{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,4]],"date-time":"2025-12-04T06:57:17Z","timestamp":1764831437556,"version":"3.46.0"},"reference-count":69,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2025,12,1]],"date-time":"2025-12-01T00:00:00Z","timestamp":1764547200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["72072031","72134002"],"award-info":[{"award-number":["72072031","72134002"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Postgraduate Research &amp; Practice Innovation Program of Jiangsu Province","award":["KYCX22_0319"],"award-info":[{"award-number":["KYCX22_0319"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Systems"],"abstract":"<jats:p>(1) Background: Public service platforms (PSPs) have become increasingly popular for delivering public services. Typically, their fixed pricing and subsidy strategies overlook the participation of various stakeholders, resulting in inefficient supply of public services. This study aims to use China\u2019s eldercare services as an example to examine its dynamic pricing and subsidy strategies. (2) Methods: Game theory was utilized to develop a two-level Stackelberg game framework considering the decision-making sequences among stakeholders with competing objectives. On this basis, the two-level Stackelberg game was solved based on the maximization of social welfare, platform profit, and utility, pursued by the government, private sector, and service providers, respectively. (3) Results: The service supply duration is determined by the service price. Specifically, when the service price falls within an appropriate range, the optimal supply duration increases with the service price. The results further show that the optimal service price increases with the platform\u2019s commission rate but declines with government subsidies. Furthermore, the optimal government subsidy increases with the platform\u2019s commission rate in a balanced market. By contrast, in an unbalanced market, where demand is either below the minimum supply or above the maximum supply, the government will withdraw subsidies entirely once the commission rate exceeds a certain threshold, thereby curbing excessive commission charges. (4) Conclusions: This study contributes to the body of knowledge of platform development by examining PSPs\u2019 dynamic pricing and government subsidy strategies. Practically, this two-level Stackelberg game framework for PSPs will help improve the efficiency of public services provision for consumers and maximize social welfare and platforms\u2019 profit for the government and private sector, respectively.<\/jats:p>","DOI":"10.3390\/systems13121085","type":"journal-article","created":{"date-parts":[[2025,12,2]],"date-time":"2025-12-02T08:49:22Z","timestamp":1764665362000},"page":"1085","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Dynamic Pricing and Subsidy Strategies in Public Service Platforms with Private Participation: A Two-Level Stackelberg Game Approach"],"prefix":"10.3390","volume":"13","author":[{"given":"Rui","family":"Liu","sequence":"first","affiliation":[{"name":"Department of Construction and Real Estate, School of Civil Engineering, Southeast University, Nanjing 211189, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Wenfei","family":"Lu","sequence":"additional","affiliation":[{"name":"Department of Construction and Real Estate, School of Civil Engineering, Southeast University, Nanjing 211189, China"},{"name":"CACC Southwest Design and Research Institute Co., Ltd., Chengdu 610225, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1140-7901","authenticated-orcid":false,"given":"Jianfeng","family":"Zhao","sequence":"additional","affiliation":[{"name":"School of Architecture and Built Environment, Northumbria University, Newcastle upon Tyne NE1 8ST, UK"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0922-6853","authenticated-orcid":false,"given":"Jingfeng","family":"Yuan","sequence":"additional","affiliation":[{"name":"Department of Construction and Real Estate, School of Civil Engineering, Southeast University, Nanjing 211189, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,12,1]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Qin, S.M., Zhang, M., Hu, H., and Wang, Y. 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