[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-83914-en":3,"doc-seo-83914-105":29,"detail-sidebar-cat-0-en-105":91},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":20,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":13,"seo_description":14,"update_tm":27,"read_time":28},83914,8796095461610,"Oliver","https://ap-avatar.wpscdn.com/davatar_276721f389ce27ea32af1340a28f341c",8,"Research & Report","Relational Multi-Agent Reinforcement Learning for Dynamic Pricing in High-Speed Railway Markets","In liberalised railway systems, operators must determine prices dynamically under partial observability, while private objectives and performance information remain hidden and regulatory rules prevent competitor communication, making strategic inference difficult for multi-agent reinforcement learning. Standard MARL methods often treat observations as unstructured vectors and ignore the market topology that shapes interactions. A relational entity-graph modelling approach represents operational units and their heterogeneous relations. An extended multi-agent twin delayed DDPG with graph convolution and attention learns robust, high-revenue pricing policies.","arXiv :2607 .05 179v 1 [ cs .LG] 6 Jul 2026  \nRelational Multi-Agent Reinforcement Learning for Dynamic Pricing in High-Speed Railway Markets  \nEnrique Adrian Villarrubia-Martina , David Muñoz-Valerob,∗, Luis Rodriguez-Beniteza , Giovanni Montanac , Luis Jimenez-Linaresa  \na Department of Technologies and Information Systems, Universidad de Castilla-La Mancha, Paseo de la Universidad 4, Ciudad Real, 13071, Spain  \nb Department of Technologies and Information Systems, Universidad de Castilla-La  \nMancha, Avenida Carlos III, s/n, Toledo, 45071, Spain c Warwick Manufacturing Group, University of Warwick, Gibbet Hill  \nRoad, Coventry, CV4 7AL, UK  \nAbstract  \nIn 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.  \n∗ Corresponding author  \nEmail addresses: [enrique.villarrubia@uclm.es](enrique.villarrubia@uclm.es) (Enrique Adrian Villarrubia-Martin), [david.munoz@uclm.es](david.munoz@uclm.es) (David Muñoz-Valero),  \n[luis.rodriguez@uclm.es](luis.rodriguez@uclm.es) (Luis Rodriguez-Benitez), [g.montana@warwick.ac.uk](g.montana@warwick.ac.uk)  \n(Giovanni Montana), [luis.jimenez@uclm.es](luis.jimenez@uclm.es) (Luis Jimenez-Linares)  \nExperimental 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](https://github. com/Kinrre/RelationalRailPricing-RL).  \nKeywords:  \nDynamic Pricing, Multi-Agent Reinforcement Learning, Deep Reinforcement Learning, Graph Neural Networks, Railway Systems  \n1. Introduction  \nThe Multi-Agent Reinforcement Learning (MARL) community has increasingly adopted graph-based approaches to model complex environments [1, 2] . Graphs are a common and very powerful practice to naturally and efficiently capture the structural relations that are fundamental to multi-agent interaction and reasoning [3] . The environments are characterised by a highly dynamic nature, where agents are constantly moving and their neighbourhood relations evolve rapidly, which creates a need for architectures capable of capturing abstract relational representations. Graph Neural Networks (GNNs) are framed as the ideal solution, precisely because they operate natively on graph structures, allowing the learning process to automatically adapt to the changing topology of the environment [4] . As agents modify their connections, GNNs maintain the ability to model interactions through message passing operations, which transforms relational variability from alimitation into an advantage, without the need to adapt the architecture of the model.  \nFocusing on railway systems, the field of application select","cbCaisHf9Fere99o","https://ap.wps.com/l/cbCaisHf9Fere99o","pdf",6243625,1,46,"English","en",105,"# Introduction\n## Graph-based MARL for dynamic relational environments\n## Railway-focused modelling: station graphs vs entity graphs\n## Proposed entity graph framework and relational state learning","[{\"question\":\"Why is dynamic pricing challenging in liberalised high-speed railway markets for multi-agent reinforcement learning?\",\"answer\":\"Because pricing decisions are made under partial observability, operators have private objectives/performance information, and regulations restrict direct communication among competitors, so agents must infer strategic interactions from limited observable market data.\"},{\"question\":\"What limitation of standard MARL approaches does the paper address?\",\"answer\":\"Standard approaches often treat observations as unstructured vectors, neglecting the market topology and structural relations that drive strategic interaction among participants.