In this study, we constructed a stochastic differential game (SDG) model for multi-stakeholder collaborative governance of quality–reputation risks in livestream e-commerce scenarios driven by quality complaints, and proposed an adaptive multi-agent collaborative response model based on dynamic event-triggering and Q-learning. We further analyzed the effectiveness conditions for collaborative governance and derived corresponding multi-stakeholder collaborative strategies under relevant factors. The major findings were threefold: (1) From the perspective of strategy adaptation, collaborative strategies were applicable to manufacturers only when the commission rate was relatively high, whereas for streamers and livestreaming platforms, such strategies were applicable only when the commission rate was relatively low. When the intensity of quality complaints was at a moderate threshold, the benefits of reputational collaborative governance were highest, prompting the system to favor collaborative mechanisms under the "quality–reputation–performance" symbiosis; once the complaint intensity deviated from this threshold, the system begin to deviate from collaboration. (2) From the perspective of quality complaints, the theoretical condition for maintaining an upward trajectory of system reputation was that complaint intensity remained relatively low in the absence of government penalties. After introducing government penalties, the external conditions for achieving Pareto optimality in the reputation trajectory were either that system traffic was weak with complaint intensity at a low or high level, or that system traffic was strong with complaint intensity at a moderate threshold. (3) Collaborative decision-making always yielded higher total system profit than decentralized decision-making, and enabled the expected value and variance of the reputation trajectory to achieve Pareto optimality while slowing its declining trend, subject to the condition that the platform's revenue coefficient (take rate) varies in the same direction as its reputation-restoration cost coefficient; with stronger synchronicity producing greater slowing effects.
Citation: Yuexiang Yang, Zhenwu Chen, Ketao Huang, Xinyi Li. A stochastic differential game approach to multi-stakeholder collaborative governance of quality–reputation risks in livestream e-commerce scenarios: a "quality–reputation–performance" symbiosis perspective[J]. AIMS Mathematics, 2026, 11(9): 28582-28627. doi: 10.3934/math.20261138
In this study, we constructed a stochastic differential game (SDG) model for multi-stakeholder collaborative governance of quality–reputation risks in livestream e-commerce scenarios driven by quality complaints, and proposed an adaptive multi-agent collaborative response model based on dynamic event-triggering and Q-learning. We further analyzed the effectiveness conditions for collaborative governance and derived corresponding multi-stakeholder collaborative strategies under relevant factors. The major findings were threefold: (1) From the perspective of strategy adaptation, collaborative strategies were applicable to manufacturers only when the commission rate was relatively high, whereas for streamers and livestreaming platforms, such strategies were applicable only when the commission rate was relatively low. When the intensity of quality complaints was at a moderate threshold, the benefits of reputational collaborative governance were highest, prompting the system to favor collaborative mechanisms under the "quality–reputation–performance" symbiosis; once the complaint intensity deviated from this threshold, the system begin to deviate from collaboration. (2) From the perspective of quality complaints, the theoretical condition for maintaining an upward trajectory of system reputation was that complaint intensity remained relatively low in the absence of government penalties. After introducing government penalties, the external conditions for achieving Pareto optimality in the reputation trajectory were either that system traffic was weak with complaint intensity at a low or high level, or that system traffic was strong with complaint intensity at a moderate threshold. (3) Collaborative decision-making always yielded higher total system profit than decentralized decision-making, and enabled the expected value and variance of the reputation trajectory to achieve Pareto optimality while slowing its declining trend, subject to the condition that the platform's revenue coefficient (take rate) varies in the same direction as its reputation-restoration cost coefficient; with stronger synchronicity producing greater slowing effects.
