Cooperation or Confrontation? An Evolutionary Game Study on Content Clipping Authorization in Live Streaming E-Commerce Under Platform Regulation

Abstract

The rapid rise of live-streaming e-commerce has fostered a new “content clipping” model, in which secondary creators edit and republish anchors’ live-streaming content to promote product sales. While this model can expand market reach and enhance revenue, it also introduces copyright disputes, regulatory challenges, and profit-sharing conflicts among platforms, anchors, and secondary creators. This study develops a three-party evolutionary game model to examine strategic choices regarding platform regulation, anchor authorization, and secondary content creation. Results reveal that excessive regulation may undermine equilibrium and profitability, while appropriate authorization can balance risk and reward. Secondary creators’ participation is sensitive to commission rates and cost–benefit trade-offs. This research contributes to the literature by integrating copyright governance into live-streaming e-commerce game theory and offers actionable insights for designing regulatory mechanisms, optimizing authorization policies, and fostering sustainable multi-party collaboration.

1. Introduction

The rapid expansion of live-streaming e-commerce has fundamentally transformed online retailing and digital content ecosystems (Wongkitrungrueng & Assarut, 2020). In recent years, live-streaming has evolved from a niche marketing tool into a mainstream sales channel, generating substantial transaction volumes and user engagement worldwide. Industry reports indicate that the global live-streaming commerce market has reached hundreds of billions of U.S. dollars in annual gross merchandise volume (GMV), with China accounting for a dominant share. In particular, the Chinese live-streaming e-commerce market has experienced sustained double-digit growth, with total GMV exceeding several trillion RMB in recent years, and live-streaming contributing an increasingly significant proportion of overall online retail sales. Major platforms such as Taobao Live, Douyin, and Kuaishou have reported rapid user growth and rising conversion rates, highlighting the effectiveness of live-streaming in influencing consumer purchasing decisions. The integration of real-time interaction, product demonstration, and social engagement has made live-streaming a highly effective mechanism for influencing consumer purchasing decisions. Alongside this growth, the reproduction and redistribution of live-streaming content have emerged as a new driver of traffic expansion and commercial value creation. In China, particularly on platforms such as Douyin, an emerging business model known as content clipping has gained increasing prominence. Under this model, secondary creators extract and re-edit segments of anchors’ live-streams into short videos and embed product links to generate sales conversions. Compared with traditional live-streaming sales, content clipping relies on fragmented and recombined content as the primary promotional medium. According to industry observations, short-video content now accounts for a substantial proportion of platform traffic, and clipped live-streaming segments often achieve higher replay rates and longer content lifecycles compared to original live broadcasts. These clipped videos can be disseminated asynchronously across multiple channels, reaching broader audiences beyond the original live-streaming context. As a result, content clipping not only amplifies exposure but also contributes to delayed conversion and repeated consumption, further extending the commercial value chain of live-streaming content.

Despite their close relationship, live-streaming and content clipping differ significantly in terms of content format, distribution mechanism, and value creation logic.

Table 1. Comparison between live-streaming and content clipping.

Dimension	Live-Streaming	Content Clipping
Content format	Real-time, continuous	Short-video, edited segments
Interaction	High (real-time interaction)	Low (asynchronous viewing)
Distribution	Platform-dependent, time-sensitive	Multi-channel, persistent
Value creation	Immediate sales conversion	Traffic expansion and delayed conversion
Content ownership	Primarily controlled by anchors	Shared or contested among multiple actors
Governance focus	Real-time moderation	Copyright protection and reuse regulation

summarizes the key differences between these two modes.

As shown in Table 1, content clipping extends the value chain of live-streaming by transforming real-time content into reusable digital assets. While this process enhances content exposure and monetization opportunities, it also introduces new governance challenges that are fundamentally different from those in traditional live-streaming settings.

First, with respect to the legality and ownership of reused live-streaming content, institutional arrangements remain fragmented and ambiguous in practice. Unauthorized secondary creators may infringe upon anchors’ content rights, while even authorized interactions often lack clear and enforceable rules governing authorization scope and revenue sharing. This ambiguity generates substantial uncertainty regarding rights protection and liability allocation. Second, in commercial practice, anchors typically receive a share of the sales revenue generated through secondary creators’ clipped content. Under such arrangements, anchors have incentives to increase authorization fees or commission rates to maximize their returns, whereas secondary creators prefer lower fees to preserve profit margins. As a result, strategic interactions over authorization terms, commission structures, and content usage emerge as critical determinants of the long-term sustainability of the content clipping model.

Within this context, the live-streaming platform plays a central and multifaceted role. As both a technology provider and a transaction intermediary, the platform supplies the infrastructure that facilitates interactions among anchors, secondary creators, and consumers (Zhou et al., 2022). At the same time, it functions as a rule setter and enforcer, exercising governance over content creation and commercial transactions (Xu et al., 2022). Insufficient platform oversight may encourage unauthorized content clipping, leading to copyright disputes, unfair competition, and ecosystem instability. In contrast, overly stringent regulation may suppress content innovation and discourage creator participation. Consequently, how platforms balance minimal regulatory intervention governance and regulatory intervention constitutes a core issue in content copyright governance and incentive coordination under the content clipping model. In practice, ambiguous supervisory boundaries and unclear penalty mechanisms further contribute to the persistence of unauthorized clipping behavior.

Although the existing literature has examined live-streaming e-commerce from multiple perspectives–including operational strategies, marketing effectiveness, revenue distribution, and platform governance (L. Chen et al., 2021; H. Chen et al., 2022; Ji et al., 2023)—research focusing on the emerging content clipping model remains limited. In particular, formal game-theoretic studies that capture the dynamic interactions among platforms, anchors, and secondary creators, as well as the long-term evolution of their strategic behaviors, are still scarce.

To address these challenges, game theory provides a useful analytical framework for examining strategic interactions among multiple agents. In particular, evolutionary game theory allows for the analysis of boundedly rational agents whose strategies evolve dynamically through repeated interactions. This approach has been widely applied in studies of platform governance, supply chain coordination, and digital content ecosystems, demonstrating its effectiveness in capturing complex adaptive behaviors. In the context of live-streaming content clipping, an evolutionary game framework is particularly suitable because it can model the gradual adjustment of strategies by platforms, anchors, and secondary creators under different incentive and regulatory mechanisms. It also enables the identification of evolutionary stable strategies (ESS), which characterize the long-term equilibrium states of the system.

Based on this perspective, this study develops a tripartite evolutionary game model. The tripartite model incorporates the platform as a key governance actor and examines the interactions among platform regulation, anchor authorization, and secondary content creation. By deriving the replicator dynamic equations, the study characterizes the evolutionary trajectories of different strategies. Furthermore, numerical simulations are conducted to explore the stability of the system under various parameter settings.

This study makes several contributions to the literature. First, it extends research on live-streaming e-commerce by explicitly incorporating content clipping as a distinct yet interconnected activity. Second, it provides a unified analytical framework to examine the interplay between platform regulation and anchor authorization, highlighting their substitution and complementarity effects. Third, it offers new insights into the governance of digital content ecosystems by identifying conditions under which cooperative equilibrium can emerge. Overall, the findings contribute to a better understanding of how to design effective governance and incentive mechanisms for the sustainable development of live-streaming content ecosystems.

2. Literature Review

The relevant literature reviewed in this paper is organized into four streams. First, we review studies on operational strategy selection in live-streaming e-commerce, focusing on collaboration mechanisms and quality improvement. Second, we examine research on marketing strategy selection, particularly the role of influencers and content characteristics in shaping consumer behavior. Third, we review the literature on regulatory issues in live-streaming e-commerce, with emphasis on policy instruments, platform governance, and compliance challenges. Finally, we summarize studies on revenue distribution, highlighting profit-sharing mechanisms among platforms, anchors, and secondary creators. Together, these four streams provide a comprehensive foundation for positioning this study within the existing literature.

2.1. Research on Live E-Commerce Operational Strategy Selection

With the rapid development of live-streaming e-commerce, the choice of operational strategies has become a research focus at the intersection of supply chain management and platform economy. Existing studies have explored this area from multiple perspectives, including platforms, streamers, and collaboration models, providing rich theoretical insights into the live-streaming e-commerce ecosystem. Regarding platform operational strategies, X. Zhang et al. (2022) examined whether e-commerce platforms should introduce live-streaming services and how to design corresponding operational mechanisms, highlighting that live streaming can enhance sales efficiency while simultaneously posing channel coordination challenges (X. Zhang et al., 2022). Zhao and Luo (2022) focused on the operational decisions of retail firms under hybrid platform models, revealing the interplay between price conflicts and network externalities when self-operated businesses compete with third-party sellers, thereby offering guidance for platform model selection (Zhao & Luo, 2022). Furthermore, Yang et al. (2025) compared two strategies within e-commerce platform supply chains-KOL (Key Opinion Leader) live streaming and manufacturer self-broadcasting-finding that platform commissions and KOL influence jointly determine the manufacturers’ optimal live-streaming strategy and indicating that, under certain conditions, a win-win outcome for both platforms and manufacturers can be achieved (Yang et al., 2025). These studies underscore the platform’s central role in live-streaming e-commerce; however, most still conceptualize platforms primarily as rule-makers and coordinators, leaving their role in content ecosystem governance-particularly in regulating content clipping behavior-insufficiently explored.

At the level of cooperation strategies between streamers and brand owners, the existing literature has largely focused on streamer type selection, contractual design, and quality control. Ye et al. (2024) examined the choice between top-tier and regular streamers from the perspective of retailers and their impact on pricing and sales, highlighting that differences in streamer influence can lead to varied channel efficiency allocations (Ye et al., 2024). Cui et al. (2024) employed a game-theoretic model to analyze the optimal contract design for product quality cooperation between brand owners and streamers, finding that when commission rates are high and streamer quality investment proportions are low, both parties can achieve profit gains, while the introduction of quality cooperation helps reduce return rates (Cui et al., 2024). Ji et al. (2023) further investigated the integration of optimal sales modes with discount strategies in live-streaming e-commerce, comparing profit differences under agency and resale models (Ji et al., 2023). These studies provide an in-depth examination of streamers as core traffic nodes within the supply chain and their interaction mechanisms with brand owners. However, most existing research assumes that streamers have full control over their content creation, leaving their authorization decisions when faced with secondary content creation largely unexplored, and failing to incorporate such behavior into analyses of streamer revenue structures and long-term cooperation strategies.

