Analysis of Heteronomy Strategies for Platform Corporate Social Responsibility Under Government Intervention

With the change in emerging technology and the economic environment, governance of the lack and alienation of platform corporate social responsibility has become more urgent. Firstly, this paper analyses the autonomy defects of the platform corporate social responsibility and illustrates the need for heteronomy of platform corporate social responsibility. Secondly, we use differential game to study the heteronomy strategies for platform corporate social responsibility: self-beneficial governance or co-beneficial governance, including the optimal governance effort level and optimal profit and optimal trajectory of the amount of governance. Then, numerical examples are used to compare the two situations. Finally, the conclusion is verified by SFIC model. The result shows that: <xref rid="deqn1-deqn3" ref-type="disp-formula">(1)</xref> The amount of governance gradually reaches a stable state over time. <xref rid="deqn1-deqn3" ref-type="disp-formula">(2)</xref> Co-beneficial governance can improve the heteronomy of platform corporate social responsibility. <xref rid="deqn1-deqn3" ref-type="disp-formula">(3)</xref> The maturity of the ecosystem in which the governance subject and platform corporation are located positively affects the amount of governance.

forms and digitalization, personal information leakage and 23 commercial non-compliance have come to light alongside 24 technological innovation. Thus, there is an urgent need to 25 strengthen the supervision of the industry. For example, 26 The associate editor coordinating the review of this manuscript and approving it for publication was Stavros Souravlas . some platform corporations illegally collect user information, 27 damage users' rights and interests, and unfair competition 28 on e-commerce platforms destroys the operating environ-29 ment. Therefore, platform corporations must exercise finan-30 cial functions based on commercial behavior, pay attention 31 to their responsibilities' performance, and actively undertake 32 social responsibilities [4]. To strengthen the regulation of the 33 new industry and protect consumer rights, the State Council 34 has taken the lead, and several ministries are involved in 35 the law of the ''platform economy''. At the same time, plat-36 form corporations' lack and alienation of social responsibility 37 have become prominent, seriously hindering the development 38 of the economy [5], [6]. According to relevant statistics, 39 back in 2014, the economic losses caused by the lack of 40 integrity of Chinese enterprises exceeded RMB 600 billion 41 per year. The issue of platform corporate social responsibility 42 consider not only internal governance mechanisms but also 98 external governance mechanisms [10]. 99 The corporate social responsibility content of corporate 100 social responsibility of the platform and the root causes of 101 autonomy defects are shown in Figure 1. The fundamental 102 reason for defects in the autonomous governance of plat-103 form companies is the unequal relationship between platform 104 companies and other stakeholders driven by profit. The main 105 manifestations are as follows: on the one hand, platform 106 companies abuse their strong position in the market, resulting 107 in monopolistic behaviors that harm the interests of bilateral 108 users. To pursue economic benefits and seize market share, 109 platform companies control supply side users by improving 110 access conditions and seeking economic benefits by weak-111 ening the choice of demand-side users. In addition, platform 112 companies force participants to withdraw from other plat-113 forms through abnormal means, preventing regular compe-114 tition between companies. However, from the perspective of 115 the sharing and openness of the platform [11], digitization and 116 intelligence have accelerated the platform's openness, and the 117 virtual characteristics of digital platforms have made gov-118 ernance more complicated. Illegal transactions may threaten 119 the interests of data-asset owners, thereby endangering social 120 and public security. Large platform companies have become 121 deeply rooted in the regional economic market because of 122 their ability to contribute fully to the development of the 123 regional economy. As a 'partner' of the government, the 124 division of rights and responsibilities has become one of 125 the most pressing issues to be addressed.

