Information Collection and Personalized Service Strategy of Monopoly under Consumer Misrepresentation

Abstract

To decrease privacy risks, consumers may choose to misrepresent themselves when they are asked to offer personal information. Using a game theoretic model, this study examines the impact of consumer misrepresentation on both a monopolistic firm and consumers. The results show that consumer misrepresentation may benefit the firm, but hurt consumers under certain conditions. In addition, we find that when the unit cost of personalized service is low, consumer misrepresentation may encourage the firm to provide a higher personalized service level. Moreover, when consumers misrepresent themselves and the firm only covers part of the market, a greater unit value of consumer private information will reduce the firm’s profit, while a greater unit cost of personalized service will increase the firm’s profit. The analysis reported here provides important insights regarding the application of consumer information in online personalized marketing and consumer privacy protection.

1. Introduction

Electronic commerce technology helps firms collect consumer personal information, such as personal identification information, browsing records, and purchasing records. With this information, firms, such as Amazon and Taobao, can recognize potential consumers and set targeted marketing strategies [1]. In return for providing private information, consumers may receive extra price discounts and personalized services from the firms. However, when disclosing personal information, consumers may experience privacy risks such as illegal information collection or unauthorized access [2,3,4,5,6]. In order to decrease their privacy risk, some consumers misrepresent themselves when firms carry out information-collecting behaviors. Typically, consumers provide false personal information or fake behavior records intentionally; for example, they may provide false personal information during the registering process, or behavior information referring to the wrong preference through browsing products that they are not interested in. Moreover, consumers may change their IP address or geographic information with privacy protection software. A few studies [7,8,9] have shown that misrepresentation is one of the main methods conducted by Internet consumers to protect their personal information. Hence, the personal information that firms obtain can be separated into two parts: true personal information and false personal information. To simplify the expression of true personal information and false personal information, in the rest of the paper, “private information” refers to “true personal information”, while “false information” refers to “false personal information”.

Some consumers prefer to provide true personal information in return for a personalized service [10,11,12,13,14], and believe that misrepresentation through providing false information will reduce their personalized service. For example, when a consumer provides false information, they may receive unrelative targeted advertising based on their provided false information. The consumer cannot obtain their desired information through advertising and may be bothered by unrelated advertising. Obviously, misrepresentation is a double-edged sword for consumers, and they need to decide whether to misrepresent themselves or not.

Misrepresentation also influences firms. On one hand, it may have a negative impact on the personalized service provided by the firm to consumers. Consumer misrepresentation with false information may mislead firms. First, firms may find it harder to recognize potential consumers, miss the consumers with demand, or choose the consumers without demand. Second, firms may provide inaccurate personalized services according to the false information, such as providing inaccurate discounts. On the other hand, misrepresentation may impact firms positively. False information can decrease the privacy risk posed to consumers, more consumers may participate in the market, and firms may obtain more demand and profits. Apparently, misrepresentation might be good for the firms, even if it degrades their personalized service. Therefore, firms need to set their personal service strategy depending on consumer misrepresentation.

The existing related literature has mostly focused on how consumer information influences the personalized services of firms and how to protect consumer private information. Few studies have investigated the impacts of consumer misrepresentation on consumers and firms. Motivated by the contradictory impacts of misrepresentation on both consumers and firms, and to fill the research gap, this study aims to answer the following research questions: How does misrepresentation impact consumers and firms? Under what conditions do consumers benefit from misrepresentation? How do the firms set their personalized service strategy considering consumer misrepresentation?

We develop a game theoretic approach to examine the impacts of consumer misrepresentation on a monopolistic firm’s personalized service strategy. Three equilibrium outcomes are derived. First, we find that consumer misrepresentation is not always bad for the firm and not always good for consumers. This finding is different from the institutional belief that misrepresentation always benefits consumers and hurts the firm. Second, we conclude that consumer misrepresentation may not decrease the firm’s personalized service level, and the firm may provide a higher personalized service level when the unit cost of personalized service is low. Finally, we conclude that, when consumers misrepresent themselves and the market is partly covered, an increase in the unit value of consumer private information has a negative impact on the firm’s profit, while an increase in the unit cost of personalized service has a positive impact on the firm’s profit.

The remainder of this paper is organized as follows. Section 2 reviews the related literature. Section 3 introduces our baseline model. Section 4 analyzes the impacts of misrepresentation on the information disclosure decisions of consumers and the personalized service strategies of firms. The conclusions and limitations of the study are given in Section 5.

2. Literature Review

Our work discusses the impacts of consumer misrepresentation on both consumers and firms. Three streams of existing literature are particularly related to our study: studies on consumer privacy protection behaviors (PPBs), the reaction of firms to consumer privacy concerns, and personalized service strategies with consumers disclosing private information.

2.1. Consumer Privacy Protection Behaviors (PPBs)

When consumers recognize that their private information is applied, they may present six typical behavioral responses, including refusal, misrepresentation, removal, negative word of mouth, complaining directly to online companies, and complaining indirectly to third-party organizations [8]. Consumers are concerned about the application of their private information and, thus, apply privacy protection behaviors including “reflection, avoidance, intervention, restriction, control and restraint” [15]. These behaviors may manifest in the following ways: deleting Cookies, clearing browsing history, falsification of personal information, and so on [2,15,16,17]. Several analytical papers have attempted to determine the factors influencing consumer PPBs. For example, Xie and Karan [18] concluded that “knowledge of and concern regarding technology ubiquity” and “companies’ business strategies” can also affect consumer PPBs. Adhikari and Panda [19] found that the privacy concerns of consumers have a significant influence on their PPBs: if they are more concerned about the application of their private information, they are more likely to adopt PPBs. However, Rodríguez-Priego [17] concluded that, if the perceived value of the service is high, consumers are less likely to adopt PPBs even if they are concerned about the application of their private information. On the other hand, PPBs can further influence the privacy concerns and reactions of the consumer [20]. Using a representative two-wave panel survey, Kruikemeier et al. [21] found that consumers with higher privacy concerns are more likely to adopt PPBs. Similarly, Wirtz et al. [22] found that the greater a consumer’s privacy concern, the greater the likelihood of the consumer to misrepresent themself and fabricate personal information. Hence, the application of consumer private information will cause consumers to adopt PPBs in order to protect their private information.

