{"id":"https://openalex.org/W4410233669","doi":"https://doi.org/10.1287/moor.2024.0478","title":"Asymptotic Nash Equilibria of Finite-State Ergodic Markovian Mean Field Games","display_name":"Asymptotic Nash Equilibria of Finite-State Ergodic Markovian Mean Field Games","publication_year":2025,"publication_date":"2025-05-09","ids":{"openalex":"https://openalex.org/W4410233669","doi":"https://doi.org/10.1287/moor.2024.0478"},"language":"en","primary_location":{"id":"doi:10.1287/moor.2024.0478","is_oa":false,"landing_page_url":"https://doi.org/10.1287/moor.2024.0478","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/A5014923299","display_name":"Asaf Cohen","orcid":"https://orcid.org/0000-0002-9211-7956"},"institutions":[{"id":"https://openalex.org/I27837315","display_name":"University of Michigan","ror":"https://ror.org/00jmfr291","country_code":"US","type":"education","lineage":["https://openalex.org/I27837315"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Asaf Cohen","raw_affiliation_strings":["Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109"],"raw_orcid":"https://orcid.org/0000-0002-9211-7956","affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109","institution_ids":["https://openalex.org/I27837315"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5013885947","display_name":"Ethan Zell","orcid":"https://orcid.org/0000-0002-8363-8418"},"institutions":[{"id":"https://openalex.org/I27837315","display_name":"University of Michigan","ror":"https://ror.org/00jmfr291","country_code":"US","type":"education","lineage":["https://openalex.org/I27837315"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Ethan Zell","raw_affiliation_strings":["Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109","institution_ids":["https://openalex.org/I27837315"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I27837315"],"apc_list":null,"apc_paid":null,"fwci":4.6502,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.93907547,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":91,"max":98},"biblio":{"volume":"51","issue":"2","first_page":"1139","last_page":"1173"},"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/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.9944000244140625,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.9909999966621399,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8564507365226746},{"id":"https://openalex.org/keywords/ergodic-theory","display_name":"Ergodic theory","score":0.7207484245300293},{"id":"https://openalex.org/keywords/nash-equilibrium","display_name":"Nash equilibrium","score":0.6503974199295044},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.5552202463150024},{"id":"https://openalex.org/keywords/markov-process","display_name":"Markov process","score":0.5493913292884827},{"id":"https://openalex.org/keywords/finite-state","display_name":"Finite state","score":0.5388792157173157},{"id":"https://openalex.org/keywords/state","display_name":"State (computer science)","score":0.4930741488933563},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.485664963722229},{"id":"https://openalex.org/keywords/mean-field-theory","display_name":"Mean field theory","score":0.4670046269893646},{"id":"https://openalex.org/keywords/stochastic-game","display_name":"Stochastic game","score":0.43074333667755127},{"id":"https://openalex.org/keywords/field","display_name":"Field (mathematics)","score":0.41011613607406616},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.364518404006958},{"id":"https://openalex.org/keywords/markov-chain","display_name":"Markov chain","score":0.2984843850135803},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.21618682146072388},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.110537588596344},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.07117512822151184}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8564507365226746},{"id":"https://openalex.org/C122044880","wikidata":"https://www.wikidata.org/wiki/Q5498822","display_name":"Ergodic theory","level":2,"score":0.7207484245300293},{"id":"https://openalex.org/C46814582","wikidata":"https://www.wikidata.org/wiki/Q23389","display_name":"Nash equilibrium","level":2,"score":0.6503974199295044},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.5552202463150024},{"id":"https://openalex.org/C159886148","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov process","level":2,"score":0.5493913292884827},{"id":"https://openalex.org/C2983497884","wikidata":"https://www.wikidata.org/wiki/Q176452","display_name":"Finite