A Study on the Design of Incentive Contracts for Platform Economy Regulation Based on Dual Principal–Agents

Abstract

A system of incentives can be established to encourage several parties to unite as a community of interest and become jointly committed to the platform economic governance. The platform economy involves progressively more complex subjects of interest and relationships, which are not the typical principal–agent one-time cooperative relationship. This study investigates the problem of regulatory incentives in the platform economy, specifically focusing on the relationship between the government, platform enterprises, and merchants. It analyzes this issue under conditions of asymmetric information by constructing and solving a dual principal–agent model. The findings indicate the following: (1) the government’s incentives and regulatory mechanisms can be considered as interchangeable to some extent, with decisions made by evaluating their respective costs; (2) the government’s optimal incentives and regulations ultimately shape the self-regulatory behavior of merchants through platform enterprises; and (3) the optimal level of incentives for both the government and the platform enterprise is influenced by factors such as the ability coefficient, the social transformation coefficient, and the merchants’ reliance on the platform enterprise. Additionally, the optimal effort level of the platform enterprise and the merchants increases with higher levels of the regulatory effort, risk sensitivity coefficient, and ability coefficient. A win–win scenario and a long-term, stable cooperative partnership can be reached by the three parties under the ideal incentive intensity. The study’s conclusions can serve as a theoretical foundation and support for the creation of incentive contracts for platform economy regulation.

1. Introduction

The platform economy defines the organizational structure of the digital economy, which fosters the creation of new digital economic models and scenarios, and serves as a catalyst and propeller for the advancement of the digital economy. While the platform economy fosters the swift expansion of the digital economy and enables its considerable affluence, it also introduces novel social risks. Characterized by diverse participating entities, extensive transaction data, information disparities between online and offline sectors, and unique network externalities, the platform economy manifests market failure in distinctive ways. Issues such as the widespread existence of counterfeit and low-quality products, cyber-industrial crime, and the adverse effects of “big data” on growth have also become more prevalent [1,2]. These difficulties pose new challenges to the regulatory framework of the digital economy and the platform economy. This presents novel problems to the regulatory framework of the digital economy and platform economy.

By the end of 2023, the cumulative valuation of Chinese digital platform enterprises surpasses US$6 trillion, encompassing approximately 279 enterprises with a market value exceeding US$1 billion [3]. Platform enterprises have experienced a significant increase in their growth rate, both in terms of size and quantity. The exponential growth of the platform economy has introduced novel complexities in its social governance and regulation, particularly the widespread occurrence of counterfeit and substandard products, cyber-industry crimes, the detrimental impact of “big data” maturation, and other related concerns. Managing data competition among platform enterprises, addressing platform monopoly, and defining the social responsibility of platform enterprises present highly intricate and delicate challenges.

In 2021, China’s platform economy saw the implementation of “stringent regulation” policies, which was prompted by the Political Bureau of the Central Committee of the Communist Party of China (“CPC”) and the Central Economic Work Conference (“CEWC”) held in December 2020. These events explicitly emphasized the importance of “strengthening anti-monopoly measures and preventing uncontrolled capital expansion”, leading to the issuance of a mandate for rigorous regulation. The December 2020 Political Conference of the CPC Central Committee and the Central Economic Work Conference both emphasized the importance of “enhancing measures against monopolies and curbing the unchecked growth of capital”, issuing a directive for “rigorous regulation”. The year 2021 saw a succession of laws and regulations on data protection, anti-monopoly, anti-unfair competition, and workers’ rights and interests issued by several governmental departments [4]. General Secretary Xi Jinping underscored the importance of maintaining a balance between promoting development and implementing regulations. He highlighted the need to regulate and standardize development activities, while also ensuring that regulations are developed in a way that supports further growth. The “Opinions on Promoting the Standardized, Healthy and Sustainable Development of the Platform Economy” was jointly issued by the National Development and Reform Commission (NDRC) and nine other departments on 19 January 2022. This document stresses the need to establish a robust regulatory framework for the platform economy and ensure its healthy and sustainable growth, in line with the strategic goal of enhancing the country’s competitive advantage. Key strategic focuses, including promoting the high-quality development of the platform economy, and forming a strategic perspective, aim to improve the development environment, strengthen innovation and development capabilities, support economic transformation and development, and establish an effective governance system for the platform economy [5]. The Opinions hold significant practical importance in promoting the coordination of governance, strengthening sectoral coordination, and adhering to the principle of integrating online and offline supervision. They also aim to enhance collaborative research and decision-making on major issues in the field of the platform economy. It is of great practical significance.

During the regulation of the platform economy, the government aims to ensure fair competition, protect consumer rights, and promote healthy economic development. Platform enterprises, on the other hand, prioritize maximizing profits alongside maintaining platform stability and attractiveness. Merchants, meanwhile, seek to expand their market share and increase their profits. These various interests are the key issues of platform economic governance. Nevertheless, the government may face challenges in comprehending the intricacies of platform enterprises and merchants’ operations and behaviors. Conversely, platform enterprises and merchants possess a greater amount of confidential information. This imbalance in information may impede the government’s ability to regulate and control platform enterprises and merchants effectively. Additionally, it may lead to platform enterprises and merchants prioritizing their own interests over the public welfare and other stakeholders. The principal–agent theory can elucidate the conflict of interest and information asymmetry between the government, platform enterprises, and merchants in the governance of platform economics.

Currently, there is significant academic interest in incentivizing platform economic regulation and conducting a quantitative analysis of incentives in platform economic regulation from many levels and perspectives. Early related studies focused on the pricing issues of platform enterprises. Subsequently, research delved into an analysis of the economic governance platform, focusing on its substance, the entities responsible for governance, the model of governance, and the establishment of the governance system.

1.1. Research Related to the Governance Content of the Platform Economy

In today’s digital era, the rise of the platform economy has significantly reshaped production, consumption, and social interaction. However, the rapid growth of the platform economy has sparked extensive discussions on governance issues as well. The most central and highly debated issues include antitrust concerns [6,7], pricing mechanisms [8,9,10,11,12], and the protection of user rights in the context of big data [7,13,14].

First, regarding the anti-monopoly debate, the issue of monopolization in the platform economy has garnered significant attention. In a competitive economy, the maximum total consumer surplus and total social welfare are expected to be achieved with the consideration of personal information protection and first-degree pricing discrimination. Nevertheless, the prohibition of price discrimination can result in an inefficient product distribution, highlighting the intricate interplay between market competition and the protection of individual rights [15,16,17]. Prior research has supported the idea that technological advancement and innovative business models might not always align with the market. It has been predicted that, under certain circumstances, the market will develop a competitive monopoly structure known as a mono-oligopoly. This highlights the significance of antitrust regulation in the platform economy [18,19,20].

Second, pricing strategies also constitute a significant aspect of platform economic governance. The vast public concern has been intensified by the phenomenon known as “big data kills maturity”, where platforms utilize user data to implement tailored pricing. In this study, Yin et al. [21] (2023) examined the possible conflicts that may arise between the rights of customers and operators of algorithmic discriminating behaviors at various phases. Relevant research has determined that conflicts may arise between operators and consumers regarding information gathering, pushing, and pricing, due to conflicting rights and interests. It emphasizes the necessity of implementing regulations to safeguard consumer rights and interests. To address this phenomenon, Lei et al. [22] (2021) and Wu et al. [23] (2020) established an evolutionary game model and a prospective benefit perception matrix, respectively, to deeply analyze the decision-making mechanism and regulatory mechanism of the “familiarization” behavior of e-commerce platforms, which provides an important reference for policy formulation.

Although antitrust and pricing methods are crucial components of platform economy governance, Denyer [24] (2023) posited that a comprehensive understanding and resolution of the difficulties presented by the platform economy require more than just these two conventional viewpoints. The convergence of fintech and network economics, exemplified by prominent Internet platforms, constitutes a novel approach to social production and the organization of daily life. Hence, it is imperative to transcend the conventional anti-monopoly viewpoint and delve into the effective governance of the platform economy from a more comprehensive standpoint.

1.2. Research on Platform Economic Governance

Prior research on platform economic governance has primarily focused on the collaborative and interdependent connection among the government, platforms, users, third parties, customers, and various other entities involved in platform governance. Li et al. [25] (2023) and Doellgast et al. [26] (2023) examined the issues such as the degree of discriminatory pricing, acknowledgment of data rights, likelihood of social exposure, and government oversight. An evolutionary game model of “merchant–platform e-commerce–government” was constructed to investigate the collaborative governance approach of the government, enterprise, and consumer in platform e-commerce. The model aimed to examine the connection between government, enterprises, and consumers. In their study, Wang et al. [27] (2020) examined the underlying “regulatory dilemma” associated with credit in platform e-commerce. They accomplished this by developing an evolutionary game model of the “merchant–platform e-commerce–government” system. The inherent “regulatory dilemma” in platform e-commerce credit was analyzed by creating an evolutionary game model of “merchant–platform e-commerce–government”. Wang et al. [28] (2022) examined consumer complaints and developed a four-party evolutionary game model that incorporates the government, e-commerce platforms, merchants, and consumers to analyze the strategic decisions made by each party. In a groundbreaking study, Xu et al. [29] (2024) developed a novel UCIP “multi-actor co-regulation” framework that involves active involvement from the government, industry associations, and platform users. Ma et al. [30] (2023) studied the small-scale interactions between individuals and the key factors that influence the evolution process. They developed a four-party evolution game model consisting of super platforms, existing platforms, entrepreneurial platforms, and governmental regulators to investigate the evolution mechanism of the duopoly.

Furthermore, some scholars have argued that the central aspect of platform governance revolves around the collaboration between government and platform enterprises. They proposed that a dual cooperative governance model, combining “government regulation + industry self-regulation,” is the most effective approach to governing cyberspace. According to Nan et al. [31] (2023), Li et al. [32] (2018), Guo et al. [33] (2019), and Lu et al. [34] (2023), they emphasized the complementary and supportive nature of government regulation and platform self-regulation. Guo et al. [33] (2019) also incorporated the concepts of dynamic balance and structural balance, along with the three regulatory approaches of ex-ante, ex-post, and ex-post. Guo et al. [33] (2019) integrated the concepts of dynamic equilibrium and structural equilibrium, along with three types of regulation: pre-event, during the event, and post-event. Two regulatory strategies were proposed: single-body dynamic equilibrium and dual-body structural equilibrium. Based on this model, a cooperative regulatory framework between the government and platforms was developed [35,36].

Currently, there is a lack of validation for quantitative techniques related to principal–agent problems in platform economic governance, despite the existing literature on the subject [9,37,38,39,40].

Extensive research revealed that a significant body of literature examined the implications and attributes of platform non-compliance, highlighting the beneficial impact of government regulation on platform economic governance. Additionally, some studies proposed strategies for the development of platform economies, providing a theoretical foundation and policy suggestions for platform economic governance. Nevertheless, there are still certain deficiencies. Initially, a substantial body of literature has extensively discussed the significance of government involvement in regulating platform monopolies, focusing on qualitative aspects and highlighting the insufficiency of current regulatory methods. The consensus is that the government should employ innovative regulatory measures to effectively address the issues of governing platform economies. Quantitatively, the number of economic restrictions on the platform is still rather low. Furthermore, while a few scholars have acknowledged the principal–agent dynamics in platform economic governance, the current study primarily focuses on the agent’s participation constraints and overlooks the principal’s minimum participation constraints. As a result, this oversight can result in a risk of financial loss despite maximizing the principal’s utility and a failure to establish effective incentives for the principal. Existing research on platform governance primarily centers around the development of incentive contracts. This approach viewed the platform enterprise as a risk-averse agent and overlooks the intricate motivations of the medical side to exert effort. Additionally, it failed to acknowledge the platform enterprise’s role as a mediator between the government and merchants.

