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The model integrated reinforcement learning, user heterogeneity modeling and small-world network synergy mechanism, adjusted the carbon credit intensity in real time by dynamic incentive generator, quantified the diminishing marginal utility effect of incentives for high-income groups by combining elastic user identifiers, and designed weather attenuation coefficients to optimize the spread of social influence. Simulation results showed that DIS-HARM significantly improves system efficiency and fairness: the peak hour passenger flow reduction rate reaches 72.2% (2.5% higher than the static strategy), the average peak hourly cost is reduced by 3.125%, and 36.5% of the incentive resources are tilted to the low-income group (83.1% coverage rate) at the same time. The model provided a theoretical tool for dynamic pricing and differentiated incentive strategies for urban transportation management, helping to achieve the dual goals of green travel and social equity.<\/jats:p>","DOI":"10.1038\/s41598-025-16632-y","type":"journal-article","created":{"date-parts":[[2025,8,21]],"date-time":"2025-08-21T06:20:57Z","timestamp":1755757257000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Optimization of dynamic incentive strategies for public transportation based on reinforcement learning and network synergy effect"],"prefix":"10.1038","volume":"15","author":[{"given":"Yifang","family":"Chen","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shunlin","family":"Wang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2025,8,21]]},"reference":[{"issue":"03","key":"16632_CR1","first-page":"985","volume":"45","author":"CX Zhou","year":"2025","unstructured":"Zhou, C. 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