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Abstract

Consumer privacy information is used to target persuasive advertising in E-commerce, which raises consumer privacy concern. Consumer privacy concern is relative to consumer’s intrinsic privacy concern and social concern over the application of consumer privacy information, known as the anchoring effect of privacy. The anchoring effect of privacy influences targeted persuasive advertising competition. With a game-theoretical model, this paper studies how asymmetric duopolistic firms compete with targeted persuasive advertising considering the anchoring effect of privacy. The results indicate that when the advantageous firm increases its advertising level, the advantageous firm gets more profit, and the disadvantageous firm gets less profit only if the anchoring effect of privacy is greater than zero. Otherwise, the disadvantageous firm gets more profit, but the advantageous firm gets less profit. Then, in equilibrium, the increase in the expected anchoring effect of privacy, expected consumer’s intrinsic privacy concern, and advertising influence power reinforce the competition asymmetry. Whereas, the increase in social concern over the application of consumer privacy information weakens the competition asymmetry.

Plain language summary

Purpose: This paper aims to analyze the competitive targeted persuasive advertising strategy considering the anchoring effect of privacy, which is relative with consumer intrinsic privacy concern and social concern. Methods: A three-stage theoretical model is established to study the targeted persuasive advertising strategy. In the model, two competitive firms compete with targeted persuasive advertising and price, and the anchoring effect of privacy, advertising persuasive power and product prices influence consumers’ purchase decisions. Conclusions: We find that when the advantageous firm increases its advertising level, only if the anchoring effect of privacy is greater than zero, the advantageous firm gets more profit, and the disadvantageous firm gets less profit. Moreover, the increase in the expected anchoring effect of privacy, expected consumer’s intrinsic privacy concern, and advertising influence power reinforce the competition asymmetry. Whereas, the increase in social concern over the application of consumer privacy information weakens the competition asymmetry. Implications: We suggest that firms should be cautious about increasing their advertising levels in competition, because they may suffer the loss with a greater advertising level due to the existence of the anchoring effect of privacy. Then, when competing with targeted persuasive advertising and price, the firm with low quality-cost margin should try to eliminate the asymmetry between itself and its competitor. Limitations: Firstly, the model in this paper does not cover all the features of the competition markets. Secondly, we just assume that persuasive advertising enhances consumer’s perceived quality, where persuasive advertising may alter consumer preference. Thirdly, it is interesting to investigate and verify our research topic with empirical approach.

Keywords

targeted advertising persuasive advertising privacy concern social concern anchoring effect

Introduction

Competitive targeted persuasive advertising is widely used in practice. For example, Miller Lite and Coors Light are the two major competitors in the U.S light beer market, they are heterogenous and preferred by different demographic groups, they target persuasive advertising to attract their competitor’s consumers (Iyer et al., 2005). Targeted persuasive advertising is targeted to special consumers based on consumer’s privacy information, it is considered to alter consumers’ utilities over the advertised product and capture consumers from the advertised firm’s competitor (Bagwell, 2007).

But some reports (Duggan et al., 2015; TRUSTe, 2014) emphasized that consumers concern about firms’ collection and application of their privacy information. Consumer privacy concern refers to consumers’ concern over how consumers control their privacy information and how their privacy information is used, it is consumer’s intrinsic attribute (Dinev et al., 2006). In reality, consumer privacy concern is also relative with the social privacy concern over privacy features of the advertised product category (or SCPF, for short). Following N. A. Zhang et al. (2022) and Masad (2011), SCPF is defined as “general feeling of being unable to maintain functional personal information.” For example, consumers are more likely to disclose their personal ID and less concerning about the using of their personal ID information when they surf on JD.com, because the public trust the security system of JD.com. But consumers concern more about the using of their personal ID when they surf an unknown website, because the public are taught that the unknown website is riskier. Hence, SCPF is more likely to be a surrounding attribute.

Consumers are sociable and knuckle under to the mainstream of the society (Gallagher, 2017), their privacy concern is not only related to consumer intrinsic privacy concern but also SCPF. As the above-mentioned example, consumers with the same intrinsic privacy concern are more willing to surf on JD.com than on an unknown website. Indeed, consumers make their decisions based on the gap between consumer intrinsic privacy concern and SCPF. In this paper, we define it as the anchoring effect of privacy. Since the anchoring effect of privacy is an important factor during consumer decision process, when firms use consumer’s privacy information to target persuasive advertising, it should be taken into consideration. Following the example of JD.com and an unknown website, consumers trust the targeted advertising on JD.com more than on the unknown website. Sometimes, consumers even do not trust the targeted advertising on the unknown website. Obviously, the anchoring effect of privacy influences persuasive advertising effectiveness, the firms’ managers should adjust their targeted persuasive advertising strategies considering this factor in a competitive situation. This paper examines how duopolistic firms compete with targeted persuasive advertising considering the anchoring effect of privacy. This research question is divided into the following questions: (1) How does the anchoring effect of privacy influence firms’ advertising and pricing competition? (2) Which firm can benefit from advertising considering the anchoring effect of privacy? (3) How do the firms set their advertising and pricing strategies?

However, few of the existing researches have studied these questions. Researchers have studied several related topics of our paper. One branch is the impact of consumer privacy concern on targeted advertising competition. Researchers (Jung, 2017; Kim et al., 2022; Toubiana et al., 2010) find that consumer privacy concern reduces targeted advertising effectiveness and the advertised firms will be worse off. Different from these researches, our paper attempts to analyze the competitive targeted persuasive advertising strategy considering the anchoring effect of privacy. Another branch is the how the anchoring effect of privacy impacts on consumers. Celebi (2015) finds that when the social feel more secure and less concern over the privacy feature, consumers might have less privacy concern. Similarly, Masad (2011) holds that the anchoring effect of privacy is another type of herb effect, which is affected by the consumer herself and the rest of her social network. N. A. Zhang et al. (2022) think consumer privacy concern is not only relative with consumers themselves but the peers in the network. Although these researches have demonstrated the existence of the anchoring effect of privacy, few of them analyze the impact of the anchoring effect of privacy on the competitive targeted advertising strategy.