In terms of content creation and derivative dissemination, research on live-streaming e-commerce has begun to pay attention to the integrated operational effects of multiple channels, such as short videos and live streaming. X. Fan and Zhang (2026) explored the strategic rationale for the simultaneous use of short videos and live streaming in social e-commerce, analyzing the “fans effect” and operational complexity arising from multi-channel coordination (X. Fan & Zhang, 2026). Niu and Ma (2024), from a market entry perspective, examined the role of online streamers within China’s live-streaming sales ecosystem, emphasizing their key function in product promotion and consumer engagement (Niu & Ma, 2024). However, existing literature generally limits content creation agents to streamers or brand owners themselves, paying little attention to the actions of third-party creators who edit and repurpose streamer-generated material. Although Xu et al. (2024) applied a three-party evolutionary game to analyze strategic decisions in live-streaming e-commerce, their focus remained on interactions among platforms, streamers, and consumers, without considering this emerging and active group of secondary creators (Xu et al., 2024). Similarly, Wu and Xiong (2012), while employing evolutionary game theory to analyze government subsidy mechanisms in reverse supply chains, provide methodological insights for multi-agent strategy evolution but are contextually far removed from the live-streaming content ecosystem (Wu & Xiong, 2012).

More importantly, within the live-streaming content ecosystem, content editors and producers-exemplified by secondary content creators-have emerged as a significant and influential group. However, existing literature lacks a systematic investigation of their behavioral motivations, revenue structures, and the allocation of rights and responsibilities between them, streamers, and platforms.

2.2. Research on Live E-Commerce Marketing Strategy Selection

As an emerging model that integrates content creation, real-time interaction, and commercial conversion, live-streaming e-commerce has made the selection and coordination of marketing strategies a prominent topic in digital marketing research. Existing literature has examined the phenomenon from the perspectives of various participants, providing a theoretical foundation for understanding the operational mechanisms of the live-streaming e-commerce ecosystem. From the platform perspective, scholars have predominantly focused on its role as a rule-maker and ecosystem coordinator. Wongkitrungrueng and Assarut (2020) investigated the central role of live streaming in fostering consumer trust and engagement in social e-commerce, emphasizing the fundamental value of platforms in creating a credible environment (Wongkitrungrueng & Assarut, 2020). Gong et al. (2022) and Li et al. (2024) further examined platform operational strategies, exploring, respectively, live-streaming strategy choices for online retailers under multi-channel sales contexts and live-streaming strategies that account for spillover effects, thereby revealing the decision logic behind traffic allocation and sales mode design (Gong et al., 2022; Li et al., 2024). Wan (2024) focused on optimal marketing strategies within live-streaming rooms, analyzing the impact of guaranteed sales versus breakthrough sales strategies on the supply chain, illustrating the platform’s critical function in incentive design and resource allocation (Wan, 2024). Y. Zhang and Xu (2024), from a value co-creation perspective, studied how live-streaming mode selection and consumer incentive mechanisms jointly drive user engagement, highlighting the platform’s role as a central coordinator of value creation (Y. Zhang & Xu, 2024). Collectively, these studies tend to treat platforms as relatively macro-level strategy formulators and rule enforcers, leaving the specificity and differentiation of their governance behaviors, as well as the direct effects on the creative actions of other micro-level ecosystem participants, largely underexplored.

Focusing on the streamer perspective, research has delved into both marketing execution and risk dimensions. Sprott et al. (2023), using a detailed possibilistic model, systematically analyzed how social media influencers’ (anchors) post characteristics and personal attributes act as central and peripheral path factors that jointly influence followers’ purchase intentions, providing a theoretical framework for understanding streamers’ persuasive mechanisms (Sprott et al., 2023). C. Zhang et al. (2025) shifted attention to the risk dimension, employing a hesitant fuzzy multi-attribute group decision-making approach to assess live-streaming marketing risks, explicitly identifying Al streamer ethical risks, VR technology promotion risks, and other factors as high-risk elements, highlighting the novel governance challenges arising from individual streamer behavior and technological applications (C. Zhang et al., 2025). H. Chen et al. (2022), based on dual-process theory, empirically examined how product information and viewing habits mediate the effect of live-streaming characteristics on purchase intentions, deepening the understanding of how streamers influence consumer decisions through content presentation (H. Chen et al., 2022). Nevertheless, most existing studies treat streamers primarily as original content producers and direct sources of risk, leaving their subsequent control over content assets (e.g., live recordings, highlight clips), authorization intentions, and the associated profit relationships with derivative content creators largely unexplored. This oversight neglects an increasingly active ecosystem segment-secondary content creation.

Secondary content creation, particularly the editing, repurposing, and dissemination of streamer-generated live content, has emerged as an important phenomenon for amplifying live-streaming impact and extending marketing lifecycles. Although Qian (2021) analyzed short-video marketing strategies in the context of social e-commerce, addressing aspects of video format and interaction, the study did not specifically focus on the secondary processing of existing live-streaming content or the associated rights, responsibilities, and profit relationships (Qian, 2021). Similarly, C. Liu et al. (2025), through text mining, examined the sentiment and thematic patterns of user-generated content in cross-border e-commerce reviews; while insightful, their focus was on consumer product evaluations rather than the creative reuse of live-streaming material (C. Liu et al., 2025). Overall, the existing literature on live-streaming e-commerce marketing strategies has delineated the platform as a provider of rules and strategic frameworks, and streamers as core content producers and risk bearers. However, the emerging and increasingly influential role of “secondary content creators” remains underexplored, particularly regarding their behavioral motivations, interactions with platform policies and streamer authorization, and the resulting triadic game dynamics that arise within the ecosystem.

2.3. Research on the Regulation of Live-Streaming E-Commerce

The rapid growth of live-streaming e-commerce and the accompanying governance challenges have prompted ongoing scholarly attention to its regulatory mechanisms. Existing research has examined platform governance and the regulation of streamer behavior, gradually forming a coherent academic trajectory. L. Chen et al. (2021) systematically reviewed research on digital platform governance and design, proposing a theoretical perspective that views platforms as “meta-organizations” and emphasizing their central role in rule-making, participant coordination, and ecosystem construction (L. Chen et al., 2021). This framework provides a foundation for understanding the basic governance logic of live-streaming e-commerce platforms. Building on this, D. He et al. (2026) focused on platform regulatory innovation in the era of data intelligence, empirically demonstrating the co-evolutionary relationship between regulatory policies and technology adoption by constructing a policy corpus and intensity indicators, highlighting the dynamic and complex nature of platform governance (D. He et al., 2026). In the specific context of live-streaming e-commerce, B. Wang et al. (2024a) developed a multi-dimensional analytical framework incorporating policy instruments, industry value chains, and governance levels, systematically evaluating policies in China’s live-streaming e-commerce industry and revealing the multi-faceted effects of policy combinations on industry development (B. Wang et al., 2024a). Collectively, these studies establish the platform’s critical role as a regulatory hub and rule designer; however, most analyses focus on dyadic relationships-either between the platform and government or the platform and merchants (anchors)-with limited attention to more complex multi-agent interactions within the platform, particularly regarding the governance of content clipping and derivative content creation.

As research perspectives extend downstream along the industry chain, streamers, as core participants in live-streaming e-commerce, have become a key focus of behavioral regulation studies. Shou et al. (2023), based on typical case studies, empirically examined the direct impact of government regulation on live-streaming e-commerce, revealing how external regulatory pressures shape both streamer and platform behavior (Shou et al., 2023). J. Fan et al. (2024) further internalized the perspective within the platform, employing evolutionary game theory to analyze platform strategies for regulating streamer integrity, incorporating behavioral economic assumptions such as prospect theory to enrich models of streamer decision-making (J. Fan et al., 2024). Barkatullah and Djumadi (2018), in a comparative study of self-regulation effectiveness in e-commerce, though not specific to live-streaming contexts, raise critical questions regarding whether self-regulatory mechanisms can provide sufficient consumer protection, offering valuable insights for considering streamer behavioral constraints (Barkatullah & Djumadi, 2018). Existing research has largely focused on streamers’ original behaviors during live sales, such as false advertising or quality misrepresentation, while downstream issues-namely, the authorized use and profit allocation of streamer-generated content within the dissemination chain and the associated regulatory implications-remain largely unexplored.

2.4. Live-Streaming Revenue Distribution

T. Y. Wang et al. (2024b) found that live anchors’ traffic effects and basic remuneration coefficients are critical for manufacturers in choosing live-streaming services over traditional promotions (T. Y. Wang et al., 2024b). Additionally, the preferences of retailers and live anchors are influenced by the contract type. The study also considered the positive Spillover Effects of traditional promotion, which increase the manufacturer’s motivation to choose traditional promotion but do not fundamentally alter the model preference of channel members. Y. He (2024) constructed a supply chain model comprising manufacturers, retailers, and live anchors and analyzed the impact of three types of contracts (sales commission only, OC; fixed fee only, OF; and combined sales commission and fixed fee, CF) on optimal decisions and profits for supply chain members (Y. He, 2024). They found that retailers tend to prefer OC contracts with highly capable anchors, while OF contracts are more beneficial to retailers and manufacturers when the fixed fee is low. CF contracts yield the highest profit for retailers when the total commission rate is low and the fixed fee is moderate. The study also explored the effects of different contracts on manufacturers’ profits, as well as contract selection strategies for retailers and anchors under varying conditions. H. Liu and Liu (2021) developed a supply chain model involving platforms and anchors, utilizing differential game theory to analyze optimal recommendation and sales effort under various revenue-sharing contracts (H. Liu & Liu, 2021). The findings indicate that a higher revenue-sharing rate set by the platform results in lower recommendation effort, potentially reducing income for both the platform and the anchor. Consequently, the study proposed a subsidy mechanism that sets a reasonable revenue-sharing rate to incentivize anchors to increase platform recommendations, achieving a win-win outcome. The study further examined optimal revenue-sharing rates under different conditions and the effect of the subsidy mechanism on enhancing total system revenue in decentralized scenarios. Peng (2024) developed a two-tier live-streaming supply chain model comprising manufacturers and anchors, analyzing the effects of three incentive mechanisms—decentralized decision-making, cost-sharing contracts, and revenue-sharing contracts—on optimal decisions and profits for supply chain members (Peng, 2024). The results indicate that cost and revenue-sharing contracts effectively enhance manufacturers’ emission reduction levels and anchors’ low-carbon promotion efforts, with revenue-sharing contracts showing superior performance. Consumer environmental awareness has a greater impact on manufacturers’ emission reduction than on anchors’ sensitivity to low-carbon promotion, and the effect of anchors’ reputation on emission reduction and profit exhibits a decreasing-then-increasing trend.

