# Dynamic multi-agent deep reinforcement learning-based pricing and incentivization approach in multimodal transportation networks

arXiv: https://arxiv.org/abs/2606.23257 · HTML: https://mlsanity.com/paper/2606.23257/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 11 of its 96 references that are in the map.
- First posted on arXiv 22 Jun 2026.

## Builds on (most cited first, 11 of 11)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Soft Actor-Critic: Off-Policy Maximum Entropy Deep Reinforcement Learning with a Stochastic Actor](https://mlsanity.com/paper/1801.01290/) (2018)
- [FairST: Equitable Spatial and Temporal Demand Prediction for New Mobility Systems](https://mlsanity.com/paper/1907.03827/) (2019)
- [Dealing With Non-stationarity in Decentralized Cooperative Multi-Agent Deep Reinforcement Learning via Multi-Timescale Learning](https://mlsanity.com/paper/2302.02792/) (2023)
- [A dynamic ridesharing dispatch and idle vehicle repositioning strategy with integrated transit transfers](https://mlsanity.com/paper/1901.00760/) (2018)
- [Regulating For-Hire Autonomous Vehicles for An Equitable Multimodal Transportation Network](https://mlsanity.com/paper/2301.05798/) (2023)
- [Dynamic Pricing in Shared Mobility on Demand Service](https://mlsanity.com/paper/1802.03559/) (2018)
- [Regulating Mobility-on-Demand Services: Tri-level Model and Bayesian Optimization Solution Approach](https://mlsanity.com/paper/2102.10382/) (2021)
- [Game Theory to Study Interactions between Mobility Stakeholders](https://mlsanity.com/paper/2104.10394/) (2021)
- [Equity Promotion in Public Transportation](https://mlsanity.com/paper/2211.14531/) (2022)
- [A multi-dimension and high-granularity equity measurement for transportation services through accessibility and reliability](https://mlsanity.com/paper/2501.14761/) (2024)

## Abstract (arXiv)

In multimodal transportation systems, shared mobility services (SMSs) are promoted for their potential to enhance flexibility and reduce congestion. However, SMS demand is often concentrated in high-density areas, which can limit the effectiveness and accessibility for various commuter groups. This uneven integration challenges transportation system efficiency, especially in terms of emissions and spatial equity. Addressing these issues requires coordination among multiple stakeholders whose objectives frequently conflict. Whereas authorities aim to ensure sustainable and equitable mobility, SMS providers focus on revenue maximization, and travelers seek to minimize personal travel costs. This paper proposes a multi-agent deep reinforcement learning framework that captures these interactions through dynamic pricing and incentivization strategies for SMSs and public transport. The framework integrates two reinforcement learning (RL) agents: (i) a public authority that allocates spatio-temporal public transport incentives to improve equity, emissions, and efficiency, and (ii) an SMS provider that dynamically adjusts fares to optimize revenue. The agents interact with the transportation system and adapt strategies in response to evolving demand, congestion, and network conditions. Numerical experiments conducted over a three-hour morning peak period show that dynamic incentivization effectively reduces congestion peaks, lowers commuters' costs by around 20% and emissions by approximately 10%, while nearly doubling public transport profit and supporting a more equitable distribution of benefits. When combined with dynamic SMS pricing, the two RL agents demonstrate the ability to balance conflicting objectives between private providers and public authorities. The proposed approach provides a decision-support tool for sustainable and equitable multimodal mobility planning.