| [1] | J. B. Luo, W. H. Xie, Research on governance mechanism of "low level" vulgar content on live broadcasting platform based on non-participating interactive public, (Chinese), Operations Research and Management Science, 31 (2022), 227–233. |
| [2] |
C. H. Hu, W. Chen, Y. J. Zhou, C. Chen, S. Y. Sun, Regulation mechanism of live streaming e-commerce based on evolutionary game theory, (Chinese), Journal of Management Sciences in China, 26 (2023), 126–141. http://doi.org/10.19920/j.cnki.jmsc.2023.06.008 doi: 10.19920/j.cnki.jmsc.2023.06.008
|
| [3] |
P. He, Q. Shang, X. J. Wang, T. Y. Wang, Z. S. Chen, Evolutionary game analysis of e-commerce supply chain considering platform supervision under the background of "live streaming+", (Chinese), Systems Engineering–Theory & Practice, 43 (2023), 2366–2379. https://doi.org/10.12011/SETP2022-2427 doi: 10.12011/SETP2022-2427
|
| [4] |
W. Xu, Y. Cao, R. Y. Chen, A multimodal analytics framework for product sales prediction with the reputation of anchors in livestream e-commerce, Decis. Support Syst., 177 (2024), 114104. https://doi.org/10.1016/j.dss.2023.114104 doi: 10.1016/j.dss.2023.114104
|
| [5] |
R. B. Yang, C. X. Yin, On the cooperative governance behavior of internet rumors based on differential games, (Chinese), Complex Systems and Complexity Science, 22 (2025), 145–153. https://doi.org/10.13306/j.1672-3813.2025.04.019 doi: 10.13306/j.1672-3813.2025.04.019
|
| [6] |
D. C. Fan, S. C. Guo, Research on differential game theory in livestreaming e-commerce platform governance under credibility crisis, (Chinese), Computer Engineering and Applications, 62 (2026), 351–362. https://doi.org/10.3778/j.issn.1002-8331.2507-0093 doi: 10.3778/j.issn.1002-8331.2507-0093
|
| [7] |
H. Sundqvist-Andberg, M. Akerman, Collaborative governance as a means of navigating the uncertainties of sustainability transformations: the case of Finnish food packaging, Ecol. Econ., 197 (2022), 107455. https://doi.org/10.1016/j.ecolecon.2022.107455 doi: 10.1016/j.ecolecon.2022.107455
|
| [8] | J. K. Yang, S. Z. Fu, G. Q. Hu, Coordination in governance or tunneling in collusion: Non-controlling shareholders' network and M & A efficiency, (Chinese), China Soft Science, 2023 (2023), 202–214. |
| [9] |
S. Yang, Y. C. Zhang, A. F. Wang, Stability of food safety social co-governance evolutionary game with multi-agent participation, (Chinese), Chinese Journal Management Science, 32 (2024), 325–334. https://doi.org/10.16381/j.cnki.issn1003-207x.2021.1008 doi: 10.16381/j.cnki.issn1003-207x.2021.1008
|
| [10] |
Y. H. Chen, Personal information sharing risks and protection countermeasures under the diversified governance mode of the internet, (Chinese), Information Science, 40 (2022), 118–123. https://doi.org/10.13833/j.issn.1007-7634.2022.11.016 doi: 10.13833/j.issn.1007-7634.2022.11.016
|
| [11] |
Y. Huang, Evolutionary game analysis of collaborative strategies in fresh e-commerce and cold chain logistics: the role of incentive mechanisms and supervision policies, Int. Rev. Econ. Financ., 104 (2025), 104773. https://doi.org/10.1016/j.iref.2025.104773 doi: 10.1016/j.iref.2025.104773
|
| [12] |
L. Yuan, Y. Z. Qi, W. J. He, X. Wu, Y Kong, T. S. Ramsey, et al., A differential game of water pollution management in the trans-jurisdictional river basin, J. Clean. Prod., 438 (2024), 140823. https://doi.org/10.1016/j.jclepro.2024.140823 doi: 10.1016/j.jclepro.2024.140823
|
| [13] | A. W. Lu, H. Y. He, Research on multi-dimensional collaborative governance of internet information service industry based on evolutionary game, (Chinese), Operations Research and Management Science, 29 (2020), 53–59. |
| [14] |
A. W. Lu, H. Y. He, Research on the function of multi-governance model in internet information service industry: an evolutionary game perspective based on multi-parameter influence, (Chinese), Chinese Journal Management Science, 29 (2021), 210–218. https://doi.org/10.16381/j.cnki.issn1003-207x.2018.1277 doi: 10.16381/j.cnki.issn1003-207x.2018.1277
|
