{"id":"https://openalex.org/W4404573808","doi":"https://doi.org/10.1007/s10957-025-02706-4","title":"Nash Equilibria in Traffic Networks with Multiple Populations and Origins\u2013Destinations","display_name":"Nash Equilibria in Traffic Networks with Multiple Populations and Origins\u2013Destinations","publication_year":2025,"publication_date":"2025-05-26","ids":{"openalex":"https://openalex.org/W4404573808","doi":"https://doi.org/10.1007/s10957-025-02706-4"},"language":"en","primary_location":{"id":"doi:10.1007/s10957-025-02706-4","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10957-025-02706-4","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10957-025-02706-4.pdf","source":{"id":"https://openalex.org/S52430896","display_name":"Journal of Optimization Theory and Applications","issn_l":"0022-3239","issn":["0022-3239","1573-2878"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Optimization Theory and Applications","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s10957-025-02706-4.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5088590159","display_name":"Rinaldo M. Colombo","orcid":"https://orcid.org/0000-0003-0459-585X"},"institutions":[{"id":"https://openalex.org/I2802148964","display_name":"Istituto Nazionale di Alta Matematica Francesco Severi","ror":"https://ror.org/01vx64p53","country_code":"IT","type":"funder","lineage":["https://openalex.org/I2802148964"]},{"id":"https://openalex.org/I79940851","display_name":"University of Brescia","ror":"https://ror.org/02q2d2610","country_code":"IT","type":"education","lineage":["https://openalex.org/I79940851"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"Rinaldo M. Colombo","raw_affiliation_strings":["INdAM Unit & Department of Information Engineering, University of Brescia, Brescia, Italy"],"raw_orcid":"https://orcid.org/0000-0003-0459-585X","affiliations":[{"raw_affiliation_string":"INdAM Unit & Department of Information Engineering, University of Brescia, Brescia, Italy","institution_ids":["https://openalex.org/I79940851","https://openalex.org/I2802148964"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5075036741","display_name":"Luca Giuzzi","orcid":"https://orcid.org/0000-0003-3975-7281"},"institutions":[{"id":"https://openalex.org/I79940851","display_name":"University of Brescia","ror":"https://ror.org/02q2d2610","country_code":"IT","type":"education","lineage":["https://openalex.org/I79940851"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Luca Giuzzi","raw_affiliation_strings":["DICATAM, University of Brescia, Brescia, Italy"],"raw_orcid":"https://orcid.org/0000-0003-3975-7281","affiliations":[{"raw_affiliation_string":"DICATAM, University of Brescia, Brescia, Italy","institution_ids":["https://openalex.org/I79940851"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5010070467","display_name":"Francesca Marcellini","orcid":"https://orcid.org/0000-0003-1619-6565"},"institutions":[{"id":"https://openalex.org/I2802148964","display_name":"Istituto Nazionale di Alta Matematica Francesco Severi","ror":"https://ror.org/01vx64p53","country_code":"IT","type":"funder","lineage":["https://openalex.org/I2802148964"]},{"id":"https://openalex.org/I79940851","display_name":"University of Brescia","ror":"https://ror.org/02q2d2610","country_code":"IT","type":"education","lineage":["https://openalex.org/I79940851"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Francesca Marcellini","raw_affiliation_strings":["INdAM Unit & Department of Information Engineering, University of Brescia, Brescia, Italy"],"raw_orcid":"https://orcid.org/0000-0003-1619-6565","affiliations":[{"raw_affiliation_string":"INdAM Unit & Department of Information Engineering, University of Brescia, Brescia, Italy","institution_ids":["https://openalex.org/I79940851","https://openalex.org/I2802148964"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5088590159"],"corresponding_institution_ids":["https://openalex.org/I2802148964","https://openalex.org/I79940851"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":{"value":2390,"currency":"EUR","value_usd":2990},"fwci":1.3614,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.77346686,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":95,"max":97},"biblio":{"volume":"206","issue":"2","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11031","display_name":"Game