This paper examines the regulatory incentive problem in the platform economy by analyzing the regulatory incentives of the government, platform enterprises, and merchants. It constructs a dual principal–agent model under conditions of asymmetric information and provides a theoretical foundation for regulating China’s platform economy through the solution and simulation of the dual principal–agent model. The primary advancements are as follows: (1) A dual principal–agent model is created to govern the relationship between the government, platform enterprises, and merchants in platform governance. An optimal contractual mechanism is designed by combining incentive and supervision mechanisms. (2) The role of platform enterprises as both principal and agent is taken into account, and the factors influencing the expected return of platform enterprises are analyzed, which provides theoretical support for the development of collaborative governance involving multiple subjects. (3) A quantitative analysis is conducted to determine the optimal incentives and supervision methods. This study performs a mathematical analysis of the most effective contract structure, taking into account optimal incentives, optimal regulation, and other relevant factors, while examining the different roles that regulatory mechanisms and incentive mechanisms can play.

This paper is structured as follows: the first part describes the platform economic regulatory incentives problem and makes assumptions about the model; the second part solves the two-layer principal–agent model; the third part analyzes and discusses the nature and characteristics of the solutions to the two-layer principal–agent model; the fourth part simulates and analyzes the two-layer principal–agent model through simulation; and the fifth (and last) part offers conclusions and recommendations for countermeasures.

2. Problem Description and Modelling Assumptions

2.1. Description of the Problem

The government plays a prominent role in implementing economic and regulatory incentives to protect consumer interests and promote the well-being of the public. Its main objective is to maximize social welfare. In contrast, merchants aim to enhance their profits. Therefore, the interests of the government and the businessmen are entirely divergent. Simultaneously, the government, due to its limited control over information, cannot directly regulate merchants and frequently relies on collaboration with platform enterprises to effectively supervise them. Owing to the presence of information asymmetry, the government faces challenges in accurately assessing the actual degree of effort exerted by platform businesses and merchants. Consequently, when the government lacks adequate motivation to regulate these entities, moral hazard frequently arises. The interaction between the government, platform enterprises, and merchants in terms of the incentives for collaborative regulation of the platform economy can be understood as a principal–agent relationship. Specifically, it is a dual principal–agent relationship, as depicted in Figure 1.

Under the incentive framework of platform economy regulation, the intricate nature of the principal–agent relationship—which is especially noteworthy due to its dual principal–agent structure—is thoroughly reflected in the cooperative regulatory system that unites the government, platform firms, and merchants. First, at the platform enterprise level, the government, as a principal, transfers some of its regulatory authority and responsibility to the platform enterprise. The expectation is that the platform enterprise will use its technological prowess and market knowledge to realize the natural integration of government regulation and self-regulation, as well as to improve the efficiency and equity of the market. The platform enterprise serves as both a sub-principal in this process, as it must further incentivize and limit merchant behavior to guarantee standardization and transparency of market transactions, and an agent, in charge of putting particular regulatory measures into place.

Secondly, the second level of principal–agent relationship is between the platform enterprise and the merchants. The platform enterprise also assigns merchants the task of managing and maintaining the market. These merchants, acting as sub-agents, are accountable for adhering to platform regulations, offering high-quality goods and services, and working together to preserve the market order. In addition to strengthening the subjects’ dependency and limitations on one another, this dual principal–agent connection necessitates the development of a more complex incentive and constraint system in order to address moral hazard and adverse selection brought on by information asymmetry. Therefore, by policy directives and regulatory measures, the government must guarantee that platform companies and merchants follow their own objectives without jeopardizing the public interest and the integrity of the market. It also must realize the robust and long-term growth of the platform economy.

2.2. Model Assumptions

The two-level principal–agent model is a theoretical framework for analyzing multi-level principal–agent relationships. The specific construction steps and computational flow are shown in Figure 2.

2.2.1. Layer 1 Principal–Agent Model Assumptions

Assumptions Regarding Output and Cost for Platform Enterprises

The platform enterprise serves as the agent at the first level of the principal–agent relationship. The principle makes the assumption that the effort levels of the platform enterprise $e_1$ and the merchant $e_2$ are continuous variables at the second level. The platform enterprise yields an output of ${\pi }_1=k_1(e_1+\varphi e_2)+{\epsilon }_1$, $k_1(k_1>0)$ is the platform enterprise’s ability to supervise and incentivize the merchant, $\varphi$($0\le \varphi \le 1$) is the coefficient of dependence, $\varphi e_2$ is the merchant’s contribution to the platform enterprise’s output, and ${\epsilon }_1$ is a stochastic variable that affects the platform enterprise’s outcome. The amount of work that the platform enterprise puts in has a big impact on the output of the platform enterprise $e_1$. This is decided by a random factor represented by the symbol ${\epsilon }_1$$~$$N(0,{\delta }_1^2)$, which has a smaller variance and a normal distribution. The effort–cost of the platform enterprise is assumed to be $C_1={\displaystyle \frac{{\lambda }_1{e}_1^2}{2}}$, ${\lambda }_1$ is the effort–cost coefficient of the platform enterprise, and the unit cost of the platform enterprise’s effort increases with its level of effort $e_1$ and the effort–cost coefficient ${\lambda }_1$.

Government Incentive Contract Assumptions for Platform Enterprises

The government will incentivize the platform enterprise based on the social benefits brought about by platform supervision, with an incentive coefficient of ${\beta }_1$($0<{\beta }_1<1$), meaning that its incentive contract is $S_G={\beta }_1{\pi }_1+{\alpha }_1$, in accordance with the proxy contract between the government and the platform enterprise. This is in addition to the fixed subsidy ${\alpha }_1$. The government and the platform enterprise adopt a collaboration model that is comparable to a fixed salary compensation when ${\beta }_1=0$, and a cooperation model that is similar to “fixed + share” when ${\beta }_1=1$. In addition to receiving the government incentive, the platform enterprise that oversees the merchants will also benefit from a better reputation among platform consumers, which will enhance the number of potential customers and product sales for the platform enterprise.

Assumption of Collusion between Platform Companies and Merchants

Due to their aligned interests, platform enterprises and merchants will conspire under government control. An example of this may be seen in Alibaba’s efforts to protect merchants in the “Alibaba VS AIC” case. In such scenario, retailers will reduce efforts to raise their creditworthiness and instead concentrate on increasing their revenue. Additionally, the platform companies will decrease their monitoring over the creditworthiness of the merchants, and approving of their behavior of maximizing their own interests and getting profit from this process. Given that the platform enterprise and the merchant have a degree of cooperation of $l$, at this time, the collusion is deemed to be $l=1-e_1$ because the platform enterprise is not taking steps to regulate it. The platform enterprise can now enjoy the collusion benefit $I_1=i_{1}l=i_1(1-e_1)$, where $i_1$ is the total benefit that can be attributed to the platform enterprise’s collusion. The greater the total benefit that can be attributed to the platform enterprise, the more collusion benefit that the platform enterprise can obtain. At the same time, the government’s social benefit will decrease when platform enterprise and merchant collide, assuming that the government’s social benefit from platform enterprise and merchant collusion will be limited to the total benefit that can be distributed $i_1$.

Assumptions about the Government’s Adoption of Regulatory Strategies

Primarily, the government will periodically carry out arbitrary inspections of platform businesses and merchants in order to detect potential collusion based on prior actions. Taking Chinese New Year of 2022, for instance, several regions around the nation have increased the monitoring and sampling of top-selling e-commerce special goods as part of specific initiatives to prevent counterfeiting. If the government uses oversight to find evidence of collusion between platform companies and retailers, it will fine the platform companies $M_1=m_{1}l=m_1(1-e_1)$, where $m_1$ is the maximum fine. Given the assumption that the government is in charge $r_1$, this probability can also be used to indicate the likelihood that the government will find out about the platform enterprise’s and the merchant’s collaboration, leading to the expectation that the platform enterprise will face consequences $E_1=m_1{r}_1\cdot (1-e_1)$.

Assumptions on Government Benefits and Cost of Risk

The social benefit output of the government as a result of regulating platform companies to protect consumer rights and interests is $F_1=h_1{e}_1+{\zeta }_1$, assuming that the government is risk-neutral. $h_1$ is the social benefit’s conversion coefficient, which shows how much the platform companies’ efforts in regulation have improved the e-commerce environment, and ${\zeta }_1$ is the stochastic factor affecting the government’s output of the social benefit, which is subject to a normal distribution. The lesser variance of the factor, ${\zeta }_1$$~$$N(0,{\sigma }_1^2)$, suggests that the platform enterprises’ effort level mostly determines the output of the government’s social benefit. The smaller its variance is, the more the output of social benefits of the government depends on the level of efforts of platform enterprises.

Assuming that, in the dual principal–agent model, the platform enterprise, acting as the intermediate principal agent and being risk-averse, has an equal expected utility and certainty revenue, and the government, acting as the principal, is neutral, their expected utility and income are equal. Assuming that the utility function of the platform enterprise exhibits an absolutely risk-averse characteristic, denoted as $u=-e^{-\rho \omega }$, where $\rho$ ($\rho >0$) represents the degree of risk aversion, and the higher the $\rho$, the lower the willingness to take risks, $\omega$ represents the platform f enterprise’s predictable income. As per Arrow–Pratt’s conclusion, the platform enterprise’s risk cost is considered to be $C_{r1}={\displaystyle \frac{{\rho }_1{\beta }_1^2{\sigma }_1^2}{2}}$, while the end agent’s merchant risk cost is expected to be $C_{r2}={\displaystyle \frac{{\rho }_2{\beta }_2^2{\sigma }_2^2}{2}}$.

2.2.2. Layer 2 Principal–Agent Model Assumptions

Merchant Output Assumptions

Due to their positive reputation, ${\pi }_2=k_2{e}_2+{\epsilon }_2$, merchants’ trustworthy behavior will yield financial benefits; $e_2$ is directly correlated with the amount of the merchants’ trustworthy efforts; $k_2$($k_2>0$) is the organization and management level capacity coefficient; ${\epsilon }_2$ is a random factor that affects the output of the merchants and follows the normal distribution ${\epsilon }_2$$~$$N(0,{\delta }_2^2)$; the smaller its variance is, the more the merchants’ output depends on the platform enterprises’ level of efforts.

Merchant’s Revenue Assumptions

The basic economic benefit that a merchant can expect to receive from selling goods through the platform enterprise is presumably $\tau {\pi }_2$($\tau >0$), or the merchant’s basic benefit coefficient; the fixed cost that the merchant must pay is $a$, or the fixed inputs that the merchant must pay, such as labor costs, fees, and tax payments. A merchant’s effort–cost coefficient is denoted by J1, the effort–cost of good faith is assumed to be $C_2={\displaystyle \frac{{\lambda }_2{e}_2^2}{2}}$, and the unit cost of a merchant’s effort rises in proportion to their effort level $e_2$ and effort–cost coefficient ${\lambda }_2$.

Assumptions on Merchant Credit Incentives by Platform Enterprises

The platform enterprise and merchant have a principal–agent contract stating that the merchant can receive a fixed subsidy ${\alpha }_2$ from the government through the platform enterprise. Additionally, the platform enterprise will provide the merchant with an incentive contract, that is, $S_B={\beta }_2{\pi }_2+{\alpha }_2$, based on the economic benefits of the reputation brought about by the supervision, with an incentive factor ${\beta }_2$ ($0<{\beta }_2<1$).

Assumptions on the Adoption of Regulatory Strategies by Platform Companies

There are two trustworthy behaviors exhibited by the vendor. Let us assume that the merchant has a negativity level of $1-e_1$ and that the consequent benefit is $I_2=i_2(1-e_2)$, with the maximum benefit amount being $i_2$. Under the assumption that the merchant has the means of supervision to keep an eye on the bad faith behavior of the merchant, the supervision strength is $r_2$ ($0<r_2<1$). If this probability is equal to the supervision strength coefficient $r_2$, then the likelihood that the platform enterprise will find out about the merchant’s bad faith behavior is higher because the supervision strength is higher. As a result, the expectation of $E_2=m_2{r}_2\cdot (1-e_2)$, where $m_2$ is the maximum penalty, is applied to the merchant’s punishment.

Assumptions on Returns and Cost of Risk for Platform Enterprises

The measure of the improvement in the e-commerce environment due to merchants’ efforts is represented by the conversion coefficient of their social benefit ($h_2$), which is $F_2=h_2{e}_2+{\zeta }_2$. The random factor affecting the platform enterprise’s social benefit output is ${\zeta }_2$, which follows the normal distribution ${\zeta }_2$$~$$N(0,{\sigma }_2^2)$, and a smaller variance indicates that a greater portion of the platform enterprise’s social benefit output is dependent on the level of merchants’ efforts.

