theta \left(s+{\delta }_d\cdot h\right)-{p_a^B}^{*}\right]d\theta \hspace{1em}={\displaystyle \frac{H^2}{16\left(-1+\lambda \mu \right)\left(-K+2\lambda \mu \right)}}.$$

(10)

(e) Social welfare:

$$S{W}^{B*}={\displaystyle \frac{H^2}{16\left(-1+\lambda \mu \right)\left(-K+2\lambda \mu \right)}}+{\displaystyle \frac{\left(-1+\lambda \right)H^2}{8{\left(-1+\lambda \mu \right)}^2\left(-K+2\lambda \mu \right)}}-\varphi \mu .$$

(11)

where $H=2\left(c-1\right)+\lambda \left(1-{\delta }_d\right)+\left(1-2c+{\delta }_d\right)\lambda \mu$,  $K=2-\lambda \left[1-{\delta }_d\left(1-\mu \right)-\mu \right]$.

First, we obtain some results of comparative statistical analysis in a pooling equilibrium with blockchain. As discussed earlier, when authentic products are infiltrated by counterfeit products, consumers face uncertainty about the type and quality of a product; in other words, consumers have product information asymmetry. Specifically, the uncertainty about product type is reflected in the proportion of counterfeit products. The information asymmetry about quality is reflected in the discounted factor of the experiential quality of counterfeit products. The reduction in the discounted factor leads to a higher degree of information asymmetry.

Proposition 1

(Effect of BCT on price, market share, and profits).  As the security level of BCT is improved (i.e., as  $\mu$  increases),

(a)

the price and market share of an authentic product increases; the profits of an authentic firm increase if $\varphi <\widehat{\varphi }$;

(b)

a deceptive counterfeiter’s market share and profits both decrease if $\lambda <{\displaystyle \frac{1}{2-\mu }}$.

The improved level of security or traceability provided by BCT reduces counterfeiting and increases consumer utility, known as the utility effect. This effect increases the price and market share of authentic products and decreases those of counterfeits. Moreover, firms trade off both positive and negative effects when choosing BCT. On the one hand, due to the security level of BCT, a branded firm obtains higher product prices and greater market demand, which is a positive effect. On the other hand, when using BCT, the company has to pay the software service fee, which has a negative effect. Thus, if the unit service fee is below a threshold, the use of BCT increases the profits of the authentic firm. In addition, if the proportion of counterfeits is not large, the use of BCT reduces the market share and profits of a counterfeit firm. Thus, in a pooling equilibrium, BCT works well when the proportion of counterfeits is less than the threshold.

Corollary 1.

(Effect of BCT on brands and counterfeiters) (a) If the unit service fee for BCT is less than a threshold i.e., $\varphi <\widehat{\varphi }$), brands should adopt BCT. (b) BCT reduces deceptive counterfeiters’ incentive to pool with the branded firm.

The adoption of BCT by brands significantly reduces the proportion of counterfeits and thus increases consumer willingness to pay. If the unit service fee for BCT is not too high, brand companies are better off with BCT. In addition, BCT reduces the incentive for fraudulent counterfeiters to join forces with an authentic company. Such an outcome illustrates the motive for anti-counterfeiting. In a pooling equilibrium, counterfeiters trade off two effects of BCT: the price effect and the demand effect. On the one hand, as the security level of BCT increases, the price of authentic products improves, leading to higher marginal profits for counterfeiters. This price effect increases the incentive for counterfeiters to enter the BCT traceability channel. On the other hand, the higher the security level of BCT, the lower the proportion of counterfeits, which reduces the demand and revenue for counterfeiters. Thus, the demand effect of BCT reduces the incentive for counterfeiters to enter the market. The demand effect of BCT on counterfeits dominates the price effect, which therefore reduces the incentive for counterfeiters to join forces with the branded firm. As a result, branded firms prefer BCT to minimize the pooling incentives for counterfeiters.

Proposition 2

(Effect of BCT on asymmetric information). If  $\lambda <{\lambda }^{\prime }$, as the security level of BCT is improved (i.e., as $\mu$ increases),

(a) the adverse impact of the asymmetric information on the authentic firm’s price, market share, and profits is mitigated (e.g., ${\displaystyle \frac{{\partial }^2{\Pi }_a^{B*}}{\partial \lambda \partial \mu }}>0$, ${\displaystyle \frac{{\partial }^2{\Pi }_a^{B*}}{\partial {\delta }_d\partial \mu }}<0$);

(b) the positive impact of the asymmetric information on the market share and profits of a deceptive counterfeiter is mitigated (e.g.,${\displaystyle \frac{{\partial }^2{D}_d^{B*}}{\partial \lambda \partial \mu }}<0$, ${\displaystyle \frac{{\partial }^2{D}_d^{B*}}{\partial {\delta }_d\partial \mu }}<0$).