To fill the research gap, we develop a three-stage game theoretical model where two heterogenous firms compete with targeted persuasive advertising and price. The three-stage game is established as follows: (1) Stage 1: firms’ advertising decisions. Both firms choose their advertising levels simultaneously and independently. (2) Stage 2: firms’ pricing decisions. Both firms set their retailing prices simultaneously and independently. (3) Stage 3: consumers’ purchase decisions. Consumers make their purchase decisions considering their preferences, privacy concerns, and SCPF. In our three-stage game theoretical model, persuasive advertising shifts the demand curve directly, because it enhances consumers’ willingness to pay (direct effect of advertising). On the other hand, consumers with different privacy concerns and SCPF are heterogeneous over the consumption (indirect effect of advertising).

The rest of this paper is organized as follows. Section “Related literature” reviews the literatures which are relevant with our work. Section “Model setup” describes the basic model and main components. Section “Equilibrium analysis” analyzes the equilibrium advertising and pricing strategies when firms compete with targeted persuasive advertising. Section “Conclusion” gives the main findings and provides the limitations of our research. All proofs are given in Appendix.

Related Literature

This paper seeks the answers to the above-mentioned questions with a game theoretical model. Our work is related with three main strands of literature: targeted persuasive advertising, consumer privacy concern, and the anchoring effect of privacy.

Firstly, targeted persuasive advertising is considered to persuade the chosen consumers to enhance/alter their purchase decisions, researchers explain how persuasive advertising impacts on firms’ competition and how firms set their targeted advertising strategy. On the one hand, the research on how persuasive advertising impacts on firms’ competition explains how persuasive advertising influences consumer’s purchase decisions and firms’ competition. Persuasive advertising tries to attract the rival’s loyal consumers with altering consumer’s perceived valuation of the advertised product, but it results in a higher price than without advertising (Von der Fehr & Stevik, 1998). Wu et.al (2009) find out that when two competitive firms can choose whether to adopt persuasive advertising or not, the one with advertising always benefits from its persuasive advertising. B. Jiang and Srinivasan (2016) examine firms’ persuasive advertising strategies with a Hotelling model, they find that the firm with low quality-cost margin increases its advertising level, meanwhile the high quality-cost margin firm decreases its advertising level when consumer preference increases. Meanwhile, Lin and Narasimhan (2020) derive that persuasive advertising helps the firm with higher-quality product to establish a competitive advantage. Choi et al. (2018) conclude that persuasive advertising leads to higher pricing competition and consumer surplus may decrease if the advertised products are less differentiated. J. Zhang et al. (2020) analyze the persuasive advertising strategies in a dual-channel supply chain, they conclude that persuasive advertising may hurt the manufacturer but benefit the retailer. In the above literature, when the persuasive advertising increases consumer’s willingness to pay, firms would like to adopt persuasive advertising because they may get more profits. Moreover, persuasive advertising helps the firm with higher-quality to maintain a competitive advantage. On the other hand, researchers study how competitive firms choose their advertising’s targeted consumers. Firms can get more profits by targeting advertising to consumers with higher preference (Iyer et al., 2005; Shaffer & Zettelmeyer, 2004; J. Zhang & He, 2019; Jiang & Wu, 2022). But when the firm target advertising to its weak segment, its rival will be hurt, because targeted advertising triggers price competition in the firm’s weak segment. März (2019) demonstrates that targeted persuasive advertising moderates the price and advertising competition under moderate levels of loss aversion and product differentiation. Arnold et al. (2022) show that in equilibrium the duopolistic firms only target advertising to their loyal consumers or their loyal consumers and switchers, but both get less profits. Based on these existing literature, we conclude that firms always target advertising to consumers who are more preferrable of them. Although the above-mentioned researched have examined how to targeted persuasive advertising, but they ignore the impact of consumer privacy concern in targeted persuasive advertising competition. In this paper, we further consider the impact of consumer privacy concern in the firms’ targeted persuasive advertising competition. We follow the assumption of these researches that persuasive advertising increases consumer’s willingness to pay, and assume firms will not target advertising to consumers who are less preferable of their products.

Our work also relates to the literature on consumer privacy concern. One branch is the relationship between consumer privacy information and privacy concern. Consumer privacy information includes consumer demographics characteristics (Cooper et al., 2022), preferences (Iyer et al., 2015; Sana, 2020), browsing history (Boerman et al., 2017), and so on. The application of consumer privacy information raises consumer privacy concern. Privacy concern is considered as a kind of interaction between individuals and external fields (Newell, 1995), different consumers have different valuations over their privacy information, and their privacy concern vary correspondingly (Beresford et al., 2012, Stuart et al., 2019). Privacy concern impacts on consumers’ online shopping behaviors (Van Slyke et al., 2006), privacy protection behaviors (Youn, 2009), and the valuations over the service based on their privacy information (Li et al., 2014). Moreover, Acquisti et al. (2020) find that consumers concern about their privacy even privacy protection exists. Another branch of studies discusses the relationship between consumer privacy concern and advertising effectiveness. Goldfarb and Tucker (2011) find that when the privacy regulation is enacted, the online advertising effectiveness is lower. Tucker (2014) concludes that consumers may click the advertising more if the firm enhances consumers’ perceived control over their privacy information. Walrave et al. (2018) examine how adolescents respond to the personalized advertising by considering their attitudes toward advertising and privacy concern. They find that high personalization can generate the most positive response, but privacy concern does not moderate the adolescents’ response over the advertising. Mpinganjira and Maduku (2019) find that consumer privacy concern has a significant negative effect on consumers’ attitudes over targeted advertising. Cooper et al. (2022) conclude that different consumers have different reactions to the application of their privacy information in targeted advertising. These papers indicate that the using of consumer privacy information will trigger consumer privacy concern and influence advertising effectiveness, but most of them treat consumer privacy concern as an absolute variable. In this paper, since targeted persuasive advertising is targeted based on consumer privacy information, we assume it raises consumer privacy concern, and we think that consumer privacy concern is a relative variable during consumer and firms’ decision process.