Theory and Applications","score":0.9865000247955322,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T11031","display_name":"Game Theory and Applications","score":0.9865000247955322,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T12592","display_name":"Opinion Dynamics and Social Influence","score":0.9818000197410583,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10698","display_name":"Transportation Planning and Optimization","score":0.977400004863739,"subfield":{"id":"https://openalex.org/subfields/3313","display_name":"Transportation"},"field":{"id":"https://openalex.org/fields/33","display_name":"Social Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/nash-equilibrium","display_name":"Nash equilibrium","score":0.6091813445091248},{"id":"https://openalex.org/keywords/destinations","display_name":"Destinations","score":0.5782070159912109},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.46046990156173706},{"id":"https://openalex.org/keywords/economic-geography","display_name":"Economic geography","score":0.3681439161300659},{"id":"https://openalex.org/keywords/computer-network","display_name":"Computer network","score":0.334030419588089},{"id":"https://openalex.org/keywords/geography","display_name":"Geography","score":0.3127228617668152},{"id":"https://openalex.org/keywords/economics","display_name":"Economics","score":0.2595682144165039},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.23721250891685486},{"id":"https://openalex.org/keywords/tourism","display_name":"Tourism","score":0.058615922927856445}],"concepts":[{"id":"https://openalex.org/C46814582","wikidata":"https://www.wikidata.org/wiki/Q23389","display_name":"Nash equilibrium","level":2,"score":0.6091813445091248},{"id":"https://openalex.org/C2776687071","wikidata":"https://www.wikidata.org/wiki/Q5265193","display_name":"Destinations","level":3,"score":0.5782070159912109},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.46046990156173706},{"id":"https://openalex.org/C26271046","wikidata":"https://www.wikidata.org/wiki/Q187097","display_name":"Economic geography","level":1,"score":0.3681439161300659},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.334030419588089},{"id":"https://openalex.org/C205649164","wikidata":"https://www.wikidata.org/wiki/Q1071","display_name":"Geography","level":0,"score":0.3127228617668152},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.2595682144165039},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.23721250891685486},{"id":"https://openalex.org/C18918823","wikidata":"https://www.wikidata.org/wiki/Q49389","display_name":"Tourism","level":2,"score":0.058615922927856445},{"id":"https://openalex.org/C166957645","wikidata":"https://www.wikidata.org/wiki/Q23498","display_name":"Archaeology","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1007/s10957-025-02706-4","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10957-025-02706-4","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10957-025-02706-4.pdf","source":{"id":"https://openalex.org/S52430896","display_name":"Journal of Optimization Theory and Applications","issn_l":"0022-3239","issn":["0022-3239","1573-2878"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Optimization Theory and Applications","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2411.12416","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2411.12416","pdf_url":"https://arxiv.org/pdf/2411.12416","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:RePEc:spr:joptap:v:206:y:2025:i:2:d:10.1007_s10957-025-02706-4","is_oa":false,"landing_page_url":"http://link.springer.com/10.1007/s10957-025-02706-4","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},{"id":"pmh:oai:iris.unibs.it:11379/627126","is_oa":true,"landing_page_url":"https://link.springer.com/article/10.1007/s10957-025-02706-4","pdf_url":null,"source":{"id":"https://openalex.org/S4306400804","display_name":"Institutional Research Information System (Universit\u00e0 degli Studi di Brescia)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I66752286","host_organization_name":"University of