| [15] | W. T. Wang, K. N. Liu, S. Wang, J. P. Ren, Y. N. Le, Research on the predicament and pathway improvement of scientific and technological achievements transformation in research hospitals from the perspective of collaborative governance, (Chinese), Science Technology Management Research, 43 (2023), 129–135. |
| [16] |
H. Y. Gao, X. T. Dai, L. H. Wu, J. X. Zhang, W. Y. Hu, Food safety risk behavior and social co-governance in the food supply chain, Food Control, 152 (2023), 109832. https://doi.org/10.1016/j.foodcont.2023.109832 doi: 10.1016/j.foodcont.2023.109832
|
| [17] | L. Yuan, X. Wu, W. J. He, D. M. Degefu, Y. Kong, Y. Kong, et al., Utilizing the strategic concession behavior in a bargaining game for optimal allocation of water in a transboundary river basin during water bankruptcy, Environ. Impact Assess. Rev., 102 (2023), 107162. https://doi.org/10.1016/j.eiar.2023.107162 |
| [18] |
Y. Wang, R. Zhang, Y. Zhao, C. H. Li, A public participation approach in the environmental governance of industrial parks, Environ. Impact Assess. Rev., 101 (2023), 107131. https://doi.org/10.1016/j.eiar.2023.107131 doi: 10.1016/j.eiar.2023.107131
|
| [19] |
Y. Song, R. Berger, M. Rachamim, A. Johnston, A. F. Colladon, Modelling the industry perspective of university–industry collaborative innovation alliances: player behavior and stability issues, Int. J. Eng. Bus. Manag., 14 (2022), 1–18. https://doi.org/10.1177/18479790221097235 doi: 10.1177/18479790221097235
|
| [20] |
X. Y. Xu, Y. Yang, Analysis of the dilemma of promoting circular logistics packaging in China: a stochastic evolutionary game-based approach, Int. J. Environ. Res. Public Health, 19 (2022), 7363. https://doi.org/10.3390/ijerph19127363 doi: 10.3390/ijerph19127363
|
| [21] |
W. X. Yang, C. L. Xie, L. D. Ma, Tripartite evolutionary game and simulation analysis of brand enhancement for geographical indications agri-food, China Agr. Econ. Rev., 16 (2024), 340–367. https://doi.org/10.1108/CAER-07-2023-0207 doi: 10.1108/CAER-07-2023-0207
|
| [22] |
L. Yuan, W. J. He, D. M. Degefu, Z. Y. Liao, X. Wu, M. An, et al., Transboundary water sharing problem: a theoretical analysis using evolutionary game and system dynamics, J. Hydrol., 582 (2020), 124521. https://doi.org/10.1016/j.jhydrol.2019.124521 doi: 10.1016/j.jhydrol.2019.124521
|
| [23] | M. Yang, D. H. Liu, Stochastic differential game model of diversified supply of emergency medical supplies led by government, (Chinese), Systems Engineering–Theory & Practice, 43 (2023), 1333–1352. |
| [24] |
M. Nerlove, K. J. Arrow, Optimal advertising policy under dynamic conditions, Economica, 29 (1962), 129–142. https://doi.org/10.2307/2551549 doi: 10.2307/2551549
|
| [25] | S. G. Zheng, D. H. Su, S. Y. Wang, W. Shang, Research on reward income sharing model of live streaming platforms, (Chinese), Systems Engineering–Theory & Practice, 40 (2020), 1221–1228. |
| [26] |
P. Xing, H. Y. You, Y. C. Fan, Optimal quality effort strategy in service supply chain of live streaming e-commerce based on platform marketing effort, (Chinese), Control and Decision, 37 (2022), 205–212. https://doi.org/10.13195/j.kzyjc.2020.1205 doi: 10.13195/j.kzyjc.2020.1205
|
| [27] |
S. Jorgensen, E. Gromova, Sustaining cooperation in a differential game of advertising goodwill accumulation, Eur. J. Oper. Res., 254 (2016), 294–303. https://doi.org/10.1016/j.ejor.2016.03.029 doi: 10.1016/j.ejor.2016.03.029
|
| [28] |
Z. J. Zhang, Z. W. Chen, M. Y. Wan, Z. Zhang, Dynamic quality management of live streaming e-commerce supply chain considering streamer type, Comput. Ind. Eng., 182 (2023), 109357. https://doi.org/10.1016/j.cie.2023.109357 doi: 10.1016/j.cie.2023.109357
|
Figures(17) / Tables(4)
Yuexiang Yang, Zhenwu Chen, Ketao Huang, Xinyi Li. A stochastic differential game approach to multi-stakeholder collaborative governance of quality–reputation risks in livestream e-commerce scenarios: a "quality–reputation–performance" symbiosis perspective[J]. AIMS Mathematics, 2026, 11(9): 28582-28627. doi: 10.3934/math.20261138
DownLoad: