2.1. Live streaming e-commerce sales

Live streaming e-commerce sales are a new business model. Brands or streamers sell their products through online video streaming. Compared with traditional e-commerce websites, live broadcasting involves an interactive, entertainment and synchronous environment, enabling real-time interaction between streamers and viewers as well as between viewers [16]. The live broadcast delivery mode of platforms such as Taobao in China is in full swing. Some international e-commerce platforms, such as Amazon and Walmart, are also aware of the advantages of live broadcast and have launched their own live commercial activities and platforms. The rapid development of live broadcasting business has brought new opportunities and challenges to academics, businesses and consumers [17].

With the rapid development of the live streaming e-commerce model [18], streamers have gradually become a new emerging profession, and a group of "Influential streamers" have gradually gained fame in this process. Different from traditional celebrity endorsements, the interaction between streamers and consumers in live broadcasts is more "down-to-earth". Therefore, consumers are more willing to make actual purchases due to the "virtual intimate relationship" established with the streamer [19,20]. Considering the creativity and interactivity of the live broadcast, the sense of social presence that consumers get during watching the live broadcast is conceptualized as a personal experience generated by watching the live broadcast [21]. Quasi-social relationships play a crucial role in increasing purchase intentions, and consumers’ perceived utilitarian value and perceived entertainment value indirectly influence their consumption intentions through their trust in the products and sellers [22]. The most prominent advantage of online live marketing lies in the seamless integration of the internet and the personal charm of streamers, with streamers and targeted audiences selecting each other, and consumers’ expectations for the level of live streaming services will further drive the development of streamers [23]. As the relationship between consumers and streamers progresses to different stages, consumers’ psychological contracts will gradually strengthen, which will also encourage them to maintain consumption stickiness [24,25]. From this, we can see that if consumers engage in consumption behaviors with a specific streamer, they may gain emotional benefits, and streamers can also expand their influence and increase their income as a result. Therefore, this study is based on the influence of consumers’ emotional factors on the design of consumer behavior patterns.

2.2. Product quality and after-sales service of live streaming e-commerce

In the booming market, high demand has promoted the continuous upgrading of product quality and after-sales service. When streamers have formed a competitive advantage in product quality and after-sales service, it can often attract more consumers’ attention and choice [26]. Similarly, high-quality after-sales service can also reverse the dynamic changes of market demand [27].

However, due to the rapid rise of live broadcast e-commerce, there are several problems to be solved. On the one hand, the phenomenon of false publicity quality occurs frequently. Some of the broadcasters abused their information superiority, perfunctorily selected products and exaggerated the efficacy of the products when selling them to induce consumers to buy [28]. On the other hand, the phenomenon of after-sales shirking responsibility should not be ignored. In the platform e-commerce live broadcast mode, the division of responsibilities is not clear, so streamers and the platform often shirk the publicity and legal responsibilities of selling products to avoid after-sales responsibilities, which seriously undermines the fair competition order of the market [29].

For the internal quality supervision of streamers on e-commerce platforms, researchers like [30] suggest that platforms can control opportunistic behaviors of sellers by establishing a seller reputation mechanism, thereby improving product quality [31–33]. In addition, some platforms ensure the quality and after-sales service of star-brand products by increasing the proportion of self-streaming by platform-brand merchants. A significant development in this regard is celebrity streamer Li Jiaqi’s transparency in product selection, demonstrated by his popular show "Every Girl’s Offer" on Bilibili, which has garnered over ten million views, facilitating direct consumer interaction with merchants and products. However, the self-interest nature of online shopping platforms means they can’t completely eliminate quality risks for consumers [34,35]. Addressing counterfeit sales in e-commerce, high-quality online word-of-mouth is identified as a key solution [36,37]. Government regulatory bodies are advised to innovate in management and guide the establishment of self-regulatory mechanisms for online reputation platforms [38,39], while e-commerce and social media platforms should establish reasonable regulatory accountability mechanisms [40,41]. In view of these problems, this paper discusses the influencing factors of streamers’ selection quality in the live broadcast delivery and how to improve the selection quality.

