{"id":"https://openalex.org/W1990967271","doi":"https://doi.org/10.1002/net.3230150303","title":"On the relationship between Nash\u2014Cournot and Wardrop equilibria","display_name":"On the relationship between Nash\u2014Cournot and Wardrop equilibria","publication_year":1985,"publication_date":"1985-09-01","ids":{"openalex":"https://openalex.org/W1990967271","doi":"https://doi.org/10.1002/net.3230150303","mag":"1990967271"},"language":"en","primary_location":{"id":"doi:10.1002/net.3230150303","is_oa":false,"landing_page_url":"https://doi.org/10.1002/net.3230150303","pdf_url":null,"source":{"id":"https://openalex.org/S191798613","display_name":"Networks","issn_l":"0028-3045","issn":["0028-3045","1097-0037"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Networks","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5027356151","display_name":"Alain Haurie","orcid":"https://orcid.org/0000-0002-5731-2772"},"institutions":[{"id":"https://openalex.org/I108192572","display_name":"HEC Montr\u00e9al","ror":"https://ror.org/05ww3wq27","country_code":"CA","type":"education","lineage":["https://openalex.org/I108192572"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"A. Haurie","raw_affiliation_strings":["Ecole des Hautes Etudes Commerciales, Montreal, Quebec, Canada H3T 1V6"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Ecole des Hautes Etudes Commerciales, Montreal, Quebec, Canada H3T 1V6","institution_ids":["https://openalex.org/I108192572"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5102990491","display_name":"Patrice Marcotte","orcid":"https://orcid.org/0000-0002-1935-2554"},"institutions":[{"id":"https://openalex.org/I108192572","display_name":"HEC Montr\u00e9al","ror":"https://ror.org/05ww3wq27","country_code":"CA","type":"education","lineage":["https://openalex.org/I108192572"]},{"id":"https://openalex.org/I4210163602","display_name":"Royal Military College Saint-Jean","ror":"https://ror.org/05mkwhv74","country_code":"CA","type":"education","lineage":["https://openalex.org/I4210163602"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"P. Marcotte","raw_affiliation_strings":["Colle\u0300ge Militaire Royal de St-Jean, St-Jean, Que\u0301bec, Canada J0J 1R0","Ecole des Hautes Etudes Commerciales, Montreal, Quebec, Canada H3T 1V6"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Colle\u0300ge Militaire Royal de St-Jean, St-Jean, Que\u0301bec, Canada J0J 1R0","institution_ids":["https://openalex.org/I4210163602"]},{"raw_affiliation_string":"Ecole des Hautes Etudes Commerciales, Montreal, Quebec, Canada H3T 1V6","institution_ids":["https://openalex.org/I108192572"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":3400,"currency":"USD","value_usd":3400},"apc_paid":null,"fwci":35.7475,"has_fulltext":false,"cited_by_count":331,"citation_normalized_percentile":{"value":0.99623234,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":100},"biblio":{"volume":"15","issue":"3","first_page":"295","last_page":"308"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10698","display_name":"Transportation Planning and Optimization","score":0.9998000264167786,"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"}},"topics":[{"id":"https://openalex.org/T10698","display_name":"Transportation Planning and Optimization","score":0.9998000264167786,"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"}},{"id":"https://openalex.org/T10524","display_name":"Traffic control and management","score":0.9811999797821045,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10298","display_name":"Urban Transport and Accessibility","score":0.9811000227928162,"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/cournot-competition","display_name":"Cournot competition","score":0.8455544710159302},{"id":"https://openalex.org/keywords/uniqueness","display_name":"Uniqueness","score":0.8225584030151367},{"id":"https://openalex.org/keywords/nash-equilibrium","display_name":"Nash equilibrium","score":0.7919760346412659},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.729749858379364},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4938989281654358},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.48487386107444763},{"id":"https://openalex.org/keywords/best-response","display_name":"Best