{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/congestion-aware-motion-planning-game-with","title":"Congestion-aware path coordination game with Markov decision process dynamics","arxiv_id":"2203.12133","date":"2022-03-23","proceeding":null,"authors":["Sarah H. Q. Li","Dan Calderone","Behcet Acikmese"],"abstract":"Inspired by the path coordination problem arising from robo-taxis, warehouse management, and mixed-vehicle routing problems, we model a group of heterogeneous players responding to stochastic demands as a congestion game under Markov decision process dynamics. Players share a common state-action space but have unique transition dynamics, and each player's unique cost is a {function} of the joint state-action probability distribution. For a class of player cost functions, we formulate the player-specific optimization problem, prove the equivalence between the Nash equilibrium and the solution of a potential minimization problem, and derive dynamic programming approaches to solve the Nash equilibrium. We apply this game to model multi-agent path coordination and introduce congestion-based cost functions that enable players to complete individual tasks while avoiding congestion with their opponents. Finally, we present a learning algorithm for finding the Nash equilibrium that has linear complexity in the number of players. We demonstrate our game model on a multi-robot warehouse \\change{path coordination problem}, in which robots autonomously retrieve and deliver packages while avoiding congested paths.","url_abs":"https://arxiv.org/abs/2203.12133v2","url_pdf":"https://arxiv.org/pdf/2203.12133v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"congestion-aware-motion-planning-game-with","repo_url":"https://github.com/lisarah/mdp_path_coordination","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}