E-Commerce Platforms’ Cross-Platform Targeted Advertising Strategies: Cooperation with Social Media Platforms or Remaining Independent

Abstract

E-commerce platforms are increasingly adopting cross-platform targeted advertising strategies, and the design of such strategies warrants attention. Focusing on cooperation between e-commerce and social media platforms, this study considers targeting precision, advertising intensity, privacy concerns and social utility on the effectiveness of targeted advertising. Using a game-theoretic model, we examine the decision between single- and cross-platform for e-commerce platforms in fully and partially overlapping user groups. The main findings indicate that (1) the social utility of social media platforms is a key factor in implementing cross-platform targeted advertising; (2) cross-platform targeted advertising is not always the optimal choice for e-commerce platforms; and (3) low-precision cross-platform strategy achieves three-party optimum in fully and partially overlapping user groups. The implications of the main findings include: (1) e-commerce platforms should prudently use social media platforms instead of relying excessively on their traffic; (2) e-commerce platforms should not regard cross-platform cooperation as the default option but as a differentiated, situation-specific decision; and (3) e-commerce platforms should promote co-creation of value and proprietary data accumulation when cooperating with social media platforms. The findings can help e-commerce platforms to choose proper targeted advertising strategy in practice. This study also provides a theoretical supplement for cross-platform targeted advertising research.

1. Introduction

Today, nearly all online advertising has some degree of targeting capability [1]. Targeted advertising refers to selecting the appropriate timing and delivering advertising content with personalized features tailored to the needs and characteristics of different types of consumers [2]. This can make advertising less costly and more effective. With the rapid development of various types of platforms, e-commerce platforms increasingly seek to broaden the scope of targeted advertising and make it more precise. Some have introduced cross-platform targeted advertising services based on inter-platform cooperation, enabling brand owners to simultaneously deliver related targeted advertisements across two or more platforms [3]. Cross-platform targeted advertising does not simply mean placing independent advertisements on multiple platforms at the same time. Rather, it involves sharing consumer-related information between platforms to deliver more precise targeted advertisements. Today, there is widespread collaborative targeted advertising between e-commerce platforms and social media platforms [4]. Examples include cooperation between JD.com [5] and WeChat [6] in China and cooperation between Amazon and X.com (Twitter) in the US. After searching for products on an e-commerce platform, consumers might subsequently receive advertisements for related products from that platform when visiting a social media site [7].

This type of collaborative cross-platform targeted advertising offers many advantages. For consumers, it provides better advertising services while reducing search costs [8,9]. For brand owners, it enables more precise delivery of product advertisements, thereby increasing profitability [10]. For e-commerce platforms, it broadens their markets and boosts sales by leveraging social media users while also improving advertising precision through social media data, ultimately enhancing the persuasiveness of advertisements and strengthening consumers’ purchase intentions [11]. For social media platforms, cooperation transforms user traffic into additional revenue [12]. Nevertheless, cross-platform targeted advertising also faces many challenges. From the consumer’s perspective, information sharing between e-commerce and social media platforms increases the risk of privacy breaches and may expose consumers to excessive advertising harassment [13]. For brand owners, cross-platform targeted advertising may lead to consumer irritation, diminishing the effectiveness of targeted advertising [14]. For e-commerce platforms, cooperation requires both revenue sharing and cooperation costs, potentially reducing income [15]. It might also cultivate new competitors, sparking conflicts between platforms [16]. For social media platforms, more precise cross-platform targeting might negatively affect user experience, leading to user attrition [17,18]. Thus, when e-commerce platforms choose to deliver cross-platform targeted advertising through social media platforms, they need to balance multiple interests, taking into account positive outcomes as well as potential drawbacks. Therefore, a key question arises for e-commerce platforms: when is the best time to adopt cross-platform targeted advertising?

Currently, many scholars have extensively examined targeted advertising strategies, particularly in single-platform settings. A few studies have focused on cross-platform targeted advertising with fully overlapping user groups and considered third-party platforms without characteristics [3]. Relatively few studies, however, have focused on the influence of social media relationships and partially overlapping user groups. In addition, previous research has explored how targeting precision [19], advertising intensity [20], and privacy concerns [21] influence e-commerce platforms’ decision-making. However, few studies have considered how these three factors interact to shape e-commerce platforms’ targeted advertising strategies. Furthermore, numerous studies have investigated optimal advertising strategies for e-commerce platforms under profit maximization [22]; yet, the optimal strategic trade-off between single-platform and cross-platform advertising has rarely been examined.

Given the aforementioned practical developments and research gaps, the goal of this study is to explore the following research questions:

(1)

What factors influence e-commerce platforms’ decision-making regarding cross-platform targeted advertising strategies in cooperation with social media platforms?

(2)

When considering the influence of social media relationships, is cross-platform targeted advertising on e-commerce platforms still effective?

(3)

How should e-commerce platforms choose between single-platform and cross-platform strategies to maximize profits in fully and partially overlapping user groups?

These questions reflect the complex interplay among multiple factors and stakeholders within the delivery of targeted advertising. Game theory, a quantitative analytical approach widely employed in theoretical modeling, is well-suited to addressing these issues. Accordingly, this study develops a game-theoretic model that incorporates factors such as targeting precision, advertising intensity, privacy concerns, and social utility to examine cross-platform targeted advertising strategies. The key stakeholders considered in the model include e-commerce platforms, social media platforms, brand owners, and consumers. In addition, this study considers the following two types of user groups: fully and partially overlapping user groups.

The remainder of this paper is organized as follows. Section 2 reviews the literature. Section 3 constructs the game-theoretic model, which consists of one brand owner, one e-commerce platform, one social media platform, and a unit mass of consumers. Section 4 derives the equilibrium outcomes and presents the corresponding analysis. Section 5 discusses the main findings, contributions, and limitations of the study. Section 6 concludes the paper and presents the managerial implications.

2. Literature Review

The literature related to this study falls into the following three main categories: the effectiveness of targeted advertising, targeted advertising incorporating the characteristics of social media platforms, and strategies for targeted advertising delivery.

2.1. The Effectiveness of Targeted Advertising

The main feature of targeted advertising is personalized ad delivery, which entails higher costs for data acquisition and analysis. Studies have found that many factors influence targeted advertising’s effectiveness, including advertising intensity [20], targeting precision [19], and consumers’ privacy concern [23,24,25,26]. Advertising intensity generally refers to the strength of advertising delivery, which can also be understood as the breadth of coverage [27]—that is, the proportion of the target audience exposed to an advertisement at least once within a specific period. Shen [28] found that in competitive online markets, firms must balance advertising intensity and costs, as high-intensity advertising does not necessarily generate higher profits. Targeting precision refers to the degree of match between an advertisement and the target audience’s needs at the time of delivery [19]. It is generally believed that the higher the targeting precision, the more effective the targeted advertising [7]. However, some studies have also found that higher targeting precision does not always improve advertising outcomes [29]. Consumers’ privacy concerns also influence the effectiveness of targeted advertising [30]. When providing data to platforms, consumers will incur privacy concern due to concerns about their own privacy, which is a form of negative utility. Investigating targeted advertising that accounts for consumers’ privacy concern, Shen et al. [31] found that owing to privacy concerns, targeted advertising is not always the optimal choice. Targeted advertising requires tracking, collecting, and analyzing consumer data, and such infringements of consumer privacy generate privacy concerns [32]. Koh et al. [33] analyzed the effect of consumer privacy concern on social welfare, finding that when user data are used for targeted advertising with privacy-sensitive consumers, consumer surplus and the effectiveness of personalized services are both reduced.

