{"id":"https://openalex.org/W4400660716","doi":"https://doi.org/10.1137/23m1608100","title":"Long-Time Behavior of Deterministic Mean Field Games with Nonmonotone Interactions","display_name":"Long-Time Behavior of Deterministic Mean Field Games with Nonmonotone Interactions","publication_year":2024,"publication_date":"2024-07-15","ids":{"openalex":"https://openalex.org/W4400660716","doi":"https://doi.org/10.1137/23m1608100"},"language":"en","primary_location":{"id":"doi:10.1137/23m1608100","is_oa":false,"landing_page_url":"https://doi.org/10.1137/23m1608100","pdf_url":null,"source":{"id":"https://openalex.org/S74141806","display_name":"SIAM Journal on Mathematical Analysis","issn_l":"0036-1410","issn":["0036-1410","1095-7154"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Mathematical Analysis","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://hdl.handle.net/11577/3525166","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5034471452","display_name":"Martino Bardi","orcid":"https://orcid.org/0000-0002-4342-268X"},"institutions":[{"id":"https://openalex.org/I138689650","display_name":"University of Padua","ror":"https://ror.org/00240q980","country_code":"IT","type":"education","lineage":["https://openalex.org/I138689650"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"Martino Bardi","raw_affiliation_strings":["Department of Mathematics \u201cT. Levi-Civita,\u201d University of Padova, via Trieste, 63, I-35121 Padova, Italy"],"raw_orcid":"https://orcid.org/0000-0002-4342-268X","affiliations":[{"raw_affiliation_string":"Department of Mathematics \u201cT. Levi-Civita,\u201d University of Padova, via Trieste, 63, I-35121 Padova, Italy","institution_ids":["https://openalex.org/I138689650"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5036280716","display_name":"Hicham Kouhkouh","orcid":"https://orcid.org/0000-0002-2632-448X"},"institutions":[{"id":"https://openalex.org/I887968799","display_name":"RWTH Aachen University","ror":"https://ror.org/04xfq0f34","country_code":"DE","type":"education","lineage":["https://openalex.org/I887968799"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Hicham Kouhkouh","raw_affiliation_strings":["RWTH Aachen University, Institut f\u00fcr Mathematik, RTG Energy, Entropy, and Dissipative Dynamics, Templergraben 55 (111810), 52062, Aachen, Germany. Current address: Department of Mathematics and Scientific Computing, NAWI, University of Graz, 8010, Graz, Austria"],"raw_orcid":"https://orcid.org/0000-0002-2632-448X","affiliations":[{"raw_affiliation_string":"RWTH Aachen University, Institut f\u00fcr Mathematik, RTG Energy, Entropy, and Dissipative Dynamics, Templergraben 55 (111810), 52062, Aachen, Germany. Current address: Department of Mathematics and Scientific Computing, NAWI, University of Graz, 8010, Graz, Austria","institution_ids":["https://openalex.org/I887968799"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5034471452"],"corresponding_institution_ids":["https://openalex.org/I138689650"],"apc_list":null,"apc_paid":null,"fwci":3.0946,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.91902368,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":96,"max":99},"biblio":{"volume":"56","issue":"4","first_page":"5079","last_page":"5098"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10067","display_name":"Stochastic processes and financial applications","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/2003","display_name":"Finance"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T10067","display_name":"Stochastic processes and financial applications","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/2003","display_name":"Finance"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.9955999851226807,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11829","display_name":"Mathematical Biology Tumor Growth","score":0.993399977684021,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8175187110900879},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.49321693181991577},{"id":"https://openalex.org/keywords/field","display_name":"Field (mathematics)","score":0.4389435052871704},{"id":"https://openalex.org/keywords/mean-field-theory","display_name":"Mean field theory","score":0.43688198924064636},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4345093369483948},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.3384212553501129},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3234803080558777},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.14306315779685974},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.1068088710308075}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8175187110900879},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.49321693181991577},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.4389435052871704},{"id":"https://openalex.org/C202213908","wikidata":"https://www.wikidata.org/wiki/Q626011","display_name":"Mean field theory","level":2,"score":0.43688198924064636},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4345093369483948},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.3384212553501129},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3234803080558777},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.14306315779685974},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1068088710308075},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/23m1608100","is_oa":false,"landing_page_url":"https://doi.org/10.1137/23m1608100","pdf_url":null,"source":{"id":"https://openalex.org/S74141806","display_name":"SIAM