Relational Multi-Agent Reinforcement Learning for Dynamic Pricing in High-Speed Railway Markets
2026-07-06 • Machine Learning
Machine LearningArtificial IntelligenceMultiagent Systems
AI summaryⓘ
The authors study how railway companies can set prices in a system where they can't openly share information due to rules against collusion. They propose a new way to represent the market as a network of smaller operational units instead of just individual companies or infrastructure, capturing how these units interact. Using this network, they improve a reinforcement learning method to better learn pricing strategies by understanding these relationships. Their experiments show this approach earns more revenue and is more stable as the market gets more complex.
multi-agent reinforcement learningpartial observabilitydynamic pricingrailway systemsgraph convolutional networkmarket topologymulti-layer relational graphattention mechanismdeep deterministic policy gradientregulatory constraints
Authors
Enrique Adrian Villarrubia-Martin, David Muñoz-Valero, Luis Rodriguez-Benitez, Giovanni Montana, Luis Jimenez-Linares
Abstract
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