Lastly, a very little of literature discusses the anchoring effect of privacy. Lai and Hui (2006) analyze the anchoring effect of privacy when consumers choose to approve the using of their privacy or not. Lowry et al. (2011) explore the relationship between culture and privacy disclosure techniques through empirical research. They find that culture affects consumer privacy concern, meanwhile, consumer privacy concern and the Internet users’ privacy awareness further affect the application of privacy disclosure technology. Teovanović (2019) finds that the impact of anchoring effect of privacy on individual consumer is different. N. A. Zhang et al. (2022) conceptualize that consumer privacy concern can be divided into self-oriented and peer-oriented privacy concern. These papers show that consumer privacy concern is not absolute, but relative.

Existing researches on persuasive advertising mostly focus on which segment of consumers should be targeted, few of them consider the anchoring effect of privacy on consumers’ purchase decisions and firms’ targeted persuasive advertising strategies. The papers of consumer privacy concern mostly focus on how consumer privacy concern impacts the advertising effectiveness and advertising competition, few of them consider the impact of the anchoring effect of privacy on consumers’ decisions. In this paper, we model the anchoring effect of privacy on consumers’ perceived utilities and purchase decisions. Furthermore, the researches on the anchoring effect of privacy study the conceptualization and impact of the anchoring effect of privacy, but seldomly analyze how the anchoring effect of privacy influences the targeted advertising strategies. Our paper differs from these papers in that, we think the anchoring effect of privacy impacts on consumers’ perceived utilities of the competitive products and purchase decisions, and influences the competitive targeted persuasive advertising strategy.

Model Description

The research method of this paper involves game theory, which has been widely-used in the fields of society and economics. Game theory, like many other disciplines that use mathematical tools to study social and economic phenomena, abstracts basic elements from complex phenomena, analyzes the mathematical models composed of these elements, examines the effects of key elements and derive the equilibrium strategies. Game models include players, players’ strategies, and players’ payoffs under different strategies. In equilibrium strategies, all participants are faced with the situation that when others do not change the strategy, their strategies at this time are the best. In other words, if one participant changes his strategy, his payoff will be reduced so that each participant will not have incentive to deviate from equilibrium strategies alone (Myerson, 2013).

Based on the game theory, we consider a unit market with two competitive firms (firm $i$ , $i = 0, 1$ ), they offer horizontally and vertically differentiated products, and compete with advertising and price. Firm $i$ chooses its advertising level $a_{i}$ and price $p_{i}$ . Consumers make their purchase decisions depending on their perceived utilities of the products. We introduce our model setting with consumer’s perceived value and firm’s expected profit function separately. The notations of our paper are summarized as in Table 1.

Table 1.

Notations Summary.No table of figures entries found.

Notations	Descriptions
$v_{i}$	Consumer’s intrinsic utility of firm $i$ ’s product
$δ_{i}$	Consumer’s extrinsic utility of firm $i$ ’s product
$V_{i}$	Consumer’s utility of firm $i$ ’s product
$γ$	The weighting factor of extrinsic utility
$p_{i}$	The price of firm $i$ ’s product
$x$	Consumer preference
$t$	Unit strength of consumer’s taste preference
$ϑ_{i}$	The intrinsic quality of firm $i$ ’s product
$σ$	The type of consumer’s privacy concern
$σ^{*}$	The social concern of privacy features
$y$	The expected demand of firm 0
$b$	General privacy concern parameter
$g$	Parameter of anchoring effect of privacy
$c_{i}$	Unit production cost of firm $i$
$a_{i}$	The advertising level of firm $i$
$k$	Persuasive power of advertising
$φ_{i}$	Consumer’s willingness to pay for firm $i$ ’s product

Consumer’s Perceived Value

We firstly introduce the consumer’s perceived value of firm $i$ ’s product. We assume each consumer has a unit demand of either product from firm $i$ , meanwhile, consumers are rational and always buy the product with the greater utility. As in Keller and Lehmann (2006), consumer’s perceived valuation reflects her complete experience of the product. Similar with Clark and Oswald (1998), we separate the utility that consumer buys from firm $i$ into two separated utility components: the intrinsic utility $v_{i}$ and extrinsic utility $δ_{i}$ . The utility function can be written as

V_{i} = v_{i} + γ δ_{i}

The weighting factor $γ > 0$ shows the importance of the extrinsic utility relative to the intrinsic utility. Assume the parameter $γ$ is constant and can be observed by the consumers.

We model the competition between the firms with a Hotelling model. Specifically, we assume the population of consumers is uniformly distributed on a unit length with two rivals locate at the extremes of the line. Each consumer needs to pay a price of $p_{i}$ to buy her “ideal” product that matches her taste as much as possible. We derive the consumer’s intrinsic utility as

v_{i} = ϑ_{i} - t | x - x_{i} | - p_{i}

$| x - x_{i} |$ shows the distance between the consumers locate at $x \in [0, 1]$ and their most preferred product, they need to pay $t | x - x_{i} |$ effort to satisfy their taste. The parameter $t$ shows the unit strength of their taste preferences, $ϑ_{i}$ indicates the intrinsic quality of the product.

Targeted persuasive advertising can be targeted to a certain segment of consumers, it may change consumer’s perceived quality of the product, which equals the consumer’s willingness to pay for the product. So, when a consumer receives firm $i$ ’s advertising, her willingness to pay for the advertised product is given by

φ_{i} = v_{i} + k a_{i}

The consumer’s willingness to pay for the advertised product is affected by both advertising and her intrinsic utility, where the weighting factor $k$ reflects the influence power of advertising and is defined as the persuasive power of advertising, it shows the effectiveness of unit advertising investment on consumer’s willingness to pay.