Here, the critical value ${\lambda }^{\prime }$ is an increasing function of $\mu$. This proposition illustrates how BCT acts on the impact of asymmetric information on authentic and counterfeit goods. Interestingly, BCT mitigates the negative impact of asymmetric information on authentic products and reduces the positive impact of asymmetric information on counterfeits. In addition to the aforementioned utility effect, BCT prevents a certain percentage of counterfeits from entering the market, thereby improving the quality of products when BCT is used, which is referred to as the quality effect. In fact, given the proportion of counterfeits $\lambda$ and their quality discount factor ${\delta }_d^{BP}$, the asymmetric information reduces the quality of products in a pooling equilibrium. BCT acts to suppress asymmetric information. Therefore, whether the effect of asymmetric information is positive or negative, BCT weakens it.

Proposition 3 

(Effect of BCT on welfare).

(a) Consumer surplus always benefits from blockchain.

(b) If the unit service fee for BCT is less than a threshold (i.e., $\varphi <\widehat{\varphi }$), blockchain improves social welfare.

We find that blockchain is beneficial to consumers, that is, higher levels of blockchain security increase consumer utility. This positive effect outweighs the negative effect of a higher price for authentic products, leading to a higher consumer surplus. However, the positive effect does not outweigh the negative effect in terms of social welfare, as blockchain also imposes costs on branded companies in addition to increasing consumer trust. Therefore, social welfare benefits from BCT only when the unit service fee for blockchain is low. This finding provides important managerial insights for policymakers.

In the context of pooling equilibrium, consumers are unable to differentiate between counterfeit goods, thus necessitating the implementation of blockchain technology as a means of combatting such illicit activities. In the context of the separating equilibrium, consumers possess the capacity to autonomously discern counterfeit goods, obviating the necessity for blockchain technology. Consequently, the primary focus of this paper is the pooling equilibrium.

5. Vertically Differentiated Competition in the Presence of Counterfeiting

Next, we consider two competing authentic firms. Each firm sells one type of product. The two products are typically authentic and premium, respectively, where a typically authentic product refers to an authentic product of standard quality, and a premium product refers to an authentic product of higher quality. The two products are imperfect substitutes. The quality of the typically authentic products $q_{a_1}$ is less than that of the premium product $q_{a_2}$. We also assume that product quality has both searchable and experiential attributes. Hence, denote that $q_{a_1}=q_a=s+h$ and $q_{a_2}=s+h^{\prime }$ ($h^{\prime }>h$), and $s=h={\displaystyle \frac{1}{2}}$. For example, some valuable herbs are available in different quality levels, such as Ginseng and Matsutake in China, and foods such as sea cucumber. They tend to have the same searchable attributes, but the experiential attributes vary greatly. There are still counterfeits on the market, and the quality of these is $q_d=s+{\delta }_{d}h$, where $0<{\delta }_d<1$. For simplicity of analysis, assume that two types of authentic products are pooled with the same proportion of counterfeits, i.e., the percentage of counterfeits is ${\displaystyle \frac{\lambda }{2}}$ for both products.

5.1. Competition Scenarios

In a duopoly market with counterfeits, three scenarios are discussed based on whether the firms adopt BCT. Scenario NN is when neither firm adopts BCT; Scenario NB denotes when the authentic firm does not adopt BCT, while the premium product firm does; Scenario BB represents when both firms use BCT. We focus on the following questions: (a) How does the use of BCT affect the competition between these firms? (b) How do the firms decide the timing to use BCT? That is, under what scenarios should BCT be adopted? (c) What is the impact of BCT on consumer surplus and social welfare? (Figure 1).

Scenario NN. We use the vertical product differentiation framework to model consumer utility. In this scenario, both firms do not adopt BCT. Consumers can purchase both products with probability ${\displaystyle \frac{\lambda }{2}}$ of being counterfeits. Thus, consumer utility of both the typically authentic and the premium product is as follows:

$$U_{a_1}^{NN}\left(\theta \right)={\displaystyle \frac{1-\lambda }{2}}\left(\theta q_{a_1}-P_{a_1}^{NN}\right)+{\displaystyle \frac{\lambda }{2}}\left(\theta q_d-P_{a_1}^{NN}\right).$$

(12)

$$U_{a_2}^{NN}\left(\theta \right)={\displaystyle \frac{1-\lambda }{2}}\left(\theta q_{a_2}-P_{a_2}^{NN}\right)+{\displaystyle \frac{\lambda }{2}}\left(\theta q_d-P_{a_2}^{NN}\right).$$

(13)