In conclusion, most current research on e-commerce live-streaming focuses on strategy selection, regulatory mechanisms, and revenue distribution. However, few studies analyze the collaboration strategies between anchors and secondary creators from the perspective of anchor authorization for secondary creation, as well as the live-streaming platform’s regulatory decision-making. As the content clipping sales model becomes increasingly popular, the analysis of the tri-party game between live-streaming platforms, anchors, and secondary creators will become more crucial. Therefore, to deeply analyze the behavioral strategies of anchors’ clipping authorization under platform regulation, this paper will employ evolutionary game theory as a methodological approach.

2.5. Research Review

Recent studies have increasingly examined revenue distribution and value allocation in live-streaming ecosystems, particularly in relation to content creators, platforms, and consumers. Existing research highlights that revenue-sharing mechanisms, commission structures, and platform incentives play a critical role in shaping the behavior of anchors and influencing sales performance.

Despite these advances, the existing literature remains fragmented in several important aspects.

First, most studies examine platform regulation, content creation, or revenue distribution in isolation, without considering the joint strategic interactions among platforms, original content creators (anchors), and secondary creators. However, in real-world live-streaming ecosystems, these actors are interdependent, and their decisions co-evolve over time.

Second, while platform governance has been widely studied, the majority of research focuses on static regulatory mechanisms, such as fixed penalties or exogenous rules. The dynamic adjustment of regulatory strategies under cost constraints and strategic feedback has received relatively limited attention.

Third, although authorization mechanisms are commonly used in practice to manage content reuse, their role as an endogenous governance tool has not been sufficiently explored in the literature. In particular, the potential substitution or complementarity between platform regulation and anchor authorization remains unclear.

Fourth, existing studies on revenue distribution primarily analyze its direct impact on individual behavior, but pay less attention to its dynamic effects on system-level stability and long-term equilibrium outcomes.

To address these gaps, this study develops a three-party evolutionary game model that explicitly incorporates platform regulation, anchor authorization, and secondary content creation. By modeling boundedly rational agents and their adaptive strategy adjustments, the framework captures the dynamic interactions among key stakeholders in the live-streaming ecosystem. In addition, the study introduces a bilateral model as a benchmark to systematically compare different reward–penalty mechanisms and their effects on cooperative behavior.

Through this approach, the paper not only bridges the gap between platform governance and content reuse literature but also provides a unified perspective on how regulatory and market-based mechanisms jointly shape the evolution of digital content ecosystems.

3. Model and Equilibrium Analysis

3.1. Assumptions and Parameters

We consider a three-party evolutionary game model consisting of a live-streaming platform (P), an anchor (A), and a secondary creator (C), aiming to characterize the strategic interactions and dynamic evolutionary processes among these agents regarding regulation, authorization, and re-creation behaviors within the live-streaming clipping ecosystem. In this model, the live-streaming platform’s strategy concerns whether to regulate the content produced by secondary creators, including copyright protection and content quality control; the anchor’s strategy is whether to authorize secondary creators to use their live-streaming materials; and the secondary creator’s strategy is whether to engage in re-creation by clipping the anchor’s live-streaming content. Based on this decision structure, the following basic assumptions are proposed:

Assumption 1. 

According to standard evolutionary game theory, all agents are assumed to be boundedly rational and to adjust their strategies over time by imitating strategies that yield higher payoffs. The replicator dynamic of each agent is constructed as the difference between the expected payoff of a given strategy and the average payoff of the population.

Assumption 2. 

If the platform chooses regulation (S), it incurs a fixed regulatory cost $C_2$ associated with content monitoring, copyright enforcement, and dispute resolution. When unauthorized clipping is detected under regulation, the platform imposes a fine $rho$ on the violating secondary creator.

Assumption 3. 

If the anchor chooses to authorize (A), they must incur an authorization cost $C_1$, encompassing administrative expenditures such as secondary creator qualification screening, contract design, and monitoring and enforcement, thereby reflecting the fixed entry barriers imposed by the authorization system. In return, the anchor charges the secondary creator a fixed authorization fee $m\left(\theta \right)$ from the income generated by the secondary creator through the use of the authorized materials. This parameter reflects the degree of linkage between the two parties in terms of ongoing revenue. Additionally, the anchor can receive a certain percentage θ of the revenue earned by the secondary creator with their clippings. This parameter reflects the degree of linkage between the two parties in terms of ongoing revenue.

Assumption 4. 

When the platform implements regulation, if a secondary creator still engages in non-compliant re-creation (E), they must pay compensation L to the anchor; if the secondary creator has obtained authorization from the anchor but fails to conduct clipping in accordance with the agreement (NE), they must also pay a contractual penalty $C_4$ to the anchor. Its function is to constrain opportunistic behavior and strengthen the enforceability of the authorization contract. When the platform does not regulate, if a secondary creator conducts re-creation without the anchor’s authorization (NA), this will cause a loss $C_3$ to the anchor, such as traffic diversion, brand dilution, or copyright infringement. This loss cannot be compensated through institutional mechanisms, reflecting the negative externalities arising from regulatory absence.

In practice, $C_1$ and $C_2$ are often higher than the immediate gains from a single unauthorized action; therefore, the model does not assume all costs are of the same magnitude. Instead, inequalities are used to characterize the relative advantage structures under different institutional settings. These inequalities serve solely to distinguish evolutionary strategy scenarios rather than impose rigid assumptions on the actual parameter values.

Assumption 5. 

The anchor’s revenue is composed of several components: First, revenue generated from selling products through their own live-streaming channel is $(P-\omega )d_1$, where P is the sales price, ω is the cost price, and $d_1$ is the sales volume. Second, authorization revenue from granting the secondary creator permission to use their content is $m\left(\theta \right)$. Additionally, the anchor earns commission revenue from the secondary creator’s sales, which is $(P-\omega )d_2\theta$, where $d_2$ is the sales volume of the secondary creator’s storefront and θ is the percentage share the anchor receives from the secondary creator’s revenue. Furthermore, the anchor benefits from additional revenue generated by the secondary creator, such as increased brand exposure, fan growth, etc., represented by T. Finally, the live-streaming platform takes a proportion η of the anchor’s total revenue.

Assumption 6. 

Set the probability that the live-streaming platform chooses to regulate secondary clippings creators as x, and the probability of not regulating as $1-x$. Set the probability of anchor authorizes the secondary clippings creator as y, and the probability of not authorizing as $1-y$. Set the probability that the secondary clippings creator edits the anchor’s material as z, and the probability of not editing as $1-z$, where $x,y,z\in [0,1]$.

It should be emphasized that, in practice, similar penalty and compensation mechanisms are widely adopted by major content platforms. For example, leading platforms such as TikTok, Douyin, and YouTube incur substantial compliance costs related to content moderation, copyright verification, and dispute resolution. Meanwhile, unauthorized reuse of content may result in revenue deductions, account restrictions, or monetary compensation paid to original creators. Consistent with prior studies on platform governance and copyright enforcement (e.g., X. Zhang et al., 2022), fines and monitoring costs in this study are treated as institutional instruments that shape strategic behavior rather than as precise monetary transfers.

In the model presented in this paper, the strategic choices of the game participants are not static but evolve dynamically over time. The live-streaming platform, the anchor, and the secondary creator all operate under bounded rationality and continuously adjust their strategies in response to changes in other players’ strategies and market feedback, with the objective of maximizing expected payoffs while mitigating potential risks.

For instance, when the regulation cost $C_2$ is excessively high, the live-streaming platform may be inclined to reduce its regulation intensity to avoid eroding overall profitability due to excessive regulatory investment. From the anchor’s perspective, when the combined benefits from authorization income $m\left(\theta \right)$ and revenue-sharing ratio $\theta$ exceed the authorization cost $C_1$, the anchor is more likely to authorize secondary creators to use live-streaming materials. Meanwhile, secondary creators trade off authorization fees, potential revenues, and the risk of penalties for non-compliance, thereby determining whether to engage in re-creation activities.

The game model is built using the presumptions listed above, as seen in Figure 1.

The relevant parameter settings are shown in

Table 2. Parameter definitions.

Notation	Explanation
x	probability that the live-streaming platform chooses to regulate secondary creators ($0<x<1$)
y	probability that the anchor chooses to authorize secondary creators ($0<y<1$)
z	probability that the secondary creator chooses to edit anchor’s video ($0<z<1$)
$m\left(\theta \right)$	Authorization fee for content clippings
$C_1$	Cost for the anchor to authorize clippings creation
$C_2$	Cost of live-streaming platform regulation
$C_3$	Loss to the anchor from secondary creators’ illegal creations in the absence of regulation by live-streaming platforms
$C_4$	Penalty for breach of contract by the secondary creator under live-streaming platform regulation
$d_1$	Quantity of products sold by the anchor in their shop window
$d_2$	Quantity of products sold by the secondary creator through their shop window
P	Product price
T	Additional revenue brought by the secondary creator to the anchor
L	Compensation paid by secondary creator to anchor for unauthorized clippings creation under live-streaming platform regulation
$\omega$	Cost price of the product
$\rho$	Fine for unauthorized clippings creation
$\eta$	Live-streaming platform commission rate
$\theta$	Anchor’s commission rate

.

Based on the above parameters, the payoff matrix of the three parties is calculated, as shown in

Table 3. Payoff matrix of live-streaming platform, anchor, and secondary creator.