2.3. Evolutionary game in live streaming e-commerce

However, despite the disclosure of numerous internal operations and the advancement of external regulation, the definition of responsibilities in the live streaming e-commerce process often remains unclear. Streamers may simultaneously assume multiple roles such as merchant and advertising spokesperson, and platforms can act both as operators and suppliers. This ambiguity often leads to a situation where streamers and platforms pass responsibility back and forth, making it challenging for consumers and official regulatory bodies to pinpoint specific responsible parties. This not only often puts platforms in a state of regulatory absence but also increases the difficulty for consumers to assert their rights. Wu et al. [42] and Li et al. [43] conducted research on the current practices of "acquaintance deception pricing" and algorithmic price discrimination by e-commerce platforms, respectively. They found that consumer oversight can effectively curb e-commerce platforms from choosing to engage in regulatory violations. Moreover, adopting reasonable incentive measures can reduce the cost of consumer supervision and promote the sustainable development of e-commerce platforms. Li et al. [44] expanded consumer regulatory channels within the regulatory mechanisms of e-commerce platforms and constructed a tripartite evolutionary game model involving e-commerce platforms, the government, and consumers under information asymmetry. This model analyzes the influencing factors and conditions for stable states in the strategic choices and behavior evolution of all parties. Fan et al. [45] highlighted issues such as counterfeit advertising and fraudulent activities arising from insufficient administrative supervision. They proposed a behavioral evolutionary game process involving platforms, consumers, and streamers. Through customer complaint handling systems and emotional monitoring systems, they aim to swiftly resolve customer complaints and predict consumer actions, thereby enhancing consumer regulation and preventing conflicts.

Through literature review, it can be seen that the success of live broadcast, as an innovative business model, largely benefits from the ingenious use and guidance of the consumer psychology of "fan economy". However, with the rapid development of live broadcast business, the quality and after-sales problems of live broadcast delivery still need to be solved. Reviewing the research of many scholars, it is found that to achieve the standardized development of live broadcast e-commerce market, all parties need to cooperate and supervise. Based on the research of these scholars, this paper extends the study to explore how changes in consumer rights protection costs influence consumers’ standards for product quality, and how platform regulatory intensity and consumer quality standards affect the seriousness of streamers’ product quality selection. To investigate the issues mentioned earlier, this paper employs a tripartite evolutionary game model to study the strategy choices and evolution of e-commerce platforms, consumers, and streamers. The tripartite game research method is widely applied in various fields, coordinated regulation of market-oriented rental housing, and is a common method for studying multi-agent systems [46,47].

Through the review of the literature mentioned above, the innovation of this paper primarily lies in three aspects: Firstly, it employs a tripartite evolutionary game approach to analyze the relationships among multiple agents. Compared to previous research methods, this approach better reflects the mutual constraints and influences among e-commerce platforms, streamers, and consumers. It facilitates the exploration of the evolution of each party’s strategic choices under the influence of multiple factors. Secondly, unlike traditional quality issues, live streaming product quality involves a broader range of subjects. Existing research often treats e-commerce platforms and streamers as a single entity to explore the quality regulation models by the government and third-party regulatory bodies. This paper distinguishes between e-commerce platforms and streamers, studying the factors influencing their profit when making strategic choices, both independently and in relation to consumers. Thirdly, the research question of this paper is based on actual phenomena, taking into account the impact of consumer rights protection costs on consumer quality requirements. It also considers how these requirements, influenced by consumer actions, affect the platforms’ punitive measures and, in turn, the subjective product selection behavior of streamers. This perspective helps fill gaps in research on how to improve the quality of product selection in live streaming e-commerce and offers practical guidance for enhancing the quality of product selection in this domain.

3.1. Model assumptions

Assumption 1: In the context of e-commerce live streaming activities, all three participating entities are bounded rationality. The strategies for the e-commerce platform are {Active cooperation, Passive cooperation}, for consumers {Strict requirements, Relaxed requirements}, and for streamers {High-quality selection, Low-quality selection}. In this context, ’High-quality selection’ for live streaming e-commerce streamer involves considering the product’s quality, user experience, and viewer demand for the products showcased in the stream; whereas ’Low-quality selection’ involves restricting their options to simply choosing brands that offer higher commissions.

Assumption 2: Streamers adopting the high-quality product selection strategy earn a profit of U₁, with the probability of encountering quality issues denoted as w₁. Conversely, opting for a low-quality product selection strategy yields a profit of U₂, with the probability of quality issues at w₂. Considering the increased workload associated with a high-quality selection strategy, it is typically assumed that U₁<U₂, as the probability of facing quality problems is lower with high-quality selection, thus w₁<w₂. When quality issues are detected, the loss faced by streamers (comprising compensation and fines levied by the platform) is F_i, which is directly proportional to the probability of the product’s quality issues, represented as F_i = w_if_i(i = 1,2; j = 1,2, where f_i corresponds to the amount lost by the e-commerce platform under active and passive cooperation strategies, assuming f₁>f₂.

Assumption 3: The active cooperation of an e-commerce platform involves proactively promoting streamers to the platform’s existing users to expand the streamers’ influence. Passive cooperation, on the other hand, entails only basic promotion, without actively directing traffic to the streamers. The profit coefficient for different cooperation modes is denoted as r_i(i = 1,2). Considering that active cooperation can increase sales and thus generate more revenue for the platform, it is assumed that r₁>r₂. Furthermore, if quality issues arise with products sold by the streamer team, the platform incurs a loss denoted as N_i, and N_j = w_in_j(i = 1,2; j = 1,2). Here, n_j represents the extent of negative impact caused by consumers choosing either strict or relaxed requirements, with the assumption that n₁>n₂. If the platform chooses active cooperation, and quality issues occur in the products sold by the streamer team, the platform will implement certain compensation measures to retain customers who might otherwise leave. The compensations provided to consumers with strict and relaxed requirements are denoted as E₁ and E₂, respectively, with the assumption that E₁>E₂.