Misrepresentation is a common intentional PPB, which enables the consumer to take control of their private information [18,23,24]. Its mechanism has been studied by economics and marketing scholars [22,25,26,27,28]. Kumar et al. [28] have concluded that the Internet makes it easy for people to misrepresent their private information. Church et al. [25] discussed the mechanism through which competition and altruism impact online disclosure behaviors considering user misrepresentation, and found that consumers are less likely to misrepresent if they are altruistic, in which case the firms may benefit. On the other hand, Drouvelis et al. [26] found that misrepresentation may result in large losses, as misrepresentation makes marketing methods less effective. Zhou et al. [29] constructed a model and found that misrepresentation leads to data noise and service failures, thus hurting both firms and consumers. In summary, misrepresentation may protect the private information of consumers, but the existing literature has reported that it may hurt firms.

Differing from the existing literature, we consider the relationship between misrepresentation and a firm’s personalized service strategy, and analyze how misrepresentation influences the decisions of both consumers and firms. Furthermore, we consider the double-edged sword of misrepresentation simultaneously, which has been seldomly considered in the abovementioned literature, but exists in practice.

2.2. Reactions of the Firms to Consumer Privacy Concerns

Consumer privacy concerns have an impact on their purchase decisions. As consumers are central to a firm’s marketing activities [30], firms should consider consumer privacy concerns during their marketing process. Ariffin et al. [31] found that consumers may not be willing to disclose their private information or purchase from the firms who ask for such information, due to their privacy concerns. Firms can also take PPBs to reduce the privacy concerns of consumers, which may reflect their corporate social responsibility [32]. Industry self-regulation, government regulation, and individual self-protection are considered to be the most important measures for decreasing consumer privacy concerns [33]. Some studies [34,35] have demonstrated that privacy statements and privacy seals are two typical forms of PPBs used by firms, the mechanisms of which differ. A privacy statement induces users to disclose private information, whereas privacy seals do not induce users to disclose their private information. In addition, privacy regulations influence the reactions of firms. Kaul [36] demonstrated the importance of privacy regulations on consumers and firms. Miller and Tucker [37] found that stating privacy regulations reduced the adoption of Electronic Medical Records (EMRs) by firms, which may hurt the hospital. Goldfarb and Tucker [38] studied the relationship between privacy regulations and targeted advertising based on consumer private information. Their findings indicated that targeted advertisements became less effective with the introduction of EU privacy regulations. Martin et al. [39] found that the transparency and control of a firm’s data management practices can mitigate consumer privacy concerns. Very few studies have considered the impact of firm privacy protections on competition between firms. Lee et al. [40] showed that privacy protection can mitigate competition if one firm protects user privacy while the other does not. Li et al. [41] stated that the supply chain members will achieve a win–win situation, as PPBs can attract more consumers. However, Liu et al. [42] derived that the firms may be hurt due to the higher cost associated with privacy protection, even if the demand increases. In summary, the existing literature has analyzed the relationships between firm PPBs and consumer privacy concerns. In particular, firm PPBs may reduce consumer privacy concerns, while consumer privacy concerns may force both the firms and consumers themselves to apply PPBs to protect their personal information.

However, most of the existing literature has only listed the possible measures that individuals may take, and few studies have focused on the effect of consumer self-protection on consumers or firms. Differing from these papers, this study considers how consumers can take actions to protect their private information, and analyzes how consumer PPBs influence the behaviors of both firms and consumers.

2.3. Personalized Service Strategy

The relationship between personalized service strategies and the disclosure of private information by consumers has been discussed [43,44,45,46,47]. Personalized services offered by firms are considered to encourage consumers to engage online [45,47]. Hann et al. [48] found that personalized services benefit both consumers and firms, and encourage consumers to disclose their private information. Chellappa and Sin [49] designed an experiment and concluded that personalized services make consumers more willing to purchase. Kim et al. [50] stated that the application of IoT technology will reduce the risk associated with disclosing personal information, and will help firms to provide more accurate personalized services, thus benefitting both the firm and consumers. However, Karwatzki et al. [44] concluded that when firms provide a personalized service based on consumers disclosing private information, they benefit only when the privacy concerns of consumers are not high. Sutanto et al. [51] studied the relationship between mobile targeted advertising and the reactions of mobile phone users, and found that users save advertising messages more frequently only when their private information is well-protected. Hence, the existing studies showed that consumers may not choose to disclose their private information in exchange for a personalized service.

Furthermore, several studies [52,53] have investigated how consumer privacy concerns impact the personalized service strategies of firms. Chellappa and Shivendu [49] examined vendor personalized strategies in a market where consumers have heterogeneous privacy concerns. They found that firms take different personalized strategies, depending on the vendor’s marginal value of information and consumer privacy concerns. Moreover, the consumer personal information provision quantity influences a firm’s personalized service investment strategy. Chellappa and Shivendu [54] concluded that the amount of consumer private information provided determines the personalized service level of a monopolistic firm, and that the firm should be cautious when applying consumer private information if consumers with high privacy concerns predominate in the market. Kim et al. [50] and Casadesus-Masanell and Hervas-Drane [55] implied that personalized service quality is concavely related to the amount of private information disclosed by consumers. Kim et al. [50] checked the relationship in the context of IoT, and found that the personalized service level is positively correlated with the volume of consumer private information. These papers indicated that even consumers concerned about the application of their private information may be willing to provide such information to obtain a personalized service.

The abovementioned studies mostly focused on how firms choose their personalized service strategy depending on the disclosure of private information by consumers, while few studied the relationship between consumer PPBs and firm personalized service strategies. We complement this stream of literature to enrich our understanding of the interactions between firms and consumers, taking into consideration consumer misrepresentation and the personalized services offered by firms.

3. Model Description

We consider a monopolistic firm, such as Amazon.com, selling products to potential consumers in a unit market. To simplify the analysis, the marginal product cost is normalized to zero, and the firm and consumers are considered to be risk-neutral.

