Tripartite Evolutionary Game Analysis of Product Quality Supervision in Live-Streaming E-Commerce

Abstract

With the rapid development of information technology, live-streaming e-commerce has risen rapidly as a new business model. However, product quality problems that exist in the development of live-streaming e-commerce continue to emerge. The influence of strategic interactions between social media influencers, live-streaming e-commerce platforms, and consumers on product quality deserves to be studied. Therefore, this paper constructs a tripartite game model of “social media influencers–the live-streaming e-commerce platform–consumers” and analyzes the dynamic evolution process of the strategy selection among subjects and influencing factors by using evolutionary game theory. This study shows that products with high functional value are more likely to stimulate consumer rights protection behavior, prompting social media influencers to shift from lax to strict quality control. But when the emotional value is high, consumers are more inclined to give up on defending their rights, which leads to the maintenance of lax quality control, and the platform supervision will be weakened accordingly. Moreover, less quality differences motivate social media influencers to choose lax quality control. An increase in quality differences will promote a shift from an equilibrium strategy to strict quality control. However, if the penalty of the platforms is not strong enough, this strategic shift will not happen. In addition, a high percentage of platform commissions can encourage influencers to implement strict quality control, while platforms can maintain weak supervision. This study’s findings provide valuable guidance for understanding and managing product quality issues in live-streaming e-commerce. In the future, the government will be considered a new player in the game in studying the impact of its policies on product quality in live-streaming e-commerce.

1. Introduction

Live-streaming e-commerce, as an innovative model of the digital economy in the field of retail, has become an emerging option for consumers [1]. Live-streaming shopping is currently popular in several regions around the world, especially in China, the United States, Southeast Asia, and some European countries. Meanwhile, due to the worldwide outbreak of the COVID epidemic in 2020, people have reduced their reliance on traditional offline shopping and turned to safer and more convenient shopping methods, which has further accelerated the development and popularization of live-streaming e-commerce [2].

However, there have been frequent product quality issues during live-streaming which have hurt consumers’ rights and led to defensive actions. According to the “Live-streaming with Goods Consumer Rights Protection Public Opinion Analysis Report (2023)”, product quality issues accounted for 34.59% of complaints. Among these, product quality issues linked to well-known influencers such as Brother Yang during live-streaming have attracted widespread attention. On World Consumer Rights Day 2024, Brother Yang was exposed for using unclean and poor-quality groove-head meat in the pork with preserved vegetables he sold via live-streaming, which is not a food ingredient, is prohibited for consumption, and grossly does not comply with food safety standards. It is evident that product quality is a fundamental concern for the management of live-streaming e-commerce.

The participants in live-streaming e-commerce include social media influencers, live-streaming e-commerce platforms, and consumers. Social media influencers and live-streaming e-commerce platforms share responsibility for ensuring product quality. Before launching products, influencers conduct quality control, which directly impacts the likelihood of quality problems. However, to save time and effort and attract more brands for collaboration, influencers may relax their quality control, leading to an increase in the probability of selling products with quality problems. Live-streaming e-commerce platforms act as intermediaries and are responsible for maintaining fair trading. When consumers encounter product quality issues, they can seek resolution on the platform. The platforms are tasked with supervising and penalizing influencers for quality issues, but they may not always take active measures due to resource constraints and may be unresponsive to consumer feedback.

Furthermore, in the live-streaming scenario, consumers will develop a willingness to purchase independently of a product’s use function due to their emotional support of social media influencers. Such emotionally driven purchasing behavior may reduce consumers’ willingness to defend their rights. Therefore, consumers are not only affected by the functional value of products, such as their actual utility and quality, but also by irrational factors such as emotional value in their purchasing decisions and defense of their own rights [3], which leads to the complexity of the issue of regulating the operation of live-streaming e-commerce.

To sum up, effective management of product quality in live-streaming e-commerce has become a major social issue facing the world. However, the behaviors of these three types of participants in live-streaming e-commerce are closely interwoven, and the dynamics of this tripartite interaction add layers of complexity to product quality management strategies. In the context of live-streaming, what are the specific relationships of interests between social media influencers, live-streaming e-commerce platforms, and consumers? What stable equilibrium state and corresponding preconditions may exist in the live-streaming e-commerce system? What factors affect the equilibrium of the system? How do participants’ strategy choices affect the evolution of the system’s equilibrium? Therefore, the objective of this research is to analyze the interrelationships and behavioral choices among live-streaming e-commerce participants, find out the reasons leading to product quality problems, explore how social media influencers manage quality control and how platforms manage product quality supervision, and propose strategies for effectively managing product quality in the live-streaming e-commerce environment. Evolutionary game theory is applied to construct a tripartite evolutionary game model of social media influencers, the platform, and consumers. We reveal the dynamic strategic choices of social media influencers, platforms, and consumers and their influencing factors, providing a theoretical basis and practical guidance for the healthy development of the live-streaming e-commerce industry.

The structure of this article is shown in Figure 1. Section 2 reviews the relevant literature. In Section 3, the parameters are reasonably estimated, and a tripartite game model is constructed. Section 4 obtains evolutionarily stable strategies and their corresponding conditions through stability analysis. Section 5 reveals the influence of different parameters on the system equilibrium strategy through sensitivity analysis. Section 6 presents conclusions and management recommendations.

Our findings show that products with high functional value are more likely to inspire consumers to defend their rights, prompting social media influencers to choose strict quality control. When the emotional value is high, consumers will tend to abandon rights protection, at which point social media influencers will maintain lax quality control strategies and platforms will tend to weakly regulate. In addition, high risk–return and low-quality differences will motivate social media influencers to choose lax quality control strategies. Interestingly, a high percentage of platform commissions can encourage influencers to implement strict quality control, while the platforms can maintain weak supervision.

2. Literature Review

2.1. Quality Issues in Live-Streaming E-Commerce

Chen et al. [4] found that the issue of product quality in live sales has become a common public concern and criticism through their analysis of online user reviews. In the traditional offline shopping model, consumers can accurately assess product quality through multiple sensory experiences, such as observing, touching, and trying out goods [5]. However, in the live-streaming e-commerce scenario, consumers mainly rely on the influencer’s explanation in their perception of product quality, which exacerbates the information asymmetry between buyers and sellers [6]. In this case, social media influencers with large fan bases and extensive influence become important signals for consumers that imply product quality [7]. However, as competition in the live-streaming e-commerce area becomes increasingly fierce, some social media influencers have begun to take advantage of the trust and emotional loyalty of their fans by resorting to lowering the level of product quality to increase revenue. For instance, in the “sugar water bird’s nest” incident, the major influencer Simba abused the trust of a large number of his fans and failed to strictly control the quality of his products, leading to a poor consumer purchasing experience and damage to the platform’s reputation and triggering the risk of co-destruction of the live-streaming e-commerce supply chain value [8]. Therefore, the problem of lax product quality control in live-streaming e-commerce needs to be solved urgently.