Assumption 4: During the live streaming e-commerce viewing process, consumers gain a benefit denoted as S₁ when they have strict requirements for the streamer, and a benefit S₂ under relaxed requirements. Since it is assumed that the streamer has a certain level of popularity, consumers derive emotional benefits when imposing strict requirements, leading to the assumption that S₁>S₂. Additionally, the loss incurred by consumers upon discovering quality issues is P₁ under strict requirements and P₂ under relaxed requirements. Considering that consumers with strict requirements will engage in rights protection activities, thus incurring certain time and economic costs when quality issues arise, it is assumed that P₁>P₂. As the cost incurred by consumers in the accountability process is often not directly proportional to the compensation received, it is assumed that P₁−P₂>E₁−E₂. If consumers have strict requirements for the streamer, and quality issues occur in the products sold, this leads to customer attrition and the associated loss for the streamer is denoted as A_i, where A_i = a_iP₁(i = 1,2). Here, a_i represents the loss for the streamer under the scenarios of high-quality or low-quality selections, with the assumption being a₁<a₂.

The notations used in this model are shown in Table 1.

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Table 1. Notations for the model.

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3.2. Model construction

Based on the assumptions and parameters mentioned earlier, the revenue matrix for the e-commerce platform, consumers, and the streamer is as shown in Table 2.

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Table 2. Strategy combination for e-commerce platform, consumer, and streamer.

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This can be specifically represented in Table 3:

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Table 3. Revenue matrix for e-commerce platform, consumer, and streamer.

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4.1. Equilibrium points of the tripartite evolutionary game system

Let the expected revenues for the e-commerce platform when choosing active cooperation and passive cooperation be M_x and M_1−x respectively. Denote their average revenue as M_a. Then, the following relationship can be established: (1) (2) (3)

Let the expected revenues for consumers when choosing strict and general requirements be M_y and M_1−y respectively. Denote their average revenue as M_b. Then, the following relationship can be established: (4) (5) (6)

Let the expected revenues for the streamer when choosing high-quality and low-quality selections be M_z and M_1−z respectively. Denote their average revenue as M_c. Then, the following relationship can be established: (7) (8) (9)

The system, composed of the above dynamic equations, is as follows: (10)

4.2. Analysis of the evolutionary paths of strategies for each entity

In a differential dynamical system, the initial values x₀,y₀, and z₀ significantly impact the system’s evolutionary outcome. Therefore, by analyzing the three-dimensional dynamical system M of the live streaming e-commerce regulatory game market, we can examine the dynamic changes in strategy choices of the three participating entities and explore the market’s evolutionary paths and patterns. Based on the nature of evolutionarily stable strategies and the stability theorem of differential equations, for the differential equation i(t) = F(i), where i = {x,y,z}, when the system is in a stable state for a certain strategy, the derivative of the system’s replicator dynamic equation F(i) must satisfy F(i) = 0 and F′(i)<0. For ease of calculation, according to Formula (10), let , we can obtain the threshold values y*,z*, and x*, leading to the following proposition.

4.2.1. E-commerce platform.

Proposition 1: For the e-commerce platform, when y = y*, where , the platform will not change its initially chosen strategy. When y<y*, the platform chooses active collaboration. Conversely, when y>y*, the platform switches to passive collaboration.

Proof: Considering that the first derivative of F(x) with respect to , let . According to the stability theorem of differential equations, for the probability of the e-commerce platform choosing active collaboration to be in a stable state, it must satisfy: F(x) = 0 and . Given that E₁>E₂,0<w₁<w₂, and z∈[0,1], it follows that . Thus, G(y) is an increasing function with respect to y. Therefore, when y = y*,F(x) = 0 and , the stable strategy is indeterminate. When y<y*,G(y)<0, satisfying the conditions F(x) = 0 and , taking x = 1 as the Evolutionarily Stable Strategy (ESS) for the e-commerce platform. When y>y*,G(y)>0, the conditions F(x) = 0 and are satisfied, taking x = 0 as ESS.

Based on the above analysis, a replicator phase diagram illustrating the strategy evolution of the e-commerce platform is drawn, as shown in Fig 2(A). From the diagram, it can be seen that when the initial state of the e-commerce platform’s strategy is in space V₁, where 0<y<y*,x = 1 is the evolutionary strategy equilibrium point. In this state, the e-commerce platform opts for an active collaboration strategy. Conversely, when the initial strategy state of the e-commerce platform is in space V₂, where y*<y<1, x = 0 is the evolutionary strategy equilibrium point, and the platform selects a passive collaboration strategy.

