Relational Multi-Agent Reinforcement Learning for Dynamic Pricing in High-Speed Railway Markets

2026-07-06

AI Summary

This study addresses the challenge of dynamic pricing in high-speed rail markets, where strategic interactions among operators are difficult to model due to partial observability and the absence of information exchange. To capture these complex interdependencies, the authors propose a relation-aware modeling approach that explicitly encodes market structure as a graph composed of operational units. By integrating relational graph convolutional networks with attention mechanisms, the method effectively represents competitive, cooperative, and connectivity relationships among agents. The framework is combined with the multi-agent twin delayed deep deterministic policy gradient (MATD3) algorithm to enable adaptive pricing decisions. Evaluated in two high-speed rail pricing scenarios of increasing complexity, the proposed approach significantly outperforms both relational and non-relational baselines, achieving notable improvements in both revenue generation and strategic stability.

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

Problem

• Dynamic Pricing
• Multi-Agent Reinforcement Learning
• Partial Observability
• Market Topology
• Strategic Interaction

Innovation

• relational graph convolutional network
• multi-agent reinforcement learning
• dynamic pricing
• entity graph modeling
• attention mechanism