2.2. Targeted Advertising Incorporating the Characteristics of Social Media Platforms

Targeted advertising is generally delivered on e-commerce platforms, social media platforms, and other types of content platforms [34,35]. Since different platforms have distinct characteristics, the features of targeted advertising and its effectiveness likewise vary. Regarding targeted advertising on social media platforms, the main mechanism involves leveraging social relationships to enhance advertising’s effectiveness [36,37,38]. Some studies have examined the attributes of social media platforms—such as social login, word of mouth, and herd effects—and their complex influence on targeted advertising delivery. Krämer et al. [39] suggested that while social login can improve targeted advertising precision, it can also intensify competition between platforms. Libai et al. [40] proposed that word of mouth creates value by accelerating the purchase behavior of customers who would have purchased anyway. Campbell [41] noted that on social media platforms, the best advertising targets are not necessarily those with the largest number of friends. Bimpikis et al. [42] suggested that firms’ advertising decisions depend on consumers’ social centrality: the greater the influence range of a given consumer, the more firms are willing to spend on advertising to them. However, as firms increase spending on central consumers, advertising effectiveness might actually diminish. Zhen et al. [43] identified herd effects as an important characteristic of social media platforms. Examining how herd effects and word of mouth influence advertising effectiveness, they found that when word of mouth is strengthened or herd effects are weakened, concealing quality information in advertisements yields the best results.

2.3. Strategies for Targeted Advertising Delivery

Regarding targeted advertising delivery strategies, early studies focused on single-platform targeted advertising. Examining advertising strategies when competing firms target different consumer segments within a market, Iyer et al. [22] found that firms prefer to advertise to consumers with strong product preferences, thereby reducing advertising expenditures. Gal-Or et al. [29] investigated the extent to which firms should allocate resources to improve the quality of delivery. They found that enhancing targeting precision can improve targeting effectiveness, but it also intensifies price competition between firms, thereby reducing profits. In other words, higher targeting precision does not necessarily lead to better outcomes. Considering the interrelationships among advertising audiences, advertising objectives, and advertising displays, Turner [44] constructed an optimization model for targeted advertising delivery and verified through experiments its ability to improve both advertising performance and firms’ profitability.

More recently, studies started to investigate advertising across multiple platforms. Lim et al. [45], for instance, analyzed synergies in digital video advertising across television, mobile television, and the internet. Their experiments showed that compared with advertising on a single platform, delivering advertisements separately across multiple platforms enhanced consumers’ perceptions of information reliability, advertising credibility, and brand owner trustworthiness, while also fostering more positive cognitive responses, thus increasing brand owner recognition and purchase intention. Athey et al. [46] studied the effect of users’ multi-platform use behavior on targeted advertising pricing, finding that as the number of multi-platform users increases, the price of targeted advertising declines. Hoeck et al. [14] investigated whether simultaneously delivering targeted advertising separately across multiple platforms undermines advertising effectiveness. They found that when consumers use multiple devices, advertising effectiveness decreases; however, delivering mobile advertisements for the same product while desktop advertisements are running mitigates this negative effect.

Today, many brand owners simultaneously deliver targeted advertising across multiple online platforms [47]. Yet, such multi-platform advertising delivery does not account for cooperation between platforms and fails to leverage the advantages of inter-platform collaboration. The interactions among advertisements across different platforms are complex: they might reinforce each other, but they might also offset one another, making it necessary to adopt appropriate strategies for multi-platform targeted advertising delivery.

Game theory is widely applied to examine issues related to targeted advertising strategies. Gal-Or et al. [29] developed a game-theoretic model to explore the trade-off between two measures—accuracy and recognition—when studying targeted advertising strategies on television. Sayedi [48] employed a game-theoretic model to investigate the effects of real-time bidding on the strategies and profits of advertisers and publishers in the context of targeted advertising. Zhou et al. [49] applied game theory to analyze the following two scenarios: (1) competing firms simultaneously engaging in both mass advertising and targeted advertising, and (2) only one firm engaging in targeted advertising. The study most closely related to ours is Liu et al. [3], who identified a phenomenon whereby e-commerce platforms deliver targeted advertising through third-party platforms, thereby establishing strategic cooperative relationships between the two parties. They referred to this strategy of leveraging inter-platform collaboration to deliver targeted advertising across multiple platforms as “collaborative cross-platform targeted advertising strategies.” By constructing a game-theoretic model of cooperation between an e-commerce platform and a third-party platform, they found that a moderate level of cross-platform targeting precision is optimal and that a Pareto zone exists in which e-commerce platforms, third-party platforms, and brand owners can all achieve higher payoffs under the cross-platform strategy. However, they did not account for the distinctive characteristics of third-party platforms.

Research on targeted advertising’s effectiveness has mainly focused on the influence of advertising intensity, targeting precision, and privacy concern on advertising outcomes. Some researchers have also recognized that platform characteristics can influence targeted advertising’s effectiveness, with social media platforms in particular relying on social relationships to shape such effectiveness. Existing studies on targeted advertising strategies have largely employed game-theoretic model and focused on single-platform targeted advertising, with relatively few examining cross-platform targeted advertising or considering cooperative relationships between platforms. We further observe that no studies have examined the effect of different platform characteristics on cross-platform targeted advertising strategies. Our study, therefore, examines cross-platform targeted advertising strategies considering the characteristics of social media platforms, as well as optimal strategy selection for e-commerce platforms between single- and cross-platform advertising.

3. Model Description

Game theory provides a theoretical framework for analyzing strategic interactions among multiple stakeholders whose outcomes depend on others’ actions. Based on this framework, game-theoretic models can be constructed to formally describe the participants, strategies, and payoff structures involved in specific economic environments. In the context of cross-platform targeted advertising cooperation between e-commerce platforms and social media platforms, the strategic decisions of participants are interdependent. Therefore, this study constructs a game-theoretic model to analyze their strategic interactions, derive equilibrium outcomes and characterize the cross-platform targeted advertising strategies of e-commerce platforms.

The model is based on the interests of the following four parties: e-commerce platforms, brand owners, social media platforms, and consumers. It incorporates both consumers’ information privacy concerns and the effect of social relationships on social media on targeted advertising, with the objective of maximizing the e-commerce platform’s profits. As shown in Figure 1, the market consists of one brand owner B, one e-commerce platform E, one social media platform S, and a unit mass of consumers.

In the baseline model, we consider only a fully overlapping user group, while in the extension, we consider a partially overlapping user group. In a fully overlapping user group, the users of the e-commerce platform and the social media platform completely coincide, such that all consumers are simultaneously users of both platforms. As shown in Figure 1, the purpose of cross-platform advertising in this case is to convert consumers who did not purchase on the e-commerce platform into purchasers on the social media platform through social sharing and dissemination.

Table 1. Descriptions of parameters and symbols.

Notation	Description
$k$	$k=B,E,S,\mathit{Ca},\mathit{Cb}$: brand owner, e-commerce platform, social media platform, privacy-sensitive and privacy-insensitive consumer
$j$	$j=H,L$: high precision and low precision, respectively
$i$	$i=1,2$: single-platform strategy and cross-platform strategy, respectively
$U_i^k$	Consumer utility
$Q_i^k$	Demand
$h_i^j$	Advertising intensity
$p_i^j$	Product price
${\Delta }^j$	Targeting precision
${\pi }_i^{\mathit{jk}}$	Profit
$\alpha$	Proportion of privacy-sensitive consumers
$\theta$	Commission paid to the e-commerce platform for product sales
$v$	Consumer valuation of the product
$f$	Per unit cost paid for cooperation with the social media platform
$ϵ$	Social utility
$m$	Loyal users of a platform in a partially overlapping user group

lists the relevant parameters.