We model the key feature that consumers make their purchase decisions depending on the others’ decisions and the anchoring effect of privacy. With consumers’ privacy information, firms can target advertising more precisely; meanwhile, consumers may get their “ideal” product more easily. But consumers differ in privacy concerns over the application of their privacy information in the targeted persuasive advertising. Some of them enjoy the convenience from targeted advertising; some are resentful of the utilization of privacy, and some do not care about the using of their privacy. In line with our model concerning the horizontal mismatch, we assume the effect of privacy concern on the perceived value of the advertised product is linear. To analyze different privacy concern of the consumers, we define there is a continuum of consumer privacy concern type $σ, σ \in [\underline{σ}, \bar{σ}]$ , where $\underline{σ} < 0 < \bar{σ}$ . Here, $\bar{σ} > 0$ represents that consumer privacy concern is positive, a positive value of $σ$ indicates that consumers would like to share their privacy information to firms, a greater value of $σ$ means that this segment of consumers will feel more convenience by offering their privacy information. On the contrary, a negative value of $σ$ shows that consumers feel the invasion of their privacy information and get a negative effect from the advertising, which results in a low probability of purchasing the advertised product. For all consumers in the market, their privacy concerns are asymmetric, that is, $\underline{σ} ≢ \bar{σ}$ . We characterize the consumers by their preferences and privacy concerns, both of the characteristics are independent and uniformly distributed over the intervals $x \in [0, 1]$ and $σ \in [\underline{σ}, \bar{σ}]$ , so consumers in the market distribute according to the following bivariate uniform distribution

f (x, σ) = {\begin{matrix} {(\bar{σ} - \underline{σ})}^{- 1} if x \in [0, 1]; σ \in [\underline{σ}, \bar{σ}] \\ 0 otherwise \end{matrix}

The expected privacy concern of all consumers is $E [σ] = \frac{\bar{σ} + \underline{σ}}{2}$ , which represents the average privacy concern of the consumers. Although firms cannot get each consumer privacy concern, but they could have the expected privacy concern of all consumers shown as $E [σ]$ . Meanwhile, the consumer knows her privacy concern separately and does not interact with others.

On the other hand, the extrinsic utility of the advertised product is relative with SCPF. Different kinds of products own different SCPF $σ^{*}$ . For example, a credit card application contains the applicant’s incoming information, most applicants do not want their incoming information to be exposed, but they do not mind their phone number being exposed during a job application. To simplify our analysis, we assume $σ^{*} \in [0, \bar{σ}]$ . Furthermore, $σ - σ^{*}$ captures the anchoring effect of privacy, it shows the gap between consumer privacy concern and SCPF. Similarly, $E (σ) - σ^{*}$ indicates the expected anchoring effect of privacy.

In our model, we divide the effect of consumer privacy concern into two parts, one is affected by the expected demand of the product. Consumers refer to the expected demand when they are asked to offer their privacy information. The expected demand of firm $0$ is denoted by $y, (y \in [0, 1])$ . The other one is the effect of consumer’s general privacy concern, which is affected by the other factors which are the same between the firms’ products.

We assume that a consumer’s extrinsic utility depends on her privacy concern. When consumers expose their privacy information, they concern the general privacy concern and the others’ consumption, which is known as Herd Effect. Herd Effect is common especially in some special goods categories, such as sex toys industry, it makes consumers who buy the sex toy less exclusive and increases her perceived extrinsic utility. Following Karni and Schmeidler (1990), we define extrinsic utility of firm $i$ ’s product as

δ_{i} = b σ + g (σ - σ^{*}) | y - x_{i} |

Where $b$ captures the general privacy concern parameter, and $g$ captures the parameter of the anchoring effect of privacy. To simplify our analysis, we assume $g = 1$ .

Firm’s Expected Profit Function

Then, we model the firm’s expected profit function. Assume firm $i$ ’s unit cost of production is $c_{i}$ . Following the assumption of standard Hotelling model, we assume firm 0 locates at $x_{0} = 0$ , and firm 1 locates at $x_{1} = 1$ .

We derive a reduced-form approach to describe the role of consumer privacy concern over targeted persuasive advertising. Each firm’s demand is affected by the advertising level $a_{i}$ , the product price $p_{i}$ and the externality of consumer privacy concern. We define a parameter $γ, γ > 0$ which represents the externality of consumer privacy concern. The targeted advertising cost of firm $i$ as $C (a_{i}) = \frac{A {a_{i}}^{2}}{2}$ , where $A$ represents the unit targeted advertising cost, the cost equation shows the diminishing marginal utility of targeted persuasive advertising. So firm $i$ ’s equilibrium profit can be given as

{π_{i}}^{*} (γ) = ({p_{i}}^{*} - c_{i}) * D_{i} ({p_{i}}^{*}, {a_{i}}^{*}, γ) - \frac{A {a_{i}}^{2}}{2}

From the above equation, with standard comparative statics, we can see that the externality of consumer privacy concern affects the equilibrium advertising level. That is to say, ${a_{i}}^{*} = argma x_{a_{i}} {π_{i}}^{*} (γ)$ , where $\frac{δ a_{i}}{δ γ} \neq 0$ . In particular, the targeted persuasive advertising influences the individual consumer’s attention and willingness to pay, we will discuss how the mechanism works in a duopoly model where each firm’s demand is constructed as firm $i$ ’s equilibrium profit equation.

In this paper, we consider the following three-stage game: Stage 1: Firm $i$ chooses its targeted advertising level $a_{i}$ and perceived product quality $ϑ_{i}$ simultaneously. Stage 2: Firm $i$ sets the product price $p_{i}$ . Stage 3: Consumers make their purchase decisions considering their preferences, privacy concerns, and SCPF.

Equilibrium Analysis

In this section, we firstly characterize the demand functions of the firms; then we analyze the interaction of targeted persuasive advertising and consumer privacy concern; thirdly, we characterize the sub-game prefect Nash equilibrium within competition.

Basic Model

We define a value $x (σ, y)$ to identify the indifferent consumers of a certain privacy concern $σ$ and the influence extent of the privacy concern $y, y \in [0, 1]$ . In our model, to cover all consumers in the market, we derive a two-dimension space $x (σ, y)$ for all privacy concerns. In the space, we assume the consumers who locate at $x = 0$ and $x = 1$ will not switch their purchase decisions whenever their privacy concern changes. Because of the externality of consumer privacy concern, consumers locate at $x \in (0, 1)$ may switch to the rival. With the above assumption, we rule out the case that only one firm occupies the whole market.