2.2. Consumer Live Purchasing and Rights Protection Behavior

Many scholars have studied consumer behavior in the live-streaming e-commerce model. From the perspective of influencers, Li et al. [9] found that the attractiveness of influencers plays the most significant role in triggering impulsive purchasing behaviors among consumers; Zhang et al. [10] found that the popularity of influencers and the time pressure in live-streaming rooms stimulate consumers to make impulsive purchases. From the perspective of platforms, Wang et al. [11] found that consumers are more likely to engage in value co-creation behaviors if the platform can respond quickly to consumer needs; Wang et al. [12] found that a high reputation for live-streaming e-commerce platforms can endorse goods and stimulate consumers’ desire to make purchases. From the perspective of consumers, Lu et al. [13] found that consumers’ emotional support for influencers can increase their purchase intention; Wang et al. [14] found that improving consumers’ perceived value and reducing shopping risks can increase their purchase intention. The above studies have found that many factors related to each subject stimulate consumers’ purchase intention through the methods of empirical research, which provides a corresponding theoretical basis for improving the business performance of these subjects in live-streaming e-commerce.

However, the factors affecting the defense of consumers’ rights and interests in the event of quality problems with products have been overlooked [15]. Parasocial relationships usually refer to one-way celebrity worship relationships between viewers and media personalities, but the rise of live-streaming e-commerce and social media influencers has prompted a shift to a quasi-social relationship, with the potential for rewards [16]. In the context of live-streaming e-commerce, influencers can establish parasocial relationships with consumers through long-term social interactions, characterized by a high degree of consumer identification, emotional support, and a fan culture [16]. When consumers face product quality problems, parasocial relationships have a significant buffering effect in alleviating consumer dissatisfaction and their willingness to defend their rights. The stronger the parasocial relationships, the lower the consumers’ willingness to defend their rights [17]. Specifically, the emotional bond established between consumers and influencers weakens consumers’ willingness to defend their rights. Therefore, if consumers purchase products for emotional support, then they tend not to defend their rights when facing product quality problems, making it rare for influencers who sell inferior products to be punished. This indirectly leads to the current situation of frequent product quality problems in live-streaming and also reveals the potential challenges faced in platform supervision.

2.3. Evolutionary Game Theory

Evolutionary game theory not only takes into account the limited rationality of the subjects, which is more relevant to actual situations, but also can analyze the stability of the strategic choices among subjects from a long-term perspective [18]. Many scholars have also used the method of evolutionary games to analyze problems with policies, norms, and other aspects. Within the context of promoting green technology innovation, Wang et al. [19] built a tripartite evolutionary game model of local governments, enterprises, and consumers; revealed three stable equilibrium states in the process of green technology innovation; and found that the government’s market regulation strategy has a positive impact on promoting enterprises’ green technology innovation and guiding consumers to buy green products. In addition, the brand benefit of enterprises’ green technology innovation strategies and the economic benefit of consumers’ green product consumption are the main factors affecting the system’s evolution. This research has enriched the theoretical basis of green development. In the context of promoting carbon neutrality, the strategic interactions between the government and power generation enterprises with different emission reduction capabilities jointly affect the effectiveness of emission reductions. Therefore, Zhang et al. [20] constructed a tripartite game model and found that government subsidies for substantial emission reductions and penalties for insufficient emission reductions are conducive to maximizing carbon emission reductions. In addition, lowering the abatement costs and increasing carbon prices can encourage enterprises to reduce their emissions. This study provides a reference for how governments can formulate policies that promote carbon reduction. In the context of banning the sale of gasoline vehicles, by constructing a tripartite evolutionary game model of consumers, automobile manufacturers, and the government, Liu et al. [21] found that increasing technical subsidies for natural gas vehicles and the production costs for gasoline vehicles and strengthening social supervision by the media are conducive to achieving an ideal equilibrium state (consumer compliance, enterprise compliance, and lax government supervision). This has important guiding significance for how the government should formulate policies to promote bans on the sale of gasoline cars. In the context of responding to public health emergencies, Xu et al. [22] constructed a tripartite evolutionary game model of local governments, enterprises, and the public. The research results show that appropriate government incentives can enhance the public’s regulatory motivation, and reasonable government subsidies to enterprises can improve enterprises’ standardized implementation of epidemic policies. This study provides theoretical support for how local governments can guide parties to achieve cooperation in fighting epidemics in public health emergencies.

In summary, evolutionary game theory can analyze the interactions and strategic choices among multiple subjects in different situations, providing a theoretical basis and practical guidance for policy formulation and decision-making. The establishment of a tripartite evolutionary game model needs to accurately identify the main participants and the relevant interest relationships within specific situations. Meanwhile, participants’ strategic assumptions are influenced by different situations. For example, in the context of promoting green technology innovation, consumers’ strategic assumptions are buying green products or buying traditional products [19]; under a policy that bans the sale of gasoline cars, consumers’ strategic assumptions are compliance or non-compliance [21]. In addition, the assumptions of participants’ returns are also affected by different situations. For example, in the context of promoting carbon neutrality, the assumptions for government benefits include regulatory costs, environmental benefits, and so on [20]; in the context of public health emergencies, the assumptions for government returns include the cost of governance, the losses within a worsening epidemic situation, and so on [22]. Therefore, this paper discusses the different factors that affect the returns of participants in the context of live-streaming e-commerce and adopts the method of evolutionary game theory to study the standardized operation of live-streaming e-commerce.

3. Model Assumptions and Construction

In the live-streaming scenario, there are usually three types of subjects involved: social media influencers, live-streaming e-commerce platforms, and consumers. Figure 2 illustrates the logical relationships between multiple subjects in live-streaming e-commerce.

We analyze product quality supervision in live-streaming e-commerce based on evolutionary game theory. The core idea of the theory is that the strategies of individuals in a group evolve over time, which contains the following two key concepts: (1) A replicated dynamic equation (RDE): This is a mathematical model that describes how strategies evolve over time within a population. It assumes that individuals will replicate themselves based on the success of their strategies (i.e., fitness), with successful strategies gradually spreading throughout the population. (2) An evolutionarily stable strategy (ESS): This is a strategy that can resist invasion under the pressure of natural selection. If a strategy is evolutionarily stable, it will be able to dominate over a sufficiently long period of time.

Evolutionary game analysis simulates the evolutionary process by comparing the expected returns of individual strategies with the average return of the population. If the expected return of a strategy exceeds the population’s average return, then under the influence of natural selection, the proportion of this strategy in the population will increase. Conversely, if a strategy’s expected return is below the population’s average return, individuals may shift towards strategies that offer higher expected returns. As strategies continue to adjust and evolve, the system may ultimately reach an evolutionarily stable strategy.

In order to systematically study the evolutionary game of live-streaming e-commerce, we put forward some reasonable hypotheses based on the main factors considered by social media influencers, live-streaming e-commerce platforms, and consumers when making strategic choices. The parameters and terms involved in this research and their meanings are shown in

Table 1. Meanings of parameters and terms.