Strategy Portfolio	Platform	Anchor	Secondary Creator
(S, A, E)	$\eta (P-\omega )(d_1+d_2)-C_2$	$(1-\eta )(P-\omega )(d_1+\theta d_2)-C_1+m\left(\theta \right)+T$	$(1-\eta )d_2(P-\omega )-\theta d_2(P-\omega )-m\left(\theta \right)$
(S, A, NE)	$\eta (P-\omega )d_1-C_2$	$(1-\eta )(P-\omega )d_1-C_1$	$-m\left(\theta \right)$
(S, NA, E)	$\eta (P-\omega )(d_1+d_2)+\rho -C_2$	$(1-\eta )(P-\omega )d_1+T+L$	$(1-\eta )d_2(P-\omega )-\rho -L$
(S, NA, NE)	$\eta (P-\omega )d_1-C_2$	$(1-\eta )(P-\omega )d_1$	0
(NS, A, E)	$\eta (P-\omega )(d_1+d_2)$	$(1-\eta )(P-\omega )(d_1+\theta d_2)-C_1+m\left(\theta \right)+T$	$(1-\eta )d_2(P-\omega )-\theta d_2(P-\omega )-m\left(\theta \right)$
(NS, A, NE)	$\eta (P-\omega )d_1$	$(1-\eta )(P-\omega )d_1-C_1$	$-m\left(\theta \right)$
(NS, NA, E)	$\eta (P-\omega )(d_1+d_2)$	$(1-\eta )(P-\omega )d_1+T$	$(1-\eta )d_2(P-\omega )$
(NS, NA, NE)	$\eta (P-\omega )d_1$	$(1-\eta )(P-\omega )d_1$	0

. The detailed derivation process is presented in Appendix A.

3.1.1. Constructing the Payoff Function

Let $U_1$ represent the live-streaming platform’s average expected payoff, $U_{11}$ represent the expected payoff of a live-streaming platform that engages in regulation, and $U_{12}$ represent the expected payoff of a live-streaming platform that does not engage in regulation. Then, we have:

$$U_{11}=\eta (P-\omega )(d_1+d_{2}yz)+\rho z(1-y)-C_2$$

(1)

$$U_{12}=\eta (P-\omega )(d_1+d_{2}z)$$

(2)

$$U_1=x{U}_{11}+(1-x)U_{12}$$

(3)

The platform’s strategy reflects a trade-off between commission revenues and regulatory costs. Regulation becomes evolutionary attractive only when enforcement benefits outweigh the fixed cost of governance.

Let $U_2$ represent the anchor’s average expected payoff, $U_{21}$ represent the expected payoff of an anchor who authorizes, and $U_{22}$ represent the expected payoff of an anchor who does not authorize. Then, we have:

$$U_{21}=(1-\eta )(P-\omega )d_1+(1-\eta )(P-\omega )\theta d_{2}z+m\left(\theta \right)z+Tz-C_1$$

(4)

$$U_{22}=(1-\eta )(P-\omega )d_1+Tz+Lxz$$

(5)

$$U_2=y{U}_{21}+(1-y)U_{22}$$

(6)

The anchor’s authorization decision depends on whether licensing revenues, revenue sharing, and indirect benefits sufficiently compensate for authorization costs and potential infringement losses.

Let $U_3$ represent the secondary creator’s average expected payoff, $U_{31}$ represent the expected payoff of a secondary creator who edits, and $U_{32}$ represent the expected payoff of a secondary creator who does not edit. Then, we have:

$$U_{31}=(1-\eta )d_2(P-\omega )-\theta d_2(P-\omega )y-m\left(\theta \right)y-(\rho +L)x(1-y)$$

(7)

$$U_{32}=-ym\left(\theta \right)$$

(8)

$$U_3=z{U}_{31}+(1-z)U_{32}$$

(9)

Secondary creators engage in content clipping when expected sales gains exceed authorization fees, revenue sharing, and potential enforcement penalties.

These expected payoff functions form the foundation of the replicator dynamic equations, where strategy evolution is driven by the difference between the payoff of a given strategy and the average payoff of the population.

The detailed derivation process is presented in Appendix A.

3.1.2. Replicator Dynamics Equations of the Three-Party Game

The replicator dynamics equation for the live-streaming platform is as follows:

$$F\left(x\right)={\displaystyle \frac{dx}{dt}}=x(1-x)\left[\rho (1-y)z-C_2\right]$$

(10)

This equation indicates that the platform’s decision to regulate depends on the trade-off between regulatory costs and the gains from penalizing violations. When the authorization rate is high and violations occur frequently, regulation is more likely to become the dominant strategy; conversely. excessively high regulatory costs weaken the platform’s incentive to supervise.

The replicator dynamics equation for the anchor is as follows:

$$\begin{array}{cc}\hfill F\left(y\right)& ={\displaystyle \frac{dy}{dt}}=y(1-y)(U_{21}-U_{22})\hfill \\ \hfill & =y(1-y)\left[m\left(\theta \right)-C_1+\theta d_2(P-\omega )(1-\eta )z+xLz\right]\hfill \end{array}$$

(11)

This equation indicates that the anchor’s decision to grant authorization depends on the comparison among authorization costs, commission revenues, and the additional value generated by secondary creators. When the combined benefits of authorization exceed its fixed costs and potential risks, the authorization strategy gradually becomes dominant.

The replicator dynamics equation for the secondary creator is as follows:

$$F\left(z\right)={\displaystyle \frac{dz}{dt}}=z(1-z)\left[(1-\eta )d_2(P-\omega )-\theta y{d}_2(P-\omega )-ym\left(\theta \right)-x(1-y)(\rho +L)\right]$$

(12)

From the perspective of secondary creators, their content clipping decisions are primarily influenced by the combined effects of revenue-sharing proportions and regulatory penalties. When clipping profits are significantly eroded by multiple deductions or when the cost of violations increases, creators are more likely to opt out of clipping activities.

The detailed derivation process is presented in Appendix B.

3.1.3. Stability Analysis of Evolutionary Game

Currently, it is unclear whether the equilibrium point is an ESS. For the stability analysis of the three-party evolutionary game, the asymptotic stability of the equilibrium point is determined by analyzing the Jacobian matrix. The expression for the Jacobian matrix is as follows:

$$J=\left[\begin{array}{ccc}{\displaystyle \frac{\partial F\left(x\right)}{\partial x}}& {\displaystyle \frac{\partial F\left(x\right)}{\partial y}}& {\displaystyle \frac{\partial F\left(x\right)}{\partial z}}\\ {\displaystyle \frac{\partial F\left(y\right)}{\partial x}}& {\displaystyle \frac{\partial F\left(y\right)}{\partial y}}& {\displaystyle \frac{\partial F\left(y\right)}{\partial z}}\\ {\displaystyle \frac{\partial F\left(z\right)}{\partial x}}& {\displaystyle \frac{\partial F\left(z\right)}{\partial y}}& {\displaystyle \frac{\partial F\left(z\right)}{\partial z}}\end{array}\right]=\left[\begin{array}{ccc}{J}_{11}& J_{12}& J_{13}\\ J_{21}& J_{22}& J_{23}\\ J_{31}& J_{32}& J_{33}\end{array}\right]$$

(13)

where: $J_{11}=(-1+2x)\left[C_2+\rho y(-1+z)\right]$, $J_{12}=\rho (-1+x)x(-1+z)$, $J_{13}=\rho (-1+x)xy$,

• $J_{21}=(-1+y)y\left[-C_4+(C_3+C_4+L-T)z\right]$,
• $\begin{array}{cc}\hfill J_{22}& =(-1+2y)\left(Lxz-m\left(\theta \right)+C_1-C_{3}z(1-x)-C_{4}x(1-z)\right)\hfill \\ & -(-1+2y)\left(d_2\theta z(1-\eta )(P-\omega )-T\left(1-z(x-2)\right)\right),\hfill \end{array}$
• $J_{23}=\left[-C_3+2T-d_2(-1+\eta )(\omega -P)\theta +(C_3+C_4+L-T)x\right](-1+y)y$,
• $J_{31}=-\left(-L-\rho +(C_4+L+\rho )y\right)(-1+z)z$,
• $J_{32}=\left[d_2(-1+\eta )(\omega -P)\theta -(C_4+L+\rho )x\right](-1+z)z$,
• $J_{33}=\left[x\left(L+\rho -(C_4+L+\rho )y\right)+d_2(-1+\eta )(\omega -P)(-1+\theta y)\right](-1+2z)$.

Let $F\left(x\right)=0$, $F\left(y\right)=0$, $F\left(z\right)=0$. The equilibrium points of the three-party game system can be derived, and the asymptotic stability of the eight local equilibrium points $E_1(0,0,0),E_2(0,1,0),E_3(0,0,1),E_4(0,1,1),E_5(1,0,0),E_6(1,1,0),E_7(1,0,1),E_8(1,1,1)$ is discussed. By substituting the equilibrium points into the formula, the corresponding Jacobian matrices for each point can be derived.

Let the Jacobian matrix corresponding to $E_1(0,0,0)$ be denoted as $J_1$:

$$J_1=\left[\begin{array}{ccc}{\lambda }_1& 0& 0\\ 0& {\lambda }_2& 0\\ 0& 0& {\lambda }_3\end{array}\right]$$

(14)

where ${\lambda }_1=-C_2,{\lambda }_2=m\left(\theta \right)-C_1+T,{\lambda }_3=d_2(\eta -1)(\omega -P).$

Similarly, by substituting the eight equilibrium points into the Jacobian matrix, the eigenvalues corresponding to the eight local stability points can be obtained, as shown in

Table 4. Eigenvalues for Different Equilibrium Points.

Equilibrium	Eigenvalue 1	Eigenvalue 2	Eigenvalue 3
$E_1(0,0,0)$	$-C_2$	$m\left(\theta \right)-C_1+T$	$d_2(1-\eta )(P-\omega )$
$E_2(1,0,0)$	$C_2$	$m\left(\theta \right)-C_1+T$	$d_2(1-\eta )(P-\omega )$
$E_3(0,0,1)$	$-C_2$	$C_3+d_2(\eta -1)(\omega -P)-T+m\left(\theta \right)$	$d_2(\eta -1)(P-\omega )$
$E_4(1,0,1)$	$C_1$	$C_3+d_2(\eta -1)(\omega -P)-T+m\left(\theta \right)$	$d_2(\eta -1)(P-\omega )$
$E_5(0,1,0)$	$C_2$	$C_2$	$-C_3-T+m\left(\theta \right)$
$E_6(1,1,0)$	$C_2$	$C_2$	$-C_3-T+m\left(\theta \right)$
$E_7(0,1,1)$	$-C_2$	$C_3+d_2(\eta -1)(\omega -P)-T+m\left(\theta \right)$	$d_2(\eta -1)(P-\omega )$
$E_8(1,1,1)$	$C_1$	$C_3+d_2(\eta -1)(\omega -P)-T+m\left(\theta \right)$	$d_2(\eta -1)(P-\omega )$

. The detailed calculation process is presented in Appendix C.