In summary, the model symbols and their meanings in this paper are shown in

Table 1. Model symbols and their meanings.

Notation	Hidden Meaning	Notation	Hidden Meaning
$e_1$	Level of effort of platform companies	$M_1$	Penalties imposed on platform enterprises by governments that find collusion
$e_2$	Merchant’s level of effort	$m_1$	Maximum penalty for breach of trust by platform companies
${\pi }_1$	Outputs of the platform’s enterprises	$r_1$	Government’s regulatory efforts
$k_1$	Ability factor of platform companies in incentivizing the monitoring of merchants	$F_1$	Social output benefits for governments
$\varphi$	Dependency factor	$h_1$	Conversion factor for social benefits
${\epsilon }_1$	Random factor	${\zeta }_1$	Stochastic factors affecting the output of government social benefits
$C_1$	Cost of effort for platform companies	$u$	Utility function of the platform firm
${\lambda }_1$	Cost-of-effort factor for platform enterprises	$C_{r1}$	Cost of risk for platform companies
${\alpha }_1$	Platform companies receive fixed subsidies	$C_{r2}$	Cost of risk for merchants
$S_G$	Government incentive contracts for platform companies	${\pi }_2$	Economic benefits of trustworthy behavior by merchants
${\beta }_1$	Government incentive factor	$k_2$	Merchant’s organizational management level capacity factor
$l$	Degree of collusion between platform companies and merchants	$\tau$	Basic revenue factor for merchants
$I_1$	Platform companies can reap the benefits of collusion	$a$	Fixed costs paid by merchants
$i_1$	Gross proceeds available for collusive distribution	$C_2$	The cost of merchant integrity efforts
${\lambda }_2$	Cost-of-effort factor for merchants	$i_2$	Maximum amount of return on merchant’s trustworthiness
${\alpha }_2$	Merchants receive a fixed subsidy	$r_2$	Regulatory efforts of platform companies
${\beta }_2$	Incentive coefficients for merchants by platform companies	$m_2$	Maximum penalty for merchant breach of contract
$S_B$	Platform business-to-business incentive contracts	$F_2$	Social benefits of business integrity
$h_2$	Conversion factor for merchant social benefits	${\zeta }_2$	Random factor

:

2.3. Dual Principal–Agent Incentive Model Construction and Analysis

The incentive contract in the dual principal–agent problem of platform economic regulation must satisfy at least two requirements: Firstly, the incentive compatibility constraint (IC) requires the government to create incentive programs that combine the platform enterprise’s and the government’s interests. Additionally, the platform enterprise must create incentive programs that align the interests of the merchant with their own interests. Moreover, the platform enterprise’s utility for credit enhancement under the government-designed incentive mechanism exceeds the merchant’s utility without participation in the incentive mechanism created by the platform enterprise. This is termed as the participation constraint (IR). The second engagement constraint (IR) is that, in accordance with the government-designed incentive mechanism, the platform enterprise’s utility in enhancing credit exceeds the utility when it does not enhance credit, and, in accordance with the platform enterprise’s incentive mechanism, the merchant’s utility in enhancing credit is greater than the utility without enhancement. Therefore, the dual principal–agent incentive mechanism is formulated as follows:

2.3.1. Government-Platform Enterprise Principal–Agent Model (First Level of Principal–Agent Relationship)

The government’s utility function $V_1$ is as follows, based on the aforementioned assumptions:

$$V_1=h_1{e}_1+{\zeta }_1+(1-{\beta }_1)\left[k_1\right(e_1+\varphi e_2)+{\epsilon }_1]-{\alpha }_1+m_1{r}_1\cdot (1-e_1)$$

(1)

Accordingly, the utility function $E\left(V_1\right)$, as anticipated by the government, is:

$$E\left(V_1\right)=h_1{e}_1+(1-{\beta }_1)\left[k_1\right(e_1+\varphi e_2\left)\right]-{\alpha }_1+m_1{r}_1\cdot (1-e_1)$$

(2)

The utility of platform enterprises $V_2$ is as follows:

$$V_2=h_2{e}_2+{\zeta }_2-{\displaystyle \frac{{\lambda }_1{e}_1^2}{2}}+{\beta }_1[k_1(e_1+\varphi e_2)+{\epsilon }_1]+{\alpha }_1+i_1(1-e_1)-m_1{r}_1\cdot (1-e_1)+(1-{\beta }_2)(k_2{e}_2+{\epsilon }_2)-{\alpha }_2+m_2{r}_2\cdot (1-e_2)-{\displaystyle \frac{{\rho }_1{\beta }_1^2{\sigma }_1^2}{2}}$$

(3)

Therefore, the expected utility function of the platform enterprise $E(V_2)$ is:

$$E(V_2)=h_2{e}_2-{\displaystyle \frac{{\lambda }_1{e}_1^2}{2}}+{\beta }_1{k}_1(e_1+\varphi e_2)+{\alpha }_1+i_1(1-e_1)-m_1{r}_1\cdot (1-e_1)+(1-{\beta }_2)k_2{e}_2-{\alpha }_2+m_2{r}_2\cdot (1-e_2)-{\displaystyle \frac{{\rho }_1{\beta }_1^2{\sigma }_1^2}{2}}$$

(4)

Consequently, the following optimization problem can be substituted for the government–platform enterprise principal–agent regulation model:

$$\begin{array}{l}E(V_1)=h_1{e}_1+(1-{\beta }_1)[k_1(e_1+\varphi e_2)]-{\alpha }_1+m_1{r}_1\cdot (1-e_1)\\ s.t.(I{R}_1)h_2{e}_2-{\displaystyle \frac{{\lambda }_1{e}_1^2}{2}}+{\beta }_1{k}_1(e_1+\varphi e_2)+{\alpha }_1+i_1(1-e_1)-m_1{r}_1\cdot (1-e_1)+(1-{\beta }_2)k_2{e}_2-{\alpha }_2+m_2{r}_2\cdot (1-e_2)-{\displaystyle \frac{{\rho }_1{\beta }_1^2{\sigma }_1^2}{2}}>U_1\end{array}$$

(5)

$$\begin{array}{l} (I{C}_1)e_1\in \arg \max [h_2{e}_2-{\displaystyle \frac{{\lambda }_1{e}_1^2}{2}}+{\beta }_1{k}_1(e_1+\varphi e_2)+{\alpha }_1+i_1(1-e_1)-m_1{r}_1\cdot (1-e_1)\\ +(1-{\beta }_2)k_2{e}_2-{\alpha }_2+m_2{r}_2\cdot (1-e_2)-{\displaystyle \frac{{\rho }_1{\beta }_1^2{\sigma }_1^2}{2}}]\end{array}$$

(6)

2.3.2. Platform Enterprise–Merchant Principal–Agent Model (Second-Level Principal–Agent Relationship)

As shown above, the expected utility function of the platform enterprise $E(V_2)$ is:

$$E(V_2)=h_2{e}_2-{\displaystyle \frac{{\lambda }_1{e}_1^2}{2}}+{\beta }_1{k}_1(e_1+\varphi e_2)+{\alpha }_1+i_1(1-e_1)-m_1{r}_1\cdot (1-e_1)+(1-{\beta }_2)k_2{e}_2-{\alpha }_2+m_2{r}_2\cdot (1-e_2)-{\displaystyle \frac{{\rho }_1{\beta }_1^2{\sigma }_1^2}{2}}$$

Based on the assumptions, the merchant’s utility function $V_3$ is as follows:

$$V_3=\tau (k_2{e}_2+{\epsilon }_2)-a-{\displaystyle \frac{{\lambda }_2{e}_2^2}{2}}+{\beta }_2(k_2{e}_2+{\epsilon }_2)+{\alpha }_2+i_2(1-e_2)-m_2{r}_2\cdot (1-e_2)-{\displaystyle \frac{{\rho }_2{\beta }_2^2{\sigma }_2^2}{2}}$$

(7)

Therefore, the merchant’s expected utility function $E(V_3)$ is:

$$E(V_3)=\tau k_2{e}_2-a-{\displaystyle \frac{{\lambda }_2{e}_2^2}{2}}+{\beta }_2{k}_2{e}_2+{\alpha }_2+i_2(1-e_2)-m_2{r}_2\cdot (1-e_2)-{\displaystyle \frac{{\rho }_2{\beta }_2^2{\sigma }_2^2}{2}}$$

(8)

Thus, it is possible to convert the platform enterprise–merchant principal–agent regulatory model into the following optimization problem:

$$\begin{array}{l}E(V_2)=h_2{e}_2-{\displaystyle \frac{{\lambda }_1{e}_1^2}{2}}+{\beta }_1{k}_1(e_1+\varphi e_2)+{\alpha }_1+i_1(1-e_1)-m_1{r}_1\cdot (1-e_1)+(1-{\beta }_2)k_2{e}_2-{\alpha }_2+m_2{r}_2\cdot (1-e_2)-{\displaystyle \frac{{\rho }_1{\beta }_1^2{\sigma }_1^2}{2}}\\ s.t.(I{R}_2)\tau k_2{e}_2-a-{\displaystyle \frac{{\lambda }_2{e}_2^2}{2}}+{\beta }_2{k}_2{e}_2+{\alpha }_2+i_2(1-e_2)-m_2{r}_2\cdot (1-e_2)-{\displaystyle \frac{{\rho }_2{\beta }_2^2{\sigma }_2^2}{2}}>U_2\end{array}$$

(9)

$$(I{C}_2)e_2\in \arg \max [\tau k_2{e}_2-a-{\displaystyle \frac{{\lambda }_2{e}_2^2}{2}}+{\beta }_2{k}_2{e}_2+{\alpha }_2+i_2(1-e_2)-m_2{r}_2\cdot (1-e_2)-{\displaystyle \frac{{\rho }_2{\beta }_2^2{\sigma }_2^2}{2}}]$$

(10)

To sum up, the platform economy regulation model based on the dual principal–agent approach is:

$$\begin{array}{l}E(V_1)=h_1{e}_1+(1-{\beta }_1)[k_1(e_1+\varphi e_2)]-{\alpha }_1+m_1{r}_1\cdot (1-e_1)\\ s.t.(I{R}_1)h_2{e}_2-{\displaystyle \frac{{\lambda }_1{e}_1^2}{2}}+{\beta }_1{k}_1(e_1+\varphi e_2)+{\alpha }_1+i_1(1-e_1)-m_1{r}_1\cdot (1-e_1)+(1-{\beta }_2)k_2{e}_2-{\alpha }_2+m_2{r}_2\cdot (1-e_2)-{\displaystyle \frac{{\rho }_1{\beta }_1^2{\sigma }_1^2}{2}}>U_1\\ (I{C}_1)e_1\in \arg \max [h_2{e}_2-{\displaystyle \frac{{\lambda }_1{e}_1^2}{2}}+{\beta }_1{k}_1(e_1+\varphi e_2)+{\alpha }_1+i_1(1-e_1)-m_1{r}_1\cdot (1-e_1)+(1-{\beta }_2)k_2{e}_2-{\alpha }_2+m_2{r}_2\cdot (1-e_2)-{\displaystyle \frac{{\rho }_1{\beta }_1^2{\sigma }_1^2}{2}}]\\ (I{R}_2)\tau k_2{e}_2-a-{\displaystyle \frac{{\lambda }_2{e}_2^2}{2}}+{\beta }_2{k}_2{e}_2+{\alpha }_2+i_2(1-e_2)-m_2{r}_2\cdot (1-e_2)-{\displaystyle \frac{{\rho }_2{\beta }_2^2{\sigma }_2^2}{2}}>U_2\\ (I{C}_2)e_2\in \arg \max [\tau k_2{e}_2-a-{\displaystyle \frac{{\lambda }_2{e}_2^2}{2}}+{\beta }_2{k}_2{e}_2+{\alpha }_2+i_2(1-e_2)-m_2{r}_2\cdot (1-e_2)-{\displaystyle \frac{{\rho }_2{\beta }_2^2{\sigma }_2^2}{2}}]\end{array}$$

3. Dual Principal–Agent Modeling

3.1. Layer 2 Principal–Agent Model Solving

The second layer of the principal–agent model is addressed first since the dual principal–agent model may be solved from the bottom up.