Parameters/Terms	Meanings
x	The probability of social media influencers choosing strict quality control.
y	The probability of a platform choosing strong supervision.
z	The probability of consumers choosing to defend their rights.
h	Platforms taking a cut of the earnings from social media influencers.
a	The positive impact on revenue when influencers choose lax quality control.
R	The benefits for social media influencers when they choose strict quality control.
$P_1/P_2$	The possibility of product problems when influencers choose strict/lax quality control.
$C_1$	Additional costs coming from a platform’s strong supervision.
F	The extent to which platforms penalize social media influencers who sell poor quality products.
E	The reputation loss for influencers when consumers defend their rights and the platforms choose weak supervision.
b	The positive impact of strong supervision on market order.
J	When a platform chooses strong supervision, consumer rights protection brings market governance benefits to the platform.
$L_1/L_2$	The commercial loss caused to the platform when social media influencers choose strict/lax quality control.
N	The functional value benefits that consumers receive from purchasing products.
W	The emotional value benefits that consumers receive from purchasing products.
$C_2$	The cost to consumers of defending their rights.
$K_1/K_2$	The probability of effectively addressing the consumer rights protection problem when a platform chooses strong/weak supervision.
S	Compensation for successful consumer rights protection.
G	Loss of consumer equity due to product quality problems.
$U_{11}$	The expected returns of social media influencers under a strict quality control strategy.
$U_{12}$	The expected returns of social media influencers under a lax quality control strategy.
$U_1$	The average returns of social media influencers under strict and lax quality control strategies.
$U_{21}$	The expected returns of the platform under a strong supervision strategy.
$U_{22}$	The expected returns of the platform under a weak supervision strategy.
$U_2$	The average returns of the platform under strong and weak supervision strategies.
$U_{31}$	The expected returns of consumers under the rights protection strategy.
$U_{32}$	The expected returns of consumers under no rights protection strategy.
$U_3$	The average returns of consumers under rights protection and no rights protection strategies.
$RDE$	The rate at which a strategy’s proportion in a population changes over time is proportional to its relative benefit.
$ESS$	A strategy that can resist invasion by alternative strategies during the process of natural selection.

.

Assumption A1. 

Relevant parameter settings for social media influencers.

(i)

There are a large number of products on the market, but their quality and variety are uncertain. Therefore, social media influencers need to manage product quality control before selling their products. The optional strategies are strict quality control and lax quality control, corresponding to the probability of $x(0\le x\le 1)$ and $(1-x)$, respectively.

(ii)

Lax quality control can reduce the costs in terms of time and energy in the quality control process, such as qualification reviews, sample evaluation, and production tracking, so the cost of strict quality control is higher than the cost of lax quality control. At the same time, lax quality control can increase cooperation with brands and the richness of products and thus obtain more admission fees and commission revenue. Considering the cost of quality control, admission fees, and commission revenue, when social media influencers choose lax quality control, the risk–return factor $a(0\le a\le 1)$ is introduced to indicate a positive impact on the revenue. If the gain with strict quality control is R, then the gain with lax quality control is $(1+a)R$.

(iii)

In real life, the strictness of product quality control is directly related to the possibility of product problems. The stricter the quality control, the lower the risk of product problems. When social media influencers choose strict quality control, the possibility of product problems is $P_1$; when quality control is lax, the possibility of product problems is $P_2(P_1<P_2)$.

Assumption A2. 

Relevant parameter settings for the live-streaming e-commerce platform.

(i)

Live-streaming e-commerce platforms have an important responsibility to ensure fair trading in terms of supervision. Therefore, platforms need to regulate the behavior of social media influencers. The available strategies are strong and weak supervision, with corresponding probabilities of $y(0\le y\le 1)$ and $(1-y)$, respectively.

(ii)

Social media influencers need to cooperate with e-commerce platforms such as TikTok, Taobao, and Jingdong for live-streaming. These platforms provide channel resources and service support for social media influencers to carry out live-streaming. Therefore, platforms will take an h-percentage of the earnings of social media influencers.

(iii)

When a platform chooses strong supervision, the platform always needs to prepare for more human and resource costs $\left(C_1\right)$ to cope with feedback on consumers’ rights protection.

(iv)

The platform’s punishment for social media influencers who sell inferior products is $P_{i}F$. In this situation, when the platform chooses strong supervision, the reputation loss of social media influencers is $bE$, where E indicates the reputational loss of the social media influencers in the presence of weak supervision, and $b(1\le b\le 2)$ indicates the positive impact of strong supervision on market order.

(v)

When a platform carries out strong supervision, consumers who choose to defend their rights assist the platform to a certain extent in rectifying the live-streaming e-commerce environment, thus bringing the potential market governance benefits J.

(vi)

When a platform carries out weak supervision, consumers who defend their rights will turn to other competitive platforms due to a poor shopping experience, resulting in commercial losses. When social media influencers choose strict quality control, the platform’s commercial loss is $L_1$; when social media influencers choose lax quality control, the platform’s commercial loss is $L_2(L_1<L_2)$.

Assumption A3. 

Relevant parameter settings for consumers.

(i)

When consumers face problematic products, the strategy they can choose is defending their rights or not defending their rights, and the corresponding probabilities are $z(0\le z\le 1)$ and $(1-z)$, respectively.

(ii)

Consumers’ purchase decisions are mainly driven by two motivations: functional motivation and emotional motivation. The functional value that consumers gain by purchasing products is N. Functional value refers to the inherent performance and attributes of a product. When consumers buy products to meet their needs in life, that is, they pay more attention to the functional value of the product, and they tend to defend their rights. The emotional value that consumers gain by purchasing products is W. Emotional value refers to the emotional support consumers show for social media influencers. When consumers have fanatical emotional devotion and loyalty to social media influencers and express their support by placing orders, that is, consumers pay more attention to the emotional value of the product, and they tend not to defend their rights.

(iii)

When consumers choose to defend their rights, the time costs of communicating with the platform and proving their point are $\left(C_2\right)$.

(iv)

The possibility of successful consumer rights protection is positively correlated with the regulatory intensity of live-streaming e-commerce platforms. The stronger the supervision, the higher the probability that consumers will successfully defend their rights. When a platform chooses strong supervision, the probability of effectively addressing the consumer rights protection problem is $K_1$, and the compensation received by the consumer is $K_{1}S$; when the platform chooses weak supervision, the probability of effectively addressing the consumer rights protection problem is $K_2(K_1>K_2)$, and the compensation received by the consumer is $K_{2}S$.

(v)

When social media influencers choose strict quality control or lax quality control, the loss of rights and interests resulting from consumer purchases is $P_{1}G$ or $P_{2}G$, respectively.

Table 2. Payoff matrix of the three-game subjects.

The Platform	Consumers	Social Media Influencers
		Strict Quality Control ($\mathbf{x}$)	Lax Quality Control ($\mathbf{1}-\mathbf{x}$)
Strong supervision (y)	Defend their rights (z)	$(1-h)R-P_{1}F-bE$	$(1-h)(1+a)R-P_{2}F-bE$
		$hR-C_1+J$	$h(1+a)R-C_1+J$
		$N-P_{1}G-C_2+K_{1}S$	$N-P_{2}G-C_2+K_{1}S$
	Do not defend their rights ($1-z$)	$(1-h)R$	$(1-h)(1+a)R$
		$hR-C_1$	$h(1+a)R-C_1$
		$W-P_{1}G$	$W-P_{2}G$
Weak supervision ($1-y$)	Defend their rights (z)	$(1-h)R-P_{1}F-E$	$(1-h)(1+a)R-P_{2}F-E$
		$hR-L_1$	$h(1+a)R-L_2$
		$N-P_{1}G-C_2+K_{2}S$	$N-P_{2}G-C_2+K_{2}S$
	Do not defend their rights ($1-z$)	$(1-h)R$	$(1-h)(1+a)R$
		$hR$	$h(1+a)R$
		$W-P_{1}G$	$W-P_{2}G$

shows a payoff matrix for social media influencers, the live-streaming e-commerce platform, and consumers.