Among the eight equilibrium points mentioned above, the eigenvalues of equilibrium points $E_1$, $E_2$, and $E_7$ satisfy ${\lambda }_3>0$, and the eigenvalues of equilibrium points $E_5$ and $E_8$ satisfy ${\lambda }_1>0$, which do not meet the Lyapunov stability condition, thus making them unstable points. By introducing constraints, equilibrium points $E_3$, $E_4$ and $E_6$ can reach a steady state.

3.1.4. Evolutionary Stability Analysis

Scenario 1. When the constraint $C_3+d_2(\eta -1)(\omega -P)\theta +m\left(\theta \right)<C_1+T$ is satisfied, equilibrium point $E_3(0,0,1)$ becomes stable, and the strategy combination of no regulate, no authorize, and edit emerges as the ESS.

From the anchor’s perspective, under the above conditions, the sum of the fixed cost of authorization $C_1$ and the potential indirect benefit T is insufficient to cover the losses and opportunity costs that may arise from not granting authorization. Consequently, the anchor lacks the incentive to authorize and tends to choose the non-authorization strategy.

At the platform level, choosing not to regulate allows the platform to avoid paying the regulatory cost $C_2$ while still earning revenue through commissions on the anchor’s sales. When the additional gains from regulation are insufficient to offset its costs, non-regulation becomes a relatively stable choice.

Under this institutional setting, secondary creators do not need to pay authorization fees and face relatively low risks of violations. With minimal entry barriers and expected costs, they are more likely to continue clipping, leading the system to converge to this stable state.

Scenario 2. When the constraint $C_3+d_2(\eta -1)(\omega -P)\theta +m\left(\theta \right)<C_1$ is satisfied, equilibrium point $E_4(0,1,1)$ becomes stable, and the strategy combination of no regulate, authorize, and edit emerges as the ESS.

In this scenario, the fixed authorization fees and revenue shares obtained by the anchor from granting authorization to secondary creators are sufficient to cover the authorization costs, making the authorization strategy economically feasible for the anchor.

Simultaneously, if the platform can still earn stable revenue through commissions without regulating, and does not incur additional regulatory costs, its intrinsic motivation to implement regulation is weak, leading it to maintain the non-regulation strategy.

In this environment, secondary creators reasonably expect that their clipping activities will not be subject to platform penalties or additional constraints; therefore, continuing content clipping becomes their dominant choice, causing the system to gradually evolve toward this stable state.

Scenario 3. When the constraints $C_1<C_4+T+m\left(\theta \right),C_4<d_2(\eta -1)(P-\omega )(\theta -1)$ are satisfied, equilibrium point $E_6(1,1,0)$ becomes stable, and the strategy combination of regulate, authorize, and no edit emerges as the ESS. The first constraint indicates that, for the anchor, although granting authorization entails a fixed cost, the direct and indirect benefits generated by authorization are sufficient to cover this cost, providing the anchor with a sustained incentive to authorize.

At the platform level, when regulation can reduce the potential external losses caused by unauthorized clipping and penalties yield a certain net benefit, it is feasible for the platform to implement regulation.

The second constraint reflects the change in incentives faced by secondary creators under an institutional environment where both regulation and authorization coexist. Since the expected benefits from clipping are insufficient to cover potential breach costs and institutional constraints, secondary creators are more likely to refrain from clipping, leading the system to stabilize at this strategy combination.

For clarity, the conditions, outcomes, and practical implications of the identified evolutionary stable strategies (ESS) are summarized in

Table 5. Conditions, Outcomes, and Practical Implications of Evolutionary Stable Strategies (ESS).

Stability Condition	ESS	Practical Implication
High authorization cost, high platform regulatory cost, and low risk of violations	$E_3(0,0,1)$	The platform chooses to turn a blind eye, the anchor chooses non-authorization, and secondary creators gain revenue through low-cost clipping, forming a “tacitly permitted gray ecosystem”.
Authorization revenue exceeds authorization cost, while the platform lacks sufficient incentives to regulate	$E_4(0,1,1)$	The anchor benefits from authorization-induced clipping-driven sales, while the platform continues to earn commission revenue without engaging in regulation. Consequently, a content diffusion model characterized by “platform tacit approval + anchor commercial authorization” emerges.
High combined authorization benefits, significant risk of violations, and regulatory gains exceeding regulatory costs	$E_6(1,1,0)$	In a high-risk and effectively regulated environment, the platform and anchor form institutional cooperation. Content clipping activities are suppressed due to increased compliance costs, driving the market back toward normative operation.

.

Proposition 1. 

In the game among the live-streaming platform, anchors, and secondary creators, when the platform’s regulatory costs are relatively high and regulatory actions can significantly increase its commission revenue, the non-regulation strategy may become the platform’s evolutionary stable choice, causing the system to converge to a non-regulated equilibrium.

In this scenario, the investment in regulation is difficult to fully offset through additional gains, leading the platform to prefer maintaining its revenue level by saving on regulatory costs. Meanwhile, if anchors have not established stable authorization incentives, platform regulation is unlikely to effectively alter the behavior of secondary creators, thereby weakening the long-term sustainability of the regulatory strategy.

At equilibrium $E_3(0,0,1)$, when the live-streaming platform refrains from regulation, it can save costs, and while the behavior of the secondary creator may pose some risks, it generally aligns with the live-streaming platform’s interests. However, at equilibrium $E_7(1,0,1)$, although the live-streaming platform opts for regulation, the anchor’s refusal to authorize and the secondary creator’s violation of editing rules persist. This may result in the live-streaming platform’s regulatory costs not yielding sufficient returns. In this scenario, the live-streaming platform not only bears the cost of regulation but, due to the anchor’s lack of authorization, also misses out on additional revenue shares, making the overall game equilibrium more difficult to achieve. Therefore, from a cost–benefit perspective, $E_7(1,0,1)$ is not a stable equilibrium point.

Proposition 2. 

Under certain conditions, the anchor authorization mechanism may partially substitute for platform regulation during the evolutionary process, allowing the system to achieve a relatively stable strategy combination even under low or absent regulation.

When anchors can effectively internalize the benefits generated by clipping through authorization to secondary creators and the platform can still earn commissions without regulating, the platform lacks intrinsic motivation to strengthen oversight. In this case, the authorization arrangement serves as the primary institutional tool for coordinating the relationship between anchors and secondary creators, while platform governance manifests more as market-based coordination rather than mandatory regulation.

At equilibrium $E_4(0,1,1)$, the anchor’s income from authorization exceeds the losses from not granting authorization, leading the live-streaming platform to lose its incentive to regulate. As the anchor authorizes the secondary creator to use their content and takes a share of the secondary creator’s revenue, they not only recover the authorization costs but also generate additional income. However, at equilibrium $E_8(1,1,1)$, where the live-streaming platform introduces regulation, the situation changes. In this equilibrium, the live-streaming platform not only has to bear regulatory costs but also faces potential losses from regulation. Meanwhile, the creative freedom of secondary creators is restricted by the live-streaming platform’s regulation, which lowers their motivation to create. As a result, $E_8(1,1,1)$ cannot reach an evolutionary equilibrium.

Proposition 3. 

When the combined costs and multiple deductions faced by secondary creators increase significantly, their incentives to participate in clipping activities may be weakened, thereby affecting the system’s evolutionary stability.

In an institutional environment with overlapping constraints, the expected net benefits for secondary creators decline, which may lead them to reduce creative input or even withdraw from content production. This result suggests that excessive regulation or imbalanced revenue distribution may, counterintuitively, diminish the vibrancy of the content ecosystem, making certain high-regulation and high-authorization strategy combinations difficult to maintain as stable outcomes in the long-term evolutionary process.

In the case of equilibrium $E_8(1,1,1)$, the revenue from secondary creators’ editing and creation primarily comes from product sales, but in this scenario, they are required to share a portion of the sales revenue with the anchor, as well as the commission taken by the live-streaming platform. If the commission percentages for both the anchor and the live-streaming platform are too high, the secondary creator’s profits will be significantly reduced. Additionally, the live-streaming platform’s regulation of secondary creators’ clippings creation does not fully eliminate the risk of unauthorized creation, which introduces uncertainty and additional compensation liabilities. At the same time, the penalties and compensation mechanisms may not effectively constrain the secondary creator’s behavior, as they may take risks and engage in unauthorized activities in pursuit of higher personal gains. Therefore, due to the complexity of revenue distribution, inadequate regulation, and misaligned incentives, $E_8(1,1,1)$ fails to reach an equilibrium state.

4. Case Study

In this section, a representative top anchor on the TikTok platform (hereafter referred to as “Anchor Q”) is selected as a case study to examine the explanatory power and mechanism consistency of the model in a real-world context. It should be emphasized that the parameter values used in this study are not derived from empirical estimates of any specific platform; rather, they are based on feasible institutional ranges and common settings in the existing literature, intended to depict relative trends under different governance environments. All parameters are normalized to comparable ranges to highlight their directional impact on the evolutionary trajectories of the three parties’ strategies, rather than to predict actual numerical levels. Therefore, the simulation results aim to validate the mechanism consistency and condition sensitivity revealed by the theoretical model. The numerical simulations were conducted using MATLAB. The replicator dynamic system was solved numerically under different parameter settings to analyze the evolutionary trajectories of the three players.

Anchor Q has a substantial fan base and operates both live-streaming sales and content dissemination channels, aligning with the basic setting of the “anchor-live-streaming platform-secondary creator” triadic interaction in the model. A sportswear product from Anchor Q’s live-streaming is selected as the object of analysis, with a procurement cost of $\omega$ = 30 CNY and a live-streaming sale price of P = 99 CNY. The live-streaming sales volume of the anchor is set as $d_1$ = 22, while the sales volume driven by secondary creators is $d_2$ = 12. Under the regulated scenario, secondary creators engaging in unauthorized clipping are required to compensate the anchor with L = 1000 CNY; under the non-regulated scenario, unauthorized clipping causes an expected loss to the anchor of $C_3$ = 838.8 CNY.

The initial strategy probabilities of all three parties are set at $0.1$ to reflect uncertainty in strategy selection. Under the parameter constraints satisfying the stability condition $E_3(0,0,1)$, the following analysis examines the effects of key parameter variations on the evolutionary trajectories of strategies.