The e-commerce platform can help brand owners directly deliver single-platform targeted advertising to consumers, or it can cooperate with the social media platform to deliver collaborative cross-platform targeted advertising simultaneously across both platforms. When delivering cross-platform targeted advertising, the e-commerce platform must determine cross-platform targeting precision $\Delta$ and advertising intensity. Cross-platform targeting precision $\Delta$ represents the degree of match between cross-platform targeted advertising and consumer demand, and it also reflects the utility consumers derive from better advertising services. Hereafter, we refer to this simply as “targeting precision.” If cross-platform targeting precision is zero ($\Delta =0$), it corresponds to the case of single-platform targeted advertising in which the e-commerce platform must instead decide on advertising intensity. Cooperation with the social media platform requires the e-commerce platform to pay the social media platform a traffic cost, with f denoting the traffic cost parameter. The e-commerce platform’s revenue comes from commissions θ earned by helping brand owners sell products. When consumers are exposed to cross-platform advertising, they may share and disseminate it on the social media platform and get social utility ϵ. In practice, the social utility may be influenced by advertising intensity and targeting precision. Therefore, ϵ might be partially endogenous to advertising intensity or targeting precision. However, for ease of calculation, we assume ϵ is a positive utility and exogenous. Consumers who are influenced through such dissemination and make a purchase are counted as cases where the e-commerce platform utilizes traffic from the social media platform.

Based on previous research related to game theory, we divide the game discussed in this paper into four stages, as shown in Figure 2. In the first stage, the e-commerce platform decides whether to cooperate with the social media platform and pay traffic cost f to disseminate product advertisements on that platform. If the e-commerce platform chooses not to cooperate, it delivers single-platform targeted advertising [3]. In this case, the e-commerce platform must decide on advertising intensity, and consumers receive a valuation v, where $v~U[0,1]$. In our model, each consumer has a common reservation value for the product, normalized to 1.

If the e-commerce platform chooses to cooperate, it delivers cross-platform targeted advertising. In this case, the e-commerce platform must decide on advertising intensity and targeting precision. Consumers arrive at the e-commerce platform and receive valuation v. In the second stage, if the e-commerce platform delivers cross-platform targeted advertising, then, based on consumers’ search records in the first step, when they log onto the social media platform, the e-commerce platform sends them product advertisements through the social media platform [50]. More precise targeting makes advertising more effective, and consumers receive better advertising services. Accordingly, consumers on the social media platform obtain a valuation of v + ∆. Since the reservation value is normalized to 1 and $v~U[0,1]$, when $v+\Delta >1$, the consumer’s effective valuation is truncated at the reservation value.

Consumers also receive extra social utility ϵ [51]. If the e-commerce platform delivers single-platform targeted advertising, consumers do not receive this additional utility. In the third stage, under single-platform and cross-platform strategies, the brand owner [52] decides on product prices respectively. In the fourth stage, consumers [53] decide whether to purchase the product based on the utility they obtain.

4. Results and Equilibrium Analysis

4.1. E-Commerce Platform Adopts a Single-Platform Targeted Advertising Strategy

Under the single-platform strategy, when consumers purchase the product at price $p_1$ their net utility is $U_1^E=v-p_1$, and so long as $U_1^E>0$, the consumer will purchase one unit of the product. Thus, demand is $Q_1^E=1-p_1$. Otherwise, the consumer leaves the platform without purchasing. Assume that advertising intensity $h_1$ is endogenous and that the brand owner sets $p_1$ to maximize profit [54]. For each product sold, the e-commerce platform charges a commission rate $\theta$, assumed to be an exogenous parameter. The brand owner’s profit is

$${\pi }_1^B=(1-\theta )p_1{Q}_1^E{h}_1$$

(1)

To maximize profit, the brand owner sets $p_1={\displaystyle \frac{1}{2}}$. The e-commerce platform then determines advertising intensity $h_1$ to maximize its own profit. The e-commerce platform’s profit is

$${\pi }_1^E=\theta p_1{Q}_1^E{h}_1-{h_1}^2/2$$

(2)

From this, we obtain $h_1={\displaystyle \frac{\theta }{4}}$. Applying backward induction [55], the following equilibrium results are derived: ${\pi }_1^E={\displaystyle \frac{{\theta }^2}{32}}$ and ${\pi }_1^B={\displaystyle \frac{(1-\theta )\theta }{16}}$.

Lemma 1.

When the e-commerce platform adopts the single-platform targeted advertising strategy, consumer demand for the product on the platform is  $Q_1^E={\displaystyle \frac{1}{2}}$, the brand owner’s equilibrium price is $p_1={\displaystyle \frac{1}{2}}$, and its profit is ${\pi }_1^B={\displaystyle \frac{(1-\theta )\theta }{16}}$. The e-commerce platform’s optimal advertising intensity is $h_1={\displaystyle \frac{\theta }{4}}$, with profit ${\pi }_1^E={\displaystyle \frac{{\theta }^2}{32}}$. At this point, the social media platform does not cooperate with the e-commerce platform, and its profit is ${\pi }_1^S=0$.

Lemma 1 shows that when the e-commerce platform adopts a single-platform targeted advertising strategy, the profits of both the brand owner and the e-commerce platform depend only on the commission rate θ paid by the brand owner for product sales. The e-commerce platform’s optimal advertising intensity increases with θ since a higher commission rate makes advertising more profitable and strengthens the platform’s incentive to advertise on behalf of the brand owner. The brand owner’s optimal price is ${\displaystyle \frac{1}{2}}$, and consumer demand is ${\displaystyle \frac{1}{2}}$; single-platform targeted advertising allows the brand owner to retain only half of the consumers.

4.2. E-Commerce Platform Adopts a Cross-Platform Targeted Advertising Strategy

If the e-commerce platform adopts a cross-platform strategy, then after consumers purchase the product at price $p_2$, their net utility is $U_2^E=v-p_2$. As long as $U_2^E>0$, the consumer will purchase; that is, $Q_2^E=1-p_2$. Consumers with $v>p_2$ have already purchased, leaving those whose utility is negative. At this point, consumers who did not purchase on the e-commerce platform receive product advertisements on the social media platform and obtain utility Δ from the better advertising service.

However, higher-quality advertising services typically entail greater privacy intrusions, causing privacy-sensitive consumers to incur privacy costs. When consumers visit an e-commerce platform and subsequently receive the same advertisement on a social media platform, they may perceive this as a violation of their privacy and thus incur a privacy cost. Consumers who view the advertisement only on the e-commerce platform incur no privacy cost. Since higher targeting precision leads to greater privacy costs, while zero accuracy results in no privacy cost, the privacy cost is specified as a quadratic function for analytical tractability. The privacy cost is denoted by ${\Delta }^2$. This quadratic specification reflects the commonly adopted assumption that privacy costs increase at an increasing rate as targeting precision rises.

Let α denote the proportion of privacy-sensitive consumers, while the proportion of privacy-insensitive consumers is given by 1 − α. Because α represents a population proportion, it is restricted to the interval α ∈ (0, 1), and the analysis focuses on the economically meaningful parameter domain in which interior solutions exist.