In the following section, we first calculate the expected returns for each participant under different strategies and then employ replicated dynamic equations to simulate and adjust these strategies. Finally, through stability analysis, we study which strategies are stable and under what conditions the strategy configuration of the population can achieve stability.

4. Stability Analysis

In live-streaming e-commerce, the strategic interaction among the three major stakeholders—social media influencers, live-streaming e-commerce platforms, and consumers—constitutes a complex game system. Due to their limited rationality or the incompleteness of market information, these participants may adjust their own strategies according to the strategies of the others to pursue the maximization of benefits. This strategy interaction is a long-term dynamic evolution process involving multiple participants, and stability analysis can determine sustainable strategies for each party in the long-term game. In this section, a stability analysis is conducted to investigate the conditions under which the strategic choices of each participant converge to a stable state, as well as elucidating which strategy combinations can emerge as stable options for all participants in the enduring dynamic interactions of live-streaming e-commerce.

4.1. Social Media Influencers

In Section 3, we construct a detailed game revenue matrix (shown in Table 2) that considers the potential benefits and costs for each party under different strategy options. On this basis, we use probability distributions to model the benefits for social media influencers when they adopt strict versus lax quality control strategies. Our methodology is widely used in the study of evolutionary games [23,24,25,26]. By probability weighting, we can obtain the expected returns $U_{11}$ and $U_{12}$ and the average returns $U_1$ of social media influencers under strict and lax quality control strategies, as shown in Appendix A. It is then possible to derive the replicated dynamic equation for social media influencers and the first-order partial derivative concerning x as follows:

$$\begin{array}{cc}\hfill & F\left(x\right)=dx/dt=x\left(U_{11}-U_1\right)=x(x-1)\left(Ra+F{P}_{1}z-F{P}_{2}z-Rah\right)\hfill \end{array}$$

(1)

$$\begin{array}{cc}\hfill & F^{\prime }\left(x\right)=dF\left(x\right)/dx=(2x-1)\left(Ra-Rah+F{P}_{1}z-F{P}_{2}z\right)\hfill \end{array}$$

(2)

According to the stability theorem of differential equations, the probability of social media influencers choosing strict quality control is in a steady state, which needs to satisfy $F\left(x\right)=0, F^{\prime }\left(x\right)<0$. Then, $F\left(x\right)=0$ yields $x=0, x=1, z\ast ={\displaystyle \frac{\mathrm{a}(h-1)R}{\mathrm{F}\left(P_1-P_2\right)}}$. When $z=z\ast$, then for any x, $F\left(x\right)=0, F^{\prime }\left(x\right)=0$. That is, the x-axis is in a steady state, and any QC strategy for social media influencers is a stable strategy. When $z\ne z\ast$, the following cases are discussed.

Case 1: If $a(h-1)R<F\left(P_1-P_2\right)<0$, then $z<z\ast$, $Ra-Rah+F{P}_{1}z-F{P}_{2}z>0$. We find that $F^{\prime }\left(x\right){{|}_{x=0}<0, F^{\prime }\left(x\right)|}_{x=1}>0, x=0$ is the only ESS.

Case 1 shows that although social media influencers are punished more for choosing lax quality control, the significant additional benefits that lax quality control can bring mean the overall net benefits outweigh those that can be achieved by adopting a strict quality control strategy. Therefore, social media influencers are more inclined to adopt a lax quality control strategy after weighing up the risks and benefits to maximize their returns.

Case 2: If $F\left(P_1-P_2\right)<a(h-1)R<0$, we analyze the following two scenarios.

(1)

When $z>z\ast$, we obtain $Ra-Rah+F{P}_{1}z-F{P}_{2}z<0$. Then, $F^{\prime }\left(x\right){{|}_{x=0}>0, F^{\prime }\left(x\right)|}_{x=1}<0, x=1$ is the only ESS.

(2)

When $z<z\ast$, we obtain $Ra-Rah+F{P}_{1}z-F{P}_{2}z>0$. Then, $F^{\prime }\left(x\right){{|}_{x=0}<0, F^{\prime }\left(x\right)|}_{x=1}>0, x=0$ is the only ESS.

Case 2 shows that social media influencers’ decisions on which quality control strategy to adopt depend on the consumer rights protection rate. When the consumer rights protection rate is greater than a certain threshold, social media influencers will choose a strict quality control strategy; in the reverse situation, they will choose a lax quality control strategy. Figure 3 summarizes the dynamic evolution path and stability of the quality control strategy chosen by social media influencers.

4.2. The Live-Streaming E-Commerce Platform

Similarly, we can obtain the expected returns $U_{21}$ and $U_{22}$ and the average returns $U_2$ of the live-streaming e-commerce platform under strong and weak supervision strategies, as shown in Appendix A. It is then possible to derive the replicated dynamic equation for the live-streaming e-commerce platform and the first-order partial derivatives concerning y as follows:

$$\begin{array}{cc}\hfill & F\left(y\right)=dy/dt=y\left(U_{21}-U_2\right)=-y(y-1)\left(Jz-C_1+L_{2}z+L_{1}xz-L_{2}xz\right)\hfill \end{array}$$

(3)

$$\begin{array}{cc}\hfill & F^{\prime }\left(y\right)=dF\left(y\right)/dy=(1-2y)\left(Jz-C_1+L_{2}z+L_{1}xz-L_{2}xz\right)\hfill \end{array}$$

(4)

According to the stability theorem of differential equations, the probability of the live-streaming e-commerce platform choosing strong supervision is in a steady state, which needs to satisfy $F\left(y\right)=0, F^{\prime }\left(y\right)<0$. For the sake of discussion, we order $Q\left(x\right)=Jz-C_1+L_{2}z+L_{1}xz-L_{2}xz$, $\mathrm{x}\ast ={\displaystyle \frac{C_1-\mathrm{z}\left(\mathrm{J}+L_2\right)}{\mathrm{z}\left(L_1-L_2\right)}}, z\ast \ast ={\displaystyle \frac{C_1}{\mathrm{J}+L_2}}$.

Case 3: When $z<z\ast \ast$, $y=0$ is an evolutionarily stable strategy; when $z>z\ast \ast$, (1) $x=x\ast$, y is entirely stable; (2) $x<x\ast$, $y=1$ is an evolutionarily stable strategy; (3) $x>x\ast$, $y=0$ is an evolutionarily stable strategy.

Proof. 