Milano-Bicocca","host_organization_lineage":["https://openalex.org/I66752286"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"},{"id":"doi:10.48550/arxiv.2411.12416","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2411.12416","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.1007/s10957-025-02706-4","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10957-025-02706-4","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10957-025-02706-4.pdf","source":{"id":"https://openalex.org/S52430896","display_name":"Journal of Optimization Theory and Applications","issn_l":"0022-3239","issn":["0022-3239","1573-2878"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Optimization Theory and Applications","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1145458839","display_name":null,"funder_award_id":"PRIN 2022","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G4105856276","display_name":null,"funder_award_id":"D53D23005620006","funder_id":"https://openalex.org/F4320311030","funder_display_name":"Istituto Nazionale di Alta Matematica \"Francesco Severi\""},{"id":"https://openalex.org/G5245466801","display_name":null,"funder_award_id":"PRIN 2022","funder_id":"https://openalex.org/F4320311030","funder_display_name":"Istituto Nazionale di Alta Matematica \"Francesco Severi\""}],"funders":[{"id":"https://openalex.org/F4320311030","display_name":"Istituto Nazionale di Alta Matematica \"Francesco Severi\"","ror":"https://ror.org/01vx64p53"},{"id":"https://openalex.org/F4320320300","display_name":"European Commission","ror":"https://ror.org/00k4n6c32"},{"id":"https://openalex.org/F4320324342","display_name":"Universit\u00e0 degli Studi di Brescia","ror":"https://ror.org/02q2d2610"},{"id":"https://openalex.org/F4320333369","display_name":"Gruppo Nazionale per l'Analisi Matematica, la Probabilit\u00e0 e le loro Applicazioni","ror":null},{"id":"https://openalex.org/F4320334045","display_name":"Gruppo Nazionale per le Strutture Algebriche, Geometriche e le loro Applicazioni","ror":null}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4404573808.pdf","grobid_xml":"https://content.openalex.org/works/W4404573808.grobid-xml"},"referenced_works_count":26,"referenced_works":["https://openalex.org/W2944036579","https://openalex.org/W4398226219","https://openalex.org/W2119826175","https://openalex.org/W2793666581","https://openalex.org/W2008670272","https://openalex.org/W2001641747","https://openalex.org/W3033770074","https://openalex.org/W2006122291","https://openalex.org/W2002373723","https://openalex.org/W3142588439","https://openalex.org/W1990967271","https://openalex.org/W2767328560","https://openalex.org/W2094238774","https://openalex.org/W2033333697","https://openalex.org/W2964008208","https://openalex.org/W2143262013","https://openalex.org/W4234761190","https://openalex.org/W2508573783","https://openalex.org/W1204325716","https://openalex.org/W4280571466","https://openalex.org/W2966664308","https://openalex.org/W2029456721","https://openalex.org/W4297563113","https://openalex.org/W2575731723","https://openalex.org/W2177295793","https://openalex.org/W4283701218"],"related_works":["https://openalex.org/W2748952813","https://openalex.org/W2087230580","https://openalex.org/W3087436147","https://openalex.org/W3133610079","https://openalex.org/W3006305005","https://openalex.org/W616705024","https://openalex.org/W1592965586","https://openalex.org/W2050388307","https://openalex.org/W1604685102","https://openalex.org/W2612871816"],"abstract_inverted_index":{"Abstract":[0],"Different":[1],"populations":[2],"of":[3,28,31,39,64],"vehicles":[4],"travel":[5,16,33],"along":[6],"a":[7,40],"network.":[8],"Each":[9],"population":[10],"has":[11],"its":[12,48],"origin,":[13],"destination":[14],"and":[15],"costs":[17],"\u2014":[18],"which":[19],"may":[20],"well":[21],"be":[22],"unbounded.":[23],"Under":[24],"the":[25,29,32,37],"only":[26],"requirement":[27],"continuity":[30],"costs,":[34],"we":[35],"prove":[36],"existence":[38],"Nash":[41],"equilibrium":[42],"for":[43,47],"all":[44],"populations.":[45],"Conditions":[46],"uniqueness":[49],"are":[50,56],"also":[51],"provided.":[52],"A":[53],"few":[54],"cases":[55],"treated":[57],"in":[58],"detail":[59],"to":[60],"show":[61],"specific":[62],"situations":[63],"interest.":[65]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-07-03T08:13:44.112507","created_date":"2024-11-21T00:00:00"}