Firstly, the optimal effort level of the merchant is determined by solving for the first-order derivative with respect to the merchant’s effort level $e_2$ and setting it to be equal to 0, i.e., in accordance with the findings of Holmstrom, et al. and the incentive compatibility constraint (IC) condition for the merchant.

$$e_2^{\ast }={\displaystyle \frac{\tau k_2+{\beta }_2{k}_2-i_2+m_2{r}_2}{{\lambda }_2}}$$

(11)

Thus, the platform enterprise–merchant principal–agent regulatory model can be represented as follows, where $e_2$ replaces $e_2^{\ast }$ in the merchant’s incentive compatibility constraint (IR) condition:

$$\begin{array}{l}E(V_2)=h_2{e}_2-{\displaystyle \frac{{\lambda }_1{e}_1^2}{2}}+{\beta }_1{k}_1(e_1+\varphi e_2)+{\alpha }_1+i_1(1-e_1)-m_1{r}_1\cdot (1-e_1)+(1-{\beta }_2)k_2{e}_2\\ -{\alpha }_2+m_2{r}_2\cdot (1-e_2)-{\displaystyle \frac{{\rho }_1{\beta }_1^2{\sigma }_1^2}{2}}\\ s.t.(I{R}_2)\tau k_2{e}_2-a-{\displaystyle \frac{{\lambda }_2{e}_2^2}{2}}+{\beta }_2{k}_2{e}_2+{\alpha }_2+i_2(1-e_2)-m_2{r}_2\cdot (1-e_2)-{\displaystyle \frac{{\rho }_2{\beta }_2^2{\sigma }_2^2}{2}}>U_2\\ (I{C}_2)e_2\in \arg \max [\tau k_2{e}_2-a-{\displaystyle \frac{{\lambda }_2{e}_2^2}{2}}+{\beta }_2{k}_2{e}_2+{\alpha }_2+i_2(1-e_2)-m_2{r}_2\cdot (1-e_2)-{\displaystyle \frac{{\rho }_2{\beta }_2^2{\sigma }_2^2}{2}}]\\ e_2={\displaystyle \frac{\tau k_2+{\beta }_2{k}_2-i_2+m_2{r}_2}{{\lambda }_2}}\end{array}$$

Theorem 1.

According to the platform enterprise–merchant credit regulation principal–agent model, the merchant receives the following optimal regulatory and incentive intensities from the platform enterprise:

$${\beta }_2^{\ast }={\displaystyle \frac{k_2(h_2+{\beta }_1{k}_1\varphi +k_2-m_2{r}_2)}{k_2^2+{\lambda }_2{\rho }_2{\sigma }_2^2}}$$

$$r_2^{\ast }={\displaystyle \frac{h_2+{\beta }_1{k}_1\varphi +k_2-{\beta }_2{k}_2}{m_2+{\lambda }_2}}$$

Proof. 

The incentive offered by the merchant must satisfy the first requirement of the incentive compatibility restriction, which is $E(U_2)=0$ when $e_2^{\ast }={\displaystyle \frac{\tau k_2+{\beta }_2{k}_2-i_2+m_2{r}_2}{{\lambda }_2}}$. The merchant’s participation constraint (IR₂) condition takes the equal sign in the optimal state, and it has:

$${\alpha }_2=U_2-\tau k_2{e}_2+a+{\displaystyle \frac{{\lambda }_2{e}_2^2}{2}}-{\beta }_2{k}_2{e}_2-i_2(1-e_2)+m_2{r}_2\cdot (1-e_2)+{\displaystyle \frac{{\rho }_2{\beta }_2^2{\sigma }_2^2}{2}}\ge 0$$

(12)

□

Substituting ${\alpha }_2$, $e_2^{\ast }$ into $E(V_2)$, the incentive model of the platform enterprise can be expressed as follows:

$$\begin{array}{l}\underset{{\beta }_2,r_2}{\max E(V_2)}=h_2{e}_2-{\displaystyle \frac{{\lambda }_1{e}_1^2}{2}}+{\beta }_1{k}_1(e_1+\varphi e_2)+{\alpha }_1+i_1(1-e_1)-m_1{r}_1\cdot (1-e_1)+(1+\tau )k_2{e}_2\\ -a-{\displaystyle \frac{{\lambda }_2{e}_2^2}{2}}+i_2(1-e_2)-{\displaystyle \frac{{\rho }_2{\beta }_2^2{\sigma }_2^2}{2}}-{\displaystyle \frac{{\rho }_1{\beta }_1^2{\sigma }_1^2}{2}}\end{array}$$

The incentive compatibility of the merchant should satisfy the first-order condition of the incentive compatibility constraint, i.e., $E^{\prime }(V_2)=0$, where:

$${\beta }_2^{\ast }={\displaystyle \frac{k_2(h_2+{\beta }_1{k}_1\varphi +k_2-m_2{r}_2)}{k_2^2+{\lambda }_2{\rho }_2{\sigma }_2^2}}$$

(13)

$$r_2^{\ast }={\displaystyle \frac{h_2+{\beta }_1{k}_1\varphi +k_2-{\beta }_2{k}_2}{m_2+{\lambda }_2}}$$

(14)

3.2. Layer 1 Principal–Agent Model Solving

To determine the optimal level of effort for the platform enterprise, solve the incentive-compatible constraint (IC) conditions for the platform enterprise by taking the first-order derivatives of $e_1$, the platform enterprise’s level of effort, and setting them to zero. This step involves substituting the optimal solutions $e_2^{\ast }$, $r_2^{\ast }$, and ${\beta }_2^{\ast }$ from the second-layer principal–agent model into the objective function and constraints of the first-layer principal–agent model.

$$e_1^{\ast }={\displaystyle \frac{{\beta }_1{k}_1-i_1+m_1{r}_1}{{\lambda }_1}}$$

(15)

Consequently, $e_1^{\ast }$ replaces $e_1$ in the incentive-compatible constraints of platform companies (IR₁) condition, which means that the principal–agent regulatory model for government-platform enterprises can be equivalent to the following:

$$\begin{array}{l}E(V_1)=h_1{e}_1+(1-{\beta }_1)[k_1(e_1+\varphi e_2)]-{\alpha }_1+m_1{r}_1\cdot (1-e_1)\\ s.t.(I{R}_1)h_2{e}_2-{\displaystyle \frac{{\lambda }_1{e}_1^2}{2}}+{\beta }_1{k}_1(e_1+\varphi e_2)+{\alpha }_1+i_1(1-e_1)-m_1{r}_1\cdot (1-e_1)+(1-{\beta }_2)k_2{e}_2-{\alpha }_2+m_2{r}_2\cdot (1-e_2)-{\displaystyle \frac{{\rho }_1{\beta }_1^2{\sigma }_1^2}{2}}>U_1\\ (I{C}_1)e_1\in \arg \max [h_2{e}_2-{\displaystyle \frac{{\lambda }_1{e}_1^2}{2}}+{\beta }_1{k}_1(e_1+\varphi e_2)+{\alpha }_1+i_1(1-e_1)-m_1{r}_1\cdot (1-e_1)+(1-{\beta }_2)k_2{e}_2-{\alpha }_2+m_2{r}_2\cdot (1-e_2)-{\displaystyle \frac{{\rho }_1{\beta }_1^2{\sigma }_1^2}{2}}]\\ e_1^{\ast }={\displaystyle \frac{{\beta }_1{k}_1-i_1+m_1{r}_1}{{\lambda }_1}}\end{array}$$

Theorem 2.

According to the government–platform enterprise credit regulation principal–agent model, the platform enterprise receives the following optimal regulatory and incentive intensities from the government:

$${\beta }_1^{\ast }={\displaystyle \frac{k_1(h_1+k_1-m_1{r}_1)}{k_1^2+{\lambda }_1{\rho }_1{\sigma }_1^2}}$$

$$r_1^{\ast }={\displaystyle \frac{h_1+k_1-{\beta }_1{k}_1}{m_1}}$$

Proof. 

The incentive offered by the platform enterprises must meet the first requirement of the incentive compatibility restriction, which is $E(U_1)=0$ when $e_1^{\ast }={\displaystyle \frac{{\beta }_1{k}_1-i_1+m_1{r}_1}{{\lambda }_1}}$. The platform enterprise’s participation constraint (IR₁) condition takes the equal sign in the optimal state, as follows:

$${\alpha }_1=U_1-[h_2{e}_2-{\displaystyle \frac{{\lambda }_1{e}_1^2}{2}}+{\beta }_1{k}_1(e_1+\varphi e_2)+i_1(1-e_1)-m_1{r}_1\cdot (1-e_1)+(1-{\beta }_2)k_2{e}_2-{\alpha }_2+m_2{r}_2\cdot (1-e_2)-{\displaystyle \frac{{\rho }_1{\beta }_1^2{\sigma }_1^2}{2}}]$$

(16)

□

Substituting ${\alpha }_1$, $e_1^{\ast }$ into $E(V_1)$, the incentive model of the platform enterprise can be expressed as the following:

$$\underset{{\beta }_1,r_1}{\max E(V_1)}=h_1{e}_1+k_1(e_1+\varphi e_2)+h_2{e}_2-{\displaystyle \frac{{\lambda }_1{e}_1^2}{2}}+i_1(1-e_1)+(1-{\beta }_2)k_2{e}_2-{\alpha }_2+m_2{r}_2\cdot (1-e_2)-{\displaystyle \frac{{\rho }_1{\beta }_1^2{\sigma }_1^2}{2}}$$

The incentive compatibility of platform enterprises should satisfy the first-order condition of the incentive compatibility constraint, i.e., $E^{\prime }(V_1)=0$, where:

$${\beta }_1^{\ast }={\displaystyle \frac{k_1(h_1+k_1-m_1{r}_1)}{k_1^2+{\lambda }_1{\rho }_1{\sigma }_1^2}}$$

(17)

$$r_1^{\ast }={\displaystyle \frac{h_1+k_1-{\beta }_1{k}_1}{m_1}}$$

(18)

4. Model Analysis and Discussion

4.1. Analysis of Factors Affecting Optimal Incentive Intensity

4.1.1. Analysis of Factors Influencing the Optimal Incentive Intensity of Government for Platform Enterprises

According to Equation (17), $k_1$, $h_1$, $m_1$, $r_1$, ${\lambda }_1$, ${\rho }_1$, and ${\sigma }_1^1$ determine the government’s ideal incentive intensity ${\beta }_1^{\ast }$ for the platform companies. It is possible to derive the following by taking the first-order derivative of ${\beta }_1^{\ast }$ with regard to $k_1$:

$${\displaystyle \frac{\partial {{\beta }^{\prime }}_1^{\ast }}{\partial k_1}}={\displaystyle \frac{-2k_1^2(h_1+k_1-m_1{r}_1)+(k_1^2+{\lambda }_1{\rho }_1{\sigma }_1^2)(h_1+2k_1-m_1{r}_1)}{{(k_1^2+{\lambda }_1{\rho }_1{\sigma }_1^2)}^2}}$$

(19)

From Equation (19): The ideal government incentive strength ${\beta }_1^{\ast }$ for platform enterprises and the platform enterprises’ coefficient of regulatory capacity $k_1$ exhibit a strong positive correlation when the conversion coefficient of social benefit is significantly smaller than the degree of regulatory punishment, ${{\beta }^{\prime }}_1^{\ast }>0$. This indicates that, as the government increases its reinforcement of platform enterprises’ incentives, its regulatory power strengthens, especially under high regulatory penalties. The ideal incentive strength ${\beta }_1^{\ast }$ of the government and the platform enterprise’s coefficient of regulatory capacity $k_1$ exhibit a strong negative link when the social benefit conversion coefficient is significantly more than the degree of regulatory penalty, ${{\beta }^{\prime }}_1^{\ast }<0$. This suggests that, the more the government tends to reduce platform enterprises’ incentives, the lower its regulatory penalty will be and the less the regulatory capability of the enterprises will be.