Consumers buy products from the firm with a given price $p$, which is exogenous. Their perceived values are different but uniformly distributed in the interval $\left[\mathrm{0,1}\right]$, and we assume that consumer $i$’s perceived value of the product is ${\theta }_i$. Following Kang et al. [56], we assume that if the collected information from a consumer is $I\left(I\in \left[\mathrm{0,1}\right]\right),$ then consumers will feel the privacy risk $I^2$. To decrease their privacy risk, consumers may choose to misrepresent themselves. Assume that the probability that a consumer provides private information is $k$; that is, the false information provided by the consumer to misrepresent themselves is equal to $1-k$. Hence, the consumer’s perceived privacy risk is $k^2$. On the other hand, disclosing private information can help consumers to obtain the personalized service, from which they can receive an additional perceived value $ek$, where e denotes the firm’s personalized service technology investment effort. To simplify the analysis, we assume that the cost of misrepresentation is zero. Therefore, the utility of consumer i when they misrepresent themselves can be given as:

$$u_i={\theta }_i+ek-k^2-p$$

(1)

The monopolistic firm collects consumer information when consumers shop on its website. It collects the personal information of consumers to provide personalized service and obtain additional revenue. In the study of Awad and Krishnan [57], the provision of a personalized service increased consumer utility when consumers buy from the firm. Following Chellappa and Shivendu [54], the firm can provide a variable personalized service level $e$. The firm should invest in improving the personalized service level; referring to Chellappa and Shivendu [54], we assume that the cost of personalized service is $\beta e^2$, where $\beta$ is the unit cost of the personalized service. Aside from the personalized service, the firm can obtain additional profit through analyzing the obtained private data. For example, the firm can recommend complementary goods to a certain product to the consumers, thus potentially gaining extra profit in the future. Hence, many Internet firms treasure consumer private information, even if they are not using the information. However, only consumer private information is profitable for the firm. Following Chellappa and Shivendu [54], we assume that the additional profit the firm can obtain from consumer private information is $\alpha k$, where $\alpha$ represents the unit value of the collected real consumer information. When the firm collects $n$ consumer personal data, the firm’s expected profit function is given as follows:

$$\pi =\left(p+\alpha k\right)n-\beta e^2$$

(2)

The timing sequence of the game in this study includes three periods. In the first period, the firm chooses its personalized service level $e$. In the second period, consumers who receive the personalized service make their purchase decisions. In the third period, the consumers who decide to buy from the firm set their misrepresentation decisions. The descriptions of the variables are presented in

Table 1. Description of Variables.

Variable	Definition
${\theta }_i$	Perceived product value of consumer $i$
$p$	Price of the product
$\alpha$	Unit value of consumer private information
$e$	Personalized service level
$k$	Proportion of private information
$\beta$	Unit cost of personalized service
$I$	Consumer’s personal information that the firm collects

.

4. Equilibrium Analysis

In this section, we first analyze the benchmark case where the monopolistic firm and consumers make decisions without misrepresentation, then examine the misrepresentation case, in which the monopolistic firm and consumers make decisions with misrepresentation. Finally, we investigate the effects of misrepresentation on the monopolistic firm and consumers. To distinguish the two cases, we adopt the superscripts $B$ and $F$ to describe the benchmark case and the misrepresentation case, respectively.

4.1. Firm Personalized Service Efforts and Consumer Purchasing Behaviors without Misrepresentation

We first analyze the case where consumers do not misrepresent; that is, all of the personal information the firm collects is the consumer’s true private information ($k=1$). Through backward induction, we first derive the expected demand in the market.

Consumers buy from the firm if their utility is not less than zero; that is, $u_B\ge 0$. Hence, the expected demand in the market is given as follows:

$$n_u^B=\left\{\begin{array}{c}\begin{array}{cc}1,& e^B\ge 1+p\end{array}\\ \begin{array}{cc}{e}^B-p,& e^B<1+p\end{array}\end{array}\right.$$

(3)

In Equation (3), all consumers in the market will buy from the firm when the personalized service level is greater than $1+p$. Otherwise, only part of consumers whose perceived utility is greater than zero will buy from the firm.

Following the abovementioned sequence, through backward induction, the monopolistic firm sets its personalized service level to maximize the expected profit. We substitute Equation (3) into Equation (2), with the first-order condition (F.O.C) of maximizing the firm’s expected profit. In this way, we can derive the equilibrium solutions as follows.

Proposition 1. 

If consumers do not misrepresent, the monopolistic firm’s optimal personalized service level is  $e^{B*}=\left\{\begin{array}{c}\begin{array}{cc}1+p,& \beta \le \frac{p+\alpha }{2\left(1+p\right)}\end{array}\\ \begin{array}{cc}\frac{p+\alpha }{2\beta },& \beta >\frac{p+\alpha }{2\left(1+p\right)}\end{array}\end{array}\right.$. Correspondingly, the expected demand and expected profit of the monopolistic firm are

$${(n}^{B*},{\pi }^{B*})=\left\{\begin{array}{c}\begin{array}{cc}\left(1,p+\alpha -\beta {\left(1+p\right)}^2\right),& \beta \le \frac{p+\alpha }{2\left(1+p\right)}\end{array}\\ \begin{array}{cc}\left(\frac{p+\alpha }{2\beta }-p,\frac{\left(p+\alpha \right)\left(p+\alpha -4\beta p\right)}{4\beta }\right),& \beta >\frac{p+\alpha }{2\left(1+p\right)}\end{array}\end{array}\right.$$

Proposition 1 shows the monopolistic firm’s optimal personalized service level, expected demand, and profit when consumers do not misrepresent. As in Equation (3), if the firm provides a personalized service level that is not less than $1+p$, all consumers will buy from the firm; hence, the expected demand is equal to one. If the firm provides a personalized service level greater than 1 + p, its expected profit will decrease; hence, the optimal personalized service level is $1+p$ when all consumers buy from the firm. When the firm offers a personalized service level of less than $1+p$, some of the consumers will choose not to buy, and the expected profit may decrease. With a given personalized service level, the expected demand equals to $e^B-p$. With the F.O.C of the firm’s profit function, we derive the optimal personalized service level to be $\frac{p+\alpha }{2\beta }$.