4.1. Simulation Setup

To enhance the transparency and reproducibility of the numerical analysis, this study provides a detailed description of the simulation process.

All simulations are implemented using MATLAB R2023a. The evolutionary dynamics are simulated based on the replicator dynamic equations derived in Equations (10)–(12). The numerical procedure consists of the following steps:

First, initial strategy proportions for the three players (platform, anchor, and secondary creator) are set within the interval $(0,1)$ to reflect bounded rationality and heterogeneous initial states.

Second, baseline parameter values are assigned according to the model assumptions and existing literature, ensuring that the payoff structure remains economically meaningful.

Third, the system of differential equations is numerically solved using standard iterative methods over a sufficiently long-time horizon to observe convergence behavior.

Fourth, sensitivity analysis is conducted by varying key parameters (e.g., regulatory cost, commission rate, authorization cost, and penalty intensity) while holding other parameters constant, in order to examine their impact on the evolutionary trajectories and equilibrium outcomes.

Finally, the simulation results are visualized through phase diagrams and evolution path plots, which illustrate the stability properties of different strategy combinations.

This step-by-step simulation design ensures that the results are robust and can be replicated under similar parameter settings.

4.2. Impact of the Anchor’s Authorization Cost

This section examines how the anchor’s authorization cost $C_1$ affects the evolutionary outcomes of the tripartite game. As the direct cost associated with granting authorization, $C_1$ captures the anchor’s expenditures on creator screening, contract design and enforcement, as well as potential reputation management. Variations in $C_1$ directly shape the anchor’s incentive to authorize and, through the resulting payoff structure, indirectly influence both the platform’s regulatory stance and secondary creators’ content clipping behavior.

As shown in Figure 2, when $C_1$ remains at a relatively low level, the fixed authorization fee is sufficient to offset the anchor’s authorization expenditures. Additionally, revenue-sharing income from secondary creators further supports the anchor’s authorization decision. Under this condition, anchors are more inclined to adopt the authorization strategy. Secondary creators, in turn, gain access to a stable source of content, which supports sustained clipping and product promotion activities. The system is therefore more likely to evolve toward a cooperative state characterized by “authorization-clipping” In such a regime, the presence of authorization partially mitigates copyright infringement risks, allowing the platform to maintain a relatively stable content environment even in the absence of strict regulatory intervention.

As $C_1$ increases, however, the net benefit of authorization gradually diminishes. Once authorization-related revenues can no longer compensate for the associated costs, the anchor’s optimal strategy shifts from authorization to non-authorization. In the absence of authorization, secondary creators engaging in content clipping face higher infringement risks and potential penalties. Nevertheless, when platform regulation remains weak, some secondary creators may still opt for unauthorized clipping in pursuit of short-term gains, leading the system to evolve toward an informal content production regime characterized by “non-authorization-clipping”.

When $C_1$ reaches a sufficiently high level, authorization ceases to be economically viable for anchors. Even potential indirect benefits, such as brand exposure or long-term reputational gains, are insufficient to offset the elevated authorization costs. In this range, anchors predominantly choose non-authorization, and stable authorization-based cooperation becomes difficult to sustain. If the platform simultaneously faces high regulatory costs, its incentive to enforce regulation is further weakened, increasing the likelihood that the system converges to a non-regulatory equilibrium.

Overall, these results suggest that the anchor’s authorization cost functions as a critical threshold variable in the evolutionary process by reshaping the relative payoff structure of authorization decisions. When authorization costs rise beyond a certain level, authorization is unlikely to emerge as an evolutionary stable strategy. This finding is consistent with the theoretical implications of Propositions 1 and 2, which indicate that under high-cost conditions, the platform and the anchor are more likely to converge toward a non-regulatory, non-authorization equilibrium.

4.3. Impact of Live-Streaming Platform Regulatory Costs

This section examines the influence of the live-streaming platform’s regulatory cost $C_2$ on the outcomes of the three-party evolutionary game. The regulatory cost $C_2$ reflects the technological and managerial resources required for content review, copyright enforcement, and institutional maintenance. Its magnitude directly determines whether the platform has the economic incentive to sustain a regulatory strategy.

As shown in Figure 3, when $C_2$ is relatively low, the platform tends to adopt a regulatory strategy. In this scenario, the revenue from penalties for violations, along with the maintenance of the platform’s content ecosystem and long-term transactional order, can effectively offset regulatory expenditures. The presence of platform regulation increases the expected cost of unauthorized clipping for secondary creators, making them more likely to comply with the authorization mechanism or reduce clipping activities. Under these conditions, the anchor’s authorization strategy is more easily supported by institutional enforcement.

As $C_2$ increases, the net benefit of regulation gradually declines. When the regulatory cost approaches or exceeds the direct and indirect gains from regulation, the platform’s optimal strategy shifts from “regulate” to “not regulate.” With weakened platform oversight, the risk of violations for secondary creators is significantly reduced, strengthening their incentives to engage in clipping and sales. Even if the anchor chooses not to authorize, unauthorized clipping may still occur extensively.

When $C_2$ rises further to a high level, the platform almost entirely loses its incentive to regulate, opting to forgo regulation in order to save costs. In the absence of effective oversight, the authorization mechanism cannot be properly enforced, the anchor’s willingness to authorize declines, and the system is more likely to converge to a “non-regulation-non-authorization-clipping” equilibrium.

Overall, the platform’s regulatory cost plays a decisive role in the evolutionary game: low regulatory costs help establish cooperative equilibrium based on institutional constraints, whereas excessively high regulatory costs weaken platform governance capacity and lead the market to revert to a state characterized by informal content production and ex-post risk-bearing.

4.4. Impact of Live-Streaming Platform Fines on Secondary Creators

This section examines the effect of the fine intensity $\rho$ imposed by the live-streaming platform on unauthorized clipping by secondary creators on the evolutionary outcomes of the three parties. The fine intensity $\rho$ represents the severity of penalties for infringement within the platform’s regulatory framework. Its mechanism operates by increasing the expected cost of violations, thereby constraining secondary creators’ strategy choices and indirectly influencing both the anchor’s authorization decisions and the platform’s own regulatory incentives.

As shown in Figure 4, when $\rho$ is relatively low, the expected penalties from unauthorized clipping are insufficient to effectively deter secondary creators. In this scenario, even if the platform nominally implements regulation, secondary creators may still choose clipping strategies to generate sales revenue, making it difficult to significantly curb violations. With limited fine revenue, the platform cannot achieve sufficient returns through regulation, reducing the attractiveness of regulatory strategies and making the system more likely to evolve toward a non-regulated state.

As $\rho$ increases, the expected cost of unauthorized clipping rises significantly, prompting secondary creators to shift their strategies toward “no clipping” or “clipping only with authorization.“ In this case, the fine mechanism exerts substantial constraint on content production behavior, and the institutional effect of platform regulation becomes evident. At the same time, higher violation costs reduce the risk of the anchor suffering infringement losses under non-authorization, thereby increasing the relative safety of participating in the authorization mechanism.

However, when $\rho$ rises further to a high level, its marginal governance effect gradually diminishes. On the one hand, excessively high fines can significantly compress the expected revenue of secondary creators, reducing their incentives to participate in content production. On the other hand, fines do not directly reduce the platform’s regulatory costs, and relying solely on increasing fine intensity is insufficient to sustain long-term regulatory incentives. In this scenario, the system’s stability remains highly dependent on the relative magnitude of regulatory costs and benefit structures.

Overall, increasing fine intensity does not fundamentally alter the platform’s strategy evolution path, indicating that the governance effectiveness of penalty mechanisms exhibits clear diminishing marginal returns if they cannot substantially improve the platform’s cost–benefit structure. This finding further complements the mechanism explanation in Proposition 1, which emphasizes that “the effectiveness of regulatory tools is constrained by the cost structure”.

4.5. Impact of Penalty for Breach of Contract

This section analyzes the effect of the breach penalty $C_4$ on the evolutionary strategies of the three parties under the scenario where the platform implements regulation and the anchor has authorized secondary creators. The breach penalty $C_4$ reflects the strength of contractual enforcement over secondary creators’ compliance, operating through contractual sanctions to reduce their incentives to deviate from agreed strategies and to provide anchors with a certain level of risk compensation.

As shown in Figure 5, when $C_4$ is relatively low, the cost for secondary creators to deviate from contractual obligations (e.g., failing to produce clips as agreed or not fulfilling promotional duties) is limited. In this case, the authorization mechanism exerts weak behavioral constraints on secondary creators. Even if the anchor chooses to authorize, uncertainty regarding compliance may persist, weakening the anchor’s willingness to grant authorization. Under such conditions, even with platform regulation in place, the system is unlikely to converge to a stable equilibrium characterized by authorized collaboration.

As $C_4$ increases, the expected cost of violating authorization agreements rises substantially, prompting secondary creators to gradually shift toward compliance. For the anchor, higher breach penalties not only provide direct economic compensation but also reduce potential post-authorization risks, thereby enhancing the relative attractiveness of choosing the authorization strategy. Within this parameter range, the system is more likely to evolve toward a stable state dominated by compliant behavior.

However, when $C_4$ further increases to a high level, its governance effect exhibits diminishing marginal returns. On one hand, excessively high breach penalties may significantly compress the expected revenue of secondary creators, reducing their willingness to participate in authorized cooperation. On the other hand, breach penalties primarily affect already authorized situations and cannot directly substitute for platform regulation or lower regulatory costs. Therefore, under conditions of high regulatory costs or unreasonable revenue distribution, merely increasing breach penalties is insufficient to ensure that the system remains stably near a cooperative equilibrium in the long run.

Overall, the breach penalty $C_4$, as a contractually endogenous enforcement mechanism, primarily functions to enhance the enforceability and credibility of authorization relationships. Moderately set penalties help alleviate anchors’ concerns about compliance risk and promote the stable evolution of authorization strategies, but their effectiveness depends on the regulatory environment of the platform and the overall cost–benefit structure. This further supports the conclusion of Proposition 3.

4.6. Impact of Secondary Creators’ Revenue for Anchors

This section examines the effect of the additional benefits T that secondary creators bring to anchors on the evolutionary strategies of the three parties. This parameter captures the indirect payoff effects generated by authorized cooperation, such as enhanced brand exposure, expansion of follower base, and accumulation of long-term commercial value. Although these benefits do not directly translate into immediate sales profits, they play an important incentive role in the anchor’s authorization decision.