Letting the above utilities be equal, i.e., $U_{a_1}^{NN}\left(\theta \right)=U_{a_2}^{NN}\left(\theta \right)$, we obtain the marginal consumer’s preference for quality as ${\theta }^{NN*}={\displaystyle \frac{P_{a_1}^{NN}-P_{a_2}^{NN}}{\left(1-\lambda \right)\left(q_{a_1}-q_{a_2}\right)}}$. The market demand for the two products is $D_{a_1}^{NN}={\theta }^{NN*}$ and $D_{a_2}^{NN}=1-{\theta }^{NN*}$, respectively. The firms maximize their profits by choosing the optimal prices for their products:

$${\Pi }_{a_1}^{NN}\left(P_{a_1}^{NN}\right)=\left(P_{a_1}^{NN}-c{q}_{a_1}\right)D_{a_1}^{NN}\cdot {\displaystyle \frac{1-\lambda }{2}}.$$

(14)

$${\Pi }_{a_2}^{NN}\left(P_{a_2}^{NN}\right)=\left(P_{a_2}^{NN}-c{q}_{a_2}\right)D_{a_2}^{NN}\cdot {\displaystyle \frac{1-\lambda }{2}}.$$

(15)

Scenario NB. In this scenario, the premium firm adopts BCT, while the typically authentic firm does not. The security level of BCT adopted by the premium firm is still indicated as $\mu$. Initially, both authentic firms have the proportion of counterfeit products as ${\displaystyle \frac{\lambda }{2}}$. Since the premium firm $a_2$ adopts BCT, the counterfeits with the proportion of ${\displaystyle \frac{\lambda \mu }{2}}$ will be blocked and thus switch to the typically authentic firm $a_1$. Therefore, the percentage of counterfeit products of $a_1$ becomes ${\displaystyle \frac{\lambda \left(1+\mu \right)}{2}}$, and that of $a_2$ becomes ${\displaystyle \frac{\lambda \left(1-\mu \right)}{2}}$. Therefore, the probability of consumers purchasing counterfeits from $a_1$ becomes ${\lambda }_{a_1}^{NB}={\displaystyle \frac{\lambda \left(1+\mu \right)/2}{\lambda \left(1+\mu \right)/2+\left(1-\lambda \right)/2}}={\displaystyle \frac{\lambda \left(1+\mu \right)}{1+\lambda \mu }}$, and from $a_2$ becomes ${\lambda }_{a_2}^{NB}={\displaystyle \frac{\lambda \left(1-\mu \right)/2}{\lambda \left(1-\mu \right)/2+\left(1-\lambda \right)/2}}={\displaystyle \frac{\lambda \left(1-\mu \right)}{1-\lambda \mu }}$. The consumer utility of the typically authentic and premium product becomes as follows:

$$U_{a_1}^{NB}\left(\theta \right)=\left(1-{\lambda }_{a_1}^{NB}\right)\left(\theta q_{a_1}-P_{a_1}^{NB}\right)+{\lambda }_{a_1}^{NB}\left(\theta q_d-P_{a_1}^{NB}\right).$$

(16)

$$U_{a_2}^{NB}\left(\theta \right)=\left(1-{\lambda }_{a_2}^{NB}\right)\left(\theta q_{a_2}-P_{a_2}^{NB}\right)+{\lambda }_{a_2}^{NB}\left(\theta q_d-P_{a_2}^{NB}\right).$$

(17)

In the same way, the marginal consumer’s preference for quality is obtained as ${\theta }^{NB*}={\displaystyle \frac{P_{a_1}^{NB}-P_{a_2}^{NB}}{K}}$, where $K=\left(1-{\lambda }_{a_1}^{NB}\right)q_{a_1}-\left(1-{\lambda }_{a_2}^{NB}\right)q_{a_2}+\left({\lambda }_{a_1}^{NB}-{\lambda }_{a_2}^{NB}\right)q_d$. The demand for two products is $D_{a_1}^{NB}={\theta }^{NB*}$ and $D_{a_2}^{NB}=1-{\theta }^{NB*}$. The profits of the two firms are as follows.

$${\Pi }_{a_1}^{NB}\left(P_{a_1}^{NB}\right)=\left(P_{a_1}^{NB}-c{q}_{a_1}\right)D_{a_1}^{NB}\left(1-{\lambda }_{a_1}^{NB}\right).$$

(18)

$${\Pi }_{a_2}^{NB}\left(P_{a_2}^{NB}\right)=\left(P_{a_2}^{NB}-c{q}_{a_2}\right)D_{a_2}^{NB}\left(1-{\lambda }_{a_2}^{NB}\right).$$

(19)