Both types of consumers decide whether to purchase from the e-commerce platform via the social media platform, and both also obtain additional social utility ϵ. Therefore, the net utility obtained via the social media platform by privacy-sensitive consumers is $U_2^{\mathit{Ca}}=v+\Delta -p_2+ϵ-{\Delta }^2$, and the net utility for privacy-insensitive consumers is $U_2^{\mathit{Cb}}=v+\Delta -p_2+ϵ$. Consumers with $0<v<p_2$ will purchase when $U_2^{\mathit{Ca}}>0$ and $U_2^{\mathit{Cb}}>0$. The corresponding product demands are

$$Q_2^E=1-p_2$$

(3)

$$Q_2^{\mathit{Ca}}=(ϵ+\Delta -{\Delta }^2)\alpha$$

(4)

$$Q_2^{\mathit{Cb}}=(ϵ+\Delta )(1-\alpha )$$

(5)

Solving via backward induction [56], if $ϵ+\Delta -{\Delta }^2>0$—that is, under low precision ($0<\Delta <{\displaystyle \frac{1+\sqrt{1+4ϵ}}{2}}$)—then the social media platform will deliver advertisements to both privacy-sensitive and privacy-insensitive consumers. If $ϵ+\Delta -{\Delta }^2\le 0$—that is, under high precision ($\Delta \ge {\displaystyle \frac{1+\sqrt{1+4ϵ}}{2}}$)—then $Q_2^{\mathit{Ca}}=0$, and the social media platform no longer delivers advertisements to privacy-sensitive consumers. The brand owner’s profit can be written as follows:

$${\pi }_2^{\mathit{LB}}=(1-\theta )p_2^L(Q_2^E+Q_2^{\mathit{Ca}}+Q_2^{\mathit{Cb}})h_2^L,0<\Delta <{\displaystyle \frac{1+\sqrt{1+4ϵ}}{2}}$$

(6a)

$${\pi }_2^{\mathit{HB}}=(1-\theta )p_2^H(Q_2^E+Q_2^{\mathit{Cb}})h_2^H,\Delta \ge {\displaystyle \frac{1+\sqrt{1+4ϵ}}{2}}$$

(6b)

Maximizing ${\pi }_2^B$ [57] yields the brand owner’s equilibrium price:

$$p_2^L={\displaystyle \frac{1}{2}}(1+{\displaystyle \frac{\Delta }{2}}+ϵ)$$

(7a)

$$p_2^H={\displaystyle \frac{1}{2}}(1+(\Delta +ϵ)(1-\alpha ))$$

(7b)

In addition, based on cooperation between the e-commerce platform and social media platform, the social media platform’s profit is

$${\pi }_2^{\mathit{LS}}=f(Q_2^{\mathit{Ca}}+Q_2^{Cb})h_2^L$$

(8a)

$${\pi }_2^{HS}=f\left(Q_2^{Cb}\right)h_2^H$$

(8b)

Given price, the e-commerce platform chooses targeting precision $\Delta$ to maximize profit; the e-commerce platform’s profit is

$${\pi }_2^{LE}=\theta p_2^L(Q_2^E+Q_2^{\mathit{Ca}}+Q_2^{\mathit{Cb}})h_2^L-{h_2^L}^2/2-f(Q_2^{\mathit{Ca}}+Q_2^{Cb})h_2^L$$

(9a)

$${\pi }_2^{HE}=\theta p_2^H(Q_2^E+Q_2^{\mathit{Cb}})h_2^H-{h_2^H}^2/2-f\left(Q_2^{Cb}\right)h_2^H$$

(9b)

When $0<\Delta <{\displaystyle \frac{1+\sqrt{1+4ϵ}}{2}}$, the solution is ${\Delta }^L={\displaystyle \frac{1}{2\alpha }}$. When $\Delta \ge {\displaystyle \frac{1+\sqrt{1+4ϵ}}{2}}$, the solution is ${\Delta }^H={\displaystyle \frac{2\frac{f}{\theta }-1}{1-\alpha }}-ϵ$. Finally, the e-commerce platform’s advertising intensity is obtained.

Substituting the equilibrium price, targeting precision, and advertising intensity into (6a), (6b), (8a), (8b), (9a), and (9b), we obtain the equilibrium profits of the brand owner, e-commerce platform, and social media platform. Proposition 1 summarizes the equilibrium outcomes.

We restrict the parameter space to ensure that the equilibrium solutions exist and remain non-negative. All parameters are assumed to lie in ranges that ensure economically meaningful interior solutions.

Proposition 1.

When the e-commerce platform adopts a cross-platform targeted advertising strategy, equilibrium solutions exist in the following two cases.

a. 

If  $0<\Delta <{\displaystyle \frac{1+\sqrt{1+4ϵ}}{2}}$, the e-commerce platform’s equilibrium targeting precision ${\Delta }^L$, equilibrium advertising intensity $h_2^L$, and equilibrium profit ${\pi }_2^{LE}$; the brand owner’s equilibrium price $p_2^L$ and equilibrium profit ${\pi }_2^{LB}$; and the social media platform’s equilibrium profit ${\pi }_2^{LS}$ are as shown in

Table 2. Equilibrium results for low- precision ($0<\Delta <{\displaystyle \frac{1+\sqrt{1+4\mathit{ϵ}}}{2}}$) and high-precision ($\Delta \ge {\displaystyle \frac{1+\sqrt{1+4\mathit{ϵ}}}{2}}$) cross-platform targeted advertising strategies in a fully overlapping user group.

$0<\Delta <\frac{1+\sqrt{1+4\mathit{ϵ}}}{2}$		$\Delta \ge \frac{1+\sqrt{1+4\mathit{ϵ}}}{2}$
${\Delta }^L$	${\displaystyle \frac{1}{2\alpha }}$	${\Delta }^H$	${\displaystyle \frac{2\frac{f}{\theta }-1}{1-\alpha }}-ϵ$
$p_2^L$	${\displaystyle \frac{1}{2}}+{\displaystyle \frac{1}{8\alpha }}+{\displaystyle \frac{ϵ}{2}}$	$p_2^H$	${\displaystyle \frac{f}{\theta }}$
$h_2^L$	${\displaystyle \frac{{(1+4\alpha (1+ϵ\left)\right)}^2\theta -16f\alpha (1+4\alpha ϵ)}{64{\alpha }^2}}$	$h_2^H$	$-{\displaystyle \frac{f(f-\theta )}{\theta }}$
${\pi }_2^{LE}$	${\displaystyle \frac{{({(1+4\alpha (1+ϵ\left)\right)}^2\theta -16f\alpha (1+4\alpha ϵ\left)\right)}^2}{8192{\alpha }^4}}$	${\pi }_2^{\mathit{HE}}$	${\displaystyle \frac{f^2{(f-\theta )}^2}{2{\theta }^2}}$
${\pi }_2^{LB}$	${\displaystyle \frac{{(1+4\alpha (1+ϵ\left)\right)}^2(1-\theta \left)\right({(1+4\alpha (1+ϵ\left)\right)}^2\theta -16f\alpha (1+4\alpha ϵ\left)\right)}{4096{\alpha }^4}}$	${\pi }_2^{\mathit{HB}}$	$-{\displaystyle \frac{f^3(f-\theta )(1-\theta )}{{\theta }^3}}$
${\pi }_2^{LS}$	${\displaystyle \frac{f(1+4\alpha ϵ)({(1+4\alpha (1+ϵ\left)\right)}^2\theta -16f\alpha (1+4\alpha ϵ\left)\right)}{256{\alpha }^3}}$	${\pi }_2^{\mathit{HS}}$	$-{\displaystyle \frac{f^2(f-\theta \left)\right(2f-\theta )}{{\theta }^2}}$

. For any $\alpha \in ({\displaystyle \frac{1}{1+\sqrt{1+4ϵ}}},1)$, ${\displaystyle \frac{f}{\theta }}\in (0,1)$, $ϵ\in ({\displaystyle \frac{7-\sqrt{17}}{8}},{\displaystyle \frac{3}{4}})$ or ${\displaystyle \frac{f}{\theta }}\in (0,{\displaystyle \frac{1}{2}}+{\displaystyle \frac{1+4ϵ+\sqrt{1+4ϵ}}{16}}+{\displaystyle \frac{1}{1+4ϵ+\sqrt{1+4ϵ}}})$, $ϵ\in (0,{\displaystyle \frac{7-\sqrt{17}}{8}})$ or ${\displaystyle \frac{f}{\theta }}\in (0,{\displaystyle \frac{1}{2}}+{\displaystyle \frac{1+4ϵ}{16}}+{\displaystyle \frac{1}{1+4ϵ}})$, $ϵ\in ({\displaystyle \frac{3}{4}},\infty )$, equilibrium solutions exist and remain non-negative.

b. 