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Fig 2. Replicator phase diagram for strategy evolution in live streaming e-commerce.

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As indicated in Fig 2(A), when 0<y<y*,x = 1 is the evolutionary strategy equilibrium point, and the e-commerce platform chooses an active collaboration strategy corresponding to volume V₁. When y<y*<1, x = 0 is the evolutionary strategy equilibrium point, and the e-commerce platform opts for a passive collaboration strategy corresponding to volume V₂. The volume V₁ is given , which simplifies to , and V₂ is given by V₂ = 1−V₁.

Corollary 1: The probability of an e-commerce platform choosing active collaboration is positively correlated with the revenue from the streamer’s high-quality selection strategy and negatively correlated with the revenue from the streamer’s low-quality selection strategy. This correlation also applies to the coefficients of revenue for active and passive collaboration strategies under specific conditions.

Proof: Based on the expression for the probability of active collaboration V₁ by the e-commerce platform, the first-order partial derivatives of various elements are calculated. For the derivative with respect to , and for . Similarly, the derivatives with respect to r₁ and r₂ are and , respectively. Defining as x_w and considering the function x_w−(1+logx_w)>0 within the interval x_w∈(0,1) implies that this function is positive. Given that r₁>r₂,E₁>E₂,U₁<U₂, and w₁<w₂, it follows that and . When the conditions and E₂(w₂−w₁)<(r₁−r₂)(U₂−U₁) are satisfied, then and .

Thus, Corollary 1 implies that securing the streamer’s revenue in high-quality product selection can discourage general collaboration by the e-commerce platform. Additionally, when the ratio of revenue from low-quality to high-quality selection by the streamer exceeds the ratio of probabilities of encountering problems , increasing the coefficient of revenue for active collaboration can encourage the platform to adopt an active collaboration strategy.

4.3. System equilibrium strategies and stability analysis

Setting F(x) = 0,F(y) = 0,F(z) = 0, which signifies no change in the system’s strategy choices, results in 15 equilibrium points. Among these, M₁,M₂,M₃,M₄,M₅,M₆,M₇,M₈ are equilibrium solutions located on the boundary of the tripartite evolutionary game’s equilibrium domain . Within this domain, there also exist M₉,M₁₀,M₁₁,M₁₂,M₁₃,M₁₄,M₁₅ that satisfy the conditions. Due to the asymmetric game resulting from information asymmetry, the evolutionary stable strategies should be pure strategies. Therefore, only the eight pure strategy local equilibrium points are discussed.

To verify the stability of the equilibrium strategies, the local stability can be determined by solving the system’s Jacobian matrix (J) [53,54]. The system’s Jacobian matrix (J) can be derived based on Eq (10).

(11)

Using the first method of Lyapunov [55,56], the stability of equilibrium points can be determined by analyzing the eigenvalues of the Jacobian matrix. If all eigenvalues of the Jacobian matrix have negative real parts, the equilibrium point is asymptotically stable. If at least one eigenvalue has a positive real part, the equilibrium point is unstable. If the Jacobian matrix has eigenvalues with zero real parts (aside from those with negative real parts), the equilibrium point is in a critical state, and its stability cannot be determined solely by the sign of the eigenvalues. By substituting the eight pure strategy points of the game into the linear transformation matrix, the eigenvalue corresponding to the equilibrium points are obtained, as shown in Table 4 below:

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Table 4. Eigenvalue corresponding to equilibrium points.

https://doi.org/10.1371/journal.pone.0305427.t004

Among the equilibrium conditions for the replicator dynamic system involving the e-commerce platform, consumer, and streamer, notable conditions include: ① ; ② ; ③ ; ④ ; ⑤ ; ⑥ ; ⑦ ; ⑧ . Based on these conditions, it is inferred that the system M has four potential evolutionary stable strategies: M₂(1,0,0),M₅(1,1,0),M₆(1,0,1), and M₈(1,1,1). This analysis reveals the complexity and the variety of stable scenarios that can emerge from the strategic interactions in this tripartite evolutionary game.

4.4. Stability analysis of equilibrium points in four scenarios

Scenario 1: Under the conditions of ②, specifically when , and w₂f₁−w₁f₁<U₂−U₁, it indicates that when the platform opts for active collaboration and the streamer selects low-quality products, the consumer’s benefits from relaxed requirements are higher than those from strict requirements. Furthermore, when consumers have relaxed requirements, the streamer’s benefits from low-quality selection exceed those from high-quality selection. Also, when consumers have relaxed requirements and the streamer opts for low-quality products, the platform’s benefits from active collaboration are greater than those from passive collaboration. As Table 5 indicates, the Jacobian matrix corresponding to the equilibrium point M₂(1,0,0) has all negative eigenvalues, making M₂(1,0,0) an equilibrium point. Therefore, {Active collaboration, Relaxed requirements, Low-quality selection} constitutes the evolutionary stable strategy in this scenario. The phase diagram of the evolutionary game model for this scenario is shown in Fig 3.