From $dQ\left(x\right)/dx=L_1-L_2<0$, we can obtain $Q\left(x\right)$ as a decreasing function. If $z<z\ast \ast$, then $x\ast <0, Q\left(x\right)=0$ when $\mathrm{x}\ast ={\displaystyle \frac{C_1-\mathrm{z}\left(\mathrm{J}+L_2\right)}{\mathrm{z}\left(L_1-L_2\right)}}$. Therefore, $x\in [0, 1]$ is clearly greater than $x\ast$, and $Q\left(x\right)<0$ holds, at which time $F^{\prime }{\left(y\right)|}_{y=0}<0$, so $y=0$ is an ESS; if $z>z\ast \ast$, then $Q\left(x\right)=0, F\left(y\right)=0, F^{\prime }\left(y\right)=0$ when $x=x\ast$, and the y-axis is in a steady state; when $x<x\ast$, then $Q\left(x\right)>0$ holds, at this time $F^{\prime }{\left(y\right)|}_{y=1}<0$, so $y=1$ is an ESS; when $x>x\ast$, then $Q\left(x\right)<0$ holds when $F^{\prime }{\left(y\right)|}_{y=0}<0$, so $y=0$ is an ESS. The proof is complete. □

Case 3 shows that when the probability of consumer rights protection is low, live-streaming e-commerce platforms tend to choose a weak supervision strategy regardless of the strategy adopted by social media influencers; when the probability of consumer rights protection is high, the strategy choice of live-streaming e-commerce platforms is related to the probability of influencers’ quality control. When the probability of strict quality control on the part of social media influencers is at the threshold, the strategy choice of live-streaming e-commerce platforms is maintained in its initial state; when the probability of strict quality control on the part of social media influencers is low, live-streaming e-commerce platforms tend towards strong supervision; when strict quality control by social media influencers has a high probability, live-streaming e-commerce platforms tend towards weak supervision. To sum up, the behavior of consumers not seeking to protect their rights will prompt live-streaming e-commerce platforms to undertake weak supervision, but if there is a high probability of consumer rights protection behavior occurring, platforms will choose strong supervision when the probability of social media influencers undertaking strict quality control is low and choose weak supervision when the probability of social media influencers undertaking strict quality control is high. Figure 4 summarizes the dynamic evolution path and stability of the supervision strategy chosen by live-streaming e-commerce platforms.

4.3. Consumers

Similarly, we can obtain the expected returns $U_{31}$ and $U_{32}$ and the average returns $U_3$ for consumers under the strategies of them defending or not defending their rights, as shown in Appendix A. It is then possible to derive the replicated dynamic equation for consumers and the first-order partial derivative concerning z as follows:

$$\begin{array}{cc}\hfill & F\left(z\right)=dz/dt=z\left(U_{31}-U_3\right)=z(z-1)\left(C_2-N+W-K_{2}S-K_{1}Sy+K_{2}Sy\right)\hfill \end{array}$$

(5)

$$\begin{array}{cc}\hfill & F^{\prime }\left(z\right)=dF\left(z\right)/dz=(2z-1)\left(C_2-N+W-K_{2}S-K_{1}Sy+K_{2}Sy\right)\hfill \end{array}$$

(6)

According to the stability theorem of differential equations, the probability of consumers choosing to defend their rights in a steady state needs to satisfy $F\left(z\right)=0, F^{\prime }\left(z\right)<0$. Then, $F\left(z\right)=0$ yields $z=0, z=1, y\ast ={\displaystyle \frac{\mathrm{N}-\mathrm{W}+K_2\mathrm{S}-C_2}{-K_1\mathrm{S}+K_2\mathrm{S}}}$. When $y=y\ast$, then for any z, $F\left(z\right)=0, F^{\prime }\left(z\right)=0$. That is, the z-axis is in a steady state, and any strategy of the consumers is a stable strategy. When $y\ne y\ast$, the following cases are discussed.

Case 4: If $N-W+K_2\mathrm{S}-C_2>0$, then $y>y\ast$, $C_2-N+W-K_{2}S-K_{1}Sy+K_{2}Sy<0$. At this point, $F^{\prime }\left(z\right){{|}_{z=1}<0, F^{\prime }\left(z\right)|}_{z=0}>0, z=1$ is the only ESS.

Case 4 shows that consumers will be more inclined to adopt a rights protection strategy when the total revenue of the compensation they receive through defense plus the actual value of the products minus the cost of rights protection is higher than the emotional value they would have gained through the purchase of products if they had not defended their rights.

Case 5: If $N-W+K_2\mathrm{S}-C_2<-K_1\mathrm{S}+K_2\mathrm{S}<0$, then $y<y\ast$, $C_2-N+W-K_{2}S-K_{1}Sy+K_{2}Sy>0$. At this point, $F^{\prime }\left(z\right){{|}_{z=0}<0, F^{\prime }\left(z\right)|}_{z=1}>0, z=0$ is the only ESS.

Case 5 shows that consumers will be more inclined not to adopt a rights protection strategy when the total revenue of the compensation they receive through defense plus the actual value of the products minus the cost of defending their rights is less than the emotional value they would have gained by purchasing products if they had not defended their rights.

Case 6: If $-K_1\mathrm{S}+K_2\mathrm{S}<N-W+K_2\mathrm{S}-C_2<0$, we analyze the following two scenarios.

(1)

When $y>y\ast$, we can obtain $C_2-N+W-K_{2}S-K_{1}Sy+K_{2}Sy<0$. At this point, $F^{\prime }\left(z\right){{|}_{z=1}<0, F^{\prime }\left(z\right)|}_{z=0}>0, z=1$ is the only ESS.

(2)

When $y<y\ast$, we can obtain $C_2-N+W-K_{2}S-K_{1}Sy+K_{2}Sy>0$. At this point, $F^{\prime }\left(z\right){{|}_{z=0}<0, F^{\prime }\left(z\right)|}_{z=1}>0, z=0$ is the only ESS.

Case 6 shows that which strategy consumers adopt depends on the probability of supervision on the part of the live-streaming e-commerce platform. When the probability of supervision by the live-streaming e-commerce platform is greater than the threshold, consumers will choose the strategy of defending their rights; in the reverse situation, they will choose the strategy of not defending their rights. Figure 5 summarizes the dynamic evolution path and stability of the defense strategy chosen by consumers.

4.4. The Tripartite Evolutionary Game System

In asymmetric dynamic games, since mixed-strategy equilibrium will not be an evolutionarily stable equilibrium, we need only analyze pure strategy equilibrium points within the evolutionary game system [27]. Letting $F\left(x\right)=0, F\left(y\right)=0, F\left(z\right)=0$, we can obtain $D_1(0,0,0), D_2(1,0,0), D_3(0,1,0), D_4(0,0,1), D_5(1,1,0), D_6(1,0,1), D_7(0,1,1),$ and $D_8(1,1,1)$ as pure strategy equilibrium points within this evolutionary game system. To analyze the stability of the equilibrium points of the evolving system, the Jacobi matrix is constructed:

$$I=\left[\begin{array}{ccc}\partial F\left(x\right)/\partial x\hfill & \partial F\left(x\right)/\partial y\hfill & \partial F\left(x\right)/\partial z\hfill \\ \partial F\left(y\right)/\partial x\hfill & \partial F\left(y\right)/\partial y\hfill & \partial F\left(y\right)/\partial z\hfill \\ \partial F\left(z\right)/\partial x\hfill & \partial F\left(z\right)/\partial y\hfill & \partial F\left(z\right)/\partial z\hfill \end{array}\right]$$

$=\left[\begin{array}{ccc}(2x-1)\left(Ra-Rah+F{P}_{1}z-F{P}_{2}z\right)& 0& x(2x-1)\left(F{P}_1-F{P}_2\right)\\ -y(y-1)\left(L_{1}z-L_{2}z\right)& (1-2y)\left(Jz-C_1+L_{2}z+L_{1}xz-L_{2}xz\right)& -y(y-1)\left(J+L_2+L_{1}x-L_{2}x\right)\\ 0& -z(z-1)\left(K_{1}S-K_{2}S\right)& (2z-1)\left(C_2-N+W-K_{2}S-K_{1}Sy+K_{2}Sy\right)\end{array}\right]$

The evolutionary game system I has five possible system evolutionary stable points: $D_1(0,0,0),D_4(0,0,1),D_6(1,0,1),D_7(0,1,1),$ and $D_8(1,1,1)$.