If  $\Delta \ge {\displaystyle \frac{1+\sqrt{1+4ϵ}}{2}}$, the e-commerce platform’s equilibrium targeting precision ${\Delta }^H$, equilibrium advertising intensity $h_2^H$, and equilibrium profit ${\pi }_2^{\mathit{HE}}$; the brand owner’s equilibrium price $p_2^H$ and equilibrium profit ${\pi }_2^{\mathit{HB}}$; and the social media platform’s equilibrium profit ${\pi }_2^{\mathit{HS}}$ are as shown in Table 2. For any  $\alpha \in ({\displaystyle \frac{1}{1+\sqrt{1+4ϵ}}},1)$, ${\displaystyle \frac{f}{\theta }}\in ({\displaystyle \frac{1}{2}}+{\displaystyle \frac{1+4ϵ+\sqrt{1+4ϵ}}{8}},1)$, and $ϵ\in (0,{\displaystyle \frac{7-\sqrt{17}}{8}})$, equilibrium solutions exist and remain non-negative.

Proposition 1 indicates that, when social media platform characteristics are taken into account, cross-platform targeted advertising admits equilibrium solutions in both the low- and high-precision ranges; the factors that chiefly affect equilibria include the social utility provided by the social media platform ϵ, the ratio of per unit traffic payment to per unit commission ${\displaystyle \frac{f}{\theta }}$, and the proportion of privacy-sensitive consumers α. When $0<\Delta <{\displaystyle \frac{1+\sqrt{1+4ϵ}}{2}}$, as the proportion α of privacy-sensitive consumers increases, the equilibrium targeting precision of cross-platform advertising decreases; in this range, equilibrium precision is independent of ϵ. When $\Delta \ge {\displaystyle \frac{1+\sqrt{1+4ϵ}}{2}}$, as α increases, equilibrium precision rises. According to the model, at this point, the e-commerce platform abandons the privacy-sensitive group; thus, the larger that the group is, the more the platform increases precision to serve the remaining consumers. In addition, the precision decision is related to the ratio of the per unit traffic payment f to the per unit commission $\theta$. That is, ${\displaystyle \frac{f}{\theta }}$. ${\displaystyle \frac{f}{\theta }}$ represents the e-commerce platform’s profitability: As ${\displaystyle \frac{f}{\theta }}$ rises, equilibrium precision rises. An increase in ${\displaystyle \frac{f}{\theta }}$ means higher costs and a smaller commission share—that is, lower profitability; thus, the platform increases precision. Finally, as the social utility ϵ provided by the social media platform increases, equilibrium precision decreases. In addition, Proposition 1 shows that when $\alpha \in ({\displaystyle \frac{1}{1+\sqrt{1+4ϵ}}},1)$, ${\displaystyle \frac{f}{\theta }}\in ({\displaystyle \frac{1}{2}}+{\displaystyle \frac{1+4ϵ+\sqrt{1+4ϵ}}{8}},1)$, and $ϵ\in (0,{\displaystyle \frac{7-\sqrt{17}}{8}})$, equilibrium solutions exist in both the low- and high-precision ranges. According to Table 2, $p_2^H>p_1$, $p_2^L>p_1$, $h_2^H<h_1$, and $h_2^L<h_1$.

When $\alpha \in ({\displaystyle \frac{1}{1+\sqrt{1+4ϵ}}},1)$, ${\displaystyle \frac{f}{\theta }}\in ({\displaystyle \frac{1}{2}}+{\displaystyle \frac{1+4ϵ+\sqrt{1+4ϵ}}{8}},1)$, and $ϵ\in (0,{\displaystyle \frac{7-\sqrt{17}}{8}})$, we have $p_2^H>p_2^L,h_2^H<h_2^L$. Compared with the single-platform strategy, the equilibrium price is higher under the cross-platform strategy. Compared with the low-precision cross-platform strategy, the equilibrium price is higher under the high-precision cross-platform strategy. Higher precision triggers consumers’ privacy concerns and raises their privacy concern. In that case, the e-commerce platform abandons privacy-sensitive consumers and instead provides better service to privacy-insensitive consumers; thus, the brand owner can raise the price. Moreover, since part of the consumer market is lost, the brand owner needs to raise prices to maintain profits. Relative to advertising intensity under the cross-platform strategy, advertising intensity is higher under the single-platform strategy. Relative to the high-precision cross-platform strategy, advertising intensity is higher under the low-precision cross-platform strategy. The lower the precision, the less effectively the consumers are identified. Consequently, the advertising service performs poorly, consumers’ utility is low, and the e-commerce platform ultimately chooses to deliver advertisements to a larger number of consumers.

4.3. Numerical Simulation

Given that the structure of equilibrium profits is relatively complex, it is difficult to directly observe how profits vary with changes in model parameters. Therefore, numerical simulations are conducted for the cross-platform targeted advertising strategy. The numerical experiment is conducted using parameter values drawn from the literature [3,31,58]. Figure 3 and Figure 4 illustrate how profits vary with the proportion of privacy-sensitive consumers (α), the platform cooperation cost (f), and targeting precision (Δ) under low- and high-precision cross-platform targeted advertising strategies.

As shown in Figure 3, an increase in the proportion of privacy-sensitive consumers (α) reduces the profits of the e-commerce platform, the brand owner, and the social media platform. Higher targeting precision (Δ) increases the profits of all three stakeholders. In contrast, as the platform cooperation cost (f) rises, profits for the e-commerce platform and the brand owner decrease, whereas the social media platform’s profit first increases and then decreases.

Figure 4 illustrates that as the proportion of privacy-sensitive consumers (α) increases, profits for the e-commerce platform, brand owner, and social media platform all decline. Increasing targeting precision (Δ) leads to higher profits for all three stakeholders. When the platform cooperation cost (f) rises, profits for e-commerce platform and brand owner decrease, whereas social media platform profit initially increases but subsequently decreases. The changes in profits under high-precision cross-platform targeted advertising are largely consistent with those under low-precision targeted advertising. It is worth noting that higher cooperation cost will inevitably have negative effects on e-commerce platform and brand owner. For social media platform, profit will rise in the short term with increasing f; however, in the long term, by adversely impacting the other two parties, the social media platform’s profit is ultimately reduced.

4.4. Comparing Single- and Cross-Platform Strategies

When the e-commerce platform sets high precision, consumers receive better advertising services and enjoy higher utility. More effective advertising brings higher conversion rates and sales. However, if precision is too high, consumers’ privacy concern also rises, which may lead the e-commerce platform to abandon privacy-sensitive consumers and thus lose part of the market. If the e-commerce platform chooses low precision, consumers’ utility is not high, but privacy concerns are lower, which may instead increase the number of consumers. Yet, it might also cause advertising waste and even perform worse than single-platform targeting, ultimately harming the platform’s profit. Therefore, when deciding whether to use cross-platform targeted advertising, the e-commerce platform needs to consider multiple factors. This subsection compares the profits of the e-commerce platform, the social media platform, and the brand owner under different equilibrium solutions.