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Fig 3. Replicator dynamic phase diagram for scenario 1.

https://doi.org/10.1371/journal.pone.0305427.g003

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Table 5. Stability analysis of equilibrium points in four scenarios.

https://doi.org/10.1371/journal.pone.0305427.t005

Scenario 2: Meeting conditions of ⑤, namely when , and , indicates that when the platform is actively collaborating and the streamer opts for low-quality selection, the consumers’ gains from strict requirements exceed those from relaxed requirements. Additionally, when consumers have strict requirements, the streamer’s benefits from low-quality selection are greater than from high-quality selection. Also, when consumers have strict requirements and the streamer selects low-quality products, the platform’s benefits from active collaboration surpass those from passive collaboration. As per Table 5, the equilibrium point M₅(1,1,0) has all negative eigenvalues in its Jacobian matrix, thus M₅(1,1,0) is an equilibrium point, and {Active collaboration, Strict requirements, Low-quality selection} is the evolutionary stable strategy in this scenario. The phase diagram for this evolutionary game model is shown in Fig 4.

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Fig 4. Replicator dynamic phase diagram for scenario 2.

https://doi.org/10.1371/journal.pone.0305427.g004

Scenario 3: Fulfilling conditions of ⑥, specifically when , and w₂f₁−w₁f₁>U₂−U₁, suggests that when the platform actively collaborates and the streamer opts for high-quality selection, the benefits for consumers having relaxed requirements exceed those from strict requirements. Moreover, when consumers have relaxed requirements, the streamer’s benefits from high-quality selection are higher than from low-quality selection. Also, when consumers have relaxed requirements and the streamer opts for high-quality products, the platform’s benefits from active collaboration are higher than those from passive collaboration. According to Table 5, the equilibrium point M₆(1,0,1) has all negative eigenvalues in its Jacobian matrix, making M₆(1,0,1) an equilibrium point. Therefore, {Active collaboration, Relaxed requirements, High-quality selection} is the evolutionary stable strategy in this scenario. The phase diagram for this evolutionary game model is illustrated in Fig 5.

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Fig 5. Replicator dynamic phase diagram for scenario 3.

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Scenario 4: Fulfilling conditions outlined in ⑧, specifically when , and , suggests that when the platform chooses active collaboration and the streamer opts for high-quality selection, the benefits for consumers adhering to strict requirements exceed those from relaxed requirements. Additionally, when consumers have strict requirements, the streamer’s benefits from high-quality selection are greater than from low-quality selection. Furthermore, when consumers have strict requirements and the streamer opts for high-quality products, the platform’s benefits from active collaboration surpass those from passive collaboration. According to Table 5, the Jacobian matrix eigenvalues corresponding to the equilibrium point M₈(1,1,1) are all negative, making M₈(1,1,1) an equilibrium point. Therefore, (Active Collaboration, Strict Requirements, High-Quality Selection) constitutes the evolutionary stable strategy in this scenario. The phase diagram of the evolutionary game model for this scenario is shown in Fig 6.

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Fig 6. Replicator dynamic phase diagram for scenario 4.

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The stability of each equilibrium point across these four scenarios is detailed in Table 5. This analysis helps to understand the dynamic interactions and potential outcomes in different strategic combinations within the live streaming e-commerce environment.

5.1. Parameter setting

Data plays a crucial role in simulation analysis, where the accuracy and reliability of the analysis need to be verified by comparison with actual data. Utilizing high-quality data helps ascertain the precision of the model and identify any potential biases or errors within it. The strategic evolution of the tripartite game among live streaming platforms, streamers, and consumers in live streaming e-commerce is relatively complex, requiring simulation analysis of four scenarios using Matlab2022a software. General data sets are derived from empirical data [23], real-world examples [23,57], and references [41,58]. The simulation parameters in this paper are set according to the simulation parameter principles found in relevant literature [59,60] and the relevant regulations of the "Consumer Rights Protection Law of the People’s Republic of China". Due to the complexity of the parameters in the model, this paper discusses the stable strategies of evolutionary games under four ideal scenarios. According to the system stability analysis, when the relationship between parameters and variables changes, the decisions of e-commerce platforms, consumers, and streamers also change, exhibiting uncertainty. The values of the simulation parameters are set as shown in Tables 6–9.

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Table 6. Simulation parameters for scenario 1.

https://doi.org/10.1371/journal.pone.0305427.t006

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Table 7. Simulation parameters for scenario 2.

https://doi.org/10.1371/journal.pone.0305427.t007

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Table 8. Simulation parameters for scenario 3.

https://doi.org/10.1371/journal.pone.0305427.t008

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Table 9. Simulation parameters for scenario 4.

https://doi.org/10.1371/journal.pone.0305427.t009

5.2. Simulation analysis of strategy evolution in live streaming e-commerce market

Scenario 1: Under the specified conditions ②, namely when , and S₁−S₂ < (E₂−E₁−P₂+P₁)w₂, the parameters are set as shown in Table 6, and the simulation results are presented in Fig 7.