Scenario BB. Since two firms use BCT, both have counterfeits with proportion ${\displaystyle \frac{\lambda \mu }{2}}$ deterred, so the proportion of counterfeits for both firms becomes ${\displaystyle \frac{\lambda \left(1-\mu \right)}{2}}$. Therefore, the probability of a consumer purchasing counterfeit products from both firms becomes ${\lambda }_{a_1}^{BB}={\lambda }_{a_2}^{BB}={\displaystyle \frac{\frac{\lambda \left(1-\mu \right)}{2}}{\frac{\lambda \left(1-\mu \right)}{2}+\frac{\left(1-\lambda \right)}{2}}}={\displaystyle \frac{\lambda \left(1-\mu \right)}{1-\lambda \mu }}$. The consumer utility obtained by purchasing typically authentic products and premium products is as follows:

$$U_{a_1}^{BB}\left(\theta \right)=\left(1-{\lambda }_{a_1}^{BB}\right)\left(\theta q_{a_1}-P_{a_1}^{BB}\right)+{\lambda }_{a_1}^{BB}\left(\theta q_d-P_{a_1}^{BB}\right).$$

(20)

$$U_{a_2}^{BB}\left(\theta \right)=\left(1-{\lambda }_{a_2}^{BB}\right)\left(\theta q_{a_1}-P_{a_2}^{BB}\right)+{\lambda }_{a_2}^{BB}\left(\theta q_d-P_{a_2}^{BB}\right).$$

(21)

We obtain the marginal consumer’s preference for quality as ${\theta }^{BB*}={\displaystyle \frac{P_{a_1}^{BB}-P_{a_2}^{BB}}{\left(1-{\lambda }_{a_1}^{BB}\right)\left(q_{a_1}-q_{a_2}\right)}}$. The market demand is $D_{a_1}^{BB}={\theta }^{BB*}$ and $D_{a_2}^{BB}=1-{\theta }^{BB*}$, respectively. The profit functions are in the following:

$${\Pi }_{a_1}^{BB}\left(P_{a_1}^{BB}\right)=\left(P_{a_1}^{BB}-c{q}_{a_1}\right)D_{a_1}^{BB}\left(1-{\lambda }_{a_1}^{BB}\right).$$

(22)

$${\Pi }_{a_2}^{BB}\left(P_{a_2}^{BB}\right)=\left(P_{a_2}^{BB}-c{q}_{a_2}\right)D_{a_2}^{BB}\left(1-{\lambda }_{a_2}^{BB}\right).$$

(23)

5.2. Analysis and Results

This section mainly discusses the BCT adoption strategies of two competing firms, as well as win-win strategies for both sides. Some comparative statistical results are also derived. Competitive scenarios beneficial to consumers and social welfare are also derived.

Proposition 4.

If the proportion of counterfeit products $\lambda$ in vertically differentiated competition is high, then premium products will lose market share.

If there are a large number of counterfeits on the market, consumers realize they have a high probability of buying counterfeits. Instead of paying higher prices for premium products, it is better to pay a lower price for typically authentic products. The phenomenon of ‘bad money driving out good money’ emerges. In particular, $\lambda$ needs to satisfy the condition of $0<\lambda <1-{\displaystyle \frac{c}{2}}$ in Scenario NN, and $0<\lambda <{\displaystyle \frac{3}{\left(4-\mu \right)}}$ in scenarios NB and BB must be fulfilled. Otherwise, premium products lose market share.

Proposition 5.

It is advantageous for the premium firm to be the first to adopt BCT, with Scenario NB being the most advantageous, followed by Scenario BB and Scenario NN being the worst, i.e., ${\Pi }_{a_2}^{NB*}$ > ${\Pi }_{a_2}^{BB*}$ > ${\Pi }_{a_2}^{NN*}$.

The price and demand for premium products are higher in Scenario NB than in Scenarios NN and BB, as shown in

Table 2. Comparisons of results in three competitive scenarios.

Firms	Typically Authentic Firm (${\mathit{a}}_1$)	Premium Firm (${\mathit{a}}_2$)
$P_{a_i}^{*}$	$P_{a_1}^{NN*}$ < $P_{a_1}^{BB*}$ < $P_{a_1}^{NB*}$	$P_{a_2}^{NN*}$ < $P_{a_2}^{BB*}$ < $P_{a_2}^{NB*}$
$D_{a_i}^{*}$	$D_{a_1}^{NB*}$ < $D_{a_1}^{BB*}$ < $D_{a_1}^{NN*}$	$D_{a_2}^{NN*}$ < $D_{a_2}^{BB*}$ < $D_{a_2}^{NB*}$
${\Pi }_{a_i}^{*}$	${\Pi }_{a_1}^{NN*}$ < ${\Pi }_{a_1}^{BB*}$ < ${\Pi }_{a_1}^{NB*}$	${\Pi }_{a_2}^{NN*}$ < ${\Pi }_{a_2}^{BB*}$ < ${\Pi }_{a_2}^{NB*}$

; therefore, the premium firm makes the highest profit in Scenario NB. In Scenario NN, where neither firm adopts BCT, the premium firm can gain a greater competitive advantage by being the first to adopt BCT in Scenario NB. However, if the authentic firm also adopts BCT in Scenario BB, the premium firm’s competitive advantage is weakened and its profits are lower than in Scenario NB. Figure 2 shows the comparison of these three competitive scenarios.