As shown in Figure 6, when T is relatively low, the indirect benefits provided by secondary creators are insufficient to offset the anchor’s authorization cost $C_1$ and potential compliance risks. Under these conditions, the anchor lacks the economic motivation to establish cooperative relationships through authorization, and the optimal evolutionary strategy is more likely to lean toward non-authorization. As a result, secondary creators’ behavior primarily depends on the intensity of platform regulation, and the system often fails to achieve a stable cooperative structure.

As T increases, the combined benefits of authorization gradually rise. When T, together with the authorization fee m and breach penalty $C_4$, ensures that the expected post-authorization payoff exceeds the authorization cost, the anchor’s authorization strategy begins to gain evolutionary advantage. In this range, authorization behavior is no longer solely driven by direct monetary returns but is significantly motivated by long-term brand value and externality benefits. Consequently, the system is more likely to converge to a stable state that incorporates authorization behavior, and a certain degree of complementarity emerges between platform regulation and the authorization mechanism.

However, when T increases further, its marginal stabilizing effect gradually diminishes. On one hand, excessively high expectations of indirect benefits may reduce the anchor’s reliance on contract enforcement and platform regulation, decreasing their sensitivity to institutional constraints in the face of potential infringement risks. On the other hand, T does not directly alter the secondary creator’s payoff structure; if revenue distribution and regulatory mechanisms are not simultaneously adjusted, strategy fluctuations may still occur. Therefore, relying solely on increased indirect benefits is insufficient to ensure that the three-party game remains stably in a cooperative equilibrium in the long run.

Overall, the parameter T enhances the intrinsic incentive for anchors to participate in authorized cooperation by increasing the comprehensive payoff of authorization, making it an important factor driving the system toward a cooperative equilibrium. Its stabilizing effect, however, requires coordination with reasonable authorization costs, contractual enforcement, and platform regulation to be fully realized. This finding is consistent with the conclusions of Propositions 1 and 2.

4.7. Impact of Live-Streaming Platform Commission Rate

This section examines the effect of the live-streaming platform’s commission rate $\eta$ on the evolutionary outcomes of the three-party game. The parameter $\eta$ reflects the proportion of sales revenue from anchors and their secondary creators that the platform retains, serving as a key determinant of the platform’s revenue structure and regulatory incentives.

As shown in Figure 7, when $\eta$ is relatively low, the platform’s marginal revenue from anchors’ and secondary creators’ sales is limited. In this case, even if the platform implements regulation, the additional revenue may be insufficient to cover the regulatory cost $C_2$, weakening the platform’s intrinsic incentive to regulate. Under this state, the behaviors of anchors and secondary creators are mainly influenced by their own payoff considerations, and the platform’s role in institutional enforcement is relatively weak.

As $\eta$ increases, the platform’s revenue from content transactions and sales activities rises significantly, enhancing the marginal return of regulatory behavior. Once the commission rate reaches a certain level, the platform’s expected payoff under regulation may exceed that under non-regulation. Even after accounting for regulatory costs $C_2$, the platform has economic incentives to enforce regulation. At this point, the regulatory strategy gradually gains evolutionary advantage, and the system is more likely to converge toward an equilibrium that includes regulatory behavior.

However, when $\eta$ increases further, its impact exhibits nonlinear characteristics. On one hand, excessively high commission rates reduce the distributable revenue available to anchors and secondary creators, diminishing their incentives to participate in authorization cooperation and content creation. On the other hand, skewed revenue allocation may exacerbate secondary creators’ avoidance behaviors or motivation for violations, thereby weakening the practical effectiveness of regulation. Under such circumstances, even if the platform has regulatory incentives, the system may still display strong strategy fluctuations and reduced stability.

In summary, the platform commission rate $\eta$ exerts a dual influence on the system’s evolutionary outcomes by simultaneously affecting the platform’s regulatory incentives and the revenue expectations of content participants. Moderate commission rates help strengthen the platform’s motivation to regulate while promoting convergence toward a stable equilibrium without significantly suppressing content supply. In contrast, excessively low or high commission rates may undermine this coordination mechanism. These findings are consistent with the analyses presented in Propositions 1 and 3.

4.8. Impact of Anchor’s Commission Rate

To further analyze the incentive role of anchors in the content clipping authorization system, this section examines the effect of the anchor’s revenue share $\theta$ on the evolutionary paths of the three-party strategies. The parameter $\theta$ directly determines the anchor’s marginal benefit from secondary creators’ sales, thereby influencing their authorization decision and, through revenue redistribution, indirectly affecting the platform’s regulatory incentives and secondary creators’ clipping behavior.

As shown in Figure 8, when $\theta$ is relatively low, the share of revenue the anchor obtains from secondary creators is limited and insufficient to cover the authorization cost $C_1$ and potential reputational risks. Under these conditions, the anchor tends to adopt a non-authorization strategy, and the system often evolves toward a non-formal content production state characterized by “non-authorization—clipping.” Since the platform can still earn commissions from the anchor’s direct live-stream sales and regulatory costs are high, the platform lacks intrinsic motivation to enforce regulation at this stage.

As $\theta$ increases, the marginal revenue that the anchor derives from secondary creators’ sales rises significantly. When the revenue share $\theta d_2(P-\omega )$ is sufficient to offset the authorization cost, the anchor’s optimal strategy gradually shifts from “non-authorization” to “authorization”. The emergence of authorization helps to formalize the boundaries of content use for secondary creators, transforming clipping behavior from an infringement-oriented mode to a cooperation-oriented mode. Within this range, even in the absence of strict platform regulation, the system may evolve toward a relatively stable state characterized by authorized collaboration.

However, when $\theta$ further increases beyond a certain threshold, the net payoff for secondary creators becomes significantly compressed. On one hand, they must pay a higher proportion of sales revenue to the anchor; on the other hand, they still face platform commissions and potential violation risks. Under such multiple revenue pressures, the incentive for secondary creators to engage in clipping declines sharply, and in some cases, they may even exit content creation. Consequently, the system may shift from an “authorization-clipping” state to a contraction equilibrium of “authorization-no clipping”.

Overall, $\theta$ exhibits a pronounced nonlinear effect on the system’s evolutionary outcomes. These results provide empirical support for the theoretical prediction in Proposition 3, which suggests that “multiple layers of revenue sharing may reduce secondary creators’ participation incentives, thereby undermining the stability of the cooperative equilibrium”.

5. Suggestions

Based on the evolutionary game analysis and numerical simulation results presented above, this study provides the following management and governance recommendations for live-streaming platforms, anchors, and secondary creators. Unlike general strategic implications, the following suggestions explicitly translate model findings into implementable measures under different institutional and cost conditions.

5.1. Recommendations for Live-Streaming Platforms: Implement Differentiated and Incentive-Compatible “Moderate Regulation”

The results indicate that whether a live-streaming platform implements regulation depends critically on whether the marginal gains from regulation can cover the associated regulatory costs. When the platform’s commission rates are low or regulatory costs are high, excessive regulation not only fails to achieve an evolutionary stable state but may also undermine the overall vitality of the content ecosystem.

To address this, platforms should adopt a differentiated governance strategy based on content types and collaboration structures.

(1) Content-based differentiation. Platforms can classify content into three categories: (i) high-value proprietary content (e.g., branded live-streaming sessions with exclusive products), (ii) traffic-oriented general content (e.g., promotional or entertainment-oriented clips), and (iii) user-generated derivative content. For high-value proprietary content, strict regulation and real-time monitoring should be applied to prevent unauthorized reuse. For general content, moderate regulation combined with traffic incentives can encourage compliant sharing. For derivative content, flexible policies (e.g., conditional authorization or revenue-sharing schemes) can be introduced to stimulate participation.

(2) Collaboration-structure-based governance. Platforms should distinguish between: (i) authorized collaboration (with formal agreements), and (ii) unauthorized or informal reuse. For authorized collaborations, platforms can reduce monitoring intensity and instead rely on contract enforcement. For unauthorized cases, platforms should apply targeted penalties only when infringement leads to significant externalities.

(3) Practical implementation example. For instance, a platform can introduce a “tiered governance system” where officially authorized clips are automatically whitelisted and enjoy higher exposure, while unauthorized clips are subject to algorithmic detection and conditional penalties. At the same time, compliant creators can receive commission rebates or traffic support, thereby increasing the relative payoff of compliant behavior.

These strategies directly correspond to Proposition 1, which shows that high regulatory costs weaken the stability of strict regulation, and highlight the importance of improving regulatory efficiency rather than intensity.

5.2. Recommendations for Anchors: Transform Authorization into a Structured and Long-Term Value Mechanism

The model analysis indicates that an anchor’s decision to authorize secondary creators depends not only on direct authorization fees and commission revenues but also on the indirect benefits generated by secondary creators, such as brand exposure and fan growth. When the combined benefits of authorization are insufficient to offset the authorization costs and potential risks, anchors tend to refuse authorization, thereby limiting content diffusion.

To enhance authorization incentives, anchors should adopt structured and forward-looking strategies.

(1) Standardized authorization mechanisms. Anchors can design tiered authorization contracts, such as: (i) basic authorization (allowing clipping with attribution), (ii) revenue-sharing authorization (requiring commission sharing), and (iii) exclusive authorization (granting rights to selected creators). This reduces negotiation costs and improves decision efficiency.

(2) Risk-control mechanisms. Clearly defined contract clauses (e.g., penalties for misuse, content scope restrictions) can reduce uncertainty and mitigate potential losses from unauthorized behavior.

(3) Practical implementation example. For example, an anchor can establish an “authorized creator program,” where selected secondary creators are granted clipping rights in exchange for a fixed commission rate and compliance with content guidelines. This not only expands content reach but also maintains brand consistency.

These strategies are consistent with Proposition 2, which highlights that authorization decisions depend on the net benefit structure and can partially substitute for platform regulation.

5.3. Recommendations for Secondary Creators: Balance Revenue Opportunities with Compliance Sustainability

The analysis shows that when secondary creators face multiple deductions and high compliance costs, their incentives to participate in content creation decline significantly, and they may even choose to withdraw, thereby destabilizing the system. This indicates that relying solely on penalties and constraints is insufficient to maintain a healthy content creation ecosystem.

Therefore, secondary creators should adopt sustainable participation strategies.