215
In terms of governance mode, from the perspective of 216 subject relationships, scholars have put forward three gov-217 ernance modes of social responsibility in the supply chain 218 system, namely decentralized, centralized, and collaborative. 219 In collaborative governance, a change in the decision-making 220 of each member affects the profits of other members. The 221 ultimate goal of collaborative governance is to ensure the 222 highest overall profit in the supply chain [22]. In addition, 223 scholars have considered the issue of social responsibility 224 in corporate technology R&D and proposed different R&D 225 strategies based on subject relations [23]. From the perspec-226 tive of institutional design and internal structure, most studies 227 examine the governance model of platform companies and 228 bilateral users from a bilateral market perspective, where 229 the goal is mainly to maximize commercial profits and the 230 governance structure is relatively simple. From the suppli-231 ers' perspective, some scholars have proposed two gover-232 nance mechanisms: evaluation and cooperation [24]. Other 233 researchers have proposed models such as single-headed 234 structures and their application scenarios [25]. Some scholars 235 have also studied the governance of social responsibility 236 from a status-role perspective, emphasizing the governance 237 status and function of governing subjects [26]. From existing 238 research, studying governance models from the perspective 239 of a corporation alone does not fully encompass all possible governance situations, which requires research using the per-241 spectives of multiple subjects.

242
In terms of methods, the differential game is used in the  actors. Since the lack of social responsibility and alienation 295 of platform companies in this system threatens the interests 296 of many subjects, the perspectives of other stakeholders in 297 the ecosystem are used to study the governance of platform 298 companies, showing sufficient rationality. As Chrislip and 299 Larson point out, the first condition for successful collabo-300 ration is that all stakeholders affected by or concerned about 301 the problem must be broadly included [38]. Awareness of 302 sustainable development is a collective responsibility [39] 303 Companies need to be concerned about the common interests 304 of stakeholders [40]. Many scholars believe that stakeholders 305 in corporate governance include shareholders, employees, 306 and other internal stakeholders. Due to the externality of 307 social responsibility itself, we must consider corporate social 308 responsibility governance from the perspective of external 309 subjects. Scholars have proposed the ecological governance 310 paradigm of social responsibility as support for this idea. 311 Thus, government departments, bilateral users, and the public 312 can govern platform corporations.

313
Clarify the leading role of the government. In China, 314 corporate social responsibility is primarily designated by 315 regulatory authorities to provide norms for platform corpora-316 tions. Currently, this is primarily led by the government. The 317 government sector is in a dominant position in the governance 318 [41], [42] of platform corporate social responsibility, and any 319 actions of platform corporate belong to the scope of gov-320 ernment management. Government regulations are usually 321 mandatory, and the government has administrative enforce-322 ment strength to legislate on social responsibility issues with 323 more vital credibility.

324
Clarify the roles of public and bilateral users. Inadequate 325 external regulation is one of the key factors leading to a lack of 326 social responsibility for platforms. There is a need to improve 327 the external regulatory network and reduce the regulatory 328 risk of platform companies, bilateral users, and the public 329 to play to their respective strengths and participate in the 330 governance of platform companies. Moreover, government 331 departments support the supervision and rights of the public 332 and users through incentives in the governance of platform 333 corporate social responsibility, which can effectively reduce 334 the risk of insufficient supervision of platform corporate 335 social responsibility. Based on the above analysis, this study takes government, 339 the public, and bilateral users as the object to study the 340 heteronomy of platform corporate social responsibility. The 341 research approach is illustrated in Figure 2.
342 Figure 2 shows that there are two ways of governance 343 for the heteronomy of platform corporate social respon-344 sibility. One is self-beneficial governance and the other 345 is co-beneficial governance. Consider that the government 346 department is dominant and shares the cost of governance 347 for both users and the public. In self-beneficial governance, 348 governing subjects pursue maximization of their interests. 349 VOLUME 10, 2022  In co-beneficial governance, the governing subjects seek to 350 maximize their overall interests.. defined as E s (t) and E g (t), respectively. The cost coefficients 359 of governance effort for the three parties are denoted as 360 k b , k s , and k g , respectively. Therefore, according to existing 361 studies [43], the cost function of governance at time t is 362 expressed as: Assumotion2: The amount of governance is expressed as T (t). 367 g denotes the impact of the government's governance effort 368 on the amount of governance and δ denotes the natural rate 369 of decay of the amount of governance. Since the governance 370 policies of platform companies are set by the government, the 371 differential equation for the process of change in the amount 372 of governance is expressed as Assumotion3: The initial benefit is 0, µ denotes the coef-375 ficient of influence of the amount of governance on gover-376 nance revenue, s denotes the coefficient of influence of public 377 scrutiny on governance revenue, b denotes the coefficient 378 of influence of bilateral users on governance revenue, and l 379 denotes the development stage of the ecosystem. The revenue 380 of governance is expressed as Assumotion4 : α(t) and β(t) denote the government's share of 384 bilateral user and public governance costs at time t, α(t) < 385 1, and β(t) < 1.

