{"id":"https://openalex.org/W4407643297","doi":"https://doi.org/10.1287/moor.2023.0148","title":"Linear Mean-Field Games with Discounted Cost","display_name":"Linear Mean-Field Games with Discounted Cost","publication_year":2025,"publication_date":"2025-02-17","ids":{"openalex":"https://openalex.org/W4407643297","doi":"https://doi.org/10.1287/moor.2023.0148"},"language":"en","primary_location":{"id":"doi:10.1287/moor.2023.0148","is_oa":false,"landing_page_url":"https://doi.org/10.1287/moor.2023.0148","pdf_url":null,"source":{"id":"https://openalex.org/S55826652","display_name":"Mathematics of Operations Research","issn_l":"0364-765X","issn":["0364-765X","1526-5471"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315699","host_organization_name":"Institute for Operations Research and the Management Sciences","host_organization_lineage":["https://openalex.org/P4310315699"],"host_organization_lineage_names":["Institute for Operations Research and the Management Sciences"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Operations Research","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/A5029240602","display_name":"Naci Sald\u0131","orcid":"https://orcid.org/0000-0002-2677-7366"},"institutions":[{"id":"https://openalex.org/I168864056","display_name":"Bilkent University","ror":"https://ror.org/02vh8a032","country_code":"TR","type":"education","lineage":["https://openalex.org/I168864056"]}],"countries":["TR"],"is_corresponding":true,"raw_author_name":"Naci Saldi","raw_affiliation_strings":["Department of Mathematics, Bilkent University, Cankaya, 06800 Ankara, Turkey"],"raw_orcid":"https://orcid.org/0000-0002-2677-7366","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Bilkent University, Cankaya, 06800 Ankara, Turkey","institution_ids":["https://openalex.org/I168864056"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5029240602"],"corresponding_institution_ids":["https://openalex.org/I168864056"],"apc_list":null,"apc_paid":null,"fwci":1.9714,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.81445087,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":95},"biblio":{"volume":"51","issue":"1","first_page":"358","last_page":"397"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10067","display_name":"Stochastic processes and financial applications","score":0.9988999962806702,"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":0.9988999962806702,"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/T10541","display_name":"Nonlinear Differential Equations Analysis","score":0.970300018787384,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T12137","display_name":"Economic theories and models","score":0.9616000056266785,"subfield":{"id":"https://openalex.org/subfields/2002","display_name":"Economics and Econometrics"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7984565496444702},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.5275190472602844},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4237551689147949},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.325279176235199},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.32245969772338867}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7984565496444702},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.5275190472602844},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4237551689147949},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.325279176235199},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.32245969772338867},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"score":0.0},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1287/moor.2023.0148","is_oa":false,"landing_page_url":"https://doi.org/10.1287/moor.2023.0148","pdf_url":null,"source":{"id":"https://openalex.org/S55826652","display_name":"Mathematics of Operations Research","issn_l":"0364-765X","issn":["0364-765X","1526-5471"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315699","host_organization_name":"Institute for Operations Research and the Management Sciences","host_organization_lineage":["https://openalex.org/P4310315699"],"host_organization_lineage_names":["Institute for Operations Research and the Management Sciences"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Operations Research","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":39,"referenced_works":["https://openalex.org/W586490843","https://openalex.org/W1559810971","https://openalex.org/W1579743691","https://openalex.org/W1973258650","https://openalex.org/W1976478782","https://openalex.org/W1977377218","https://openalex.org/W1977794212","https://openalex.org/W1983321045","https://openalex.org/W1983997656","https://openalex.org/W1986431940","https://openalex.org/W1997001104","https://openalex.org/W2010654234","https://openalex.org/W2011000015","https://openalex.org/W2013479759","https://openalex.org/W2013876250","https://openalex.org/W2038686546","https://openalex.org/W2056099894","https://openalex.org/W2211095476","https://openalex.org/W2592426095","https://openalex.org/W2888559564","https://openalex.org/W2902676408","https://openalex.org/W2904233225","https://openalex.org/W2911251896","https://openalex.org/W2953246643","https://openalex.org/W2962856092","https://openalex.org/W2963134136","https://openalex.org/W2964034900","https://openalex.org/W3044306006","https://openalex.org/W3048890299","https://openalex.org/W3123224094","https://openalex.org/W3124359942","https://openalex.org/W3130179182","https://openalex.org/W4210364010","https://openalex.org/W4233762729","https://openalex.org/W4288947489","https://openalex.org/W4297852499","https://openalex.org/W4300093168","https://openalex.org/W4301791716","https://openalex.org/W4310300362"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W2142036596","https://openalex.org/W2072657027","https://openalex.org/W2962838298","https://openalex.org/W2600246793"],"abstract_inverted_index":{"In":[0],"this":[1,35],"paper,":[2],"we":[3,84,139],"introduce":[4],"discrete-time":[5],"linear":[6,78,120],"mean-field":[7,48,66,75,79,137],"games":[8,76],"subject":[9],"to":[10],"an":[11,112,157],"infinite-horizon":[12],"discounted-cost":[13],"optimality":[14],"criterion.":[15],"At":[16],"every":[17],"time,":[18],"each":[19,60],"agent":[20,26,61],"is":[21,37,69,94,104,111],"randomly":[22],"coupled":[23],"with":[24,162],"another":[25],"via":[27,39],"their":[28,44],"dynamics":[29],"and":[30,54,77,128,155],"one-stage":[31,56],"cost":[32,57],"function,":[33],"where":[34,107],"randomization":[36],"generated":[38],"the":[40,47,51,55,65,70,87,99,119,129,132,136,141,144],"empirical":[41],"distribution":[42],"of":[43,59,101,115,123,131],"states":[45],"(i.e.,":[46],"term).":[49],"Therefore,":[50],"transition":[52,133],"probability":[53,134],"function":[58,114],"depend":[62],"linearly":[63],"on":[64],"term,":[67,138],"which":[68],"key":[71],"distinction":[72],"between":[73],"classical":[74],"games.":[80],"Under":[81],"mild":[82],"assumptions,":[83],"show":[85],"that":[86],"policy":[88],"obtained":[89],"from":[90],"infinite":[91,145],"population":[92,146],"equilibrium":[93,152,161],"[Formula:":[95,108],"see":[96,109],"text]-Nash":[97],"when":[98],"number":[100],"agents":[102],"N":[103],"sufficiently":[105],"large,":[106],"text]":[110],"explicit":[113],"N.":[116],"Then,":[117],"using":[118],"programming":[121],"formulation":[122],"Markov":[124],"decision":[125],"processes":[126],"(MDPs)":[127],"linearity":[130],"in":[135,143],"formulate":[140],"game":[142],"limit":[147],"as":[148],"a":[149,163],"generalized":[150],"Nash":[151],"problem":[153],"(GNEP)":[154],"establish":[156],"algorithm":[158],"for":[159],"computing":[160],"convergence":[164],"guarantee.":[165]},"counts_by_year":[{"year":2025,"cited_by_count":1}],"updated_date":"2026-02-21T06:11:54.161237","created_date":"2025-10-10T00:00:00"}