Same as above: (1) The government’s ideal incentive strength ${\beta }_1^{\ast }$ for platform enterprises is substantially positively connected with the social benefit conversion coefficient $h_1$, according to ${{\beta }^{\prime }}_1^{\ast }>0$. This demonstrates that a government’s quality increases with its social benefit. This suggests that the government’s social benefit is better and that it prefers to increase platform enterprise incentives more when the social benefit conversion coefficient is higher. (2) The government’s ideal incentive strength ${\beta }_1^{\ast }$ for platform enterprises is highly negatively connected with the coefficient of the regulatory strength $r_1$ and the maximum penalty amount $m_1$, ${{\beta }^{\prime }}_1^{\ast }<0$. This implies that platform companies will be deterred if the government enacts strict regulations and stiffens penalties in response to learning of the speculative activities of these companies. The more the government does this, the less motivation platform companies have to operate. (3) There is a strong positive correlation between the government’s optimal incentive strength ${\beta }_1^{\ast }$ for platform enterprises, their coefficient of effort–cost ${\lambda }_1$, and their coefficient of risk aversion ${\rho }_1$, when the conversion coefficient of social benefit is significantly lower than the degree of regulatory punishment, ${{\beta }^{\prime }}_1^{\ast }>0$. This suggests that the government tends to increase platform enterprise incentives the more effort and less willingness to take risks there are when the regulatory penalty is larger. Platform enterprises’ coefficient of effort–cost ${\lambda }_1$ and coefficient of risk aversion ${\rho }_1$ are strongly negatively correlated with the optimal incentive strength of the government when the conversion coefficient of social benefit is significantly larger than the degree of regulatory punishment, ${{\beta }^{\prime }}_1^{\ast }<0$. This shows that platform enterprises are more likely to be willing to assume the risks associated with speculative activity and to put in less effort when the government’s regulatory penalty is minimal, thus weakening the platform enterprises’ incentives. (4) The ideal government incentive strength ${\beta }_1^{\ast }$ for platform enterprises and the variance ${\sigma }_1^2$ of the social output benefits of platform enterprises show a strong positive correlation when the conversion coefficient of social benefits is significantly smaller than the degree of regulatory punishment, ${{\beta }^{\prime }}_1^{\ast }>0$. This suggests that the government prefers to increase platform enterprise incentives when its regulatory penalty is higher and the social output advantages of these businesses fluctuate less. The ideal government incentive strength ${\beta }_1^{\ast }$ and the variance ${\sigma }_1^2$ of the social output benefits of the platform enterprises exhibit a strong negative association when the conversion coefficient of social benefits is significantly more than the degree of regulatory penalty, ${{\beta }^{\prime }}_1^{\ast }<0$. This implies that, the more the government tends to reduce platform enterprises’ incentives, the more fluctuating the social output benefits of those enterprises are when the regulatory penalty imposed by the government is minor.

4.1.2. Analysis of Factors Influencing the Optimal Incentive Strength of Platform Companies for Merchants

According to Equation (21), ${\beta }_1$, $k_1$, $\varphi$, $k_2$, $h_2$, $m_2$, $r_2$, ${\lambda }_2$, ${\rho }_2$, and ${\sigma }_2^2$ determine the platform enterprise’s ideal incentive strength ${\beta }_2^{\ast }$ for the merchant. It is possible to derive the following by taking the first-order derivative of ${\beta }_2^{\ast }$ with regard to $k_2$:

$${\displaystyle \frac{\partial {{\beta }^{\prime }}_2^{\ast }}{\partial k_2}}={\displaystyle \frac{-2k_2^2(h_2+{\beta }_1{k}_1\varphi +k_2-m_2{r}_2)+(k_2^2+{\lambda }_2{\rho }_2{\sigma }_2^2)(h_2+{\beta }_1{k}_1\varphi +2k_2-m_2{r}_2)}{{(k_2^2+{\lambda }_2{\rho }_2{\sigma }_2^2)}^2}}$$

(20)

Equation (20) demonstrates a strong positive correlation between the optimal incentive strength of the platform enterprise to the merchants ${\beta }_2^{\ast }$, and the merchant’s organization and management level $k_2$, when the conversion coefficient of the government’s and the merchants’ social benefits and the platform enterprise’s incentive strength are significantly smaller than the platform enterprise’s regulatory penalty, ${{\beta }^{\prime }}_2^{\ast }>0$. This indicates that the platform enterprise is inclined to increase the merchant’s incentives as the merchant’s organizational management level and the platform enterprise’s regulatory penalty rise. The ideal incentive strength of the platform enterprise to the merchant ${\beta }_2^{\ast }$ and the coefficient of the merchant’s organization and management level $k_2$ exhibit a strong negative correlation when the conversion coefficient of social benefits and the government’s incentives to the platform enterprise are significantly larger than the regulatory punishment of the platform enterprise, ${{\beta }^{\prime }}_2^{\ast }<0$. This implies that the government tends to lessen the incentives for platform enterprises when the regulatory penalties imposed by the platform enterprises are greater and the merchants’ organizational management level is lower.

Same as above: (1) The government’s incentive strength ${\beta }_1$, the platform enterprise’s supervisory ability $k_1$, the merchants’ degree of reliance $\varphi$ on the platform enterprise, the conversion coefficient $h_2$ of the social benefits of the merchants, and the optimal incentive strength ${\beta }_2^{\ast }$ of the platform enterprise for the merchants all exhibit strong positive correlations, ${{\beta }^{\prime }}_2^{\ast }>0$. This suggests that, the greater the merchants’ reliance on the platform enterprise, the higher the conversion coefficient of the merchants’ social benefits, the stronger the government’s incentive strength for the platform enterprise, the stronger the supervisory ability of the platform enterprise, and the stronger the platform enterprise’s supervision of the merchants, the better the platform enterprise’s benefit. (2) The maximum penalty amount $m_2$ and the platform enterprise’s supervision strength $r_2$ have a strong negative correlation with the platform enterprise’s optimal incentive strength ${\beta }_2^{\ast }$ for merchants, ${{\beta }^{\prime }}_2^{\ast }<0$. This implies that the platform enterprise will serve as a deterrent for merchants and be more likely to reduce their incentives if it implements a strict supervision policy and stiffens the penalties after learning of the merchants’ speculative activities. (3) When the government’s incentive strength for the platform enterprise and the conversion coefficient of the merchants’ social benefits are significantly smaller than the platform enterprise’s regulatory penalty, ${{\beta }^{\prime }}_2^{\ast }>0$, and when the platform enterprise’s optimal incentive strength for the merchants ${\beta }_2^{\ast }$, and the merchants’ cost of effort ${\lambda }_2$ and risk aversion ${\rho }_2$ exhibit a strong positive correlation, this suggests that the merchant is less eager to take risks and more inclined to put forth effort when the platform enterprise’s regulatory penalty is higher. Additionally, the platform enterprise tends to increase the merchant’s incentives. The ideal incentive strength of the platform enterprise to the merchants ${\beta }_2^{\ast }$, and the merchants’ cost of effort ${\lambda }_2$ and risk aversion ${\rho }_2$ exhibit a strong negative correlation when the conversion coefficient of the social benefit of merchants and the government’s incentive strength to the platform enterprise are significantly larger than the regulatory penalty of the platform enterprise, ${{\beta }^{\prime }}_2^{\ast }<0$. This suggests that the merchant is less inclined to exert effort and take on the risk of speculative conduct when the platform enterprise’s regulatory penalty is minimal, and, thus, the platform enterprise’s motivation is weakened. (4) There is a strong positive correlation between the variance of the merchant’s output benefits ${\sigma }_2^2$, and the optimal incentive strength of the platform enterprise to the merchants ${\beta }_2^{\ast }$, when the conversion coefficient of the merchants’ social benefits and the government’s incentive strength to the platform enterprise are much smaller than the platform enterprise’s regulatory penalty, ${{\beta }^{\prime }}_2^{\ast }>0$. This implies that the platform enterprise tends to improve the incentives for merchants and that there is less fluctuation in the social benefits of merchants when the regulatory penalty of the platform enterprise is higher. The optimal incentive strength of platform enterprises for merchants ${\beta }_2^{\ast }$, and the variance of merchants’ output benefits ${\sigma }_2^2$ exhibit a strong negative correlation when the conversion coefficient of merchants’ social benefits and the government’s incentive strength for platform enterprises are both significantly larger than the degree of regulatory punishment of platform enterprises, ${{\beta }^{\prime }}_2^{\ast }<0$. This suggests that the platform enterprise prefers to reduce the incentives for merchants when its regulatory penalty is minor and the variability of the merchant’s output benefit is bigger.

4.2. Analysis of Factors Affecting Optimal Regulatory Intensity

4.2.1. Analysis of Factors Influencing the Optimal Intensity of Government Regulation of Platform Companies

According to Equation (18), $h_1$, $m_1$, ${\beta }_1$, and $k_1$ determine the government’s optimal regulatory intensity $r_1^{\ast }$ for the platform companies. It is possible to derive the following by taking the first-order derivative of $r_1^{\ast }$ with regard to $m_1$:

$${\displaystyle \frac{\partial r_1^{\ast }}{\partial m_1}}=-{\displaystyle \frac{h_1+k_1-{\beta }_1{k}_1}{m_1^2}}$$

(21)

The optimal regulatory intensity $r_1^{\ast }$ of the government on the platform enterprise and the maximum punishment amount $m_1$ when the government discovers the speculative activity of the platform enterprise show a strong negative link, as can be seen from Equation (21), where there is ${r^{\prime }}_1^{\ast }<0$ when $h_1+k_1-{\beta }_1{k}_1>0$. This suggests that, if the government finds out about the platform enterprise’s speculative behavior, it only needs to impose a larger maximum punishment amount before the platform enterprise gives up on its speculative behavior. Furthermore, while stricter regulation of e-commerce platforms does not necessarily lead to increased social benefits, it does result in the government tending to loosen its regulation of platform enterprises more. There is ${r^{\prime }}_1^{\ast }>0$ when $h_1+k_1-{\beta }_1{k}_1<0$; the government finds out about the speculative activity of the platform enterprises, and there is a substantial positive correlation between the maximum punishment amount $m_1$ and the optimal regulatory intensity $r_1^{\ast }$ of the government over the firms. This suggests that the government is more prepared to regulate e-commerce platforms through higher levels of penalty and regulation due to their increased conversion factor of social benefits.

Same as above: (1) When ${r^{\prime }}_1^{\ast }>0$, the optimal regulatory intensity $r_1^{\ast }$ of the government on the platform enterprise and the conversion coefficient $h_1$ of the social benefits of the platform enterprise show a strong positive correlation. This implies that the government would want to accomplish greater social benefits through regulation to prevent speculation, resulting in a higher conversion factor of social benefits for platform companies. (2) When ${r^{\prime }}_1^{\ast }<0$, the optimal regulatory intensity $r_1^{\ast }$ of the government to the platform enterprise shows a strong negative correlation with the incentive coefficient $k_1$ of the government to the merchants and the coefficient ${\beta }_1$ of the regulatory ability of the platform enterprise. This indicates that, the larger the government’s incentive coefficient for merchants is, the stronger the platform enterprise’s regulatory ability is, and the platform enterprise will avoid speculative behavior. Therefore, the government has less of a need to strengthen the regulation of the speculative behavior of platform enterprises.