386
Assumotion5: The discount rate is r, and the revenue distri-387 bution rates of bilateral users, the public, and the government 388 are n b , n s , and n g , respectively. In a state of self-beneficial governance, the government is 392 the prominent leader responsible for formulating macro-393 policy governance, including incentives for bilateral users 394 and the public, such as reduction and exemption of related 395 fees. Citing the numerical expression of the subject relation 396 proposed by Jiang Yue and other scholars from China [44], 397 the bilateral users and the public determine their governance 398 efforts, and the profit functions of the bilateral users, the 399 public, and the government are as follows: The optimal strategies for governance subjects in the case 408 of self-beneficial governance are as follows: The optimal trajectory of the change process of the amount 413 of governance is: The optimal profit of bilateral users is: The optimal profit of public is: The optimal profit of government is: The optimal profit of self-beneficial governance is The dynamic stochastic control method is used to solve  Taking the partial derivatives for the HJB equations E b , E s 436 and E g respectively: Obtain the solutions to (24), (25), and (26). It turns out to 451 be a binary one-degree function of T . Let Eventually, (11), (12) and (13) of Theorem1 is proved.

461
Then, substituting b u g back to (29) we obtain :  The optimal strategies of governance subjects in the case 472 of cooperative governance are: The optimal trajectory of the change process of amount of 475 governance is: The optimal profit of co-beneficial governance is: In co-beneficial governance, the decision-making goal is 484 to maximize the profits of the three parties, and the profit 485 functions are as follows: Satisfy the following HJB equation: 491 Taking the partial derivatives for the HJB equations E b , E s 492 and E g respectively: Substituting (39) back to (38), then we obtain as in (40), 495 shown at the bottom of the next page. From (40), is a binary 496 one-degree function of T . Let Substituting (41) back to (40), then we obtain: Eventually, (36) of Theorem2 is proved.

509
Substituting (44) back to (4), then we obtain: Solving (45), the optimal trajectory of the change process 512 of governance quantity is obtained as follows: Eventually, (35) of Theorem2 is proved.

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The following propositions are obtained by comparing 518 the optimal strategies of governance subjects, the optimal 519 trajectory of the change process of governance quantity, opti-520 mal profit of co-beneficial governance, and self-beneficial since the revenue distribution rate is constantly greater than 0,  (E g (t)) in the co-beneficial and self-beneficial cases is neg-561 atively correlated with the cost coefficients of the govern-562 ment's governance effort(k g ), the natural rate of decay of the 563 amount of governance(δ), and the discount rate(r).

564
In both the co-beneficial and self-beneficial cases, optimal 565 profit is positively related to the coefficient of influence 566 of governance volume on governance revenue, development 567 stage of the ecosystem(l), and revenue distribution rate(n i ), 568 and negatively related to the cost coefficients of governance 569 effort(k i ), discount rate(r), and natural rate of decay of the 570 amount of governance(δ).