Following the standard Hotelling model, the indifference curve of consumer’s utility from purchasing two firms’ products is given as

\begin{matrix} x (σ, y) = \\ \frac{t + (ϑ_{0} - ϑ_{1}) - (p_{0} - c_{0} - p_{1} + c_{1}) + γ (σ - σ^{*}) (2 y - 1)}{2 t} \end{matrix}

To guarantee the above assumption exists, we assume the horizontal mismatch caused by the externality of privacy concern satisfies $t > \frac{γ (\bar{σ} - \underline{σ})}{2}$ . In our model, to simplify the analysis, we consider that consumer preference is the main factor affecting consumers’ optimal choices.

Derived from the above indifference curve, the set of consumers with different privacy concern $σ \in [\underline{σ}, \bar{σ}]$ who buy firm $i$ ’s product is given as

x \leq \frac{t + (ϑ_{0} - ϑ_{1}) - (p_{0} - c_{0} - p_{1} + c_{1}) + γ (σ - σ^{*}) (2 y - 1)}{2 t}

The gross expected demand of firm 0 is

\begin{matrix} D_{0} = \frac{1}{\bar{σ} - \underline{σ}} \int_{\underline{σ}}^{\bar{σ}} \int_{0}^{\frac{t + (ϑ_{0} - ϑ_{1}) - (p_{0} - c_{0} - p_{1} + c_{1}) + γ (σ - σ^{*}) (2 y - 1)}{2 t}} 1 dxd σ \end{matrix}

And firm 1’s demand equals to $D_{1} = 1 - D_{0}$ .

Hence, firm $i$ ’s demand with a given price $p_{i}$ and perceived quality $ϑ_{i}$ is derived as

D_{i} = \frac{1}{2} + \frac{(ϑ_{i} - ϑ_{1 - i}) - (p_{i} - c_{i} - p_{1 - i} + c_{1 - i})}{2 [t - γ (E (σ) - σ^{*})]}

Firm $i$ ’s demand is increasing with the intrinsic quality (vertical difference) and decreasing in price (price competition). When $ϑ_{i} \neq ϑ_{1 - i}$ or $p_{i} - c_{i} \neq p_{1 - i} - c_{1 - i}$ , the firms’ demands are asymmetric. Only if $ϑ_{i} - p_{i} - c_{i} > ϑ_{1 - i} - p_{1 - i} - c_{1 - i}$ , firm $i$ ’s demand $D_{i} > D_{1 - i}$ . We can find that if a firm is willing to get more market share, it could improve the consumer’s perceived quality with advertising or her intrinsic utility with a lower cost than its rival. But it may be reminiscent of price competition. To ensure no firm can capture the whole market, we assume that $ϑ_{i} - c_{i} - ϑ_{1 - i} + c_{1 - i} < \frac{9 A [t - γ (E (σ) - σ^{*})] - k^{2}}{3 A [t - γ (E (σ) - σ^{*})] - k^{2}}$ .

Meanwhile, the anchoring effect of privacy, the expected privacy concern and SCPF affect the sensitivity to the mismatch between consumers and their preferable products, and then affect the demand.

Theorem 1. When $ϑ_{i} - p_{i} - c_{i} > ϑ_{1 - i} - p_{1 - i} - c_{1 - i}$ , firm $i$ ’s demand increases with an increasing anchoring effect of privacy and expected privacy concern, but decreases with an increasing SCPF $σ^{*}$ , that is, $\frac{\partial D_{i}}{\partial (E (σ) - σ^{*})} > 0$ , $\frac{\partial D_{i}}{\partial E (σ)} > 0$ , $\frac{\partial D_{i}}{\partial σ^{*}} < 0$ .

Theorem 1 indicates the anchoring effect of privacy, the expected privacy concern and SCPF can influence the firm’s demand. The firm with higher quality-cost margin benefits from a greater anchoring effect of privacy and expected privacy concern, but suffers the loss from the increasing SCPF. A greater anchoring effect of privacy enhances consumer’s perceived value of the product and expands the differentiation between the firms which results in a greater asymmetric demand. Similarly, a greater expected privacy concern also makes consumers hard to change their purchase decisions. Since the anchoring effect of privacy and expected privacy concern always benefit the firm with higher quality-cost margin, in practice, firms should try to get a higher quality-cost margin in competition to achieve competitive advantages. A lower SCPF makes consumers concern more about their own privacy during their purchase. For example, Netherlands is an open society to sex, the social privacy concern connected to sex toys is low. So, when they purchase sex toys in Netherlands, they may not concern about the privacy about sex toys. But in India, the situation is opposite, Indian society treat sex as one of top privacy, the social privacy concern connected to sex toys is very high. Due to the different SCPF, the sex toy sales volume in Netherland is much larger than that in India, even India has a much larger population than Netherland. Hence, in practice, the firm with higher quality-cost margin needs to reduce SCPF to maintain its competitive advantage. Oppositely, to eliminate the disadvantage of lower quality-cost margin, the firm with lower quality-cost margin should make the public pay more attention to SCPF.

The Interaction of Advertising and Anchoring Effect of Privacy

Following the role of persuasive advertising, a higher advertising level can enhance consumer’s willingness to pay. When one firm choose a different advertising level (assume firm 0 chooses a higher advertising level), it will lead to a shift of the indifference curve of the consumer utility function. Because consumers get a higher perceived quality $ϑ_{i}$ from a higher advertising level $a_{i}' (a_{i}' > a_{i})$ of firm $i$ . Since $ϑ_{i}$ has an enhancing effect on the demand, we can derive that while all consumers benefit from the increase in intrinsic utility due to a higher advertising level of firm $i$ , the individual consumer’s extrinsic utility affected by the privacy concern changes correspondingly.

Since quality has a demand-enhance effect, the reference sales $y$ is updated accordingly ( $y$ increases to $y'$ ). It leads to a clockwise rotation of the indifference curve through point ( $0, y'$ ) around the point $x (σ^{*}, y^{*})$ , as Figure 1 shows. The rotation is generated by the anchoring effect of privacy. With an increase in firm $0$ ’s advertising level, all consumers benefit equally in intrinsic utility, but the extrinsic utility is affected differently to individuals. We can easily have that the anchoring effect of privacy affects the advertising demand-enhancing effect on consumers with privacy concern $σ$ .

Figure 1.

Changes of the indifference curve when firm 0 increases its advertising level.