response","score":0.42703455686569214},{"id":"https://openalex.org/keywords/economics","display_name":"Economics","score":0.3955515921115875}],"concepts":[{"id":"https://openalex.org/C16520705","wikidata":"https://www.wikidata.org/wiki/Q601799","display_name":"Cournot competition","level":2,"score":0.8455544710159302},{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.8225584030151367},{"id":"https://openalex.org/C46814582","wikidata":"https://www.wikidata.org/wiki/Q23389","display_name":"Nash equilibrium","level":2,"score":0.7919760346412659},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.729749858379364},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4938989281654358},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.48487386107444763},{"id":"https://openalex.org/C32407928","wikidata":"https://www.wikidata.org/wiki/Q2733833","display_name":"Best response","level":3,"score":0.42703455686569214},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.3955515921115875},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1002/net.3230150303","is_oa":false,"landing_page_url":"https://doi.org/10.1002/net.3230150303","pdf_url":null,"source":{"id":"https://openalex.org/S191798613","display_name":"Networks","issn_l":"0028-3045","issn":["0028-3045","1097-0037"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Networks","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/8","display_name":"Decent work and economic growth","score":0.5}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":27,"referenced_works":["https://openalex.org/W1972221945","https://openalex.org/W1972868509","https://openalex.org/W1981267404","https://openalex.org/W1986598958","https://openalex.org/W1994621621","https://openalex.org/W2006122291","https://openalex.org/W2023736708","https://openalex.org/W2024936298","https://openalex.org/W2025565923","https://openalex.org/W2033619170","https://openalex.org/W2039230544","https://openalex.org/W2042114124","https://openalex.org/W2047382992","https://openalex.org/W2067186438","https://openalex.org/W2071609006","https://openalex.org/W2078338432","https://openalex.org/W2078433128","https://openalex.org/W2081255621","https://openalex.org/W2125913552","https://openalex.org/W2156920109","https://openalex.org/W2177295793","https://openalex.org/W2738992722","https://openalex.org/W3142300713","https://openalex.org/W3217016363","https://openalex.org/W4231269780","https://openalex.org/W4235413659","https://openalex.org/W4238881924"],"related_works":["https://openalex.org/W2803931294","https://openalex.org/W4389370903","https://openalex.org/W2282604764","https://openalex.org/W1554758635","https://openalex.org/W2245247999","https://openalex.org/W2500870930","https://openalex.org/W2354539280","https://openalex.org/W2955320052","https://openalex.org/W4248623114","https://openalex.org/W3119844974"],"abstract_inverted_index":{"Abstract":[0],"A":[1,29],"noncooperative":[2],"game":[3],"is":[4,32,52],"formulated":[5],"on":[6],"a":[7,60,66],"transportation":[8],"network":[9],"with":[10,16],"congestion.":[11],"The":[12,45],"players":[13],"are":[14,20,43],"associated":[15],"origin\u2010destination":[17],"pairs,":[18],"and":[19,34,38],"facing":[21],"demand":[22],"functions":[23],"at":[24],"their":[25],"respective":[26],"destination":[27],"nodes.":[28],"Nash\u2010Cournot":[30,50],"equilibrium":[31,51],"defined":[33],"conditions":[35],"for":[36],"existence":[37],"uniqueness":[39],"of":[40,48],"this":[41],"solution":[42],"provided.":[44],"asymptotic":[46],"behavior":[47],"the":[49],"then":[53],"shown":[54],"to":[55,65],"yield":[56],"(under":[57],"appropriate":[58],"assumptions)":[59],"total":[61],"flow":[62],"vector":[63],"corresponding":[64],"Wardrop":[67],"equilibrium.":[68]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":9},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":9},{"year":2021,"cited_by_count":9},{"year":2020,"cited_by_count":19},{"year":2019,"cited_by_count":16},{"year":2018,"cited_by_count":14},{"year":2017,"cited_by_count":12},{"year":2016,"cited_by_count":21},{"year":2015,"cited_by_count":14},{"year":2014,"cited_by_count":19},{"year":2013,"cited_by_count":14},{"year":2012,"cited_by_count":8}],"updated_date":"2026-06-23T06:36:01.041984","created_date":"2025-10-10T00:00:00"}