572
To further analyze the decision results in both cases, sev-573 eral examples are used to demonstrate the changes in the 574 amount and profit of governance, along with the MATLAB 575 simulation software to perform simulations. Because it is 576 difficult to obtain real data on the corporate social respon-577 sibility governance of the platform, the setting of simulation 578 parameters is based on the analysis of the action mechanism 579 of the governance subject and considering the impact of other 580 aspects. First, we consider the characteristics of the variables 581 in the model. Second, referring to a related study [45], [46], 582 [47], assume that the initial amount of governance is zero and 583 the sum of the revenue of the governance rate is 1. In addition, 584 other parameters are assigned as follows:  Figure 4 shows the change in optimal profit over time 588 in the two cases. The profits of both co-beneficial and 589 self-beneficial governance show a decreasing trend from a 590 specific value to zero because, as the volume of governance 591 increases over time, the demand for governance decreases, 592 resulting in a decrease in revenue. Clearly, as the volume of 593 governance increases, the benefits to the subject of gover-594 nance decrease. As governance increases, the lack and alien-595 ation of social responsibility become fully managed. This 596 phenomenon shows that social responsibility pursues social 597 goals and conflicts with commercial interest.  co-beneficial governance. From Figure 6, it can be seen 612 that the optimal trajectory of the amount of governance 613 increases gradually over time and finally reaches stability. 614 In self-beneficial governance, for each additional unit of l, 615 the growth rates of the amount of governance accounted 616 for 18.92%, 15.91%, 13.46%, 11.86%, and 10.45% of the 617 original amount of governance, respectively. In co-beneficial 618 governance, for each additional unit of l, the growth 619 rate of the amount of governance accounted for 44.86%, 620 37.39%, 32.05%, 28.04%, and 24.92% of the original amount 621 of governance, respectively. Whether it is self-beneficial 622 governance or co-beneficial governance, although the pro-623 portion of the increase is different, the amount of increase 624 is the same. This shows that the higher the maturity of 625 the platform corporate innovation ecosystem, the higher is 626 the amount of governance. Moreover, the growth rate of 627 co-beneficial governance is more elevated, indicating that 628 under the same conditions, compared with self-beneficial 629 governance, co-beneficial governance can produce higher 630 amount of governance and better governance efficiency. The 631 amount of governance rises as the maturity of the innova-632 tion ecosystem in which the platform corporation is located 633 increases, suggesting that the more stable the relationship 634 between the subjects of the innovation ecosystem, the more 635 conducive it is to the governance of the lack of social respon-636 sibility and alienation of the platform corporation. 637 Figure 7 shows the influence of the parameter on 638 the amount of governance in the case of self-beneficial 639 governance and co-beneficial governance. As shown in main factor in the governance of the lack and alienation of 666 platform corporate social responsibility.

667
It can be seen from Figures 6-8 that compared with self-668 beneficial governance, co-beneficial governance can achieve 669 a higher amount of governance, and platform corporate social 670 responsibility governance gives priority to co-beneficial 671 governance.
672 Figure 9 shows the influences of k g and δ on the amount 673 of governance in the case of co-beneficial governance. 674 As shown in Figure 9, the amount of governance decreases 675 as the decay rate increases, and the amount of governance 676 decreases as the cost coefficients of governance effort for the 677 government increase. This phenomenon shows that when the 678 decay rate of the amount of governance is relatively large, 679 governance is hurt.

681
The SFIC model is a typical model for analyzing collabora-682 tive governance problems. The connotation of collaborative 683 governance in this model is the same as that of co-beneficial 684 governance; therefore, the idea of the SFIC model is used to 685 describe co-beneficial governance. Ansell and Gash identi-686 fied four main variables affecting collaborative governance 687 by analyzing 137 cases: starting conditions, facilitative 688 leadership, collaborative processes, and institutional design. 689 Stakeholders are included in the formal strategy of the gov-690 ernment decision-making process [48], the SFIC model is 691 suitable for research on the collaborative governance of 692 platform corporations. The model's starting conditions and 693 facilitative leadership are used to analyze the co-beneficial 694 governance of the heteronomy of platform corporate social 695 responsibility.   According to the comparative analysis of numerical simula-757 tion results and the amount of governance and profit obtained, 758 it can be seen that the governance effect of co-beneficial 759 governance on platform corporate social responsibility is bet-760 ter. Based on the numerical analysis results combined with 761 the SFIC model, this section presents the system design of 762 co-beneficial governance.