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Fig 7. Evolutionary simulation for scenario 1.

https://doi.org/10.1371/journal.pone.0305427.g007

Based on the above parameter settings, the process of strategy evolution in the system is depicted in the following Fig 7.

The simulation depicted in Fig 7 indicates that the equilibrium stable strategy M₂(1,0,0), representing {Active collaboration, Relaxed requirements, Low-quality selection}, is prevalent under these conditions. It is observed that when the costs associated with protecting consumer rights are high, it diminishes consumer initiative to defend their rights, leading them to be more lenient in their quality requirements during shopping. In this situation, where consumers are less demanding about quality issues, the e-commerce platform opts for active collaboration. Given the consumers’ low demands and the platform’s weaker punitive measures for quality issues, streamers are more inclined to choose low-quality products. The {Active collaboration, Relaxed requirements, Low-quality selection} becomes the evolutionary stable strategy, and the simulation results of the evolutionary game corroborate the theoretical analysis of Scenario 1.

Scenario 2: Fulfilling conditions of ⑤, specifically when , and S₂−S₁ < (E₁−E₂−P₁+P₂)w₂, the parameters are set as shown in Table 6, and the simulation results are presented in Fig 8.

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Fig 8. Evolutionary simulation for scenario 2.

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The system strategy evolution process based on the above parameters is as shown in Fig 8.

From the simulation shown in Fig 7, it is evident that the equilibrium stable strategy M₅(1,1,0), representing {Active collaboration, Strict requirements, Low-quality selection}, is the prevalent outcome. This suggests that as the costs associated with protecting consumer rights decrease, consumers tend to raise their expectations regarding product quality. Despite the increased costs associated with active collaboration, the combined benefits for the e-commerce platform and streamer from active collaboration still outweigh those from general collaboration, leading the platform to choose active collaboration. However, due to the still weak punitive measures of the platform for quality issues, the cost savings from streamers choosing low-quality products outweigh the losses incurred from consumers’ heightened standards. Therefore, streamers continue to opt for a low-quality selection strategy. The {Active collaboration, Strict requirements, Low-quality Selection} becomes the evolutionary stable strategy, validating the theoretical analysis of Scenario 2 through evolutionary game simulation results.

Scenario 3: Meeting conditions of ⑥, specifically when , and S₂−S₁ = (E₁−E₂−P₁+P₂)w₂, the parameters are set as shown in Table 8, and the simulation results are presented in Fig 9.

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Fig 9. Evolutionary simulation for scenario 3.

https://doi.org/10.1371/journal.pone.0305427.g009

Based on the parameter settings mentioned above, the strategy evolution process of the system is illustrated in Fig 9.

The simulation reveals that the equilibrium stable strategy M₆(1,0,1), representing {Active collaboration, Relaxed requirements, High-quality selection}, is the prevalent outcome. This indicates that due to the significant benefits obtained by e-commerce platforms in active collaboration with streamers, platforms often opt for active collaboration. When the costs associated with protecting consumer rights are high, it diminishes consumer initiative to defend their rights, leading them to be more lenient in their quality requirements during shopping. Despite consumers having lower expectations of streamers, the strong punitive measures of the platform for quality issues mean that the gains from streamers choosing low-quality products are insufficient to offset the losses caused by quality problems, naturally inclining streamers to opt for high-quality selections. The {Active collaboration, Relaxed requirements, High-quality selection} becomes the evolutionary stable strategy, validating the theoretical analysis of Scenario 3 through evolutionary game simulation results.

Scenario 4: Fulfilling conditions of ⑧, specifically when , and S₂−S₁ < (E₁−E₂−P₁+P₂)w₁, the parameters are set as shown in Table 9, and the simulation results are presented in Fig 10.

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Fig 10. Evolutionary simulation for scenario 4.

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Based on the aforementioned parameter settings, the system strategy evolution process is illustrated in Fig 10.

From the simulations, it is evident that the equilibrium stable strategy M₈(1,1,1), representing {Active collaboration, Strict requirements, High-quality selection}, is the prevalent outcome. This scenario reveals that due to significant benefits from active collaboration between e-commerce platforms and streamers, platforms often choose active collaboration. As the costs associated with protecting consumer rights decrease, consumers tend to raise their quality requirements for streamers. In this situation, with consumers imposing strict requirements and platforms exerting strong punitive measures for quality issues, the risk of losses from quality problems is high. Consequently, streamers naturally lean towards reducing the likelihood of quality issues and adopt high-quality selection strategies. The {Active collaboration, Strict requirements, High-quality selection} becomes the evolutionary stable strategy, confirming the validity of the theoretical analysis for Scenario 4 through evolutionary game simulation results.