4.2.2. Analysis of Factors Influencing the Optimal Regulatory Intensity of Merchants by Platform Enterprises

According to Equation (14), ${\beta }_1$, $k_1$, $\varphi$, $h_2$, $m_2$, ${\beta }_2$, ${\lambda }_2$, and $k_2$ determine the platform enterprise’s optimal regulatory intensity $r_2^{\ast }$ for merchants. It is possible to derive the following by taking the first-order derivative of $r_1^{\ast }$ with regard to $m_1$:

$${\displaystyle \frac{\partial r_2^{\ast }}{\partial m_2}}=-{\displaystyle \frac{h_2+{\beta }_1{k}_1\varphi +k_2-{\beta }_2{k}_2}{{(m_2+{\lambda }_2)}^2}}$$

(22)

$${\displaystyle \frac{\partial r_2^{\ast }}{\partial {\lambda }_2}}=-{\displaystyle \frac{h_2+{\beta }_1{k}_1\varphi +k_2-{\beta }_2{k}_2}{{(m_2+{\lambda }_2)}^2}}$$

(23)

From Equations (22) and (23), the ideal regulatory strength of the platform enterprise to the merchants $r_2^{\ast }$, the platform enterprise’s maximum punishment amount after realizing the merchants’ speculative behaviors $m_2$, and the cost coefficient of the merchants’ efforts ${\lambda }_2$ exhibit a strong negative correlation when the conversion coefficient of the merchants’ social benefits and the government’s incentive strength to the platform enterprise are both significantly smaller than the platform enterprise’s regulatory punishment degree, ${r^{\prime }}_2^{\ast }<0$. This suggests that, the more a merchant tries to be honest and the larger the maximum penalty that the platform enterprise will impose after learning of their speculative behavior, the more likely it is that the merchant will give up their speculative behavior and that the platform enterprise will weaken their regulation. A strong positive correlation is observed between the optimal regulatory intensity of the platform enterprises on the merchants $r_2^{\ast }$, the platform enterprise’s maximum punishment amount after realizing the merchants’ speculative behaviors $m_2$, and the cost coefficient of the merchants’ efforts ${\lambda }_2$, when the conversion coefficient of the merchants’ social benefits and the government’s incentives to the platform enterprises are both significantly larger than the regulatory penalties of the platform enterprises, ${r^{\prime }}_2^{\ast }>0$. Because the merchant’s social benefits have a higher conversion factor, this means that, the more effort the merchant puts in, the more the government is likely to regulate the merchant through harsh punishment.

Same as above: (1) There is a strong positive correlation between the following: When ${r^{\prime }}_2^{\ast }>0$, the optimal regulatory intensity of the platform enterprise on the merchants $r_2^{\ast }$, the incentive intensity of the government on the platform enterprise ${\beta }_1$, the coefficient of the platform enterprise’s regulatory ability $k_1$, the degree of dependence of the merchants on the platform enterprise $\varphi$, and the conversion coefficient of the merchants’ social benefits $h_2$ all show a strong positive correlation. The government’s incentives, their own regulatory capacity, the merchants’ dependence on them, and the platform enterprises’ desire to realize more social benefits through regulation to prevent speculative behaviors all seem to be correlated with the merchants’ higher conversion coefficient of social benefits. (2) The ideal regulatory intensity of the platform enterprise for merchants $r_2^{\ast }$, r < 0, shows a strong negative link with the platform enterprise for merchants’ incentive coefficient ${\beta }_2$ and the merchant’s organizational management level’s coefficient $k_2$. This suggests that a merchant’s organizational management level is greater and that the merchant refrains from engaging in speculative conduct the larger the platform enterprise’s incentive coefficient to the merchant. The less the platform company has to tighten its oversight of merchants’ speculative activity, the better.

4.3. Analysis of Factors Influencing the Optimal Level of Effort

4.3.1. Analysis of Factors Influencing the Optimal Effort Level of Platform Companies

According to Equation (15), ${\beta }_1$, $k_1$, $i_1$, ${\lambda }_1$, $m_1$, and $r_1$ determine the optimal effort level of platform enterprises $e_1^{\ast }$. It is possible to derive the following by taking the first-order derivative of $e_1^{\ast }$ with regard to ${\lambda }_1$:

$${\displaystyle \frac{\partial e_1^{\ast }}{\partial {\lambda }_1}}={\displaystyle \frac{{\beta }_1{k}_1-i_1+m_1{r}_1}{{\lambda }_1^2}}$$

(24)

According to Equation (24), there is a strong negative correlation between the optimal level of the platform enterprise’s effort $e_1^{\ast }$ and the coefficient of the platform enterprise’s cost of effort $i_1$, when $i_1$ is larger. This indicates that, when the platform enterprise is in collusion with merchants and allocating a larger total benefit, ${e^{\prime }}_1^{\ast }<0$, this suggests that the marginal cost of the platform enterprise’s work steadily rises, its effort level constantly declines, and, finally, it tends to the steady state when the total revenue distributed by the collusion between the platform business and the merchant is bigger. In other words, the platform enterprise is less inclined to exert further effort to control speculative conduct at this time because the higher marginal cost of his work has a greater negative impact. In contrast, he is more inclined to make more of an effort to control speculative activity when the platform enterprise’s overall advantage from its collaboration with merchants is minimal.

Same as above: (1) We can observe that: When ${e^{\prime }}_1^{\ast }>0$, the platform enterprise’s optimal effort level $e_1^{\ast }$ exhibits a strong positive correlation with the government’s incentive coefficient to the platform enterprise ${\beta }_1$, the platform enterprise’s regulatory ability coefficient $k_1$, the maximum amount of punishment meted out after the government uncovers the platform enterprise’s speculative behaviors $m_1$, and the level of government regulation of the platform enterprise $r_1$. This suggests that platform enterprises will work harder the more government incentives and regulation there are for e-commerce platforms, the more platform enterprises are regulated, and the more severely platform enterprises are punished for engaging in speculative conduct. Platform companies are more inclined to work harder when they receive government incentives. Platform companies’ activities will be encouraged by the government’s tight supervision over their speculative behavior as its regulatory measures intensify. The internal engine that propels the platform enterprise’s efforts is also the enhancement of its own supervision level. (2) There is a strong negative correlation between the optimal level of the platform enterprise’s effort $e_1^{\ast }$ and the larger total revenue allocated by the platform enterprise in collusion with merchants $i_1$. This implies that, when the overall revenue distributed by the platform enterprises in collaboration with the merchants increases, the amount of effort on the part of the platform enterprises eventually diminishes. This echoes Marx’s statement that “with 10 percent profit, it is used everywhere; with 20 percent, it comes alive; with 50 percent, it causes positive risk-taking; with 100 percent, it makes men defy all laws; and with 300 percent, it makes men unafraid to commit crimes, or even to fear the danger of being hanged”.

4.3.2. Analysis of Factors Influencing Merchants’ Optimal Level of Effort

According to Equation (11), ${\beta }_2$, $k_2$, $i_2$, ${\lambda }_1$, $m_2$, $r_2$, and $\tau$ determine the optimal effort level of merchant $e_2^{\ast }$. It is possible to derive the following by taking the first-order derivative of $e_2^{\ast }$ with regard to ${\lambda }_2$:

$${\displaystyle \frac{\partial e_2^{\ast }}{\partial {\lambda }_2}}={\displaystyle \frac{\tau k_2+{\beta }_2{k}_2-i_2+m_2{r}_2}{{\lambda }_2^2}}$$

(25)

According to Equation (25), the merchant’s ideal level of effort and its cost of effort coefficient, ${\lambda }_2$, exhibit a strong negative correlation when $i_2$ is large, that is, when the revenue produced by the merchant’s speculative conduct is large, ${e^{\prime }}_2^{\ast }<0$. Accordingly, the merchant’s effort steadily rises in the marginal cost as the advantages from speculative activity increase, and the effort level finally falls until reaching a stable state. Stated differently, the merchant is less motivated to exert additional effort to steer clear of speculative conduct at this time due to the greater negative impact of higher marginal costs. Conversely, the merchant is more inclined to exert effort to refrain from engaging in speculative activity because it yields a lower benefit.

Same as above: (1) When ${e^{\prime }}_2^{\ast }>0$, the merchant’s optimal effort level $e_2^{\ast }$ demonstrates a strong positive correlation with the platform enterprise’s incentive coefficient to the merchant ${\beta }_2$, the merchant’s ability coefficient of organization and management level $k_2$, the maximum amount of punishment the merchant can receive after the platform enterprise detects speculative behavior $m_2$, the intensity of the platform enterprise to the merchant $r_2$, and the merchant’s basic gain coefficient $\tau$. This suggests that merchants will exert more effort to increase their level of rewards and oversight from e-commerce platforms, as well as their organizational management competency and amount of punishment for engaging in speculative behavior. Additionally, merchants will be more motivated to increase their basic benefits. Platform companies’ incentives encourage merchants to put in more effort. The platform company’s tight control over the merchant’s speculative behavior will encourage the merchant’s efforts as its regulatory efforts grow. Base revenue increases with a merchant’s organizational and managerial prowess, and platform companies are more internally motivated to incentivize effort. (2) When ${e^{\prime }}_2^{\ast }<0$, the revenue that a merchant generates from their speculative activity is strongly correlated with their ideal degree of effort $e_2^{\ast }$. This implies that, as speculative revenue from speculating increases, the merchant’s effort level drops and their propensity to participate in speculative activity grows.

Conclusion 1: There is an overlap between incentives and regulatory mechanisms.

The aforementioned analysis demonstrates that regulatory mechanisms and incentives are interrelated. In order to encourage platform companies and merchants to put in more effort, the government or platform enterprises can enhance either incentives or regulatory measures. This implies that the information barrier will be broken by the government or platform companies introducing a regulatory system, which will also reduce the likelihood of merchant speculation and increase merchant effort.

Conclusion 2: The ideal degree of government incentives ${\beta }_1^{\ast }$, the ideal amount of regulation $r_1^{\ast }$, and the ideal level of effort put out by platform enterprises $e_1^{\ast }$ are all unaffected by the second layer of the principal–agent relationship in the first tier.

Because platform enterprises and merchants have direct contractual relationships or business connections that allow platforms to directly influence merchants’ business behaviors, Conclusion 2 suggests that platform enterprises are the primary entities responsible for the speculative behaviors of merchants. Platform companies can also keep an eye on the trading habits, product quality, after-sale support, and other activities of merchants by utilizing a variety of tools and methods. Platform enterprises are better equipped to carry out their supervision duties as a result of these technological and management capabilities.

Conclusion 3: The optimal amount of effort by the merchant $e_2^{\ast }$ is positively impacted by the ideal level of incentives from the platform enterprise to the merchant ${\beta }_2^{\ast }$, through the level of incentives ${\beta }_1^{\ast }$ from the government to the platform enterprise.

According to Equations (11), (13) and (14), the following can be obtained:

$$e_2^{\ast }={\displaystyle \frac{k_2^2(h_2+{\beta }_1{k}_1\varphi +k_2-m_2{r}_2)+(\tau k_2-i_2+m_2{r}_2)(k_2^2+{\lambda }_2{\rho }_2{\sigma }_2^2)}{{\lambda }_2(k_2^2+{\lambda }_2{\rho }_2{\sigma }_2^2)}}$$

(26)

As demonstrated by Conclusion 3, the combined incentives from platform companies and the government have a positive impact on merchants’ optimal effort levels. With a rise in incentives, the government and platform companies will also impose stricter regulations on merchant speculation and raise merchant standards. This is expected to encourage merchants to refrain from engaging in speculative activity. Equation (26)demonstrates that the platform companies’ incentives have the ability to directly increase the effort level of the merchants.

5. Numerical Examples and Analysis

Through numerical examples and simulation analysis, this part explores the key parameters and conclusions in order to more intuitively grasp the conclusions of this research and the corresponding model outcomes. For the purpose of this study, we primarily use up-to-date information about how the government regulates platform businesses and merchants, placing it within a realistic framework [41,42,43,44,45,46]. The base data are taken as follows: $k_1=1$, $h_1=2$, ${\rho }_1=0.5$, ${\lambda }_1={\lambda }_2=2$, $i_1=i_2=1$, ${\sigma }_1^2={\sigma }_2^2=1$, $m_1=3$, $r_1=r_2=0.5$, $\varphi =0.5$, $\tau =0.5$, $k_1=2$, $h_2=2$, ${\rho }_2=0.5$, ${\beta }_1={\beta }_2=1$, $m_2=2$, $r_2=0.5$, $\tau =1$, and $e_1=e_2=2$. The primary research objectives of the numerical simulation are as follows: (1) the relationship between the government’s incentive intensity ${\beta }_1$ for platform enterprises and their capability coefficient $k_1$, their transformation coefficient of social benefits $h_1$, their maximum punishment amount $m_1$ after the government uncovers their speculative behavior, and their effort–cost coefficient ${\lambda }_1$; (2) the relationship between the platform enterprise’s incentive strength ${\beta }_2$ and the merchant’s dependence on it $\varphi$, as well as the platform enterprise’s incentive strength to the government ${\beta }_1$, the platform enterprise’s capability coefficient $k_1$, the maximum penalty amount that the platform enterprise will impose upon discovering the merchant’s speculative behaviors $m_2$, and the merchant’s organizational capability coefficient $k_2$; (3) the correlation between the effort level $e_1$ of the platform enterprise and the coefficient of effort–cost ${\lambda }_1$ of the platform enterprise, the coefficient of capability $k_1$ of the platform enterprise, the intensity of the government’s supervision as $r_1$, the coefficient of risk sensitivity ${\rho }_1$, and the coefficient of transformation of the social benefit $h_1$; (4) the correlation between the merchant’s effort level $e_2$ and the merchant’s organizational capability coefficient $k_2$, the government’s incentive strength for the platform enterprise ${\beta }_1$, the merchant’s dependence on the platform enterprise $\varphi$, and the merchant’s effort–cost coefficient ${\lambda }_2$; and (5) the correlation between the expected utility $E(V_2)$ of the platform enterprise and the effort level of the platform enterprise $e_1$, the effort level of the merchant $e_2$, the transformation coefficient of the social benefit $h_2$, and the capability coefficient $k_1$ of the platform enterprise.