763
The institutional design of co-beneficial governance is the 764 design of basic rules and behavioral norms in governance. 765 In co-beneficial governance, including the code of conduct of 766 the governance subject, the government should fully consider 767 the opinions of bilateral users and the public when issuing 768 corresponding systems and regulations to ensure openness 769 of the governance process. In addition, the openness and 770 transparency of the formulation process should be consid-771 ered. Finally, the governance subject governs the platform 772 corporation in a good system.

773
Existing research on platform corporate social responsibil-774 ity and external stakeholders is mostly descriptive. This study 775 used the differential game method to describe the hetero-776 geneity of social responsibility from a dynamic perspective. 777 In addition, this method can be used to study the influence 778 of different parameters on governance and to provide a basis 779 for the strategic choice of governance subjects. Finally, the 780 SFIC model is applied to social responsibility governance 781 to verify the conclusions of the simulation research, which 782 further ensures the accuracy of the conclusions. With the development of advanced technologies such as 786 digital technology and artificial intelligence, a new form of 787 organization, the platform enterprise, has emerged. Platform 788 companies connect bilateral users through their platforms 789 to match supply and demand efficiently. However, at the 790 same time, there is also a lack of alienation from social 791 responsibility, where large platform enterprises have a vast 792 influence and are more likely to use their dominant position 793 to the detriment of other participants. Hence, it is crucial to 794 study the governance of the lack of and alienation from social 795 responsibility. This paper considers the shortcomings of 796 self-centered governance in autonomous governance, using 797 a stakeholder perspective that considers government, the 798 public, and bilateral users as other regulated subjects. It con-799 structs a self-interest governance decision-making model 800 with self-interest as the primary objective and a co-benefit 801 governance decision-making model with the common good 802 as the primary purpose. This paper discusses the optimal 803 strategy of the three actors, the change in the amount of 804 governance over time, the optimal trajectory of total profits, 805 and the impact of relevant parameters on socially responsible 806 governance.

807
Conclusion 1 is that the degree of governance effort 808 and governance is highest for government, the public, and 809 bilateral users under co-beneficial governance decisions.
Combined with the change in the amount of governance, the 811 amount of governance is more significant in the co-beneficial 812 case than in the self-beneficial case; therefore, co-beneficial 813 governance is a better governance strategy. 814 Conclusion 2 is that the amount of governance gradually 815 increases with time and finally reaches a specific stable value, 816 and the overall profit gradually decreases with time.  issues. Although co-beneficial governance can achieve the 858 highest overall profit for the three governance subjects, it is 859 essential to pay attention to the profit of each of the three 860 governance subjects to determine their initiative of the gover-861 nance subjects. Therefore, there should be a specific mecha-862 nism for distributing benefits when co-beneficial governance 863 is conducted. Government departments must adhere to the 864 implementation of macro-controls to provide strong support 865 for corporate development. In addition, in terms of environ-866 ment, as the ecosystem where the governance subjects are 867 located develops more maturely, the inter-subject dependency 868 relationship becomes more stable, which provides a superior 869 external force in socially responsible governance. From the 870 market environment perspective, the market environment also 871 determines the development of enterprises. Social supervi-872 sion plays a vital role in the behavior of enterprises. External 873 public opinion can prompt platform enterprises to fulfill their 874 social responsibilities.

876
This study focuses on the self-beneficial and co-beneficial 877 governance situations in socially responsible governance and 878 studies the amount of governance and profit changes in 879 governance to propose governance strategies, but does not 880 delve into the issue of governance mechanisms in socially 881 responsible governance. In addition, considering the devel-882 opmental maturity of the ecosystem, future research can 883 further consider using a numerical representation of ecosys-884 tem development stages to explore the impact of ecosystem 885 development stages on socially responsible governance. 886 ity and employee innovation performance: A cross-layer study mediated 933 by employee intrapreneurship,'' SAGE Open, vol. 11, no. 2, Apr. 2021, 934 Art. no. 215824402110214.