(1)

When $W>N-C_2+K_{2}S$, the evolutionarily stable strategy for the system is $D_1(0,0,0)$.

(2)

When $F{P}_2-F{P}_1-Ra+Rah<0, L_2<C_1-J, W<N-C_2+K_{2}S$, the evolutionarily stable strategy for the system is $D_4(0,0,1)$.

(3)

When $F{P}_1-F{P}_2+Ra-Rah<0, L_1<C_1-J, W<N-C_2+K_{2}S$, the evolutionarily stable strategy for the system is $D_6(1,0,1)$.

(4)

When $F{P}_2-F{P}_1-Ra+Rah<0, L_2>C_1-J, W<N-C_2+K_{1}S$, the evolutionarily stable strategy for the system is $D_7(0,1,1)$.

(5)

When $F{P}_1-F{P}_2+Ra-Rah<0, L_1>C_1-J, W<N-C_2+K_{1}S$, the evolutionarily stable strategy for the system is $D_8(1,1,1)$.

Proof. 

According to Lyapunov’s method, when all the eigenvalues in the Jacobi matrix are less than 0, the point is stable; when there are positive and negative eigenvalues, the point is a saddle point; and when all the eigenvalues are greater than 0, the point is unstable [28]. We can take the following Jacobi matrix as an example:

$$I_2=\left[\begin{array}{ccc}Rah-Ra& 0& 0\\ 0& -C_1& 0\\ 0& 0& N-C_2-W+K_{2}S\end{array}\right]$$

The eigenvalue $V_1=Rah-Ra$, $V_2=-C_1$, $V_3=N-C_2-W+K_{2}S$ can be obtained. Because this paper assumes $0<a<1,$$0<h<1$, and $C1>0$. Therefore, when $W>N-C_2+K_{2}S$, $V_1<0, V_2<0$ and $V_3<0$, which meets the judgment condition for a stable point, and $D_1(0, 0, 0)$ is the system’s evolutionarily stable strategy. When $W<N-C_2+K_{2}S$, $V_1<0, V_2<0$ and $V_3>0$, and the point is a saddle point. Similarly, the local stability of the other equilibrium points can be judged, as shown in

Table 3. Stability analysis of equilibrium points.

Equilibrium Points	Eigenvalue ${\mathit{V}}_1$	Eigenvalue ${\mathit{V}}_2$	Eigenvalue ${\mathit{V}}_3$	Symbolic Judgement
$D_1(0,0,0)$	$Rah-Ra$	$-C_1$	$N-C_2-W+K_{2}S$	$(-, -, \ast )$
$D_2(1,0,0)$	$Ra-Rah$	$-C_1$	$N-C_2-W+K_{2}S$	$(+, -, \ast )$
$D_3(0,1,0)$	$Rah-Ra$	$C_1$	$N-C_2-W+K_{1}S$	$(-, +, \ast )$
$D_4(0,0,1)$	$F{P}_2-F{P}_1-Ra+Rah$	$J-C_1+L_2$	$C_2-N+W-K_{2}S$	$(\ast , \ast , \ast )$
$D_5(1,1,0)$	$Ra-Rah$	$C_1$	$N-C_2-W+K_{1}S$	$(+, +, \ast )$
$D_6(1,0,1)$	$F{P}_1-F{P}_2+Ra-Rah$	$J-C_1+L_1$	$C_2-N+W-K_{2}S$	$(\ast , \ast , \ast )$
$D_7(0,1,1)$	$F{P}_2-F{P}_1-Ra+Rah$	$C_1-J-L_2$	$C_2-N+W-K_{1}S$	$(\ast , \ast , \ast )$
$D_8(1,1,1)$	$F{P}_1-F{P}_2+Ra-Rah$	$C_1-J-L_1$	$C_2-N+W-K_{1}S$	$(\ast , \ast , \ast )$

Note: “+”, “−”, and “∗”, respectively, indicate that the eigenvalue of the point is “positive”, “negative”, and “uncertain”.

. □

5. Sensitivity Analysis

In this section, we conduct a sensitivity analysis on factors such as risk–return, commercial loss, and functional value to comprehend how the model or system responds to variations in the input parameters, thereby providing support and guidance in the decision-making process. Sensitivity analysis is crucial for validating the stability analysis, emphasizing the model’s robustness in the face of parameter variations. Furthermore, by evaluating the effects of parameter changes on the system stability and strategic decisions, we can identify the key drivers of system evolution. This understanding facilitates recognition of how strategies evolve over time and the potential stable states that may arise under varying circumstances. To visually represent the changes in the system’s evolutionary equilibrium points due to differing parameters and to extract additional managerial insights, we performed a sensitivity analysis using Matlab R202la(America). The initial values were established based on reasonable assumptions about the parameters and stability conditions, as shown in

Table 4. The initial values of the relevant parameters.

ESS	${\mathit{D}}_1(0,0,0)$	${\mathit{D}}_4(0,0,1)$	${\mathit{D}}_6(1,0,1)$	${\mathit{D}}_7(0,1,1)$	${\mathit{D}}_8(1,1,1)$
a	$0.2$	$0.4$	$0.2$	$0.4$	$0.2$
b	$1.5$	$1.5$	$1.5$	$1.5$	$1.5$
h	$0.3$	$0.3$	$0.3$	$0.3$	$0.3$
R	100	100	100	100	100
$P_1$	$0.2$	$0.2$	$0.2$	$0.2$	$0.2$
$P_2$	$0.5$	$0.5$	$0.5$	$0.5$	$0.5$
F	50	50	50	50	50
E	20	20	20	20	20
$K_1$	$0.8$	$0.8$	$0.8$	$0.8$	$0.8$
$K_2$	$0.2$	$0.2$	$0.2$	$0.2$	$0.2$
S	50	50	50	50	50
$C_1$	25	25	25	10	10
$C_2$	5	5	5	5	5
N	20	50	50	20	50
W	50	20	20	20	20
G	10	10	10	10	10
J	5	5	5	15	5
$L_1$	10	10	10	10	10
$L_2$	15	15	30	15	15

.

5.1. Impacts of Social Media Influencers

5.1.1. The Risk–Return Factor

The risk–return factor refers to the extra admission fees and commission revenue gained when a social media influencer chooses a lax quality control strategy. To explore the impact of different risk–return factors on each subject, we set the risk–return factors as $a=0.4$, $a=0.3$, and $a=0.2$ for simulation, and the results are shown in Figure 6, where x, y, and z represent the probability values for the social media influencers’, live-streaming e-commerce platform’s, and consumers’ strategies, respectively.