The demand-enhancing effect of increasing advertising level is reinforced for the consumer whose privacy concern is higher than SCPF, and weakened for the consumer whose privacy concern is lower than SCPF. With a given SCPF, consumer can benefit from providing privacy information when her privacy concern is higher than SCPF. It results in a demand-enhancing effect. On the contrary, when consumer privacy concern is lower than SCPF, even her privacy concern is positive, she suffers the loss from exposing her privacy information. Therefore, those consumers whose privacy concerns are higher than SCPF are more attractive to the heavily advertised brand.

We compare the demands before ( $a_{i}$ ) and after ( $a_{i}', a_{i}' > a_{i}$ ) the increasing of targeted advertising level in two different ways: consumers with same privacy concern $σ$ and the whole market. With the analysis, we derive that the demand-enhance effect caused by the increment of advertising level for consumer segments with the same privacy concern $σ$ is

\begin{matrix} x' - x = & (\frac{k}{2 t} + \frac{k γ (σ - σ^{*})}{2 t [t - γ (E (σ) - σ^{*})]}) \\ \int_{a_{i}}^{a_{i}'} d \hat{a_{i}}, (a_{i}' > a_{i}, σ \in [\underline{σ}, \bar{σ}]) \end{matrix}

Targeted persuasive advertising impacts the consumers with the same privacy concern directly and indirectly. $\frac{k}{2 t} \int_{a_{i}}^{a_{i}'} d \hat{a_{i}}$ shows the direct effect of targeted persuasive advertising, and it’s constant for all consumers. Firm $i$ can get a positive demand increment due to the direct effect of targeted persuasive advertising. $\frac{k γ (σ - σ^{*})}{2 t (t - γ (E (σ) - σ^{*}))} \int_{a_{i}}^{a_{i}'} d \hat{a_{i}}$ indicates the indirect effect of targeted persuasive advertising. The indirect effect of targeted persuasive advertising varies with the expected privacy concern and SCPF. Therefore, we have

Lemma 1. When firm $i$ increases its advertising level, an increasing anchoring effect of privacy leads to the increment of demand from the indirect effect of targeted persuasive advertising. When $E (σ) > σ^{*}$ , firm $i$ can get an increment of demand from the indirect effect of targeted persuasive advertising; when $E (σ) < σ^{*}$ , firm $i$ gets a reduction of demand from the indirect effect of targeted persuasive advertising; and when $E (σ) = σ^{*}$ , two firms compete within the standard Hotelling model. An increasing SCPF $σ^{*}$ results in reducing the increment of demand caused by the indirect effect of targeted persuasive advertising.

Lemma 1 shows that the anchoring effect of privacy, expected privacy concern, and SCPF impact on the increment of demand caused by the indirect effect of targeted persuasive advertising. When the anchoring effect of privacy increases, consumers could get more perceived value with a greater advertising level of firm $i$ , who could capture more consumers. But the impact of the expected privacy concern $E (σ)$ on the increment of demand varies. If $E (σ)$ is greater than SCPF, it means more consumers would like to disclose the privacy information, both the firms and consumers can benefit. On the contrary, the consumers do not like to disclose their privacy information because the society focus on the privacy connected with the product. In extreme situations, firms may suffer the loss from advertising because the society are not like to exposure the privacy connected with the product. Then, A higher SCPF $σ^{*}$ indicates that the society concern more on the privacy related with the product. Consumers are not willing to disclose more privacy information even they can benefit more from the advertising. Sometimes, a higher SCPF may hurt the demand from the consumers with the same privacy concern.

In Lemma 1, when firm $i$ chooses to increase its advertising level, it should pay more attention to the relationship between the expected privacy concern $E (σ)$ and SCPF $σ^{*}$ , because it may lose part of the potential demand when $E (σ) < σ^{*}$ . On the other hand, firm $i$ should try to increase the anchoring effect of privacy which could help itself to get more potential demand.

The aggregate demand equals to the sum-up of individual demand across consumers who are affected by the targeted persuasive advertising.

Theorem 2. When firm $i$ increases its advertising level, the increment of the aggregate demand results from the adding-up of individual effect across consumers, it is increasing in the expected privacy concern, and it’s decreasing in SCPF, that is $\frac{d {D_{i}}^{2}}{dE (σ) d a_{i}} > 0$ , $\frac{d {D_{i}}^{2}}{d σ^{*} d a_{i}} < 0$ .

Theorem 2 shows that an increase in the expected privacy concern $E (σ)$ can make the advertising more effective with a given SCPF. When consumers are more likely to disclose their privacy information, they can pay less efforts to buy the product, both firms and some of the consumers benefit from a higher $E (σ)$ . On the other hand, when SCPF $σ^{*}$ increases, it means the society concern more about the privacy connected with the product, consumers do not like to disclose their privacy information, as a result, the advertising effectiveness reduces.

Corollary 1. When firm $i$ increases its advertising level, it may suffer the loss when the expected anchoring effect of privacy satisfies $E (σ) - σ^{*} > \frac{t}{γ}$ .

Corollary 1 indicates that the increasing advertising level of firm $i$ may hurt its potential demand. The reason is that when the expected anchoring effect of privacy is greater, the gap between the expected privacy concern and SCPF is larger, the increment of advertising level will decrease consumer’s perceived value of firm $i$ ’s product, and the demand decreases. Hence, when firm $i$ decides to increase its advertising level, it should try to reduce the expected anchoring effect of privacy to establish its advantage, and if the expected anchoring effect of privacy is too large, firm $i$ should not increase its advertising level.

Nash Equilibrium Solutions and Analysis

There exists the sub-game prefect Nash equilibrium of the game in our paper. With a given $ϑ_{i}$ , firm $i$ sets its equilibrium price $p_{i}$ to maximizes its profit $π_{i}$ . Firm $i$ ’s profit is

π_{i} (p_{i}) = (p_{i} - c_{i}) D_{i} - \frac{A {a_{i}}^{2}}{2}

With first order condition to maximize the profit function $π_{i} (p_{i})$ , we can derive firm $i$ ’s price

p_{i} = t - γ (E (σ) - σ^{*}) + \frac{ϑ_{i} - ϑ_{1 - i} + 2 c_{i} - c_{1 - i}}{3}

Hence, when two firms choose their advertising levels simultaneously, firm $i$ ’s profit can be expressed as $π_{i} (ϑ_{i}) = \frac{{(3 [t - γ (E (σ) - σ^{*})] + ϑ_{i} + k a_{i} - ϑ_{1 - i} - k a_{1 - i} - c_{i} + c_{1 - i})}^{2}}{18 (t - γ (E (σ) - σ^{*}))} - \frac{A {a_{i}}^{2}}{2}$ . Then, we can derive the sub-game prefect Nash equilibrium of the game.