5.1. Analysis of Factors Influencing the Incentive Strength of Platform Companies for Merchants ${\beta }_1$

As the capability coefficient $k_1$ and the social benefit transformation coefficient $h_1$ of the platform enterprises vary, Figure 3 illustrates how the government incentive intensity ${\beta }_1$ exhibits a downward distortion. However, the distortion will continue to decrease as $h_1$ declines. The government incentive intensity ${\beta }_1$ has a tendency that increases as the social benefit transformation coefficient rises, increases with the platform enterprise’s capability coefficient, and decreases with the latter. This indicates that, in the first place, the government will often boost the incentive intensity to push platform enterprises to enhance their own capabilities—such as technology, service, and management—when their capability coefficient is low. This is due to the fact that platform enterprises require greater resources and assistance in order to expand quickly during their early stages. Nonetheless, the government may suitably lower the incentive intensity when the platform enterprise’s capability steadily strengthens, or as its capability coefficient rises. This is due to the fact that platform businesses already possess a certain level of self-regulation and market competition, and the government’s incentive role is comparatively lessened. Secondly, the social benefit transformation coefficient indicates how much platform enterprise regulation contributes to the social economy. In order to encourage platform enterprise regulation and further expand its social benefit, the government will increase the incentive intensity in proportion to the increase in the social benefit conversion coefficient, which indicates the platform enterprise regulation’s contribution to the social economy. The rationale for the government’s incentive-based approach to platform enterprise regulation is to guarantee that these businesses comply with legal requirements and offer consumers dependable, secure, and superior products and services.

As the government learns about the platform enterprises’ speculative activity, Figure 4 illustrates how the government incentive intensity ${\beta }_1$ rises with an increase in the social benefit transformation coefficient $h_1$ but falls with an increase in the maximum punishment $m_1$. This pattern suggests that, if the government decides to raise the maximum penalty amount after learning about the platform enterprises’ speculative activity, the government’s incentive intensity will drop in tandem. Put another way, by stiffening the penalties, the government seeks to curtail the speculative actions of platform companies, thus lowering the expenses and hazards associated with regulation. From an economic perspective, stiffer penalties make platform companies’ non-compliance more expensive, which lessens their incentive to act in a speculative manner. As a result, the government does not need to use strong incentives during the regulatory process to entice platform companies to comply. In addition, by stepping up the intensity of incentives, the government pushes platform companies to aggressively carry out their social obligations and increase the scope of their social benefits. This method of thoughtful deliberation supports the robust, orderly, and high-quality growth of the e-commerce sector as a whole as well as the sustained development of platform businesses.

Figure 5 shows that the government incentive intensity ${\beta }_1$ rises when the platform enterprise’s effort–cost coefficient ${\lambda }_1$ rises, but increases when the social benefit transformation coefficient $h_1$ rises. When the platform enterprise’s effort–cost coefficient B rises, the government incentive intensity A falls. In the event that platform enterprises must allocate significant financial, material, and human resources towards countering counterfeit and substandard goods and safeguarding the rights and interests of consumers, and the incentives provided by the government prove insufficient to offset these costs, the platforms may opt to scale back on their efforts to combat these issues, thereby exacerbating speculative behaviors.

5.2. Analysis of Factors Influencing the Incentive Strength of Merchants by Platform Companies ${\beta }_2$

Figure 6 illustrates how the platform enterprise’s incentive intensity ${\beta }_2$ exhibits a downward distortion in response to changes in the merchant’s reliance on platform enterprise $\varphi$ and organizational capability coefficient $k_2$. However, this distortion will lessen as the coefficient decreases. With a rise in the merchant’s organizational capability coefficient $k_2$ and an increase in the merchant’s reliance on the platform enterprise $\varphi$, the platform enterprise’s incentive intensity tends to increase and decrease. This implies that, in general, the platform enterprise’s incentive intensity increases in tandem with the merchant’s increased dependency on the platform enterprise. This is because the platform is more important to the merchant for sales and promotions, and, as a result, the platform can guarantee the merchant’s engagement and loyalty by offering bigger incentives. Nevertheless, there may be a downward distortion to this increase in incentive intensity, which is not linear. The increase in incentive intensity provided by the platform enterprise may progressively decline following a certain point of increased merchant reliance. The degree of this distortion may decrease in tandem with the reduction in specific elements, such as regulatory expenses, market competition, and so on. Platform companies might be more equipped or more ready to offer ongoing incentives when these outside influences lessen. Secondly, the operational and managerial effectiveness of a merchant is reflected in its organizational capacity factor. A rise in an e-commerce merchant’s organizational capability coefficient indicates improved sales and operational activity management. Initially, when the merchant’s organizational capability factor rises, the platform enterprise’s incentive intensity may also rise. This is so that high-performing merchants can receive more rewards from the platform since they can increase their sales and market share. Nonetheless, the platform enterprise’s incentive intensity may tend to decline as the merchant’s organizational competence coefficient rises to a particular point. This can be because the platform does not need to offer as many outside incentives because the merchant is now more self-driven.

As seen by Figure 7, the platform enterprise’s incentive intensity ${\beta }_2$ rises in proportion to the merchant’s reliance $\varphi$ on it, but it falls in proportion to the maximum punishment $m_2$ imposed by the platform enterprise upon discovering the merchant’s speculative activity. This implies that, in general, platform companies that regulate merchants’ speculative activities must continue to be appealing to merchants while also successfully controlling such behaviors. As a result, platform businesses can vary the incentive intensity based on the level of speculative activity and the reliance of merchants. In order to preserve the fairness and order of the platform, the platform enterprise will increase incentives when merchants are heavily dependent on it and speculative behavior is low. When speculative behavior increases, however, the platform enterprise will lessen the incentive intensity by imposing harsher penalties. The incentive intensity of platform businesses exhibits a diminishing trend with an increase in the maximum penalty that these firms impose for the speculative behaviors of merchants. This indicates a trade-off between platform enterprises’ incentives and regulation. Platform companies will not need to offer as many incentives if they impose harsh penalties for speculative activity because merchants will be less inclined to do so out of a concern for taking on unnecessary risk.

Figure 8 illustrates how platform enterprises’ incentive intensity ${\beta }_2$ is trending upward in tandem with the government’s incentive intensity ${\beta }_1$ and their capacity coefficient $k_1$. Consequently, the platform enterprise will offer merchants incentives that are more intense. Second, when the platform enterprise’s capability coefficient rises, its management quality and operational efficiency climb as well. This allows it to better control merchant behavior and discourage speculative activity. Platform businesses with high-capacity coefficients are also better able to offer a variety of incentives in order to satisfy the demands of various merchants and strengthen their position in the market.

5.3. Analysis of Factors Influencing the Effort Level of Platform Companies $e_1$

Figure 9 illustrates this: as the platform enterprises’ effort–cost coefficient ${\lambda }_1$ rises, so does their level of effort $e_1$; conversely, as the government regulation effort $r_1$ rises, the amount of effort A rises. This is a reliable measure of the platform companies’ level of effort. This implies that the expense of expanding the platform enterprises’ regulatory effort is reflected in the effort–cost coefficient. The cost of each extra unit of regulatory effort made by platform enterprises rises in proportion to an increase in this coefficient. As a result, platform companies may decide to scale back their regulatory efforts due to financial constraints. Platform businesses will come under more external pressure and scrutiny as government regulation grows. The fee that platform enterprises must pay rises in proportion to each unit of increased regulatory effort when the cost of effort coefficient rises. When government regulatory efforts expand, platform enterprises are subject to increased external pressure and scrutiny. Platform companies will typically step up their regulatory efforts to make sure that their platform activities are in compliance with the standards in order to abide by the government’s regulatory obligations, prevent potential penalties, and mitigate any bad effects. In summary, platform companies balance the advantages and disadvantages of controlling merchant conduct. Platform companies may lower their level of effort when their effort–cost coefficient is high, that is, when the cost of increasing regulatory effort is high. However, platform companies would typically step up their regulatory efforts in response to increased government regulation in order to minimize potential consequences and fines. This underscores that external government regulatory initiatives have a significant impact on platform enterprises’ regulatory conduct in addition to internal cost–benefit analyses. The regulatory actions of platform corporations are greatly influenced by the government’s responsibility in upholding consumer rights and interests as well as in maintaining market order.

According to Figure 10, platform enterprises’ effort levels $e_1$ increase in tandem with their competence coefficients $k_1$ and government monitoring $r_1$. However, it should be noted that they are comparatively more susceptible to government oversight. This indicates that platform enterprises, firstly, recognize that, when their capability coefficient increases, they must exert a greater effort to guarantee the platform’s steady operation, optimize the user experience, and boost the market’s competitiveness. This approach includes the stringent regulation of platform rules, service quality, and user safety in addition to technology innovation and human investment.

On the other hand, there is a greater effect of government regulation intensity on the level of effort that platform enterprises put forth. This implies that platform companies respond to regulatory pressure from the government by changing their tactics and ways of operating more quickly. Platform companies are well aware of the severe legal repercussions and market hazards they would encounter if they breach regulatory rules, which contributes to this sensitivity. The government has considerable regulatory power and influence over the platform economy. Furthermore, platform enterprises’ proactive and adaptable approach to handling regulatory difficulties is shown in their sensitivity. Platform organizations will demonstrate proactive and adaptable approaches to regulatory challenges, continually enhancing their efforts and strengthening platform self-correction to ensure compliance with legal requirements and regulations.

According to Figure 11, although platform enterprises are somewhat sensitive to the social benefit conversion coefficient, their effort level $e_1$ increases with increases in both their own risk sensitivity coefficient ${\rho }_1$ and social benefit conversion coefficient $h_1$. This implies that platform enterprises’ risk sensitivity coefficient, in the first place, indicates the weight they give to possible hazards. Platform enterprises are more likely to step up their regulatory efforts in an attempt to reduce the risks associated with inadequate regulation, like lawsuits and reputational damages, when the risk sensitivity coefficient rises. Additionally, platform enterprises’ regulatory efforts can be translated into real societal benefits, as measured by the social benefit transformation coefficient. Increasing the caliber of products, defending the rights and interests of customers, and encouraging honest competition in the marketplace are all part of this. When the social benefit conversion coefficient grows, it suggests that platform enterprises’ regulatory efforts can be more successfully converted into social well-being, which encourages platform enterprises to implement even more regulations. Lastly, a platform enterprise may be more concerned with the social consequences of its regulatory actions if it has a higher sensitivity to the social benefit transformation coefficient. The platform company’s emphasis on social responsibility or its strategic goals for long-term market development may be the cause of this sensitivity. The platform enterprise adapts its level of regulatory effort more quickly in response to changes in the social benefit conversion factor.