The platform’s strategy stabilizes towards weak supervision, and the consumer’s strategy stabilizes towards rights protection. When the risk–return factor is high, the strategy choice of social media influencers tends to be lax quality control, and when the risk–return factor is low, social media influencers tend to have strict quality control. This suggests that a lower risk–return factor can induce the three parties in live-streaming e-commerce to reach a steady state (1,0,1); social media influencers choose the strict quality control strategy, the platform chooses a weak supervision strategy, and consumers choose the strategy of defending their rights.

5.1.2. The Ratio of the Probability of Product Problems under Different QC Strategies

The probability of product quality problems is affected by the degree of quality control. When influencers choose strict quality control, the probability of product quality problems can be reduced. To explore the impact of different probabilities of quality problems on each subject, we set $P_2/P_1=1.5$, $P_2/P_1=2.5$, and $P_2/P_1=4$ for simulation, and the results are shown in Figure 7.

When $P_2/P_1$ is small, social media influencers tend to choose the lax quality control strategy and take their chances. With the expansion of the difference in the probability of product quality problems, the system equilibrium strategy also changes, from lax quality control, weak supervision, and rights protection to strict quality control, weak supervision, and rights protection. It should be noted that at this time, the value of F is large, so the probability of quality problems with products affects the strategy choice of influencers. If the value is small, the strategy choice of influencers will not be affected by the probability of quality problems with products. Therefore, the live-streaming e-commerce platform needs to severely punish product quality problems in live-streaming, which is an effective means to constrain and regulate the behavior of social media influencers’ product selection.

5.2. Impacts of the Live-Streaming E-Commerce Platform

5.2.1. Commercial Losses

Commercial losses of live-streaming e-commerce platforms often stem from weak supervision and an inability to effectively protect consumers’ rights, which lead to a collapse of consumer trust in the platforms and drives them to other competitive live-streaming e-commerce platforms that can provide better shopping protection. The loss of consumers not only weakens the platform’s user base but also triggers a domino effect, leading to the loss of more potential consumers and ultimately causing significant commercial losses. To explore the impact of changes in the commercial losses of the platform on each subject, the commercial losses are set to $L_1=10$, $L_1=15$, and $L_1=20$ for simulation, and the results are shown in Figure 8.

With an increase in commercial losses for the live-streaming e-commerce platform, the system equilibrium strategy shifts from strict quality control, weak supervision, and rights protection to strict quality control, strong supervision, and rights protection. This indicates that when the commercial losses caused by weak supervision of the platform exceed the sum of the additional costs and market governance benefits of strong supervision of the platform, the platform will be forced to turn to a strong supervision strategy due to its inability to withstand the commercial losses caused by the massive loss of users who defend their rights.

5.2.2. Strong Supervision Costs and Market Governance Benefits

When the live-streaming e-commerce platform implements a strong supervision strategy, it will spend more human and resource costs to respond to consumer rights feedback, but at the same time, it can also gain market governance benefits. To explore the impact of changes in strong supervision costs and the market governance benefits for the live-streaming e-commerce platform on each subject, we set the costs of strong supervision as $C_1=25$, $C_1=15$, and $C_1=10$ and the market governance benefits as $J=5$, $J=15$, and $J=25$ for simulation, and the results are shown in Figure 9 and Figure 10.

When the costs of strong regulation decrease or the benefits of market governance increase, the platform tends to adopt a strong supervision strategy. This indicates that the market governance benefits gained by the platform under strong supervision, after deducting the supervision costs, exceed the commercial losses under weak supervision. Although the platform faces increased supervision costs in the short term, in the long run, a strong supervision strategy will enhance the platform’s overall credibility and user satisfaction and bring more significant market governance benefits to ensure the sustainable development and long-term profitability of the platform.

5.2.3. Percentage of Platform Commissions

To explore the impact of changes in the percentage of platform commissions on each subject, we set the percentage of platform commissions as $h=0.1$, $h=0.2$, and $h=0.3$ for simulation, and the results are shown in Figure 11.

When consumers choose the rights protection strategy, the equilibrium strategy of the system changes from lax quality control, strong supervision, and rights protection to strict quality control, weak supervision, and rights protection as the percentage of platform commissions becomes higher. In this instance, the profit margins caused by social media influencers’ lax quality control strategies are compressed, while the platform’s strong supervision increases the cost of violations, meaning influencers face a higher level of punishment. Therefore, under this dual pressure, influencers turn to strict quality control strategies to improve product quality and consumer satisfaction, thereby remaining competitive and profitable. With the general adoption of strict quality control strategies by social media influencers, the overall quality of products on the market improves, which means reduced consumer complaints due to quality issues and lowered supervision pressure on platforms. Therefore, with fewer product quality issues, live-streaming e-commerce platforms tend to adopt a weak supervision strategy to reduce their operating costs.

5.3. Impacts of Consumers

5.3.1. Functional Value and the Success Rate of Rights Protection

Consumers’ functional value gains are mainly derived from the satisfaction of their life needs, that is, the material performance gains they can obtain when purchasing the products recommended by social media influencers. The success rate of rights protection refers to the probability that the platform can effectively deal with and safeguard consumers’ rights when they encounter product quality problems. To explore the impact of different functional value gains and success rates of rights defense on each subject, we set $N=20$, $N=40$, and $N=60$, and $K_2=0.2$, $K_2=0.3$, and $K_2=0.4$ for simulation, and the results are shown in Figure 12 and Figure 13.

The system’s equilibrium strategy changes from lax quality control, weak supervision, and no rights protection to strict quality control, weak supervision, and rights protection as the functional value gain increases or as the success rate of consumers in defending their rights increases. This shows that when the functional value of the products purchased by consumers becomes higher and higher, consumers are more inclined to defend their rights. This phenomenon is consistent with the reality that consumers invest more money in these products and are more sensitive to the product quality. In addition, as the success rate of rights defense rises, consumers are more confident in protecting their reasonable interests through rights defense. At the same time, as the proportion of consumers who defend their rights increases, social media influencers face a greater risk of being penalized by platforms, which prompts them to adjust their management strategies and shift from lax quality control to strict quality control.

5.3.2. Emotional Value

When consumers choose to purchase products recommended by social media influencers, they can obtain mental pleasure and satisfaction, namely emotional value gains. To explore the influence of different emotional value gains of consumers on each subject, we set $W=20$, $W=40$, and $W=60$ for simulation, and the results are shown in Figure 14.

With a gradual increase in the emotional value gains consumers receive based on their purchasing behavior, the system’s equilibrium strategy changes from lax quality control, strong supervision, and rights protection to lax quality control, weak supervision, and no rights protection. The logic behind this shift is that consumers’ strong emotional reliance on and support for social media influencers causes them to often choose not to defend their rights when there are problems with their products in order to maintain an emotional connection with influencers. The existence of this phenomenon not only weakens consumers’ willingness to defend their rights but also affects the supervision strategy of live-streaming e-commerce platforms. Due to consumers generally not defending their rights, the platforms may see no need to implement strict supervision measures and thus turn to a weak supervision strategy. In an environment of weak supervision, social media influencers are easily driven by profit and choose the less costly lax quality control strategy to maximize their revenue. This ultimately leads to stability of the strategies of each subject (lax quality control, weak supervision, and no rights protection). In the long run, the overall operating environment of the live-streaming e-commerce platforms will gradually deteriorate. The key to promoting the orderly and healthy development of live-streaming e-commerce platforms is to change this current market equilibrium. Consumers should realize that excessive emotional maintenance and blind support for social media influencers will adversely affect the positive development of the market. Therefore, consumers should actively defend their rights when encountering product problems and even protect their interests through legal means. At the same time, platforms should also assume responsibility for supervision in order to promote strict quality control on the part of social media influencers and achieve the long-term stable development of live-streaming e-commerce.