Journal on Mathematical Analysis","issn_l":"0036-1410","issn":["0036-1410","1095-7154"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Mathematical Analysis","raw_type":"journal-article"},{"id":"pmh:oai:www.research.unipd.it:11577/3525166","is_oa":true,"landing_page_url":"https://hdl.handle.net/11577/3525166","pdf_url":null,"source":{"id":"https://openalex.org/S4377196283","display_name":"Research Padua  Archive (University of Padua)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I138689650","host_organization_name":"University of Padua","host_organization_lineage":["https://openalex.org/I138689650"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:www.research.unipd.it:11577/3525166","is_oa":true,"landing_page_url":"https://hdl.handle.net/11577/3525166","pdf_url":null,"source":{"id":"https://openalex.org/S4377196283","display_name":"Research Padua  Archive (University of Padua)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I138689650","host_organization_name":"University of Padua","host_organization_lineage":["https://openalex.org/I138689650"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G171175040","display_name":null,"funder_award_id":"320021702/GRK2326","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G3346728545","display_name":null,"funder_award_id":"CRG2021-4674","funder_id":"https://openalex.org/F4320322320","funder_display_name":"King Abdullah University of Science and Technology"}],"funders":[{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"},{"id":"https://openalex.org/F4320322320","display_name":"King Abdullah University of Science and Technology","ror":"https://ror.org/01q3tbs38"},{"id":"https://openalex.org/F4320333369","display_name":"Gruppo Nazionale per l'Analisi Matematica, la Probabilit\u00e0 e le loro Applicazioni","ror":null}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":37,"referenced_works":["https://openalex.org/W1487586009","https://openalex.org/W1522579744","https://openalex.org/W1951267103","https://openalex.org/W1988313155","https://openalex.org/W2001209238","https://openalex.org/W2038686546","https://openalex.org/W2077743708","https://openalex.org/W2119707575","https://openalex.org/W2191482861","https://openalex.org/W2282360864","https://openalex.org/W2504932549","https://openalex.org/W2594297941","https://openalex.org/W2619441451","https://openalex.org/W2755331706","https://openalex.org/W2791784110","https://openalex.org/W2884088755","https://openalex.org/W2890024345","https://openalex.org/W2977953343","https://openalex.org/W3023486662","https://openalex.org/W3082044992","https://openalex.org/W3083240464","https://openalex.org/W3098467712","https://openalex.org/W3098636910","https://openalex.org/W3101852205","https://openalex.org/W3104281263","https://openalex.org/W3104707106","https://openalex.org/W3119203894","https://openalex.org/W3170277341","https://openalex.org/W3180237281","https://openalex.org/W3205280976","https://openalex.org/W3212285838","https://openalex.org/W4210718478","https://openalex.org/W4230008158","https://openalex.org/W4301264158","https://openalex.org/W4360980644","https://openalex.org/W4361225955","https://openalex.org/W4362630994"],"related_works":["https://openalex.org/W2938786841","https://openalex.org/W2004478840","https://openalex.org/W2982120024","https://openalex.org/W4388553927","https://openalex.org/W2038629209","https://openalex.org/W2059761707","https://openalex.org/W2320117397","https://openalex.org/W2040944759","https://openalex.org/W4380147916","https://openalex.org/W4283749635"],"abstract_inverted_index":{"We":[0,32,111],"consider":[1],"deterministic":[2],"mean":[3],"field":[4],"games":[5],"(MFGs)":[6],"in":[7,28],"all":[8,106],"Euclidean":[9],"space":[10],"with":[11,16,39,62,79],"a":[12,29,41,51,127],"cost":[13,42,80,98],"functional":[14,81],"continuous":[15],"respect":[17],"to":[18,75,126,141,144],"the":[19,22,36,54,63,69,73,88,97,100,109,113,116,119,123,130,135,138],"distribution":[20,117],"of":[21,53,58,72,103,115,118,122,129,137,147,151],"agents":[23,120],"and":[24,46,121],"attaining":[25],"its":[26],"minima":[27,104],"compact":[30],"set.":[31],"first":[33,59],"show":[34],"that":[35,96],"static":[37],"MFG":[38,56,132],"such":[40],"has":[43,99],"an":[44],"equilibrium,":[45],"we":[47,67,94],"build":[48],"from":[49],"it":[50],"solution":[52,128],"ergodic":[55,131],"system":[57,133],"order":[60],"PDEs":[61],"same":[64,101],"cost.":[65],"Next":[66],"address":[68],"long-time":[70],"limit":[71],"solutions":[74],"finite":[76],"horizon":[77,136],"MFGs":[78,148],"satisfying":[82],"various":[83],"additional":[84],"assumptions,":[85],"but":[86],"not":[87],"classical":[89],"Lasry-Lions":[90],"monotonicity":[91],"condition.":[92],"Instead":[93],"assume":[95],"set":[102],"for":[105],"measures":[107],"describing":[108],"population.":[110],"prove":[112],"convergence":[114],"value":[124],"function":[125],"as":[134],"game":[139],"tends":[140],"infinity,":[142],"extending":[143],"this":[145],"class":[146],"some":[149],"results":[150],"weak":[152],"KAM":[153],"theory.":[154]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2024,"cited_by_count":3}],"updated_date":"2026-04-28T14:05:53.105641","created_date":"2024-07-16T00:00:00"}