Proposition 6.

For the typically authentic firm, if ${\displaystyle \frac{1}{2}}<h^{\prime }<h^{\widehat{\prime }}$, Scenario NB is also optimal, followed by Scenario BB and then Scenario NN, i.e., ${\Pi }_{a_1}^{NB*}$ > ${\Pi }_{a_1}^{BB*}$ > ${\Pi }_{a_1}^{NN*}$. Specifically,

(a) ${\Pi }_{a_1}^{NB*}$ > ${\Pi }_{a_1}^{NN*}$, this suggests that the premium firm adopting BCT can offer a free ride to the typically authentic firm.

(b) ${\Pi }_{a_1}^{BB*}$ > ${\Pi }_{a_1}^{NN*}$.

(c) If ${\displaystyle \frac{1}{2}}<h^{\prime }<h^{\widehat{\prime }}$, ${\Pi }_{a_1}^{NB*}$ > ${\Pi }_{a_1}^{BB*}$.

The result of ${\Pi }_{a_1}^{NB*}$ > ${\Pi }_{a_1}^{NN*}$ seems to be a counterintuitive conclusion. This is because if the premium firm is the first to adopt BCT, it will drive some of the counterfeits to the typically authentic firm and increase the probability that consumers will buy counterfeit versions of typically authentic products, thus reducing the demand for authentic products. In addition, the adoption of BCT by the premium firm increases consumer confidence in and utility of premium products, which also increases the price of premium products. However, typically authentic products also have room for price increases. The price increase effect for typically authentic products outweighs the sales decrease effect. Thus, the premium firm’s decision to adopt BCT first increases the typically authentic firm’s profit, which is the spillover effect of BCT on the value of both firms.

The adoption of BCT by both firms leads to an increase in the price of both products, where $P_{a_1}^{NN*}$ < $P_{a_1}^{BB*}$. However, the rise in prices reduces the sales of the typically authentic product, i.e., $D_{a_1}^{NN*}$ > $D_{a_1}^{BB*}$. Since the effect of the price increase is greater than the effect of the sales decrease, the profits of the authentic firm are higher in Scenario BB than in Scenario NN.

Mechanism behind the “free-ride”. Let ${\pi }_a=(p_a-c_a)D_a$ be the standard firm’s profit. When the premium firm adopts blockchain, two forces act on ${\pi }_a$: (i) Demand contraction—some consumers upgrade to the premium product because $\mu$ raises their expected experiential quality; and (ii) Competitive softening—vertical distance widens, so the standard firm’s optimal best response raises $p_a$ to extract surplus from the lower-taste segment. In the parameter region identified in Proposition 6, the price-increase effect dominates the quantity-loss effect, yielding $\Delta {\pi }_a>0$ despite $\Delta D_a<0$. Intuitively, authenticity certification by the premium firm relaxes head-to-head pressure in vertical differentiation, allowing the standard firm to free-ride on improved sorting and charge a higher margin.

Although the introduction of BCT may increase sales of authentic products, it may also increase competition between firms, thereby reducing the price of authentic products. Moreover, if the quality of the premium products is not high, the competition between firms is greater as there is less to differentiate the premium products from the authentic products. Therefore, it is not appropriate for the authentic firm to adopt BCT at the same time as the premium firm, as shown in Figure 3. If the quality of premium products is sufficiently high, the competition between firms is not fierce, so the authentic firm can also adopt BCT, as shown in Figure 4.

Corollary 2.

If the quality of the premium product is below a certain threshold, Scenario NB is a win-win situation for both the typically authentic firm and the premium firm.

This result can be obtained by Propositions 5 and 6. The best BCT selection strategy is for the premium firm to adopt BCT while the typically authentic firm does not adopt BCT, as shown in Figure 5. In this scenario, the Pareto optimum is achieved. The management implication is that when premium products face imperfect substitution competition from typically authentic products, premium firms should be the first to adopt BCT and typically authentic firms should not follow.

Proposition 7.

(a) Effect of $\lambda$. (i) The profits of both typically authentic and premium firms decrease with $\lambda$ in Scenarios NN and BB. (ii) The profits of both firms increase or decrease with $\lambda$ in Scenario NB.

(b) Effect of $\mu$. (i) The profits of both typically authentic and premium firms increase with $\mu$ in Scenario BB. (ii) The profits of a premium firm increase with $\mu$, and the profits of a typically authentic firm increase or decrease with $\mu$ in Scenario NB.

(c) Effect of $h^{\prime }$. (i) The profits of both typically authentic and premium firms increase with $h^{\prime }$ in Scenarios NN and BB. (ii) The profits of a typically authentic firm increase with $h^{\prime }$, and the profits of a premium firm increase or decrease with $h^{\prime }$ in Scenario NB.

