[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-83731-en":3,"doc-seo-83731-105":30,"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":21,"is_downloadable":21,"audit_status":21,"page_count":22,"language":23,"language_code":24,"site_id":25,"html_lang":24,"table_of_contents":26,"faqs":27,"seo_title":13,"seo_description":14,"update_tm":28,"read_time":29},83731,549758252649,"Ivy","https://ap-avatar.wpscdn.com/avatar/8000253669c5317157?_k=1778319167496531819",8,"Research & Report","Congestion Games with Heterogeneous Valuations: An Optimal Transport Approach","Emerging urban mobility and logistics settings involve agents with heterogeneous destination valuations who compete for shared congested resources such as charging stations, delivery hubs, or cloud services. Existing congestion-game and resource-allocation models fail to jointly represent multidimensional destination preferences and aggregate congestion externalities. A new nonatomic congestion game framework models destination valuations on a measure space, characterizes Nash equilibria and social optima, and yields finite-dimensional threshold-vector representations via dual potentials. The analysis uses Kantorovich duality to provide a geometric view and partitions the valuation space that determines choices.","arXiv :2607 .03625v 1 [ cs .GT] 3 Jul 2026  \nCongestion Games with Heterogeneous Valuations: An Optimal Transport Approach  \nPan-Yang Su 1[0000−0003−2551−828X], Negar Mehr2[0000−0002−1045−4423], and Shankar Sastry 1[0009−0000−9021−7235]  \n1 Department of Electrical Engineering and Computer Sciences, University of  \nCalifornia, Berkeley, Berkeley, CA 94720, USA [pan_yang_su@berkeley.edu](pan_yang_su@berkeley.edu) , [sastry@eecs.berkeley.edu](sastry@eecs.berkeley.edu)  \n2 Department of Mechanical Engineering, University of California, Berkeley,  \nBerkeley, CA 94720, USA  \n[negar@berkeley.edu](negar@berkeley.edu)  \nAbstract. In emerging urban mobility and logistics applications, such as advanced air mobility, electric vehicle charging, and shared service systems, agents with heterogeneous valuations choose among multiple destinations while sharing congested network resources. However, existing congestion game and resource allocation models do not simultaneously capture heterogeneous destination preferences and aggregate congestion externalities. We introduce a new nonatomic congestion game framework in which agents are endowed with heterogeneous destination valuations modeled by a measure space. We characterize Nash equilibria and social optima in this setting and show that both admit finite-dimensional representations in terms of threshold vectors and dual potentials. These structures induce a partition of the valuation space that determines agents’destination choices. Our analysis leverages Kantorovich duality from optimal transport theory and provides a new geometric perspective on congestion games with heterogeneous valuations.  \nKeywords: Congestion games · Semi-discrete matching · Optimal transport.  \n1 Introduction  \nA New Congestion Game Model. In everyday commuting, travelers choose among different destinations (e.g., restaurants, tourist spots, supermarkets) based on their heterogeneous valuations, traffic conditions, and the limited capacity of the destinations themselves. For example, when electric vehicle owners need to charge, they select stations by weighing specific destination activities and travel times against the hard limits of available charging plugs. Similarly, in service systems such as delivery hubs or cloud servers, users choose among service locations with different types or prices, where increased demand leads to longer delays and strict resource capacities must be respected.  \nIn all these scenarios, an agent’s utility can be modeled by the difference between their heterogeneous valuation of a destination and the delay induced by  \n2 P.-Y. Su et al.  \ncongestion. However, despite their common structure, these problems cannot be directly captured by classical models. Congestion games handle aggregate delaysand route choices but typically assume homogeneous agents or one-dimensional valuation distribution. Conversely, resource allocation and matching models accommodate heterogeneous valuations but abstract away from endogenous congestion. To bridge this gap, we propose a new congestion game model that explicitly integrates multidimensional, agent-specific valuations with aggregate, endogenous congestion and strict resource capacities.  \nTheoretical Contributions. Our framework bridges two classical lines of research: nonatomic congestion games [36, 37] and semi-discrete matching problems [4, 48] . Combining heterogeneous valuations and aggregate congestion externalities from these two models requires new techniques. In classical congestion games [36, 37], agents are homogeneous, allowing the characterization of Nash equilibria and social optima to be solved via finite-dimensional convex optimization. Even when heterogeneous agents are introduced via elastic demand [13], their types are typically one-dimensional, which permits a straightforward threshold argument (high-valuation agents vs. low-valuation agents) .  \nIn our model, however, agents choose among multiple destinations, making valuations multid","cbCaioRKypUuXPrf","https://ap.wps.com/l/cbCaioRKypUuXPrf","pdf",787033,2,1,37,"English","en",105,"# Introduction\n## A New Congestion Game Model\n## Theoretical Contributions\n## An Emerging Application","[{\"question\":\"What problem does the paper address in congestion game modeling?\",\"answer\":\"It addresses how to model agents with heterogeneous, multidimensional destination preferences while also capturing aggregate congestion externalities and strict capacity limits.\"},{\"question\":\"How does the proposed framework represent heterogeneous destination valuations?\",\"answer\":\"It models agents’ destination valuations using a measure space within a new nonatomic congestion game framework.\"},{\"question\":\"What mathematical tool does the paper use to characterize equilibria and optima?\",\"answer\":\"It leverages Kantorovich duality from optimal transport theory, leading to finite-dimensional representations through threshold vectors and dual 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problem does the paper address in congestion game modeling?","Question",{"text":75,"@type":76},"It addresses how to model agents with heterogeneous, multidimensional destination preferences while also capturing aggregate congestion externalities and strict capacity limits.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"How does the proposed framework represent heterogeneous destination valuations?",{"text":80,"@type":76},"It models agents’ destination valuations using a measure space within a new nonatomic congestion game framework.",{"name":82,"@type":73,"acceptedAnswer":83},"What mathematical tool does the paper use to characterize equilibria and optima?",{"text":84,"@type":76},"It leverages Kantorovich duality from optimal transport theory, leading to finite-dimensional representations through threshold vectors and dual 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