The intuition behind this is as follows. When the unit cost of the personalized service level is low, it means that the marginal expected profit is great, and offering a greater personalized service level can help the firm cover the whole market and obtain more profit. However, when the unit cost of the personalized service level is high, the marginal excepted profit decreases. To maximize the expected profit, the firm needs to decrease its service level, and only some of the consumers will buy from the firm.

Hence, the monopolistic firm should choose its personalized service level strategy depending on the unit cost of personalized service. When the unit cost of personalized service is low, it should set a personalized service level equal to $1+p$ and, thus, cover the whole market; otherwise, it should decrease its personalized service level to maximize its expected profit, which results in the scenario where only part of the market is covered by the firm’s personalized service.

Corollary 1 is derived from Proposition 1 and summarizes how the product price, unit value of consumer private information, and unit cost of personalized service affect the firm’s optimal personalized service level, demand, and expected profit. To make the expressions in the rest of the paper clearer, we define that, if $n^{B*}=1$, the market is fully covered; otherwise, the market is partly covered.

Corollary 1. 

If consumers do not misrepresent themselves,

(1) 

When the market is fully covered, (i) $\frac{{de}^{B*}}{dp}>0$. (ii) If $\alpha <1$, $\frac{{d\pi }^{B*}}{dp}<0$; if $\alpha >1and\beta >\frac{1}{2}$, $\frac{{d\pi }^{B*}}{dp}<0$; if$\alpha >1and\beta <\frac{1}{2}$, when $p<\frac{1}{2\beta }-1$, $\frac{{d\pi }^{B*}}{dp}>0$; otherwise, $\frac{{d\pi }^{B*}}{dp}<0$.

(2) 

When the market is partly covered, (i) $\frac{{de}^{B*}}{dp}>0$. (ii) If $\beta >\frac{1}{2}$, $\frac{{dn}^{B*}}{dp}<0$; otherwise,$\frac{{dn}^{B*}}{dp}>0$. (iii) If $\beta <\frac{1}{4}$, $\frac{{d\pi }^{B*}}{dp}>0$; if $\frac{1}{4}<\beta <\frac{1}{2}$, when $p<\frac{2\beta -1}{1-4\beta }\alpha$, $\frac{{d\pi }^{B*}}{dp}>0$; otherwise, $\frac{{d\pi }^{B*}}{dp}<0$; if $\beta >\frac{1}{2}$,$\frac{{d\pi }^{B*}}{dp}<0$.

Corollary 1 shows the relationship between the product price and the firm’s optimal personalized service level, demand, and expected profit. It is clear that an increasing product price encourages the firm to provide a greater personalized service level in both cases, as the firm can obtain more marginal profit with a greater personalized service level. However, the relationship between the product price and the demand and expected profit varies with the parameters $\alpha$ and $\beta$ in the two different cases. In Corollary 1, it is interesting to note that when the market is fully covered, a greater product price may decrease the firm’s expected profit even if the unit value of consumer private information is high. When the unit value of consumer private information $\alpha$ is low, no matter the unit cost of personalized service $\beta$, the expected profit always decreases. This is because when $\alpha$ is low, it means the expected additional profit is low; however, when the cost of personalized service increases, it leads to a decreasing marginal profit. Hence, the expected profit decreases in price. Similarly, when $\alpha >1\mathrm{a}\mathrm{n}\mathrm{d}\beta >\frac{1}{2}$, the marginal expected profit decreases with increasing price. Meanwhile, when $\alpha >1\mathrm{a}\mathrm{n}\mathrm{d}\beta <\frac{1}{2}$, the unit value of consumer private information $\alpha$ is high while the unit cost of personalized service $\beta$ is low. If the product price is lower than $\frac{1}{2\beta }-1$, the expected profit increases with $p$ as, in this scenario, the marginal expected profit increases with $p$ and is always greater than zero; thus, the firm always obtains more profit with increasing product price. In contrast, if the product price is greater than $\frac{1}{2\beta }-1$, the personalized service cost increases, thus decreasing the marginal expected profit, which is always less than zero.

When the market is partly covered, an increase in product price affects the expected demand differently. When the unit cost of personalized service is high ($\beta >\frac{1}{2}$), the marginal expected profit is always less than zero, and decreases with increasing product price. To maximize its profit, the firm should reduce the personalized service level until the marginal expected profit is equal to zero. A lower personalized service level leads to less demand. On the other hand, when the unit cost of personalized service is low ($\beta <\frac{1}{2}$), the firm should increase its personalized service level to cover more consumers until the marginal expected profit is equal to zero. When the firm increases its personalized service level, the expected demand increases. Similar to the analysis in the case where all consumers are covered, we can derive the relationship between the product price and the expected profit. However, in Corollary 1, when the unit cost of personalized service is in the middle range ($\frac{1}{4}<\beta <\frac{1}{2}$), the expected profit first increases and then decreases with the product price, and the trend differs from that of the demand; that is, if $p>\frac{2\beta -1}{1-4\beta }\alpha$, the firm has more demand but less profit with an increasing product price. The reason for this is that an increase in $p$ increases the firm’s personalized service level, but also increases the cost of personalized service. When $p>\frac{2\beta -1}{1-4\beta }\alpha$, the marginal expected profit is less than zero and decreases with $p$.

Corollary 1 indicates that if the firm increases its product price, it should provide a higher personalized service level correspondingly. Meanwhile, the firm should not increase its product price blindly—an increasing product price can only help them to obtain more profit in the scenario where the unit value of consumer private information is high and the unit cost of personalized service is low.

Based on Proposition 1, we derive the following corollary.

Corollary 2. 

If consumers do not misrepresent themselves,

(1) 

When the market is fully covered, (i)  $\frac{{de}^{B*}}{d\alpha }=0$; $\frac{{d\pi }^{B*}}{d\alpha }>0$. (ii) $\frac{{de}^{B*}}{d\beta }=0$; $\frac{{d\pi }^{B*}}{d\beta }<0$.