5.3. Impact of parameter on strategy evolution stability

In the early stages of development for short video and social live streaming e-commerce platforms, e-commerce platforms often chose active collaboration, proactively pushing their original user base towards streamers. At this time, both consumers and streamers were typically in a wait-and-see state. Consequently, consumers had relaxed requirements while watching live streaming, and streamers, seeking to avoid risks and unwilling to invest heavily, opted for low-quality selections. In this scenario, the initial strategies for the e-commerce platforms, consumers, and streamers align with M₂(1,0,0), choosing {Active collaboration, Relaxed requirements, Low-quality selection}. The parameter values are set as previously indicated in Table 6, with the initial probabilities for x,y, and z being set at 0.4. The evolutionary simulation for this decision scenario is presented in Fig 11.

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Fig 11. Evolutionary simulation for initial decision M₂(1,0,0).

https://doi.org/10.1371/journal.pone.0305427.g011

This simulation illustrates how the dynamics of strategy evolution are influenced by initial decisions and parameter settings in the live streaming e-commerce context. It demonstrates the interaction between platform collaboration strategies, consumer requirements, and streamer product selection under specific initial conditions. Understanding these dynamics is crucial for e-commerce platforms, consumers, and streamers to adapt their strategies effectively in response to evolving market conditions and user behavior trends.

5.3.1. Analysis of factors influencing consumer decisions.

The transition from M₂(1,0,0) to M₅(1,1,0) represents a shift in consumer decisions from relaxed to strict requirements. Based on the eigenvalues at these equilibrium points, the change in consumer decisions is primarily associated with the parameters P_i,E_i, and S_i. Therefore, the study focuses on the impact of variations in these three parameters. The critical conditions for the transition from M₂ to M₅ are and S₂−S₁ = (E₁−E₂−P₁+P₂)w₂. When P₁≤7, the condition is satisfied, and the critical point becomes only S₂−S₁ = (E₁−E₂−P₁+P₂)w₂.

(1) When P₁ decreases, satisfying and S₂−S₁ = (E₁−E₂−P₁+P₂)w₂, the stable point transitions from M₂(1,0,0) to M₅(1,1,0) as shown in Fig 12(A). In a low P₁ state (P₁ = 7), when P₂ increases, satisfying S₂−S₁ = (E₁−E₂−P₁+P₂)w₂, the stable point shifts from M₂(1,0,0) to M₅(1,1,0) as depicted in Fig 12(B).

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Fig 12. Evolutionary simulation from M₂(1,0,0) to M₅(1,1,0).

https://doi.org/10.1371/journal.pone.0305427.g012

(2) Similarly, in a low P₁ state, when E₁ increases, the stable point transitions from M₂(1,0,0) to M₅(1,1,0), as shown in Fig 13(A). Also, in a low P₁ state, when E₂ decreases, the stable point shifts from M₂(1,0,0) to M₅(1,1,0) as depicted in Fig 13(B). Since S₂−S₁ = (E₁−E₂+P₂−P₁)w₂ is the critical condition for the transition from M₂(1,0,0) to M₅(1,1,0), when S₂−S₁ = (E₁−E₂+P₂−P₁)w₂, both M₂(1,0,0) and M₅(1,1,0) are in a stable state, and consumers can choose either. In such a scenario, the probability of choosing strict requirements y will stabilize but will be neither 1 nor 0. A similar situation was also reported in Liu et al. [61].

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Fig 13. Evolutionary simulation from M₂(1,0,0) tp M₅(1,1,0).

https://doi.org/10.1371/journal.pone.0305427.g013

(3) In a low P₁ state, when S₁ increases, the stable point shifts from M₂(1,0,0) to M₅(1,1,0), as shown in Fig 14(A). Similarly, when S₂ decreases in a low P₁ state, the stable point transitions from M₂(1,0,0) to M₅(1,1,0) as illustrated in Fig 14(B).

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Fig 14. Evolutionary simulation from M₂(1,0,0) to M₅(1,1,0).

https://doi.org/10.1371/journal.pone.0305427.g014

As shown in the figures above, increasing the emotional gains S₁ and compensations E₁ received by consumers for strict requirements can prompt a shift in consumer decision-making from relaxed to strict requirements. Similarly, reducing the cost P₁ of consumer accountability in strict requirement scenarios also leads to a shift from relaxed to strict requirements. Conversely, if the benefits and compensations received under relaxed requirements increase, along with a decrease in the cost of accountability, consumers are likely to revert their decision from strict back to relaxed requirements.