5.4. Analysis of Factors Influencing Merchant Effort Levels $e_2$

Figure 12 demonstrates that, when the intensity of government incentives for platform enterprises ${\beta }_1$ and merchants’ organizational capability coefficient $k_2$ increase, there is a downward distortion in merchants’ effort level $e_2$. However, this distortion continues to decrease as merchants’ organizational capability coefficient $k_2$ increases. This implies that, first, merchants may experience increased performance pressure or expectations in response to intensifying government incentives for platform corporations, which may prompt them to temporarily pursue more effective sales or operational techniques. But, in their quest for instant gratification, retailers risk ignoring long-term sustainable initiatives like customer service optimization and product quality enhancement due to the strong incentives. Because of this, a merchant’s level of effort could show a “downward distortion”, which would make it seem efficient in the short term but potentially hurt the company in the long run. Second, the potential of a merchant to react to government incentives rises with its organizational capacity coefficient. This implies that merchants can pursue performance while maintaining stability and sustainability in their level of effort. When the organizational competence coefficient rises, the downward distortion in merchants’ effort levels thus decreases.

Overall, this situation might suggest that, when regulating platform businesses, the government should take into account the various organizational capacities of merchants when creating incentive programs to prevent policies that are too general and cause distortions in the effort levels of merchants. In order to adapt more effectively to market shifts and government incentives while achieving long-term sustainable development, retailers need to concurrently aggressively strengthen their own organizational capacities.

Figure 13 illustrates this relationship: the merchant’s effort level A rises with the merchant’s reliance on platform company B, but it falls with the merchant’s effort–cost coefficient C. This implies that a merchant’s effort level rises in tandem with its dependence on the platform enterprise. Wohllebe [41] (2022) and Engert, et al. [42] (2022) also note that retailers depend more and more on e-commerce platforms since they offer them convenient shopping options and excellent business chances. Merchants typically step up their efforts to maintain a positive relationship with the platform and take advantage of these commercial prospects, such as by optimizing customer service and improving product quality. Second, a merchant’s effort level falls even as its effort–cost coefficient rises. A merchant may believe that the costs are too high and reduce effort when their operating cost coefficient, also known as the effort–cost coefficient, above a certain threshold (e.g., 10%). Conversely, quality merchants are generally able to maintain a good effort level, achieve cost control, and achieve operational benignity when the operating cost coefficient is kept within the range of 4–7% [43] (Han et al., 2022).

5.5. Analysis of Factors Influencing the Expected Utility of Platform Companies $E(V_2)$

The expected utility $E(V_2)$ of the platform enterprise rises as the capability coefficient $k_1$ and the social benefit transformation coefficient $h_2$ rise, as shown in Figure 14. The expected utility effect of the two for the platform enterprise is comparatively constant. This shows that: firstly, the social benefit conversion coefficient represents the degree to which the socio-economic and cultural-development-promoting function that e-commerce platforms play is converted into the platform’s actual value. As the capability coefficient increases, platforms can expedite order processing, streamline distribution, and logistics, enhance customer support quality, and reduce operational costs, all of which contribute to increased profitability. Platform businesses may process orders more quickly, streamline distribution and logistics, raise the caliber of customer support, and more, as the capability coefficient grows, which lowers operating costs and boosts profitability. Second, the predicted utility of the platform is enhanced by the mutual reinforcement of the platform enterprise capacity and the coefficient of transformation of social benefits. Enhancing social benefits adds to the platform’s legitimacy, appeal, and profitability on the one hand; increasing the platform enterprise’s capability, on the other hand, helps to maximize operational effectiveness and service quality, which, in turn, enhances social benefits even more. They both collaborate on the anticipated utility of platform businesses, creating a positive feedback loop. The predicted usefulness of platform enterprises will rise in tandem with improvements in the capability and social benefit transformation coefficients, hence advancing the platform’s realization of sustainable development.

Ultimately, the expected utility of platform enterprises rises in tandem with the platform enterprises’ capability and social benefit transformation coefficients, and their respective effects on the expected utility of platform enterprises are largely consistent. This implies that, in order to achieve the platform’s long-term development, focus should be given to enhancing the platform’s capacity and social benefit during the platform enterprise monitoring process.

Figure 15 illustrates how the effort level $e_1$ of the e-commerce platform and the effort level $e_2$ of the merchants cause a negative distortion in the expected utility $E(V_2)$ of the platform enterprises. This demonstrates that, when the merchant effort increases, the projected utility of the platform improves and then drops, and the distortion becomes more noticeable as the e-commerce platform effort increases.

First, as merchants put in more effort, platform enterprises’ predicted utility first rises. This is due to the fact that the merchant’s efforts may be seen in the form of improved products and services, more forceful marketing initiatives, etc., all of which enhance platform functionality and user happiness, ultimately raising platform income. However, the predicted utility of the platform company may start to decrease when the merchant’s effort level surpasses a particular level. This might be the result of an increase in the merchant’s effort–cost, which compresses profit margins. It might also trigger unfavorable events like price wars and hostile competition, all of which could be harmful to the platform’s overall goals. Second, the e-commerce platform’s own degree of effort has a greater influence on the distortionary dynamics of predicted utility than does the merchants’ level of effort. This is because e-commerce platforms have more power and authority over marketing, technical innovation, and regulations. This is conceivable for two reasons: First, e-commerce platforms might overinvest in specific areas, including marketing and expansion, which would squander money and reduce productivity. Second, the platform’s reputation and interests could be harmed if there are oversight flaws or misconduct that leads to unfair competition among merchants, the spread of counterfeit goods, and other issues. Third, while technological innovations can enhance the operational efficiency and service quality of platforms, they may also bring about technical risks, security risks, and other issues that require platforms to invest more resources to deal with.

The aforementioned downward distortion implies that platform companies’ regulatory conduct should be balanced in order to allow merchants’ and platform enterprises’ efforts to further the platform’s overall development without compromising the intended utility. To uphold fair competition and market order, platform enterprises should enhance their regulatory efforts. At the same time, they should sanely direct merchants’ efforts to steer clear of aggressive and excessive competition. Furthermore, platform enterprises must make modest investments in their own level of effort in order to prevent resource waste and falling efficiency. They must balance the advantages and disadvantages of technological innovation and market marketing to make sure that investment returns are optimized.

6. Conclusions and Recommendations

Beginning with the background of collaborative platform economy regulation, this paper constructs a dual principal–agent model and solves and simulates the dual principal–agent model in order to analyze the regulatory incentive problem of government–platform enterprise–merchant, a tripartite subject of regulatory incentives of the platform economy under the condition of asymmetric information. This allows the investigation of the primary factors influencing the optimal incentive intensity, the optimal regulatory intensity, and the optimal level of effort. The following are the precise findings and managerial insights:

(1) Platform companies will ultimately impact merchants’ self-regulatory conduct through the government’s optimal incentives and regulation in the process of platform economic governance. Collaboration between the government, platform companies, and merchants is essential to achieve this broad, deep, and lasting impact.

Firstly, governments can offer a variety of incentives, such as tax breaks, financial aid, or other policy support, to motivate platform companies to better fulfill their regulatory obligations. Platform businesses may be more inclined to impose stringent management and oversight in order to preserve the stability and well-being of the platform ecosystem as a result of these incentives. To control and limit the operational behavior of platform enterprises, the government must establish a number of laws, rules, and regulatory policies. To make sure that platform enterprises may function legally, these regulatory regulations may include provisions for consumer rights protection, data protection, and anti-unfair competition.

Secondly, platform companies act as intermediaries between the public sector and retailers. Platform companies will develop the necessary internal policies and procedures to oversee and manage merchants in compliance with legal and regulatory standards as well as government incentives. Platform companies will monitor and assess merchants’ business practices in real time to ensure they adhere to platform guidelines as well as applicable laws and regulations. They will do this by using technological tools and data analysis.

Ultimately, platform businesses will enhance their oversight and management of merchants and raise the penalty for non-compliance with the best possible government incentives and regulations. Merchants must gradually increase their awareness of self-discipline and adhere to platform rules, laws, and regulations in order to grow steadily on the platform over time. Over time, this self-control conduct on the platform will become the standard and a habit, increasing the platform’s legitimacy and competitiveness.

(2) Platform companies and the government can support merchants in the platform economic governance process by implementing monitoring mechanisms; on the other hand, incentives and regulations have a certain relationship and must be closely monitored to achieve the optimal governance outcome. The government and platform companies must thoroughly analyze the relationship between incentives and regulation, as well as the associated changes in costs and benefits, as part of the platform economic governance process. The optimal governance effect can be achieved and the long-term, robust growth of the platform economy can be encouraged by thoughtfully combining and adjusting incentives and restrictions.

Governments and platform enterprises must consider the expenses related to implementing incentives and regulations. While the costs of regulatory measures include items like technical inputs and enforcement costs, the costs of incentives include things like tax incentives and financial outlays for funding support. To ensure the efficacy and sustainability of incentive and regulatory measures, the link between costs and benefits must be considered during implementation. There are definite advantages to enacting regulations and incentives. Regulations can preserve market order and fair competition while fostering the robust growth of the platform economy. Incentive measures can lower the cost and risk of noncompliance by merchants and improve their willingness and motivation to comply. It is crucial that we evaluate whether the benefits outweigh the costs to guarantee the economic and social benefits of the incentive and regulatory measures.

(3) The external regulation of businesses and merchants falls under the category of external incentives in the economic governance of platforms. These entities also require internal incentives to raise the overall level of governance by raising the bar for their own work, raising the coefficient of transformation of social benefits, and so forth. Building a pleasant and healthy atmosphere is essential to achieving this goal because it helps merchants and platform enterprises understand the value of sustainable development and self-improvement.

In the first place, platform companies should motivate merchants to add more value by setting up a fair incentive system. To help them differentiate themselves from the competition, this involves—but is not limited to—offering technical support, marketing support, training materials, and other help. Platform companies should also promote the transformation of social benefits at the same time, pushing merchants to prioritize sustainable development and social responsibility over economic gains, and boosting the social benefit transformation factor through doable initiatives.

Second, increasing this kind of intrinsic incentive can strengthen the cohesiveness and centripetal force of the entire platform in addition to encouraging platform businesses and merchants to practice self-control and self-improvement. Platform businesses and merchants will become more involved in the economic governance of the platform when they recognize how well their development styles complement one another. This will create a positive feedback loop and engagement.

(4) All stakeholders must cooperate to maximize the overall benefits in the platform economy governance process in order to maintain long-term cooperation between the government, platform companies, and merchants.

The government must first create and amend pertinent laws and regulations to provide a transparent and unambiguous regulatory framework for the platform economy. It should also promote the innovation and growth of the platform enterprises, safeguard the rights and interests of consumers, and uphold a fair and competitive market environment by offering policy support and guidance. This lays the groundwork for long-term collaboration by fostering a relationship of mutual trust between the government, platform companies, and merchants.

Second, in order to make sure that their business operations are lawful and compliant, platform companies should proactively adhere to the rules and laws established by the government and improve internal management. Simultaneously, platform companies ought to consistently enhance their technological proficiency and service caliber in order to furnish merchants with an enhanced and more convenient trading environment and facilitate their augmentation of operational effectiveness. Platform companies should also actively engage with the government, provide input on market demands and conditions, and work together to support the robust growth of the platform economy.

Lastly, in order to guarantee that the caliber of the products and services they sell fulfill the requirements, retailers must adhere completely to the platform’s guidelines. Merchants should also actively engage in platform activities, build strong working relationships with the platform, and work together to increase market competitiveness and brand influence. Merchants should also be aware of what customers want, deliver high-quality goods and services, gain the confidence and goodwill of customers, and support the growth of the platform economy.

The dual principal–agent model, in summary, offers a helpful analytical framework for the platform economy’s regulatory incentive problem. By creating a fair incentive structure, the government, platform companies, and merchants can work together to effectively coordinate the relationship and support the platform economy’s healthy development. In order to create an ideal contractual system, this study creatively builds a dual principal–agent model for the government, platform enterprise, and merchant in platform economy governance. This model integrates incentives and monitoring measures. The unique role that the platform enterprise plays in the dual principal–agent relationship—that is, as both the government’s agent and the merchants’ principal—is then thoroughly examined. Quantitative techniques are used to analyze the contract structure under optimal regulatory and incentive mechanisms. The interaction and substitution effects between regulatory and incentive mechanisms are also covered. However, the relationship between the parties in platform economic governance is more complex and involves multiple tasks; additionally, the benefits will vary over time, and future research will focus on this topic instead of the static study of regulatory incentives in platform economic governance.