In Scenario NB, due to the adoption of BCT by the premium firm, the percentage of counterfeits among the authentic products is higher than among the premium products. Moreover, ${\displaystyle \frac{\partial {\lambda }_{a_1}^{NB}}{\partial \lambda }}>{\displaystyle \frac{\partial {\lambda }_{a_2}^{NB}}{\partial \lambda }}$, i.e., as the total proportion of counterfeits in the market increases, the probability of counterfeiting the authentic product is greater than that of counterfeiting the premium product. Therefore, the utility of buying the typically authentic product decreases more, changing the competitive landscape between the two firms. In other words, the typically authentic firm has a significant competitive disadvantage, while the premium firm has a competitive advantage. Although $\lambda$ increases the probability that a consumer purchases counterfeits, thus reducing consumer utility. However, the effect is not always negative due to the asymmetric competition between typically authentic and premium firms in Scenario NB. In Scenarios NN and BB, both firms are symmetric and an increase in $\lambda$ does not change the competitive landscape, so the profits of the two firms decrease with $\lambda$.

In Scenario NB, the adoption of BCT by premium firms is not always detrimental to typically authentic firms; moreover, the profits of the authentic firm increase when the effect of increasing the price of the authentic product outweighs the effect of increasing the probability of buying counterfeits so that Scenario NB can become a win-win scenario. This result that the profits of both typically authentic and premium firms increase with $\mu$ in Scenario BB is intuitive.

In Scenario NB, the shift in the competitive landscape engenders an enhanced competitive posture for a premium firm. An escalation in prices exerts a more substantial impact on demand, consequently precipitating a decline in the profits of the aforementioned premium firm. Consequently, in Scenario NB, the assumption that superior quality invariably yields favorable outcomes for the premium product is not substantiated (

Table 3. Variation in variables with parameters in three scenarios.

Scenarios	Scenario NN		Scenario NB			Scenario BB
Parameters	$\lambda$	$h^{\prime }$	$\lambda$	$\mu$	$h^{\prime }$	$\lambda$	$\mu$	$h^{\prime }$
$P_{a_1}^{ij*}$	$-$	$+$	$+/-$	$+$	$+$	$-$	$+$	$+$
$P_{a_2}^{ij*}$	$-$	$+$	$+/-$	$+$	$+$	$-$	$+$	$+$
$D_{a_1}^{ij*}$	$+$	$\backslash$	$+/-$	$-$	$+$	$+$	$-$	$\backslash$
$D_{a_2}^{ij*}$	$-$	$\backslash$	$+/-$	$+$	$-$	$-$	$+$	$\backslash$
${\Pi }_{a_1}^{ij*}$	$-$	$+$	$+/-$	$+/-$	$+$	$-$	$+$	$+$
${\Pi }_{a_2}^{ij*}$	$-$	$+$	$+/-$	$+$	$+/-$	$-$	$+$	$+$

(Note. ‘$+$’ means that the left variable increases with the upper parameter; ‘$-$’ means that the left variable decreases with the upper parameter, ‘$\backslash$’ means parameter has no definition or relevant influence relationship in the corresponding scenario.)

).

Proposition 8.

The comparative results on consumer surplus and social welfare are obtained as follows.

(a) Consumer surplus. If $0<\lambda <{\displaystyle \frac{3}{4}}$, $C{S}^{NB*}$ < $C{S}^{BB*}$.

(b) Social welfare. (i) $S{W}^{NB*}$ < $S{W}^{BB*}$. (ii) If ${\displaystyle \frac{\left(66+3\sqrt{70}\right)}{92}}<\lambda <1$, $S{W}^{NN*}$ < $S{W}^{BB*}$.

Although Scenario NB is the optimal scenario for firms, consumers demonstrate a clear preference for Scenario BB. This is because consumers have a high probability of purchasing counterfeits in Scenario NB, which results in a suboptimal consumption experience. By contrast, in Scenario BB, consumers have the lowest probability of purchasing counterfeits and benefit from the most favorable shopping environment.

Scenario BB exhibits higher social welfare in comparison to Scenario NB. Additionally, Scenario BB surpasses Scenario NN, particularly in scenarios characterized by a substantial presence of counterfeit goods in the market. Consequently, from the perspective of social welfare, Scenario BB emerges as the more optimal case.

6. Extensions

In the following sections, we delve into the intricacies of two model variations and demonstrate the robustness of the fundamental model’s outcomes when confronted with alternative model specifications. We keep the welfare accounting as consumer surplus plus firms’ profits net of $F\left(\mu \right)$.

