Competitive Multi-Operator Reinforcement Learning for Joint Pricing and Fleet Rebalancing in AMoD Systems

Dynamic pricing in competitive retail markets requires strategies that adapt to fluctuating demand and competitor behavior. In this work, we present a systematic empirical evaluation of multi-agent reinforcement learning (MARL) approaches-specifically MAPPO and MADDPG-for dynamic price optimization under competition. Using a simulated marketplace environment derived from real-world retail data, we benchmark these algorithms against an Independent DDPG (IDDPG) baseline, a widely used independent learner in MARL literature. We evaluate profit performance, stability across random seeds, fairness, and training efficiency. Our results show that MAPPO consistently achieves the highest average returns with low variance, offering a stable and reproducible approach for competitive price optimization, while MADDPG achieves slightly lower profit but the fairest profit distribution among agents. These findings demonstrate that MARL methods-particularly MAPPO-provide a scalable and stable alternative to independent learning approaches for dynamic retail pricing.

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.

In liberalised railway systems, operators must set prices dynamically in an environment with partial observability, as they retain private information about their objectives and performance, where regulatory constraints prohibit communication or direct information exchange between competitors to prevent explicit collusion. Consequently, agents must learn to infer strategic interactions only from observable market data which presents a significant challenge for multi-agent reinforcement learning, where standard approaches typically treat observations as unstructured vectors, ignoring the underlying market topology that governs strategic interactions. To address this, an entity graph modelling approach is proposed, which represents the environment as a graph of operational units, rather than decision-making agents or static infrastructure, encoding competition, coordination, and connectivity relations between entities. Then, an extension of the multi-agent twin delayed deep deterministic policy gradient algorithm with graph-based representation learning processes the features of the entities through a multi-layer relational graph convolutional network and aggregates them via a learnt attention mechanism. Experimental results in a rail pricing reinforcement learning environment show that this novel framework achieves higher revenue and stability in two different settings of increasing market complexity compared to a representative selection of relational and non-relational baselines. The code is publicly available at: https://github.com/Kinrre/RelationalRailPricing-RL