Proposition 2.

Compared with the single-platform strategy, when  $\alpha \in ({\displaystyle \frac{1}{1+\sqrt{1+4ϵ}}},1),{\displaystyle \frac{f}{\theta }}\in (0,{\displaystyle \frac{9}{16}}+{\displaystyle \frac{ϵ}{4}}),ϵ\in (0,\infty )$, it always holds that ${\pi }_2^{LE}>{\pi }_1^E$. When $\alpha \in ({\displaystyle \frac{1}{1+\sqrt{1+4ϵ}}},1),{\displaystyle \frac{f}{\theta }}\in ({\displaystyle \frac{1}{2}}+{\displaystyle \frac{1+\sqrt{1+4ϵ}}{16}}+{\displaystyle \frac{ϵ}{4}},1),ϵ\in (0,{\displaystyle \frac{{(\sqrt[3]{16})}^2-1}{4}})$, it always holds that ${\pi }_2^{LE}<{\pi }_1^E$. When $\alpha \in ({\displaystyle \frac{1}{1+\sqrt{1+4ϵ}}},1),{\displaystyle \frac{f}{\theta }}\in ({\displaystyle \frac{1}{2}}+{\displaystyle \frac{1+4ϵ+\sqrt{1+4ϵ}}{8}},1),ϵ\in (0,{\displaystyle \frac{7-\sqrt{17}}{8}})$, it always holds that ${\pi }_2^{HE}<{\pi }_1^E$. Within the cross-platform strategy itself, when $\alpha \in ({\displaystyle \frac{1}{1+\sqrt{1+4ϵ}}},1),{\displaystyle \frac{f}{\theta }}\in ({\displaystyle \frac{1}{2}}+{\displaystyle \frac{1+4ϵ+\sqrt{1+4ϵ}}{8}},1),ϵ\in (0,{\displaystyle \frac{7-\sqrt{17}}{8}})$, it always holds that ${\pi }_2^{LE}>{\pi }_2^{HE}$.

Proposition 2 shows that, relative to the single-platform strategy, under a low-precision cross-platform strategy, the e-commerce platform’s profit can exceed that under the single-platform strategy under certain conditions. Under a high-precision cross-platform strategy, the e-commerce platform’s profit is always lower than under the single-platform strategy. Comparing cross-platform strategies, the e-commerce platform’s profit under low precision is always higher than under high precision.

Considering the e-commerce platform’s profit alone, higher precision does not necessarily yield better advertising performance or higher profit. Under certain conditions, single-platform profit may exceed that under low-precision cross-platform strategies, or it may be lower. Indeed, both the low-precision cross-platform strategy and the single-platform strategy can outperform the high-precision cross-platform strategy. Therefore, from the e-commerce platform’s standpoint, overly high-precision cross-platform targeting performs worse.

Proposition 3.

When  $\alpha \in ({\displaystyle \frac{1}{1+\sqrt{1+4ϵ}}},1),{\displaystyle \frac{f}{\theta }}\in (0,{\displaystyle \frac{9}{16}}+{\displaystyle \frac{ϵ}{4}}),ϵ\in (0,\infty )$, we have ${\pi }_2^{LE}>{\pi }_1^E$; compared with the single-platform strategy, the low-precision cross-platform strategy is superior. When $\alpha \in ({\displaystyle \frac{1}{1+\sqrt{1+4ϵ}}},1),{\displaystyle \frac{f}{\theta }}\in ({\displaystyle \frac{1}{2}}+{\displaystyle \frac{1+4ϵ+\sqrt{1+4ϵ}}{8}},1),ϵ\in (0,{\displaystyle \frac{7-\sqrt{17}}{8}})$, we have ${\pi }_2^{HE}<{\pi }_2^{LE}<{\pi }_1^E$; compared with cross-platform strategies, the single-platform strategy is superior.

Proposition 3 states that a cross-platform strategy is not always better for the e-commerce platform than a single-platform strategy. Since cross-platform cooperation requires paying cooperation costs to the social media platform, if the gains from cooperation do not cover those costs, the e-commerce platform will choose not to cooperate and will deliver single-platform advertising. Between low-precision and high-precision cross-platform strategies, low precision is better, because high precision may cause the platform to abandon privacy-sensitive consumers and thereby lose a portion of demand. When making decisions, the e-commerce platform should consider its own profitability ${\displaystyle \frac{f}{\theta }}$ and the social utility ϵ offered by the social media platform. This also indicates that targeting precision is not necessarily “the higher, the better”; in some cases, relatively coarse targeting performs better.

Proposition 4.

For the social media platform, ${\pi }_2^{LS}>{\pi }_1^S$ and ${\pi }_2^{HS}>{\pi }_1^S$. For the brand owner, when $\alpha \in ({\displaystyle \frac{1}{1+\sqrt{1+4ϵ}}},1)$, ${\displaystyle \frac{f}{\theta }}\in (0,1)$, $ϵ\in (0,\infty )$, it always holds that ${\pi }_2^{LB}>{\pi }_1^B$. When $\alpha \in ({\displaystyle \frac{1}{1+\sqrt{1+4ϵ}}},1)$, ${\displaystyle \frac{f}{\theta }}\in ({\displaystyle \frac{1}{2}}+{\displaystyle \frac{1+4ϵ+\sqrt{1+4ϵ}}{8}},{\displaystyle \frac{4+{(1216-192\sqrt{33})}^{1/3}+4{(19+3\sqrt{33})}^{1/3}}{24}})$, $ϵ\in (0,{\displaystyle \frac{-19+8{(19-3\sqrt{33})}^{1/3}+8{(19+3\sqrt{33})}^{1/3}}{24}}-{\displaystyle \frac{\sqrt{-599+48{(19-3\sqrt{33})}^{1/3}+48{(19+3\sqrt{33})}^{1/3}+128{((19-3\sqrt{33})(19+3\sqrt{33}))}^{1/3}}}{24}})$, it always holds that ${\pi }_2^{\mathit{HB}}>{\pi }_1^B$.

Proposition 4 indicates that under cross-platform strategies, the social media platform always earns positive profits. For the social media platform, there is incentive to cooperate with the e-commerce platform to obtain cooperation fees and increase profit. Hence, cross-platform strategies are always beneficial for the social media platform. Under low-precision cross-platform strategies, the brand owner’s profit is always higher than under the single-platform strategy. Under certain conditions, the brand owner’s profit under a high-precision cross-platform strategy exceeds that under the single-platform strategy. For the brand owner, a low-precision cross-platform strategy is safer, better ensuring profit than is the case under a single-platform strategy. Meanwhile, a high-precision cross-platform strategy requires taking into account the e-commerce platform’s profitability ${\displaystyle \frac{f}{\theta }}$ and the social utility ϵ provided by the social media platform. Only when the platform’s profitability is relatively high and social utility is relatively low does the brand owner’s profit under high-precision cross-platform targeting exceed that under the single-platform strategy.

Proposition 5.

Under the low-precision cross-platform strategy, a Pareto zone exists. When  $\alpha \in ({\displaystyle \frac{1}{1+\sqrt{1+4ϵ}}},1)$, ${\displaystyle \frac{f}{\theta }}\in (0,{\displaystyle \frac{9}{16}}+{\displaystyle \frac{ϵ}{4}})$, and $ϵ\in (0,\infty )$, the e-commerce platform can choose between the low-precision cross-platform strategy and the single-platform strategy, and we have ${\pi }_2^{LE}>{\pi }_1^E,{\pi }_2^{LB}>{\pi }_1^B,{\pi }_2^{LS}>{\pi }_1^S$. Under the low-precision cross-platform strategy, a three-party optimum is achieved.