(1) Platform selection strategy. Creators should prioritize platforms with transparent rules, moderate commission rates, and stable authorization mechanisms to reduce uncertainty.

(2) Compliance-oriented operation. Engaging in authorized clipping and adhering to platform regulations can reduce the risk of penalties and improve long-term returns.

(3) Practical implementation example. For instance, a secondary creator can choose to collaborate with anchors offering clear authorization policies and stable revenue-sharing schemes, rather than relying on short-term gains from unauthorized clipping that may result in penalties or account restrictions.

These findings align with Proposition 3, which demonstrates that high costs and compressed revenue space suppress participation incentives, emphasizing the need for a balanced cost–benefit structure.

Overall, the above recommendations highlight that effective governance in live-streaming ecosystems should rely on a combination of differentiated regulation, incentive alignment, and collaborative mechanisms, rather than unilateral control or purely punitive approaches.

6. Discussion

6.1. Interpretation of ESS Conditions

This study identifies several evolutionary stable strategy (ESS) conditions (e.g., E3, E4, and E6), which characterize different long-term equilibrium of the system. These equilibriums reflect distinct governance regimes in the live-streaming content ecosystem and provide insights into how strategic interactions among platforms, anchors, and secondary creators evolve over time.

Specifically, E3 corresponds to a regime in which platform regulation is sustained, unauthorized clipping is effectively constrained, and cooperative behavior is partially achieved. This equilibrium emerges when the expected penalty revenue outweighs the regulatory cost, ensuring that supervision remains a viable strategy. E4 reflects a mixed or transitional state in which the system does not converge to full cooperation or full opportunism, but instead stabilizes under intermediate parameter conditions. E6 represents a cooperative equilibrium characterized by platform non-regulation, anchor authorization, and active participation of secondary creators. This equilibrium highlights the possibility that decentralized coordination mechanisms can replace centralized enforcement under appropriate incentive structures.

Together, these ESS conditions illustrate that the system may converge to fundamentally different outcomes depending on parameter configurations, and that the stability of each equilibrium depends on the alignment of economic incentives across all participants.

6.2. Regulation Effectiveness and Platform Governance

One of the central findings of this study is that excessive platform regulation may undermine system stability, especially when regulatory costs are high or enforcement is inefficient. This result provides an important complement to the literature on platform governance discussed in Section 2.3.

Existing studies generally emphasize the role of platform regulation in mitigating opportunistic behaviors and maintaining market order. Stronger supervision is often viewed as a necessary condition for ensuring compliance and protecting intellectual property rights. However, our evolutionary analysis suggests that regulation is not always self-sustaining. When the cost of monitoring and enforcement exceeds the expected benefits, platforms may gradually withdraw from active supervision, leading the system to evolve toward a non-regulatory equilibrium.

This finding extends the platform governance literature by highlighting the endogenous limitation of regulatory mechanisms. Rather than assuming that platforms can enforce rules at negligible cost, the model explicitly incorporates regulatory costs and shows how they shape long-term strategic choices. In this sense, the study provides a more dynamic perspective on governance, where regulation is not exogenously imposed but evolves as part of the strategic interaction among agents.

6.3. Authorization as a Substitute for Regulation

Another key insight of this study is the role of anchor authorization as a potential substitute for platform regulation. In particular, E6 demonstrates that when authorization mechanisms are sufficiently attractive, the system can converge to a cooperative equilibrium even in the absence of strong platform intervention.

This finding contributes to the literature by reframing authorization not merely as a legal arrangement, but as an economic coordination mechanism. In contrast to centralized regulation, authorization operates through incentive alignment: by granting permission and sharing revenues, anchors transform potentially infringing activities into mutually beneficial cooperation.

Compared with existing studies, which often treat regulation and authorization as independent governance tools, this study reveals a substitution effect between them. When authorization is well-designed—through appropriate pricing, revenue-sharing, and access conditions—it can reduce the need for costly platform supervision. This insight suggests that decentralized governance mechanisms may, under certain conditions, achieve outcomes comparable to or even better than centralized enforcement.

6.4. Revenue Distribution and Creator Behavior

The model also highlights the sensitivity of secondary creators’ behavior to revenue distribution parameters, particularly the effective returns from clipping activities. This finding directly relates to Proposition 3 and extends the literature on live-streaming revenue distribution discussed in Section 2.4.

Prior research has shown that revenue-sharing mechanisms play a critical role in shaping the incentives of content creators and platform participants. Our results further demonstrate that small changes in commission rates or net returns can significantly alter the evolutionary trajectory of the system. When the net return from clipping exceeds a certain threshold, secondary creators are more likely to engage in clipping activities, even in the presence of regulatory pressure. Conversely, when returns are low or penalties are substantial, clipping behavior diminishes.

This sensitivity implies that revenue distribution is not only a static contractual arrangement but also a dynamic driver of system evolution. By incorporating bounded rationality and adaptive behavior, the model shows how revenue-sharing schemes influence not only immediate decisions but also long-term equilibrium outcomes. In this sense, the study provides a dynamic extension to the existing literature on profit allocation in live-streaming ecosystems.

6.5. Theoretical Implications and Contribution

Overall, this study contributes to the literature in three main aspects.

First, it integrates platform regulation, anchor authorization, and secondary content creation into a unified evolutionary game framework, thereby capturing the interdependence among these mechanisms. Second, it demonstrates that governance outcomes are not determined solely by regulatory intensity, but by the interaction between regulation and market-based coordination mechanisms. Third, it highlights the importance of dynamic analysis in understanding digital platform ecosystems, where strategies evolve over time rather than being fixed.

By linking the ESS conditions to existing research on platform governance and revenue distribution, this study provides a more comprehensive and nuanced understanding of how live-streaming content ecosystems can be effectively managed. The findings suggest that future research should pay greater attention to the interaction between centralized and decentralized governance mechanisms, as well as to the dynamic nature of strategic behavior in digital platforms.

7. Conclusions

7.1. Contributions

This study focuses on the increasingly prevalent phenomenon of content clipping in live-streaming e-commerce and constructs a three-party evolutionary game model comprising the live-streaming platform, anchors, and secondary creators to systematically analyze the dynamic interactions among platform regulation, anchor authorization, and secondary creator clipping behavior. Unlike existing studies that primarily focus on a single actor or static game structures, this paper adopts an evolutionary perspective. It depicts how the strategies of all participants gradually adjust under bounded rationality, influenced by payoff structures and institutional constraints, and ultimately converge to different stable states.

Theoretical contributions of this study are threefold. First, it explicitly defines “content clipping for sales” as an institutionalized commercial activity situated between content reuse and derivative content creation, and integrates copyright authorization and platform regulation into a unified analytical framework, thereby addressing a gap in the literature on governance of secondary content creation. Second, through evolutionary stability analysis, it reveals the critical roles of regulatory costs, authorization incentives, and revenue distribution in determining the stability of different strategy combinations, indicating that high-intensity regulation or multiple layers of revenue compression do not necessarily lead to more stable governance outcomes. Third, supported by numerical simulations, the study further demonstrates how variations in key parameters affect system equilibrium through evolutionary pathways, providing a mechanistic explanation for incentive imbalances in live-streaming platform content governance.

From a practical perspective, this study provides more concrete and actionable guidance for different stakeholders.

For live-streaming platforms, the results suggest implementing a differentiated and incentive-compatible governance strategy. Instead of uniformly intensifying regulation, platforms should classify content types (e.g., proprietary commercial content, traffic-oriented content, and derivative content) and adopt targeted policies, such as stricter control over high-value content and more flexible governance for derivative content. In addition, platforms can enhance compliance incentives through mechanisms such as commission optimization, traffic support for authorized content, and selective enforcement of penalties.

For anchors, authorization should be treated as a long-term value investment rather than a short-term transactional decision. By establishing standardized authorization schemes (e.g., tiered authorization or revenue-sharing agreements) and clearly defining contractual responsibilities, anchors can expand content reach while maintaining control over intellectual property. This approach helps transform authorization into a stable strategic choice in the evolutionary process.

For secondary creators, sustainable participation depends on balancing revenue opportunities with compliance requirements. Creators should prioritize collaboration with platforms and anchors that offer transparent rules and stable revenue-sharing mechanisms, and actively adopt authorized clipping strategies to reduce regulatory risks and ensure long-term returns.

7.2. Limitations

Although this study provides certain insights in terms of theoretical modeling and mechanism analysis, several unavoidable limitations remain. First, the study adopts a highly abstract evolutionary game framework and does not incorporate micro-level data from actual platforms or individual actors. Consequently, the findings primarily reflect potential mechanisms rather than direct predictions of real-world behavior. This implies that the results should be interpreted as “evolutionary outcomes that may arise under specific conditions” rather than universally applicable empirical facts.

Second, the model assumes a single live-streaming platform, a single anchor, and representative secondary creators, neglecting complex scenarios in reality such as multi-platform competition, anchor heterogeneity, and variations in secondary creator scale. While this simplification helps to highlight core mechanisms, it also limits the model’s explanatory power in highly competitive or multi-agent environments.

Additionally, platform regulation is simplified to a binary choice of “regulate vs. not regulate’ without capturing regulatory intensity, enforcement modalities, or dynamic adjustment processes. This, to some extent, constrains the ability to reflect the diversity of governance strategies employed by real-world platforms.

Finally, while this study focused on the game equilibrium states and short-term dynamic changes, it neglected the impact of long-term trends and potential transformations. With technological advancements and market changes, the live-streaming industry may face new opportunities and challenges. Future research could examine the impact of long-term trends and potential transformations on game equilibrium.

7.3. Future Research

Future research can extend this study in several directions. First, multi-platform competition or platform-differentiated governance mechanisms can be incorporated to analyze how inter-platform competition influences regulatory incentives and the cross-platform strategy choices of content creators. Second, heterogeneity among anchors and secondary creators such as differences in influence, bargaining power, or risk preferences can be further considered to enhance the model’s ability to capture real-world behavior.

Additionally, future studies could leverage empirical platform data or case studies to test the evolutionary mechanisms proposed in this paper, thereby establishing a closer link between theoretical analysis and empirical evidence. Finally, as technologies such as algorithmic recommendations, automated content review, and smart contracts become increasingly integrated into live-streaming platforms, exploring how technological governance tools can be incorporated into the evolutionary game framework represents another important direction for future research.