(2) 

When the market is partly covered, (i) $\frac{{de}^{B*}}{d\alpha }>0$; $\frac{{dn}^{B*}}{d\alpha }>0$; if $\beta \le \frac{1}{2}$, $\frac{{d\pi }^{B*}}{d\alpha }>0$; if $\beta >\frac{1}{2}$, when $\alpha <\left(2\beta -1\right)p$, $\frac{{d\pi }^{B*}}{d\alpha }<0$, when $\alpha >\left(2\beta -1\right)p$, $\frac{{d\pi }^{B*}}{d\alpha }>0$. (ii) $\frac{{de}^{B*}}{d\beta }<0$, $\frac{{dn}^{B*}}{d\beta }<0$, $\frac{{d\pi }^{B*}}{d\beta }<0$.

In Corollary 2, the firm sets its personalized service level depending only on the product price and coverage of the whole market. Based on consumer $i$’s utility function, the additional profit of consumer private information and the cost of personalized service are not related. Meanwhile, as the product price is given, increasing unit value only increases the additional expected profit of the firm, and an increasing unit cost of personalized service only increases the cost for the firm.

In the case that only part of the market is covered, an increasing unit value of consumer private information may reduce the firm’s expected profit when the unit value of consumer private information is low and the unit cost of personalized service is high. The explanation for this is as follows: an increasing unit value of consumer private information increases the personalized service level and the potential demand, but also increases the cost simultaneously. As a result, the marginal expected profit decreases and is less than zero. Hence, the expected profit decreases with the unit value of consumer private information.

Corollary 2 suggests that if the firm can cover the whole market, it should try its best to fully explore the value of consumer private information. However, if it only covers the market partly, it should be cautious when exploring the value of consumer private information. In particular, when the unit cost of personalized service is high and the unit value of consumer private information is relatively low, the firm should not try to explore the value of consumer private information.

4.2. Firm Personalized Service Efforts and Consumer Purchasing Behaviors under Misrepresentation

In this section, we assume that consumers will misrepresent themselves when they perceive privacy risk when their personal information is collected by the monopolistic firm. Following the timing sequence in Section 3, through backward induction, we first derive the optimal proportion of private information. Consumers attempt to maximize their utility as far as possible based on Equation (1). Considering the F.O.C, we can derive the response function for the optimal proportion of private information:

$$k^F\left(e\right)=\frac{e^F}{2}$$

(4)

Equation (4) shows that when the monopolistic firm provides a greater personalized service level, consumers will disclose more private information. Intuitively, it is a win–win game: the firm provides a greater personalized service level, which encourages consumers to disclose more private information; meanwhile, when consumers disclose more private information, the firm can provide a greater personalized service level.

Similar to the analysis in Section 4.1, consumer $i$ buys the firm’s product if $u_i^F\left({\theta }_i\right)\ge 0$. As the maximized potential demand is one, we separate our analysis into two parts: one where the market is fully covered, and another where the market is partly covered. When the market is fully covered, consumer $i$’s minimized utility function is

$$ek-k^2-p\ge 0$$

(5)

When the market is partly covered, consumer $i$’s utility function is given as Equation (1), and consumers whose utility satisfies $u_i^F\left({\theta }_i\right)\ge 0$ will buy from the firm. Hence, we can derive the expected demand function as follows:

$$n_u^F\left(e^F\right)=\left\{\begin{array}{c}\begin{array}{cc}1,& e^F\ge 2\sqrt{p}\end{array}\\ \begin{array}{cc}\frac{{\left(e^F\right)}^2}{4}+1-p,& e^F<2\sqrt{p}\end{array}\end{array}\right.$$

(6)

In Equation (6), if the personalized service level is greater than $2\sqrt{p}$, all consumers in the market will buy from the firm; otherwise, only part of the consumers buy from the firm, and the expected demand increases with the firm’s personalized service level. Combining Equation (2) and Equation (6), and considering the F.O.C, we can derive the equilibrium solutions when consumers misrepresent themselves as follows.

Proposition 2. 

If consumers misrepresent themselves, the monopolistic firm’s optimal personalized service level is  $e^{F*}=\left\{\begin{array}{c}\begin{array}{cc}\frac{\alpha }{4\beta },& \beta \le \frac{\alpha }{8\sqrt{p}}\end{array}\\ \begin{array}{cc}2\sqrt{p},& \frac{\alpha }{8\sqrt{p}}<\beta <\frac{p}{4}+\frac{\alpha \left(1+2p\right)}{8\sqrt{p}}\end{array}\\ \frac{4}{3\alpha }\left(2\beta -\frac{p}{2}-\sqrt{{\left(2\beta -\frac{p}{2}\right)}^2-\frac{3}{4}{\alpha }^2(1-p)}\right),\beta \ge \frac{p}{4}+\frac{\alpha \left(1+2p\right)}{8\sqrt{p}}\end{array}\right.$. Correspondingly, the expected demand and expected profit of the monopolistic firm are ${(n}^{F*},{\pi }^{F*})=\left\{\begin{array}{c}\begin{array}{cc}\left(1,p+\frac{{\alpha }^2}{16\beta }\right),& \beta \le \frac{\alpha }{8\sqrt{p}}\end{array}\\ \begin{array}{cc}\left(1,\left(1-4\beta \right)p+\alpha \sqrt{p}\right),& \frac{\alpha }{8\sqrt{p}}<\beta <\frac{p}{4}+\frac{\alpha \left(1+2p\right)}{8\sqrt{p}}\end{array}\\ \left(n_1^{F*},{\pi }_1^{F*}\right),\beta \ge \frac{p}{4}+\frac{\alpha \left(1+2p\right)}{8\sqrt{p}}\end{array}\right.$, where $n_1^{F*}=\frac{8\left[\left(2\beta -\frac{p}{2}\right)\left(2\beta -\frac{p}{2}-\sqrt{{\left(2\beta -\frac{p}{2}\right)}^2-\frac{3}{4}{\alpha }^2(1-p)}\right)\right]}{9{\alpha }^2}+\frac{2}{3}\left(1-p\right)$ and ${\pi }_1^{F*}=\frac{16\left[\left({\left(2\beta -\frac{p}{2}\right)}^2-\frac{3}{4}{\alpha }^2(1-p)\right)\left(2\beta -\frac{p}{2}-\sqrt{{\left(2\beta -\frac{p}{2}\right)}^2-\frac{3}{4}{\alpha }^2(1-p)}\right)\right]+12{\alpha }^2\left(1-p\right)\left(\beta +2p\right)}{27{\alpha }^2}$.