Proposition 5 shows that cross-platform strategies can generate a three-party optimum for the e-commerce platform, the social media platform, and the brand owner. When the e-commerce platform can choose only between the low-precision cross-platform strategy and the single-platform strategy, it may select the low-precision cross-platform strategy. In this case, the profits of the e-commerce platform, the brand owner, and the social media platform under low-precision cross-platform targeting all exceed their profits under the single-platform strategy. When $\alpha \in ({\displaystyle \frac{1}{1+\sqrt{1+4ϵ}}},1)$, ${\displaystyle \frac{f}{\theta }}\in ({\displaystyle \frac{1}{2}}+{\displaystyle \frac{1+4ϵ+\sqrt{1+4ϵ}}{8}},1)$, and $ϵ\in (0,{\displaystyle \frac{7-\sqrt{17}}{8}})$, the e-commerce platform can choose from among three strategies, and ${\pi }_2^{HE}<{\pi }_2^{LE}<{\pi }_1^E$ holds. For the e-commerce platform the single-platform strategy is superior, though not for the brand owner or the social media platform. To achieve the three-party optimum, the e-commerce platform should focus on its own profitability ${\displaystyle \frac{f}{\theta }}$ when making decisions. As long as ${\displaystyle \frac{f}{\theta }}$ lies within an appropriate range, a three-party optimum can be achieved under the low-precision cross-platform strategy.

4.5. Comparing Fully and Partially Overlapping User Groups

In the preceding sections, we examined cross-platform advertising by e-commerce platforms in a fully overlapping user group. Here, we extend the model and consider a partially overlapping user group. The analysis shows that under this extension, the main conclusions drawn from the baseline model continue to hold.

In the real world, platforms may have their own loyal users. In a partially overlapping user group, some consumers are users of only the e-commerce platform or only the social media platform, while some are users of both (Figure 5). In this case, cross-platform targeted advertising enables social-media-only users to see the advertisement and make a purchase. We assume the shares of loyal users of the e-commerce platform and the social media platform are both m and the share of dual-platform users is 1 − 2m. In practice, platforms may differ in terms of market size and the proportion of loyal users. A platform with a larger loyal user base may possess stronger bargaining power in cross-platform cooperation and capture a greater share of the resulting benefits. However, for analytical tractability, the model assumes that the e-commerce platform and the social media platform have identical shares of loyal users. The e-commerce platform first decides whether to cooperate with the social media platform. If it does not cooperate, it chooses the single-platform strategy. In that case, single-platform targeted advertising covers both dual-platform users and e-commerce-only users.

The resulting equilibrium under the single-platform strategy is $p_1={\displaystyle \frac{1}{2}}$ for the brand owner’s price and ${\pi }_1^B={\displaystyle \frac{{(1-m)}^2(1-\theta )\theta }{16}}$ for its profit. The e-commerce platform’s optimal advertising intensity is $h_1={\displaystyle \frac{(1-m)\theta }{4}}$, with profit ${\pi }_1^E={\displaystyle \frac{{(1-m)}^2{\theta }^2}{32}}$. Under the cross-platform strategy, consumers in all three categories see the advertisement with certain probabilities, but the e-commerce platform’s loyal users do not see advertisements on the social media platform because they do not use it.

Table 3. Equilibrium results for low-precision ($0<\Delta <{\displaystyle \frac{1+\sqrt{1+4\mathit{ϵ}}}{2}}$) and high-precision ($\Delta \ge {\displaystyle \frac{1+\sqrt{1+4\mathit{ϵ}}}{2}}$) cross-platform targeted advertising strategies in a partially overlapping user group.

$0<\Delta <\frac{1+\sqrt{1+4\mathit{ϵ}}}{2}$		$\Delta \ge \frac{1+\sqrt{1+4\mathit{ϵ}}}{2}$
${\Delta }^L$	${\displaystyle \frac{1}{2\alpha }}$	${\Delta }^H$	${\displaystyle \frac{2\frac{f}{\theta }-1}{(1-m\left)\right(1-\alpha )}}-ϵ$
$p_2^L$	${\displaystyle \frac{1}{2}}+{\displaystyle \frac{1-m}{8\alpha }}+{\displaystyle \frac{(1-m)ϵ}{2}}$	$p_2^H$	${\displaystyle \frac{f}{\theta }}$
$h_2^L$	${\displaystyle \frac{{(1+4\alpha (1+ϵ)-m(1+4\alpha ϵ\left)\right)}^2\theta -16f\alpha (1-m\left)\right(1+4\alpha ϵ)}{64{\alpha }^2}}$	$h_2^H$	$-{\displaystyle \frac{f(f-\theta )}{\theta }}$
${\pi }_2^{LE}$	${\displaystyle \frac{{({(1+4\alpha (1+ϵ)-m(1+4\alpha ϵ\left)\right)}^2\theta -16f\alpha (1-m\left)\right(1+4\alpha ϵ\left)\right)}^2}{8192{\alpha }^4}}$	${\pi }_2^{\mathit{HE}}$	${\displaystyle \frac{f^2{(f-\theta )}^2}{2{\theta }^2}}$
${\pi }_2^{LB}$	${\displaystyle \frac{{(1+4\alpha (1+ϵ)-m(1+4\alpha ϵ\left)\right)}^2(1-\theta \left)\right({(1+4\alpha (1+ϵ)-m(1+4\alpha ϵ\left)\right)}^2\theta -16f\alpha (1-m\left)\right(1+4\alpha ϵ\left)\right)}{4096{\alpha }^4}}$	${\pi }_2^{\mathit{HB}}$	$-{\displaystyle \frac{f^3(f-\theta )(1-\theta )}{{\theta }^3}}$
${\pi }_2^{LS}$	${\displaystyle \frac{f(1-m\left)\right(1+4\alpha ϵ\left)\right({(1+4\alpha (1+ϵ)-m(1+4\alpha ϵ\left)\right)}^2\theta -16f\alpha (1-m\left)\right(1+4\alpha ϵ\left)\right)}{256{\alpha }^3}}$	${\pi }_2^{HS}$	$-{\displaystyle \frac{f^2(f-\theta )(2f-\theta )}{{\theta }^2}}$

reports the equilibrium results.

Using the method presented in Section 4, we obtain the brand owner’s equilibrium price and profit; the e-commerce platform’s equilibrium advertising intensity, equilibrium targeting precision, and equilibrium profit; and the social media platform’s equilibrium profit.

Proposition 6.

Similar to the fully overlapping user group, in the partially overlapping user group, a cross-platform strategy is superior to a single-platform strategy only under certain conditions, and a Pareto optimum exists. When  $\alpha \in ({\displaystyle \frac{1}{1+\sqrt{1+4ϵ}}},1)$, $m\in (0,{\displaystyle \frac{1}{2}})$, ${\displaystyle \frac{f}{\theta }}\in (0,{\displaystyle \frac{17}{32}}+{\displaystyle \frac{ϵ}{8}})$, $ϵ\in (0,{\displaystyle \frac{7-\sqrt{17}}{8}})\cup ({\displaystyle \frac{4\sqrt{2}-1}{4}}-{\displaystyle \frac{\sqrt{1+8\sqrt{2}}}{8}},{\displaystyle \frac{4\sqrt{2}-1}{4}})\cup ({\displaystyle \frac{7}{4}},\infty )$, we have ${\pi }_2^{LE}>{\pi }_1^E,{\pi }_2^{LB}>{\pi }_1^B,{\pi }_2^{LS}>{\pi }_1^S$. Under the low-precision cross-platform strategy, a three-party optimum can be achieved.