6. Conclusions and Management Implications

6.1. Conclusions

This paper considers product quality issues and consumer preferences in live-streaming e-commerce and analyzes the stability of the strategic choices of each subject, the stability of the combination of equilibrium strategies within the game system, and the impact of key factors by constructing a tripartite evolutionary game model of social media influencers, live-streaming e-commerce platforms, and consumers. Furthermore, the validity of the cases is verified by a numerical simulation analysis. The following conclusions are obtained based on the above research.

(i)

In the evolutionary game system of live-streaming e-commerce, there are five possible evolutionarily stable strategies for the system. They are lax quality control, weak supervision, and no rights protection; lax quality control, weak supervision, and rights protection; strict quality control, weak supervision, and rights protection; lax quality control, strong supervision, and rights protection; and strict quality control, strong supervision, and rights protection.

(ii)

When the emotional value obtained by the consumers exceeds the compensation obtained by the consumers through rights protection and the actual value of the products minus the cost of rights protection, the strategy of the three parties will eventually stabilize at lax quality control, weak supervision, and no rights protection. In this context, the live-streaming e-commerce industry faces an undesirable phase of development driven by excessive consumer fandom.

(iii)

Consumers’ purchase decisions under different motivations will affect their choice of rights protection. When the functional value of the products is higher, consumers are more motivated to choose a rights defense strategy. In this context, the strategic equilibrium state for social media influencers will undergo a leap, and the strategic choice will shift from a lax quality control strategy to a strict quality control strategy. When the purchase of products brings higher emotional value to consumers, consumers are more inclined not to defend their rights, and the strategy of social media influencers stabilizes at lax quality control. In this context, the strategic equilibrium state for the live-streaming e-commerce platform will jump, shifting from strong supervision to weak supervision.

(iv)

A higher risk–return factor or a lower probability of quality problemscan make social media influencers more motivated to choose a lax quality control strategy. As the difference in the probability of quality problems continues to increase, the equilibrium strategy will shift from lax quality control to strict quality control. It should be noted that if the platform’s punishment for quality problems is lower, the effect of the probability of quality problems is not significant, and this will not motivate influencers to change their strategy. Another interesting finding is that a high percentage of platform commissions can encourage influencers to implement strict quality control, while the platforms can maintain weak supervision.

6.2. Management Implications

Based on the above conclusions, the following management recommendations are proposed from the perspectives of social media influencers, live-streaming e-commerce platforms, and consumers, respectively.

(i)

Social media influencers should establish a rigorous collaborative screening mechanism, conducting a thorough qualification review and credibility assessment of potential partners, for example, gaining an in-depth understanding of a merchant’s market reputation and its product quality management system. Consumers have higher expectations and sensitivity to the quality of products with a high functional value, and social media influencers must adopt stricter quality control measures when promoting and selling these high-value goods. This can help to reduce consumer dissatisfaction and complaints arising from quality issues. In the event of product quality problems, social media influencers should take a positive and sincere attitude, apologize to consumers and compensate them according to the law, and promise to strictly control the quality of their products in the future and accept consumers’ supervision at all times. In addition, social media influencers can enhance the transparency of their operations by disclosing their selection criteria and quality control processes, such as listing the key factors considered in product selection and displaying product-related quality certifications and testing reports. Social media influencers should become quality guardians and trust-maintainers to maintain long-term competitiveness and promote the healthy and sustainable development of the industry.

(ii)

Live-streaming e-commerce platforms should use data mining algorithms to conduct an in-depth analysis of massive data resources such as transaction history and consumer rights protection records to identify areas with a high incidence of product quality problems, changing trends in social media influencers’ reputations, and hot topics within consumer complaints. At the same time, relying on artificial intelligence and big data analysis, an intelligent risk warning model can be built to effectively identify possible violations on the basis of lax quality control by social media influencers. For live-streaming business activities judged as high-risk, platforms should establish a quick response mechanism. Once it is found that there are product quality problems in live-streaming, platforms must punish this severely, such as lowering credit ratings, suspending live-streaming for some time, or even banning it to constrain and regulate the product selection behavior of social media influencers. In addition, to improve the quality of service of their platforms, platforms need to establish perfect training systems, improve the work efficiency and problem-solving abilities of their customer service specialists, and reduce the waiting time for feedback on user rights. Furthermore, consumers’ rights protection behavior will deter social media influencers from lax quality control somewhat, so it plays a key role in the product quality governance system. Platforms should encourage consumers to participate in the daily governance of the platform and strengthen the enthusiasm of consumers for participating in supervision. For example, platforms can set up a public honor roll to recognize consumers who actively participate in feedback and make constructive comments. They can also receive exclusive coupons or sweepstakes. These incentive mechanisms aim to strengthen consumer supervision of social media celebrities and encourage them to cooperate with e-commerce live-streaming platforms in carrying out co-governance.

(iii)

For consumers, it is crucial for them to maintain rational consumption choices. In the context of live-streaming with goods, the consumption model based on the fan economy often leads to the excessive involvement of emotional factors in consumers’ decision-making processes, which is not conducive to the creation of a rational and healthy consumption environment. Consumers need to maintain a certain distance from social media influencers and avoid excessive investment of time and energy. In addition, consumers should make purchase decisions based on objective product information and their actual personal needs and avoid irrational consumer behaviors due to blind admiration and following of influencers, which is conducive to managing product quality issues in live-streaming. Consumers can set a shopping budget for themselves and regularly assess whether their consumption behavior is in line with their personal consumption philosophy and life goals. If consumers encounter product quality problems, they should actively defend their rights to platforms to safeguard their legitimate rights and interests and assist the platform in effectively managing unregulated behavior on the part of social media influencers. When influencers or platforms fail to deal with problems, consumers should pursue their rights through other legal channels, forcing social media influencers to improve the strictness of their product selection and urging platforms to strengthen their supervision efforts. In summary, rational consumer purchasing behavior and active rights protection actions can help promote a more standardized and healthy live-streaming e-commerce environment.

6.3. Limitations and Future Research

This paper conducted a game strategy analysis with social media influencers, live-streaming e-commerce platforms, and consumers as the participants, as well as analyzing the influence of related factors on the equilibrium of the system’s strategy, and put forward feasible suggestions for the standardized operation of live-streaming e-commerce. However, this study still has some limitations.

This paper only considered the interactions between the main participants in live-streaming e-commerce and their impact on product quality supervision without considering the role of the government in regulating market operations. Therefore, introducing the government as a new game participant, constructing a multi-party game model with the participation of the government included, and analyzing the influence mechanism of government policies and regulatory measures on the quality of live-streaming e-commerce products will be our future research directions.