Theorem 3. When both firms engage in targeted persuasive advertising, firm $i$ ’s profit-maximizing price and advertising level in the sub-game prefect Nash equilibrium are given as

\begin{matrix} p_{i}^{*} & = t - γ (E (σ) - σ^{*}) + c_{i} \\ + \frac{3 A [t - γ (E (σ) - σ^{*})] (ϑ_{i} - ϑ_{1 - i} + c_{1 - i} - c_{i})}{9 A [t - γ (E (σ) - σ^{*})] - k^{2}} \end{matrix}

and

a_{i}^{*} = \frac{k}{2} (\frac{1}{3 A} + \frac{ϑ_{i} - ϑ_{1 - i} + c_{1 - i} - c_{i}}{9 A [t - γ (E (σ) - σ^{*})] - k^{2}})

Firms’ equilibrium advertising level is affected by the advertising persuasive power. If the advertising persuasive power tends to zero, firms are not willing to invest in advertising because advertising has no demand-enhancing effect. However, the equilibrium price is influenced by the expected anchoring effect of privacy $E (σ) - σ^{*}$ . When the firms are symmetric, the equilibrium prices are affected by $E (σ)$ and SCPF only. With a higher $E (σ)$ , firms may reduce their prices, because consumers are not willing to disclose their privacy information, a lower price may offset consumer loss from privacy information disclosure. On the other hand, a higher SCPF can increase the equilibrium price, because a higher SCPF encourages firms to get more privacy information from consumers and charge a higher price.

Corollary 2. When two firms compete with targeted persuasive advertising, the aggregate equilibrium advertising level is fixed and equals to $\frac{k}{3 A}$ .

Corollary 2 shows the aggregate equilibrium advertising level depends only on the unit advertising cost $A$ and the advertising persuasive power $k$ . When the unit advertising cost is higher, firms do not intend to advertise because they need to pay more advertising cost to attract a consumer. When the advertising persuasive power increases, firms may benefit from advertising more because it increases consumer’s perceived value of the advertised product. In a word, Corollary 2 shows that advertising plays a role of business-stealing. Hence, in practice, when firms compete with targeted persuasive advertising, they should be more aggressive, because the optimal advertising level is fixed, if the firm is not aggressive, its competitor may capture more consumers.

Following Anderson and De Palma (2006), the “quality-cost margin” is given as $ϑ_{i} - c_{i}$ . To simplify the analysis, we assume that firm 0’s quality-cost margin is greater than firm 1’s. From Theorem 3, we can observe the following corollaries.

Corollary 3. The relationship between firm $i$ ’s price and advertising level in equilibrium are given as follows, (i) when $E (σ) - σ^{*} > \frac{t}{γ}$ , $\frac{\partial p_{i}^{*}}{\partial a_{i}^{*}} < 0$ ; (ii) when $E (σ) - σ^{*} < \frac{t}{γ}$ , $\frac{\partial p_{i}^{*}}{\partial a_{i}^{*}} > 0$ ; (iii) when $E (σ) - σ^{*} = \frac{t}{γ}$ , $\frac{\partial p_{i}^{*}}{\partial a_{i}^{*}} = 0$ .

Bagwell (2007) indicates that the persuasive role of advertising makes the heavily advertised product more expensive than the less advertised product, because persuasive advertising improves consumer’s willingness to pay. Corollary 3 suggests that when the anchoring effect of privacy is less than $\frac{t}{γ}$ , the relationship between the equilibrium price and advertising level is positive, firms try to transfer their advertising cost to consumers by charging a higher price. Corollary 3 also indicates that when the anchoring effect of privacy is greater than $\frac{t}{γ}$ , firms charge a lower price with a greater advertising level. Because in this scenario, the effect of targeted persuasive advertising is weakened on consumers, and the firms involve in price competition. In a special scenario where the anchoring effect of privacy equals to $\frac{t}{γ}$ , the equilibrium price has no connection with the advertising level, because the effect of both firms’ advertising on consumers are the same and offset.

Furthermore, we discuss how the marginal changes of the expected anchoring effect of privacy, the expected privacy concern, SCPF, and advertising persuasive power influence the competition. Based on Theorem 3, we derive that

Corollary 4. When the expected anchoring effect of privacy $E (σ) - σ^{*}$ increases, the advertising levels, demands, and prices in equilibrium are more asymmetric.

Corollary 4 indicates that when the expected anchoring effect of privacy increases, the market structure is more asymmetric, which results in a greater market concentration. Similarly, when the expected anchoring effect of privacy is greater, firm 0 invests more in advertising which could capture more consumers from firm 1, and it is more profitable with a higher price. To reduce the disadvantage, firm 1 needs to reduce its price. Hence, the increasing expected anchoring effect of privacy reinforces the price asymmetry.

Corollary 5. When the expected privacy concern increases, the demands, advertising levels, and prices in equilibrium are more asymmetric. When SCPF increases, the demands, advertising levels, and prices in equilibrium are less asymmetric.

Corollary 5 shows that a marginal increment of the expected privacy concern makes the market structure more asymmetric, it also increases the market concentration. Both firms try to capture more consumers to enhance their market power. Firm 0’s advantage of quality-cost margin is enhanced, and the consumer’s extrinsic utility increases with the increasing expected privacy concern. Differently, an increasing SCPF moderates the asymmetries between the firms. A higher SCPF indicates that consumers suffer less pressure from purchasing the product, it reduces the advertised firm’s market power, and moderates the price and advertising competition, the market structure is less asymmetric.

Corollary 6. In equilibrium, the increase of advertising persuasive power reinforces asymmetries of advertising levels, but it reinforces the asymmetry of prices when $E (σ) - σ^{*} > \frac{t}{γ}$ , otherwise, it weakens the asymmetry of prices.