Proposition 2 shows the monopolistic firm’s optimal personalized service level, expected demand, and profit when consumers misrepresent themselves. Following the timing sequence in Section 3, consumers make their misrepresentation decisions depending on the firm’s service level. Intuitively, the firm should increase its personalized service level to encourage consumers to provide more private information, until it captures all the consumers in the market. However, as providing a personalized service is costly, a higher personalized service level increases the cost and may decrease the expected profit. Therefore, the firm may choose a different personalized service strategy to maximize its expected profit when the unit cost of personalized service is high.

Proposition 2 also shows that, even if the firm captures all consumers in the market, it is still driven to choose a higher personalized service level when the unit cost of personalized service is less than $\frac{\alpha }{8\sqrt{p}}$. The reason for this is that a low unit cost of personalized service decreases the marginal cost and increases the firm’s marginal expected profit. Hence, even if the firm captures all the consumers in the market, it should increase its personalized service level when the unit cost of personalized service is low.

Corollary 3. 

If consumers misrepresent themselves,

(1) 

When the market is fully covered, (i) when  $\beta \le \frac{\alpha }{8\sqrt{p}}$, $\frac{{de}^{F*}}{dp}=0$; otherwise, $\frac{{de}^{F*}}{dp}>0$. (ii) When $\frac{\alpha }{8\sqrt{p}}<\beta <\frac{p}{4}+\frac{\alpha \left(1+2p\right)}{8\sqrt{p}}$, if $\alpha <\frac{1-p}{\sqrt{p}}andp>\frac{{\alpha }^2}{4{\left(4\beta -1\right)}^2}$, $\frac{{d\pi }^{F*}}{dp}<0$; otherwise, $\frac{{d\pi }^{F*}}{dp}>0$.

(2) 

When the market is partly covered, (i) when $\beta <\frac{4+3a^2}{16}$, $\frac{{de}^{F*}}{dp}>0$; otherwise, $\frac{{de}^{F*}}{dp}<0$.

Corollary 3 shows the relationship between the firm’s optimal strategies and price. In Corollary 3(1), the market is fully covered. When the unit cost of personalized service is low, if the monopolistic firm increases its price, it will not increase its personalized service level simultaneously. This is because when the unit cost of personalized service is low, the monopolistic firm captures all consumers in the market when it offers a service level equal to $\frac{\alpha }{4\beta }$. Even if it increases the price, consumers will not misrepresent themselves more, so the service level does not need to be increased. However, when the unit cost of personalized service is high, it should increase the price to maintain the marginal profit. Notably, the relationship between the firm’s profit and price differs. Corollary 3(1) indicates that when the firm increases the price, even when increasing the service level, which increases the cost, it may obtain more profit. From Corollary 3(1), in the scenario where the unit value of consumer private information is low and the price is high, an increasing price may reduce the firm’s profit as, in this scenario, the firm should provide a greater service level to attract consumers; however, consumers will misrepresent themselves more, thus reducing the firm’s additional profit. Hence, in practice, the firm should avoid increasing its price in this scenario, or it should explore the value of consumer information.

In Corollary 3(2), the market is partly covered. When the unit cost of personalized service is low, the monopolistic firm increases its service level with an increasing price. The reason for this is that a greater price may increase the marginal profit of the firm and, to capture more consumers, the firm can increase its personalized service level. However, the relationships between the expected demand/profit and the price are complicated and non-linear, given that consumers may misrepresent themselves depending on the personalized service level, which has an impact on the additional profit and service cost. To provide a reasonable and smooth analysis of this paper, we do not provide the details.

Based on Proposition 2, we derive the following corollary.

Corollary 4. 

If consumers misrepresent,

(1) 

When the market is fully covered, (i) if  $\beta \le \frac{\alpha }{8\sqrt{p}}$, $\frac{{de}^{F*}}{d\alpha }>0$; otherwise, $\frac{{de}^{F*}}{d\alpha }=0$; $\frac{{d\pi }^{F*}}{d\alpha }>0$. (ii) If $\beta \le \frac{\alpha }{8\sqrt{p}}$, $\frac{{de}^{F*}}{d\beta }<0$; otherwise, $\frac{{de}^{F*}}{d\beta }=0$; $\frac{{d\pi }^{F*}}{d\beta }<0$.

(2) 

When the market is partly covered, (i) $\frac{{de}^{F*}}{d\alpha }>0$; $\frac{{dn}^{F*}}{d\alpha }>0$, $\frac{{d\pi }^{F*}}{d\alpha }<0$. (ii) $\frac{{de}^{F*}}{d\beta }<0$; $\frac{{dn}^{F*}}{d\beta }<0$, $\frac{{d\pi }^{F*}}{d\beta }>0$.

Corollary 4 shows how the unit value of consumer private information and unit cost of personalized service impacts the monopolistic firm’s optimal decisions when consumers can misrepresent themselves.

When the market is fully covered, while the unit cost of personalized service is low, a greater unit value of consumer private information leads to a higher personalized service level, with the marginal profit increasing. Similarly, a greater unit cost of personalized service leads to a lower personalized service level, as the marginal profit decreases. However, when the unit cost of personalized service is at a medium level, the monopolistic firm does not change its personalized service level when the unit value of consumer private information or the unit cost of personalized service increases; in this case, the marginal profit is only related to the price, and cost of personalized service is equal to the additional profit. Then, Corollary 4(1) shows that a greater unit value of consumer private information leads to a higher expected profit (as the marginal profit increases) and a greater unit cost of personalized service leads to a lower expected profit (as the cost of personalized service increases and is greater than the additional profit).

Hence, when consumers misrepresent themselves and the market is fully covered, the monopolistic firm should try to explore the value of consumer private information and reduce its unit cost of personalized service.