6.1. Nonuniform Consumer Preference Distribution

In the basic model outlined in Section 3, it is assumed that consumer preferences for quality exhibit a uniform distribution from 0 to 1. In this section, the circumstances under which the probability density of consumer preferences follows a step-wise function, as noted by Kwark et al. [46], are investigated. In particular, we assume distinct consumer groups: the first group $\alpha$ is distributed uniformly between $\left[0, 1+\beta \right]$; the second group $1-\alpha$ is distributed uniformly between $\left[0, 1\right]$. It is observed that the probability density is higher on the left side of the distribution range $\left[0, 1\right]$ than on the right side $\left[1, 1+\beta \right]$. When $\beta =0$, this distribution is equivalent to the fundamental model.

As the model analysis remains constant, the results specific to the monopoly are the sole focus of this discussion. In the absence of BCT, the marginal consumer is equivalent to that of the basic model. The demand function is as follows:

$$D_a^N=\left(1-\lambda \right)\left[\left(1-\alpha \right)\left(1-{\theta }^{N*}\right)+\alpha \left(1-{\displaystyle \frac{{\theta }^{N*}}{1+\beta }}\right)\right].$$

(24)

In the presence of BCT, the demand function is as follows:

$$D_a^B={\displaystyle \frac{1-\lambda }{1-\lambda \mu }}\left[\left(1-\alpha \right)\left(1-{\theta }^{B*}\right)+\alpha \left(1-{\displaystyle \frac{{\theta }^{B*}}{1+\beta }}\right)\right].$$

(25)

The profit functions and the solving procedure are consistent with those of the basic model. It can be verified that the primary results of the basic model hold qualitatively in the case of a non-uniform distribution of consumer preferences. In particular, the effect of BCT on prices, demand, and profits (as presented in Proposition 1 and 3), and the impact of BCT on asymmetric information (as presented in Proposition 2) are qualitatively the same as in the basic model.

6.2. Considering BCT Costs in the Competition

In the basic model in Section 5, the costs of BCT in a vertically differentiated competition are not taken into consideration. In this section, the cost of BCT traceability services for firms that adopt BCT is considered in three scenarios. Analogous results to those in the basic model are obtained.

Proposition 9.

If $0<\varphi <\mathit{min}\left\{{\varphi }_1,{\varphi }_2\right\}$ and ${\displaystyle \frac{1}{2}}<h^{\prime }<h^{\widehat{\prime }}$, the three scenarios are in the order of NB > BB > NN for both a premium firm and a typically authentic firm.

(a) For a premium firm, if $0<\varphi <{\varphi }_1$, ${\tilde{\Pi }}_{a_2}^{NB*}$ > ${\tilde{\Pi }}_{a_2}^{BB*}$ > ${\tilde{\Pi }}_{a_2}^{NN*}$.

(b) For a typically authentic firm, if ${\displaystyle \frac{1}{2}}<h^{\prime }<h^{\widehat{\prime }}$ and $0<\varphi <{\varphi }_2$, ${\tilde{\Pi }}_{a_1}^{NB*}$ > ${\tilde{\Pi }}_{a_1}^{BB*}$ > ${\tilde{\Pi }}_{a_1}^{NN*}$.

We generalize the fee to $F_i\left({\mu }_i\right)$ with $F_i^{\prime }(\cdot )>0$ and $F_i^{\prime \prime }(\cdot )\ge 0$. The NB > BB > NN ranking (Proposition 9) continues to hold when marginal fees lie below a threshold governed by demand sensitivities and quality gaps. If $F_i^{\prime }$ is very high at the relevant ${\mu }_i$, BB may lose its welfare edge over NN because firm-side costs dominate consumer gains. This preserves the main insight: NB is privately optimal under moderate fees, whereas BB maximizes consumer surplus and often welfare when counterfeit prevalence is high, creating a classic externality wedge.

The same results as the basic model can be obtained when the marginal cost of the BCT is not too high. Conversely, when the cost of BCT traceability is elevated, adopting BCT becomes disadvantageous. When considering BCT costs, Scenario NB emerges as a mutually beneficial scenario for both firms. These direction-only checks (extreme $\mu$; high marginal fees; quality weights; demand elasticity; marginal subsidies to $F\left(\mu \right)$) provide qualitative robustness without changing the paper’s main comparative-statics conclusions.

6.3. Implementation of Conditions and Managerial Guidance

Operationalizing $\mu$. Interpret $\mu$ as the share of source counterfeits prevented from entering the authentic channel through governance (batch-level sampling coverage, multi-stage inspections, tamper-evident seals, cryptographic anchoring, and dispute-resolving smart contracts). Higher $\mu$ requires more intensive and auditable processes. Let the one-off service fee be a monotone increasing (possibly convex) function $F\left(\mu \right)$; the baseline linear form used in Section 4.2, $F\left(\mu \right)=\varphi \mu$, is a tractable special case.