5.3.2. Analysis of factors influencing streamer decisions.

The transition from M₅(1,1,0) to M₈(1,1,1) reflects a shift in the streamer’s decision-making from low-quality to high-quality selection. Based on the eigenvalues at these equilibrium points, we can deduce that the changes in the streamer’s decisions are mainly influenced by U_i and w_i. Therefore, the study focuses on the impact of these two parameters. Assuming the initial stable point is M₅(1,1,0) with parameter values as shown in Table 7, the critical condition for the transition from M₅(1,1,0) to M₈(1,1,1) is .

(1) When U₁ increases or U₂ decreases, satisfying , the stable point shifts from M₅(1,1,0) to M₈(1,1,1) as shown in Fig 15(A) and 15(B).

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Fig 15. Evolutionary Simulation from M₅(1,1,0) to M₈(1,1,1).

https://doi.org/10.1371/journal.pone.0305427.g015

(2) Similarly, when w₁ decreases, the stable point shifts from M₅(1,1,0) to M₈(1,1,1) as shown in Fig 16(A). Conversely, when w₂ increases, the stable point transitions from M₅(1,1,0) to M₈(1,1,1) as depicted in Fig 16(B).

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Fig 16. Evolutionary simulation from M₅(1,1,0) to M₈(1,1,1).

https://doi.org/10.1371/journal.pone.0305427.g016

The simulations above reveal that the decision-making of streamers is positively correlated with the rewards U_i associated with different selection strategies and negatively correlated with the probability w_i of product issues under each selection strategy. Given that the probability of quality issues is higher with low-quality selection, streamers are inclined to choose high-quality products to minimize penalties. Conversely, if the platform’s regulatory measures are weak, streamers may opt for low-quality selections to maximize profits. This underscores the critical role of platform regulations and the impact of potential rewards and penalties in shaping streamer behavior in the live streaming e-commerce environment.

5.3.3. Analysis of factors influencing e-commerce platform decisions.

In the initial stages of live streaming e-commerce development, with streamers choosing low-quality selections, the entire process of the evolutionary game is studied. Assuming the initial stable point is M₅(1,1,0) with parameters as specified in Table 7, a temporary and unstable emergence of M₃(0,1,0) occurs when the active collaboration reward coefficient r₁ of the platform is reduced to 0.4. As r₁ is further decreased to 0.3, the evolutionary stable point bypasses M₃(0,1,0) and directly transitions to M₁(0,0,0). The strategy evolution process of the system under these conditions is depicted in Fig 17.

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Fig 17. Evolutionary simulation from M₅(1,1,0) to M₁(0,0,0).

https://doi.org/10.1371/journal.pone.0305427.g017

Fig 17 demonstrates that when the active collaboration reward coefficient r₁ for the e-commerce platform is high, the platform tends to choose active collaboration. However, as r₁ decreases, a sequence of transitions in the stability of the system is observed. Initially, a reduction in r₁ leads to a change in the stable point from M₅(1,1,0) to M₃(0,1,0), as the profits for the platform under M₅(1,1,0) and M₃(0,1,0) conditions become less favorable. Subsequently, the stable point shifts from M₃(0,1,0) to M₁(0,0,0) as the consumer benefits under M₃(0,1,0) and M₁(0,0,0) conditions S₁−w₂P₁<S₂−w₂P₂ also decrease. Then, as , the stable point moves from M₁(0,0,0) to M₂(1,0,0). Finally, the condition causes the stable point to shift back from M₂(1,0,0) to M₅(1,1,0), creating a cyclical pattern.

When r₁ is further reduced to 0.3 or lower, the final evolutionary stable strategy becomes M₁(0,0,0), characterized by passive collaboration from the e-commerce platform, relaxed consumer requirements, and low-quality selection by streamers. This state fails to stimulate active participation among the system’s stakeholders, potentially leading the live streaming e-commerce market into a low-end and chaotic state. This underscores the crucial role of maintaining appropriate incentives and collaboration levels to foster a healthy and dynamic market environment.

Similarly, as shown in Fig 18, when r₂ increases to 0.6 or higher, the final evolutionary strategy also becomes M₁(0,0,0), characterized by general cooperation of e-commerce platforms, general consumer requirements, and general product selection by streamers. This state fails to stimulate active participation from system stakeholders, potentially leading the live streaming e-commerce market into a low-end and disordered state, which is not conducive to maintaining a healthy shopping environment. This highlights the importance of the profit coefficient of e-commerce platforms to the entire evolutionary system.

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Fig 18. Evolutionary simulation from M₅(1,1,0) to M₁(0,0,0).

https://doi.org/10.1371/journal.pone.0305427.g018

Simultaneously, the reductions in r₁ and r₂ correspond to the intense competition among e-commerce platforms observed in real life. When r₁ decreases, the strategic choice of e-commerce platforms shifts from active cooperation to general cooperation, whereas a reduction in r₂ sways the platforms’ decision-making towards active cooperation. Moreover, the decrease in r₁ and r₂ also leads to streamers opting for general product selections, and the ultimate market outcome is that both reductions further diminish the profits of e-commerce platforms.