Proposition 6 shows that in the partially overlapping user group, a low-precision cross-platform strategy can still deliver a three-party optimum for the e-commerce platform, the social media platform, and the brand owner. We find that in a partially overlapping user group, the equilibrium cases are the same as in a fully overlapping user group. Cross-platform targeted advertising strategies also exhibit different equilibrium outcomes at different precision levels. In addition, changes in product price and advertising intensity are identical to those in the fully overlapping user group. Changes in targeting precision are similar, with one difference: under the high-precision cross-platform strategy, as loyal consumers decrease, targeting precision declines. Comparing the equilibrium results, we find that the single-platform and cross-platform strategies in the partially overlapping user group are essentially consistent with those in the main model.

In partially overlapping user group, the e-commerce platform’s decision is jointly determined by the proportion of privacy-sensitive consumers, the shares of loyal users, the e-commerce platform’s profitability and the social utility provided by the social media platform. By contrast, under the single-platform targeted advertising strategy, the e-commerce platform’s decision only depends on its commission rate and the shares of loyal users.

Different from fully overlapping user group, in partially overlapping user group, the e-commerce platform should consider the shares of loyal users. Only when the proportion of privacy-sensitive consumers, the shares of loyal users, the e-commerce platform’s profitability and the social utility all lie within certain ranges can generate a win–win–win outcome for e-commerce platforms, social media platforms, and brand owners.

5. Discussion

For cooperation between e-commerce and social media platforms, this study constructs a game-theoretic model to study e-commerce platforms’ choice of targeted advertising strategies. The main findings are as follows.

(1)

The social utility of social media platforms is a key factor in implementing cross-platform targeted advertising. Cross-platform targeted advertising strategies exhibit different equilibrium outcomes at different precision levels. In fully overlapping user group, these are jointly determined by the proportion of privacy-sensitive consumers, the e-commerce platform’s profitability and the social utility provided by the social media platform. By contrast, under the single-platform targeted advertising strategy, the e-commerce platform’s decision depends solely on its commission rate. In partially overlapping user group, equilibrium outcomes are also determined by the shares of loyal users.

(2)

Cross-platform targeted advertising is not always the optimal choice for e-commerce platforms. Whether in fully or partially overlapping user group, if the gains from cooperation can offset cooperation costs, the e-commerce platform will choose a low precision cross-platform strategy; otherwise, a single-platform strategy is preferable. In terms of the e-commerce platform’s profit alone, higher precision does not necessarily deliver better advertising performance or higher profit.

(3)

Low-precision cross-platform strategy achieves three-party optimum in fully and partially overlapping user groups. Although targeting is relatively coarse under low precision, the consumer base is larger, privacy intrusions are fewer, and consumers receive the social utility of the social media platform. As a result, relatively high sales can be achieved. Therefore, the e-commerce platform can maintain relatively high profits while facilitating synergistic gains for both the brand owner and the social media platform.

Based on these findings, managerial implications are listed below.

(1)

E-commerce platforms should prudently use social media platforms instead of relying excessively on their traffic. In the long run, increasing traffic dependence may reshape the balance of power between e-commerce platforms and social media platforms, which could influence the stability of cooperative advertising arrangements. In practice, increasing reliance on external traffic sources may gradually strengthen the bargaining power of social media platforms. As e-commerce platforms become more dependent on third-party traffic, social media platforms may gain greater leverage in advertising cooperation. This dynamic dependence could affect the long-term sustainability of the three-party optimal outcome identified in this study. E-commerce platforms can reduce their dependence on external channels by developing proprietary communities, membership programs, and customer repurchase mechanisms. Membership programs and repurchase mechanisms may help mitigate privacy-related attrition risks associated with cross-platform data sharing. Taking JD.com as an example, after ending its partnership with WeChat, the platform may strengthen its connection with members to enhance user loyalty and reduce reliance on external traffic sources. By strengthening user loyalty, these mechanisms encourage consumers to maintain long-term relationships with the platform even when privacy concerns arise. As a result, they can help e-commerce platforms stabilize their user base and reduce the potential negative effects of privacy concerns on user retention.

(2)

E-commerce platforms should not regard cross-platform cooperation as the default option but as a differentiated, situation-specific decision. Consider the case of the partnership between JD.com and WeChat, which has experienced both the establishment and dissolution of its cooperation [59]. On one hand, cooperation allows JD.com to obtain user traffic from WeChat; on the other hand, non-cooperation compels JD.com to allocate budgets flexibly to new channels such as TikTok and offline stores. In the long term, non-cooperation may drive JD.com to pursue a digital transformation of its supply chain, fostering a multi-polar growth structure [60]. When deciding whether to cooperate with social media platforms, e-commerce platforms should identify the actual situation. Evaluating their own profitability, the proportion of privacy sensitive consumers, the shares of loyal users, the social utility and the type of user group is necessary. Under certain conditions, a single-platform targeted advertising strategy may be more cost-effective.

(3)

E-commerce platforms should promote co-creation of value and proprietary data accumulation when cooperating with social media platforms. Compared with single-platform and high-precision cross-platform advertising strategies, low-precision cross-platform advertising strategy may achieve a win–win–win outcome for e-commerce platforms. When promoting co-creation of value, e-commerce platforms can choose low-precision cross-platform advertising strategy. However, low-precision cross-platform advertising strategy relies more heavily on third-party user traffic. From a long-term perspective, a portion of user data may remain within the social media platform, potentially limiting the e-commerce platform’s ability to accumulate proprietary data. Taking JD.com as an example, WeChat’s vast social data enable JD.com to leverage external data resources to support its data infrastructure without incurring substantial costs. However, once the partnership ends, JD.com may incur considerable costs to rebuild its own dataset. This consideration further suggests that e-commerce platforms should adopt cross-platform strategies cautiously.

This study makes three main contributions. First, research on cross-platform targeted advertising strategies between e-commerce platforms and social media platforms remains scarce. By examining cross-platform strategies across different user groups, the study enriches the literature on targeted advertising. Second, it extends the application of game theory to targeted advertising and provides managerial insights through a game-theoretic model that explains the mechanisms of cross-platform targeted advertising delivery. Third, the findings enable e-commerce platforms to better understand the advantages and disadvantages of cross-platform strategies, supporting more informed decisions between single- and cross-platform advertising.

This study has several limitations. First, the study does not include empirical evidence to validate the theoretical results. Second, regulatory aspects, such as data protection regulations and privacy laws, are not incorporated into the model. Third, the model does not consider competition among platforms and the influence of different cooperation mechanisms.

6. Conclusions

This paper uses game theory to analyze the optimal advertising strategy for e-commerce platforms choosing between single-platform and cross-platform targeted advertising in collaboration with social media platforms. Intuitively, higher targeting precision would appear to be more beneficial. However, through a game-theoretic model under fully and partially overlapping user group, the findings reveal that e-commerce platforms do not necessarily need to adopt cross-platform strategies; in some cases, single-platform targeted advertising may be more effective. When cross-platform strategies are adopted, lower targeting precision—that is, relatively less specific targeting—may yield better outcomes. Furthermore, when implementing cross-platform targeted advertising, the social utility provided by social media platforms should be carefully considered.

This study can be extended in various directions. First, investigating these issues by empirical method is an immediate extension. Second, considering the impact of privacy protection regulations could better reflect real-world strategic decision-making and yield deeper insights. Third, as this study focuses only on single cooperative relationships between platforms, extending the analysis to different cooperation mechanisms and competition among platforms would enrich the analysis.