When the market is partly covered, a greater unit value of consumer private information leads to a higher personalized service level and captures more consumers, but yields less profit. In this scenario, a greater unit value of consumer private information indicates a higher marginal profit, and, so, the firm increases its personalized service level to attract more consumers. However, when the personalized service level increases, consumers will misrepresent themselves more, which may reduce the marginal profit; meanwhile, the cost of personalized service increases, and, thus, the expected profit decreases when the unit value of consumer private information increases. Then, a greater unit cost of personalized service leads to a less personalized service level and fewer consumers, but more profits. In this scenario, a greater unit cost of personalized service indicates that it will cost the firm more to provide a greater personalized service level. To maximize its profit, the monopolistic firm should decrease its personalized service level to reduce the personalized service cost, which results in less consumer demand. However, the marginal profit increases as the decrease in unit personalized service cost is greater than the decrease in unit additional profit; hence, the monopolistic firm can obtain more profit with a higher unit cost of personalized service.

Hence, when consumers misrepresent themselves and the market is partly covered, the monopolistic firm should be more cautious when exploring the value of consumer private information and reduce the unit cost of personalized service.

4.3. Comparison Analysis

Consumers misrepresenting may have an impact on the monopolistic firm’s optimal strategy. In this section, we compare the optimal strategies obtained when consumers do not misrepresent with those when consumers misrepresent themselves.

Based on Proposition 1 and Proposition 2, we first compare the optimal personalized service level and analyze the effect of misrepresentation on the firm’s personalized service level. We obtain the following results:

Proposition 3. 

Based on the optimal personalized service levels in Proposition 1 and Proposition 2,

(1) 

if $\alpha <\frac{2p\sqrt{p}\left(1-p\right)}{\left(1+p\right)\left(2p+1\right)-4\sqrt{p}}$

(i) 

When  $\beta <\frac{\alpha }{4\left(p+1\right)}$,  $e^F>e^B$;

(ii) 

When  $\frac{\alpha }{4\left(p+1\right)}<\beta \le \frac{p+\alpha }{2\left(1+p\right)}$,  $e^F<e^B$;

(iii) 

When $\frac{p+\alpha }{2\left(p+1\right)}<\beta <\frac{p\left(p+\alpha \right)+\left(p+\alpha \right)\sqrt{p^2+3\left(\alpha p+2p+\alpha \right)\alpha }}{4\left(\alpha p+2p+\alpha \right)}$: a) If $p>\frac{1}{3}$and $\frac{4p\left(1-p\right)}{\left(p+1\right)\left(3p-1\right)}<\alpha <\frac{2p\sqrt{p}\left(1-p\right)}{\left(1+p\right)\left(2p+1\right)-4\sqrt{p}}$, $e^F>e^B$; b) If $p\le \frac{1}{3}$or $\alpha <\frac{4p\left(1-p\right)}{\left(p+1\right)\left(3p-1\right)}$, $e^F<e^B$.

(iv) 

When $\beta >\frac{p\left(p+\alpha \right)+\left(p+\alpha \right)\sqrt{p^2+3\left(\alpha p+2p+\alpha \right)\alpha }}{4\left(\alpha p+2p+\alpha \right)}$, $e^F<e^B$.

(2) 

if $\alpha >\frac{2p\sqrt{p}\left(1-p\right)}{\left(1+p\right)\left(2p+1\right)-4\sqrt{p}}$

(i) 

When $\beta <\frac{\alpha }{4\left(p+1\right)}$, $e^F>e^B$;

(ii) 

When$\frac{\alpha }{4\left(p+1\right)}<\beta <\frac{p+\alpha }{4\sqrt{p}}$,  $e^F<e^B$;

(iii) 

When $\frac{p+\alpha }{4\sqrt{p}}<\beta <\frac{p}{4}+\frac{\alpha \left(2p+1\right)}{8\sqrt{p}}$, a) If $p\le \frac{1}{2}$ or $\alpha <\frac{2p\left(1-\sqrt{p}\right)}{2p-1}$, $e^B>e^F$; b) If $p>\frac{1}{2}$ and $\alpha >\frac{2p\left(1-\sqrt{p}\right)}{2p-1}$, $e^F>e^B$.

(iv) 

When $\frac{p}{4}+\frac{\alpha \left(2p+1\right)}{8\sqrt{p}}\le \beta \le \frac{p+\sqrt{p^2+12{\alpha }^2\left(p+\alpha \right)}}{8}$, a) if $\alpha >\frac{\left[{\left(2p+1\right)}^2-12p^2\right]+\sqrt{△}}{24p}$, $e^F<e^B$; b) if $\alpha <\frac{\left[{\left(2p+1\right)}^2-12p^2\right]+\sqrt{△}}{24p}$, $e^F>e^B$; where $△={\left(12p^2-{\left(2p+1\right)}^2\right)}^2+96\left(2p+1\right)p^2\sqrt{p}$.

(v) 

When  $\frac{p+\sqrt{p^2+12{\alpha }^2\left(p+\alpha \right)}}{8}<\beta <\frac{p\left(p+\alpha \right)+\left(p+\alpha \right)\sqrt{p^2+3\left(\alpha p+2p+\alpha \right)\alpha }}{4\left(\alpha p+2p+\alpha \right)}$,  $e^F>e^B$;

(vi) 

When $\beta >\frac{p\left(p+\alpha \right)+\left(p+\alpha \right)\sqrt{p^2+3\left(\alpha p+2p+\alpha \right)\alpha }}{4\left(\alpha p+2p+\alpha \right)}$, $e^F<e^B$.

Based on the comparison results of $e^F$ and $e^B$, we find that when the unit cost of personalized service is low, the monopolistic firm provides a higher personalized service level if consumers misrepresent themselves. When the unit cost of personalized service is high, the monopolistic firm provides a lower personalized service level if consumers misrepresent themselves.

However, when the unit cost of personalized service is at a medium level, the comparison results vary with the unit value of consumer private information, the unit cost of personalized service, and the product price. When the unit value of consumer private information is low while the product price is high, the monopolistic firm provides a higher personalized service level if consumers misrepresent themselves. Otherwise, the monopolistic firm provides a lower personalized service level if consumers misrepresent themselves. When the unit value of consumer private information is high while the price is high, the monopolistic firm provides a higher personalized service level if consumers misrepresent themselves. Furthermore, when the unit cost of personalized service is relatively high, the monopolistic firm also provides a higher personalized service level if consumers misrepresent themselves.