\"},{\"question\":\"How does the proposed method model the environment and learn representations?\",\"answer\":\"It uses an entity graph where operational units are vertices and heterogeneous edges encode competition, coordination, and connectivity relations. Graph convolutional processing with an attention mechanism produces compact, learnable relational state representations used in an actor-critic framework.\"}]",1784191419,116,{"code":4,"msg":30,"data":31},"ok",{"site_id":24,"language":23,"slug":32,"title":13,"keywords":33,"description":14,"schema_data":34,"social_meta":86,"head_meta":88,"extra_data":90,"updated_unix":27},"relational-multi-agent-reinforcement-learning-for-dynamic-pricing-in-high-speed-railway-markets","",{"@graph":35,"@context":85},[36,53,68],{"@type":37,"itemListElement":38},"BreadcrumbList",[39,43,47,50],{"item":40,"name":41,"@type":42,"position":20},"https://docshare.wps.com","Home","ListItem",{"item":44,"name":45,"@type":42,"position":46},"https://docshare.wps.com/document/","Document",2,{"item":48,"name":12,"@type":42,"position":49},"https://docshare.wps.com/document/research-report/",3,{"item":51,"name":13,"@type":42,"position":52},"https://docshare.wps.com/document/relational-multi-agent-reinforcement-learning-for-dynamic-pricing-in-high-speed-railway-markets/83914/",4,{"url":51,"name":13,"@type":54,"author":55,"headline":13,"publisher":57,"fileFormat":60,"inLanguage":23,"description":14,"dateModified":61,"datePublished":62,"encodingFormat":60,"isAccessibleForFree":63,"interactionStatistic":64},"DigitalDocument",{"name":9,"@type":56},"Person",{"url":40,"name":58,"@type":59},"DocShare","Organization","application/pdf","2026-07-17","2026-07-16",true,{"@type":65,"interactionType":66,"userInteractionCount":20},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71,77,81],{"name":72,"@type":73,"acceptedAnswer":74},"Why is dynamic pricing challenging in liberalised high-speed railway markets for multi-agent reinforcement learning?","Question",{"text":75,"@type":76},"Because pricing decisions are made under partial observability, operators have private objectives/performance information, and regulations restrict direct communication among competitors, so agents must infer strategic interactions from limited observable market data.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"What limitation of standard MARL approaches does the paper address?",{"text":80,"@type":76},"Standard approaches often treat observations as unstructured vectors, neglecting the market topology and structural relations that drive strategic interaction among participants.",{"name":82,"@type":73,"acceptedAnswer":83},"How does the proposed method model the environment and learn representations?",{"text":84,"@type":76},"It uses an entity graph where operational units are vertices and heterogeneous edges encode competition, coordination, and connectivity relations. Graph convolutional processing with an attention mechanism produces compact, learnable relational state representations used in an actor-critic framework.","https://schema.org",{"og:url":51,"og:type":87,"og:title":13,"og:site_name":58,"og:description":14},"article",{"robots":89,"canonical":51},"index,follow",{"doc_id":7,"site_id":24},{"code":4,"msg":5,"data":92},[93,97,101,105,110,115,120,123,128,131,135],{"id":20,"doc_module":4,"doc_module_name":45,"category_name":94,"show_sort_weight":95,"slug":96},"Story & Novel",90,"story-novel",{"id":46,"doc_module":4,"doc_module_name":45,"category_name":98,"show_sort_weight":99,"slug":100},"Literature",80,"literature",{"id":52,"doc_module":4,"doc_module_name":45,"category_name":102,"show_sort_weight":103,"slug":104},"Exam",70,"exam",{"id":106,"doc_module":4,"doc_module_name":45,"category_name":107,"show_sort_weight":108,"slug":109},5,"Comic",60,"comic",{"id":111,"doc_module":4,"doc_module_name":45,"category_name":112,"show_sort_weight":113,"slug":114},6,"Technology",50,"technology",{"id":116,"doc_module":4,"doc_module_name":45,"category_name":117,"show_sort_weight":118,"slug":119},7,"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":45,"category_name":12,"show_sort_weight":121,"slug":122},30,"research-report",{"id":124,"doc_module":4,"doc_module_name":45,"category_name":125,"show_sort_weight":126,"slug":127},9,"Religion & Spirituality",20,"religion-spirituality",{"id":126,"doc_module":4,"doc_module_name":45,"category_name":129,"show_sort_weight":126,"slug":130},"World Cup","world-cup",{"id":132,"doc_module":4,"doc_module_name":45,"category_name":133,"show_sort_weight":132,"slug":134},10,"Lifestyle","lifestyle",{"id":136,"doc_module":4,"doc_module_name":45,"category_name":137,"show_sort_weight":106,"slug":138},19,"General","general"]