state","level":3,"score":0.5388792157173157},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.4930741488933563},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.485664963722229},{"id":"https://openalex.org/C202213908","wikidata":"https://www.wikidata.org/wiki/Q626011","display_name":"Mean field theory","level":2,"score":0.4670046269893646},{"id":"https://openalex.org/C22171661","wikidata":"https://www.wikidata.org/wiki/Q1074380","display_name":"Stochastic game","level":2,"score":0.43074333667755127},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.41011613607406616},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.364518404006958},{"id":"https://openalex.org/C98763669","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov chain","level":2,"score":0.2984843850135803},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.21618682146072388},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.110537588596344},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.07117512822151184},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1287/moor.2024.0478","is_oa":false,"landing_page_url":"https://doi.org/10.1287/moor.2024.0478","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":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":34,"referenced_works":["https://openalex.org/W1485289509","https://openalex.org/W1648295671","https://openalex.org/W1951267103","https://openalex.org/W2001038345","https://openalex.org/W2011000015","https://openalex.org/W2028316825","https://openalex.org/W2038686546","https://openalex.org/W2119707575","https://openalex.org/W2138405426","https://openalex.org/W2146662761","https://openalex.org/W2749028154","https://openalex.org/W2755331706","https://openalex.org/W2799984760","https://openalex.org/W2914331054","https://openalex.org/W2962739421","https://openalex.org/W2963993278","https://openalex.org/W2964078161","https://openalex.org/W2964128536","https://openalex.org/W2964140724","https://openalex.org/W3000371736","https://openalex.org/W3015784824","https://openalex.org/W3047552776","https://openalex.org/W3101852205","https://openalex.org/W3103922228","https://openalex.org/W3104707106","https://openalex.org/W3164756548","https://openalex.org/W3181839803","https://openalex.org/W3212873270","https://openalex.org/W4210364010","https://openalex.org/W4243669201","https://openalex.org/W4256330275","https://openalex.org/W4307279931","https://openalex.org/W4321149741","https://openalex.org/W4360985384"],"related_works":["https://openalex.org/W2390585021","https://openalex.org/W412641959","https://openalex.org/W50969306","https://openalex.org/W4292101436","https://openalex.org/W2341040961","https://openalex.org/W4287207389","https://openalex.org/W2779828239","https://openalex.org/W3154976382","https://openalex.org/W2044004505","https://openalex.org/W2951177262"],"abstract_inverted_index":{"Mean":[0],"field":[1],"games":[2,7],"(MFGs)":[3],"model":[4],"equilibria":[5,105,140],"in":[6,52,154],"with":[8,28,94],"a":[9,47,86],"continuum":[10],"of":[11,18,81,136],"weakly":[12],"interacting":[13],"players":[14],"as":[15],"limiting":[16],"systems":[17],"symmetric":[19],"n-player":[20,54],"games.":[21],"We":[22,56,75,109,128],"consider":[23],"the":[24,41,53,62,67,72,77,82,95,102,111,118,124,134,137,151],"finite-state,":[25],"infinite-horizon":[26],"problem":[27],"ergodic":[29,119],"cost.":[30],"Assuming":[31],"Markovian":[32],"strategies,":[33],"we":[34,100,145],"first":[35],"prove":[36],"that":[37],"any":[38],"solution":[39],"to":[40,46,132],"MFG":[42,112],"system":[43,113],"gives":[44],"rise":[45],"[Formula:":[48],"see":[49],"text]-Nash":[50],"equilibrium":[51],"game.":[55],"follow":[57],"this":[58],"result":[59],"by":[60,84,122],"proving":[61],"same":[63],"is":[64],"true":[65],"for":[66,90,150],"strategy":[68],"profile":[69],"derived":[70],"from":[71],"master":[73,120],"equation.":[74],"conclude":[76],"main":[78],"theoretical":[79],"portion":[80],"paper":[83],"establishing":[85],"large":[87],"deviation":[88],"principle":[89],"empirical":[91],"measures":[92],"associated":[93],"asymptotic":[96,103,138],"Nash":[97,104,139],"equilibria.":[98],"Then,":[99],"contrast":[101],"using":[106],"an":[107,147],"example.":[108],"solve":[110,117],"directly":[114],"and":[115,141],"numerically":[116],"equation":[121],"adapting":[123],"deep":[125],"Galerkin":[126],"method.":[127],"use":[129],"these":[130],"results":[131],"derive":[133,146],"strategies":[135],"compare":[142],"them.":[143],"Finally,":[144],"explicit":[148],"form":[149],"rate":[152],"functions":[153],"dimension":[155],"two.":[156]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":1}],"updated_date":"2026-06-26T08:34:08.712188","created_date":"2025-10-10T00:00:00"}