Adoption corridor. The firm’s gain from $\mu$ combines a utility/quality effect and a cost effect $F\left(\mu \right)$. Adoption is advisable when the marginal benefit at the interior optimum exceeds the marginal fee (Proposition 1 and its corollary).

Product classes. Categories with a high experiential component enjoy stronger benefits because $\mu$ directly alleviates asymmetric information on experiential quality.

Governance playbook. Effective roll-out requires (i) credible third-party or consortium governance, (ii) verifiable data-capture at source, (iii) random audits with public attestation, and (iv) clear consumer-facing provenance cues.

6.4. Policy Implications

The government should indeed implement subsidy policies with the objective of encouraging firms to adopt blockchain technology, a course of action which has the potential to engender benefits social welfare.

Blockchain technology is a powerful enforcement tool for intellectual property systems, providing goods with tamper-proof ‘digital IDs’. It can effectively track authenticity and preserve evidence of infringement. While it does not replace intellectual property law, it does enhance its protection and enforcement capabilities in actual markets through technological means, thereby helping to build a more trustworthy business environment. Therefore, this paper argues that the government should encourage firms to adopt blockchain technology to supplement the intellectual property system.

Our results reveal a tension: consumers prefer BB (lowest counterfeit incidence), while firms may prefer NB (premium adopts; standard does not) when quality gaps and fees satisfy threshold conditions. Policymakers can close this wedge via marginal subsidies or tax credits tied to $\mu$, public-procurement requirements for traceability, and standardized auditing protocols that reduce $F\left(\mu \right)$.

7. Conclusions

Counterfeit products are causing significant harm to a wide range of industries around the world. The advent of blockchain technology holds considerable promise in addressing this issue by ensuring the integrity and traceability of data, thereby counteracting the proliferation of counterfeit goods to a certain extent. However, the issue of counterfeiting at the source remains largely unaddressed by the scholarly community. This study aims to address this gap by examining how authentic firms make decisions regarding BCT adoption strategies within a monopoly and competitive duopoly context.

The findings of this study demonstrate that, in general, firms should adopt BCT if the cost is not high. Furthermore, it is demonstrated that the adoption of BCT is advantageous to social welfare in a monopoly. Furthermore, the study demonstrates that BCT serves as a deterrent for deceptive counterfeiters, discouraging them from collaborating with the branded firm. However, in a duopoly market where both firms sell premium products, the adoption of BCT may not be optimal. Conversely, in a duopoly market where one firm specializes in premium products and the other in authentic products, with the premium product having a quality below a certain threshold, Scenario NB becomes a win-win scenario. The results of this study demonstrate that premium firms should be the primary adopters of BCT to combat counterfeiting, while authentic firms should refrain from adopting it. Notwithstanding this, the scenario in which both firms adopt BCT is found to be more beneficial to consumer surplus and social welfare than the scenario in which only premium firms adopt it.

This paper posits several research hypotheses for future investigation. Firstly, an exploration is conducted of the competitive landscape of two firms in the context of counterfeiting. In subsequent research, it would be worthwhile considering competition between two supply chains and their BCT adoption strategies. Secondly, the study posits the hypothesis that authentic premium products possess higher experiential quality than authentic products, yet both exhibit equivalent searchable quality. Further consideration could be given to premium products having higher experiential and searchable quality than authentic products. Thirdly, it is assumed that BCT is provided by a third party, such as JD Blockchain, or AntChain in China. However, it is noteworthy that certain corporations establish their own blockchain networks, such as Walmart and Amazon. Consequently, a potential avenue for future research could involve the examination of how companies utilize their own established BCT traceability networks to combat counterfeit goods.

8. Scope and Limitations

The present paper is subject to certain limitations in terms of its applicability, in addition to some significant constraints in the model’s assumptions. For instance, decision-making scenarios are generally confined to industries such as apparel, cosmetics, and luxury goods on online shopping platforms. In these sectors, counterfeit products can accurately replicate the search attributes of genuine items, yet they often fall short in replicating experiential attributes. In addition, this study is bounded by several modeling choices that clarify where our results are expected to hold. First, the game is static and single-period; dynamic reputation, learning from reviews, and repeated interactions are abstracted away. Second, before data are uploaded to the blockchain, observable signals are assumed to be perfectly mimicable by deceptive counterfeiters, rationalizing a pooling information environment. Third, consumer heterogeneity follows a uniform distribution; relaxing this to step-wise densities preserves qualitative results (Section 6.1). Fourth, the security level $\mu$ is taken as an implementable governance choice but enters the model as an exogenous parameter to firms’ price games (Section 4.2). Fifth, we abstract from multi-channel frictions, inventory dynamics, and contract enforcement risks. Under these boundary conditions, comparative statics and adoption-timing insights—especially the superiority of Scenario NB under a threshold on premium quality and service fees—remain valid. Future work can endogenize $\mu$, allow noisy third-party verification, and study dynamic learning with reputational spillovers.