Hence, if consumers misrepresent, the monopolistic firm should be cautious with respect to increasing its personalized service level to attract more consumers. In particular, its optimal choice is increasing the personalized service level only when the unit cost of the personalized service level is low. However, if the unit cost of the personalized service level is high, its optimal choice is decreasing the personalized service level.

Furthermore, based on Propositions 1 and 2, we compare the expected demand if the market is partly covered, and derive the following results:

Proposition 4. 

When the market is partly covered, if  $\alpha <\frac{2p\sqrt{p}\left(2+p\right)}{\left(2p+1\right)\left(4-p\right)-12\sqrt{p}}$, $n^F<n^B$; otherwise, $n^F>n^B$.

In Proposition 4, when the market is partly covered and the unit value of consumer private information is low, the monopolistic firm receives less demand if consumers misrepresent themselves. The reason for this is the low unit value of consumer private information resulting in a low additional profit, which may cause the monopolistic firm to reduce its personalized service level. This reduced personalized service level cannot attract more consumers, leading to lower consumer demand.

Proposition 4 indicates that consumer misrepresentation has an impact on the demand of the monopolistic firm, in a manner that varies with the unit value of consumer private information. When the unit value of consumer private information is low, consumer misrepresentation reduces the demand; otherwise, it enhances the demand.

Next, we compare the profit when consumers misrepresent with that when consumers do not misrepresent. We have

Proposition 5. 

(1) When the market is fully covered, if  $0<p<1$  and $\frac{2\alpha -\alpha \sqrt{3-2\alpha p-p^2}}{4{\left(1+p\right)}^2}\le \beta \le \frac{\alpha }{8\sqrt{p}}$, or $0.1951<p<1$ and $\frac{\alpha }{8\sqrt{p}}\le \beta \le \frac{a\left(1-\sqrt{p}\right)}{{\left(1-p\right)}^2}$, ${\pi }^B>{\pi }^F$; otherwise, ${\pi }^B<{\pi }^F$.

(2) When the market is partly covered, there exists a threshold $\frac{p}{4}+\frac{\alpha \left(1+2p\right)}{8\sqrt{p}}\le \beta \le F(\alpha ,p)$, ${\pi }^B>{\pi }^F$; otherwise, ${\pi }^B<{\pi }^F$.

Proposition 5 shows that even when consumers misrepresent, the monopolistic firm can still obtain good outcomes. Hence, in practice, the firm should not be severe about consumer misrepresentation.

5. Conclusions

5.1. Main Findings and Implications

Consumer personal data can benefit firms. Acknowledging this fact, firms can take measures to encourage consumers to disclose their private information. However, the disclosure of private information is a double-edged sword for consumers. To reduce privacy risks while still obtaining benefits, some consumers choose to misrepresent themselves through the use of falsified information. The existing literature has focused on the effect of privacy protection by organizations on both consumer privacy behaviors and firm strategies, but few studies have focused on the effects of consumer misrepresentation, which is a typical measure of consumer self-privacy protection, on both firms and consumers. Using a game-theoretic model, this study analyzed the influence of consumer misrepresentation in a monopolistic market. In our model, consumers decide the quantity of falsification regarding their private information, while the firm decides its service level.

The results show that consumer misrepresentation may not decrease the firm’s payoff. Hence, the firm should not be opposed to misrepresentation, as the unit cost of personalized service and the marginal cost of misrepresentation moderate the effects of misrepresentation on both consumers and the firm. The results also indicate that, under misrepresentation, a consumer does not disclose less private information and the number of disclosing consumers may decrease. Meanwhile, under misrepresentation, the firm may still provide a higher personalized service level than when consumers do not misrepresent. Furthermore, the unit cost of personalized service, the unit value of consumer private information, and the product price have different impacts on the firm’s optimal decisions. If consumers misrepresent when the market is partly covered, a greater unit value of consumer private information will reduce the firm’s profit, while a greater unit cost of personalized service increases the firm’s profit.

Our paper fulfilled the research on the relationship between consumer PPBs by misrepresentation and firm personalized service strategies, which is ignored by the existing research. The key implications of the study comprise two parts. First, if the privacy concerns of consumers are high, the firm must prevent these consumers from misrepresenting. This is because misrepresentation discourages consumers with high privacy concerns from disclosing, and the firm profits less from these consumers under misrepresentation. Otherwise, if the privacy concerns of consumers are low, the firm does not have to take measures to stop misrepresentation. Under this scenario, the firm should adjust its service strategy according to the value of consumer private information and the marginal cost of misrepresentation. For example, if the value of consumer private information is neither too high nor too low and the marginal cost of misrepresentation is high, the firm can provide a low service level to consumers. Second, the existing literature has concluded that misrepresentation is a good way to decrease the privacy risks perceived by consumers and encourages consumers to disclose, while this study reached a different conclusion. Misrepresentation is not always an efficient means for consumers to decrease privacy risks. Both benefits (the personalized service level) and costs (privacy risk and the opportunity cost of misrepresentation) have great effects on consumers.

5.2. Limitations and Future Work

We studied the effects of misrepresentation on both a monopolistic firm and consumers by comparing the scenarios when consumers misrepresent and when consumers do not misrepresent. In this study, we simplified the assumptions regarding the consumer’s and firm’s decision-making processes in a static monopolistic market. Therefore, it would be meaningful and interesting to analyze the topic considering the complexity of consumer and firm decision making and market dynamics in a competitive market. Meanwhile, we did not consider the relationship between consumer misrepresentation behaviors and their privacy concerns. In future research, it would be valuable to consider such a relationship in order to check the robustness of our findings. Furthermore, consumer misrepresentation may lead to ethical problems, and investigating the ethical implications—such as consumer trust, privacy, and transparency—in the content of the digital market is another research direction. Finally, while we applied a game theoretic model to investigate the impacts of consumer misrepresentation on consumers and firms, it would be interesting to validate these findings with empirical evidence.