Advertising is an effective tool in competition when it plays the persuasive role. Corollary 6 shows that an increasing advertising persuasive power reinforces firm 0’s market power. Firm 0 always advertises more to gain more profit, but firm 1 may increase or decrease its advertising level. Since firm 1’s quality-cost margin is low, if it invests more in advertising, its marginal profit will decrease and suffer more loss, so it decreases its advertising level. Hence, when the advertising persuasive power increases, the equilibrium advertising levels are more asymmetric. But the impact of an increasing advertising persuasive power on the equilibrium prices varies. When $E (σ) - σ^{*} > \frac{t}{γ}$ , advertising can help firm 0 to capture more consumers, firm 1 has to reduce its price to offset the influence of the heavier advertising level of firm 0, hence, the equilibrium prices are more asymmetric. But when $E (σ) - σ^{*} < \frac{t}{γ}$ , firm 0’s investment in advertising hurts its profit, it should reduce its price to attract its loyal consumers, on the other hand, firm 1 can get more profit with a higher price, hence, the equilibrium prices are less asymmetric.

Corollary 4 to 6 explains the factors that influence firms’ competition. The firm with greater quality-cost margin could always benefit from the increase of the expected anchoring effect of privacy, expected privacy concern, and advertising persuasive power, but may be worse off with a greater SCPF. Hence, when SCPF is low, firms should increase their quality-cost margin to establish competitive advantage; when SCPF is high, they should try to be homogeneous with their competitors.

Conclusion

Consumer privacy information is used to target persuasive advertising, it triggers consumer privacy concern and influences consumers’ purchase decisions. With a three-stage theoretical model, this paper mainly discussed how the duopolistic firms compete with targeted persuasive advertising considering the anchoring effect of privacy.

Main Findings

The main finding of this paper is that when one of the duopolistic firms increases its advertising level, targeted persuasive advertising hurts the firm but benefits its rival if the anchoring effect of privacy is negative. The finding is different with Wu et al. (2009) and contradict with common sense, where the advertising investment benefits the higher advertised firm due to the demand-enhancing effect of persuasive advertising. The reason is that, when the anchoring effect of privacy is negative, consumer’s perceived utility of the higher advertised firm will reduce, but his perceived utility of the lower advertised firm will not change, more consumers will buy from the rival, the demand of the higher advertised firm reduces, meanwhile the advertising cost increases, hence, the higher advertised firm gets less profit but its rival gets more profit.

Then, based on the equilibrium prices and advertising levels in the model, we find that the firm with higher quality-cost margin advertises more and charges a higher price. The increases in the expected consumer privacy concern and advertising persuasive power will reinforce the asymmetry of the equilibrium prices, advertising levels, and demands. Furthermore, an increase in SCPF will weaken the asymmetry of the equilibrium prices, advertising levels, and demands. Finally, an increase in the anchoring effect of privacy reinforces the asymmetry of the equilibrium advertising levels and demands, but under certain conditions, it could soften the asymmetry of the equilibrium prices.

Managerial Implications

Our findings can help firms to effectively set their competitive targeted persuasive advertising and pricing strategies considering the anchoring effect of privacy. We suggest that firms should be cautious about increasing their advertising levels in competition, because they may suffer the loss with a greater advertising level due to the existence of the anchoring effect of privacy. Firms should pay more attention to consumers whose privacy concern is lower than SCPF, because these consumers’ perceived utilities of the advertised firm decrease rapidly and are more likely to change their purchase decisions, it results in a lower profit of the advertised firm. Accordingly, firms should focus on the consumers whose privacy concern is higher than SCPF.

Then, when competing with targeted persuasive advertising and price, the firm with low quality-cost margin should try to eliminate the asymmetry between itself and its competitor. On the contrary, the firm with high quality-cost margin should reinforce the asymmetry in the competition. Specially, firms should pay more attention to the anchoring effect of privacy because it directly influences the firms’ advertising and pricing strategies, and the disadvantageous firm should try to weaken the anchoring effect of privacy as well as the quality-cost margin.

Finally, our findings are helpful for the market regulators, they should try to increase SCPF, since a greater SCPF may moderate the advertising and price competition, and reduces the asymmetry of the competitive firms which ensures the competitiveness of the market and benefits consumers.

Limitations and Future Research

Our research contributes to the connection between targeted persuasive advertising and consumer privacy information, especially the researches on the anchoring effect of privacy. But there are several limitations. Firstly, the model in this paper does not cover all the features of the competition markets. We simply treat that the relationship between consumer privacy concern and SCPF is independent. It will be interesting to analyze the firms’ advertising and pricing strategies when the relationship is dependent. Meanwhile, we assume that persuasive advertising enhances consumer’s perceived quality, where persuasive advertising may also alter consumer preference. It will be meaningful to analyze firms’ advertising and pricing strategies when persuasive advertising alters consumer preference. Moreover, in our game theoretical model, we simply adopt linear function to describe consumer’s perceived utility, it is meaningful to adopt other forms of functions to describe consumer’s perceived utility and study how firms compete with targeted advertising strategy considering the anchoring effect of privacy. Finally, it is interesting to investigate and verify our research topic with empirical approach. We hope to address these researches in the future.

Footnotes

Appendix

Declaration of Conflicting Interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work is supported by National Natural Science Foundation of China (Grant No. 72371069, 71871054).

ORCID iD

Yuxiang Zhang

Data Availability Statement

Data sharing not applicable to this article as no datasets were generated or analyzed during the current study.

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“Anchoring Effect” of Privacy in Targeted Persuasive Advertising Competition

Abstract

Plain language summary

Keywords

Introduction

Related Literature

Model Description

Consumer’s Perceived Value

Firm’s Expected Profit Function

Equilibrium Analysis

Basic Model

The Interaction of Advertising and Anchoring Effect of Privacy

Nash Equilibrium Solutions and Analysis

Conclusion

Main Findings

Managerial Implications

Limitations and Future Research

Footnotes

Appendix

Declaration of Conflicting Interests

Funding

ORCID iD

Data Availability Statement

References