{"id":"https://openalex.org/W1986431940","doi":"https://doi.org/10.1109/tac.2013.2289711","title":"Risk-Sensitive Mean-Field Games","display_name":"Risk-Sensitive Mean-Field Games","publication_year":2013,"publication_date":"2013-11-19","ids":{"openalex":"https://openalex.org/W1986431940","doi":"https://doi.org/10.1109/tac.2013.2289711","mag":"1986431940"},"language":"en","primary_location":{"id":"doi:10.1109/tac.2013.2289711","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2013.2289711","pdf_url":null,"source":{"id":"https://openalex.org/S184954342","display_name":"IEEE Transactions on Automatic Control","issn_l":"0018-9286","issn":["0018-9286","1558-2523","2334-3303"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Automatic Control","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/A5073493112","display_name":"Hamidou Tembin\u00e9","orcid":"https://orcid.org/0000-0002-1604-8223"},"institutions":[{"id":"https://openalex.org/I71920554","display_name":"King Abdullah University of Science and Technology","ror":"https://ror.org/01q3tbs38","country_code":"SA","type":"education","lineage":["https://openalex.org/I71920554"]}],"countries":["SA"],"is_corresponding":true,"raw_author_name":"Hamidou Tembine","raw_affiliation_strings":["KAUST Strategic Research Initiative Center for Uncertainty Quantification in Computational Science and Engineering, King Abdullah University of Science and Technology, Thuwal, Saudi Arabia","KAUST Strategic Res. Initiative Center for Uncertainty Quantification in Comput. Sci. & Eng., King Abdullah Univ. of Sci. & Technol., Thuwal, Saudi Arabia"],"affiliations":[{"raw_affiliation_string":"KAUST Strategic Research Initiative Center for Uncertainty Quantification in Computational Science and Engineering, King Abdullah University of Science and Technology, Thuwal, Saudi Arabia","institution_ids":["https://openalex.org/I71920554"]},{"raw_affiliation_string":"KAUST Strategic Res. Initiative Center for Uncertainty Quantification in Comput. Sci. & Eng., King Abdullah Univ. of Sci. & Technol., Thuwal, Saudi Arabia","institution_ids":["https://openalex.org/I71920554"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5081500464","display_name":"Quanyan Zhu","orcid":"https://orcid.org/0000-0002-0008-2953"},"institutions":[{"id":"https://openalex.org/I157725225","display_name":"University of Illinois Urbana-Champaign","ror":"https://ror.org/047426m28","country_code":"US","type":"education","lineage":["https://openalex.org/I157725225"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Quanyan Zhu","raw_affiliation_strings":["Department of Electrical and Computer Engineering, University of Illinois at Urbana-Champaign, Urbana, IL, USA","Dept of Electr. & Comput. Engg, Univ. of Illinois at Urbana-Champaign, Urbana, IL, USA"],"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, University of Illinois at Urbana-Champaign, Urbana, IL, USA","institution_ids":["https://openalex.org/I157725225"]},{"raw_affiliation_string":"Dept of Electr. & Comput. Engg, Univ. of Illinois at Urbana-Champaign, Urbana, IL, USA","institution_ids":["https://openalex.org/I157725225"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5019604570","display_name":"Tamer Ba\u015far","orcid":"https://orcid.org/0000-0003-4406-7875"},"institutions":[{"id":"https://openalex.org/I157725225","display_name":"University of Illinois Urbana-Champaign","ror":"https://ror.org/047426m28","country_code":"US","type":"education","lineage":["https://openalex.org/I157725225"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Tamer Basar","raw_affiliation_strings":["Department of Electrical and Computer Engineering, University of Illinois at Urbana-Champaign, Urbana, IL, USA","Dept of Electr. & Comput. Engg, Univ. of Illinois at Urbana-Champaign, Urbana, IL, USA"],"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, University of Illinois at Urbana-Champaign, Urbana, IL, USA","institution_ids":["https://openalex.org/I157725225"]},{"raw_affiliation_string":"Dept of Electr. & Comput. Engg, Univ. of Illinois at Urbana-Champaign, Urbana, IL, USA","institution_ids":["https://openalex.org/I157725225"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5073493112"],"corresponding_institution_ids":["https://openalex.org/I71920554"],"apc_list":null,"apc_paid":null,"fwci":18.162,"has_fulltext":false,"cited_by_count":183,"citation_normalized_percentile":{"value":0.99207406,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":100},"biblio":{"volume":"59","issue":"4","first_page":"835","last_page":"850"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10067","display_name":"Stochastic processes and financial applications","score":0.9998000264167786,"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":0.9998000264167786,"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/T12011","display_name":"Insurance, Mortality, Demography, Risk Management","score":0.9950000047683716,"subfield":{"id":"https://openalex.org/subfields/3317","display_name":"Demography"},"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/T10471","display_name":"Climate Change Policy and Economics","score":0.9879000186920166,"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/hamilton\u2013jacobi\u2013bellman-equation","display_name":"Hamilton\u2013Jacobi\u2013Bellman equation","score":0.8685070276260376},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7459069490432739},{"id":"https://openalex.org/keywords/stochastic-differential-equation","display_name":"Stochastic differential equation","score":0.6598545908927917},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5814070701599121},{"id":"https://openalex.org/keywords/affine-transformation","display_name":"Affine transformation","score":0.547424852848053},{"id":"https://openalex.org/keywords/mean-field-theory","display_name":"Mean field theory","score":0.5140413045883179},{"id":"https://openalex.org/keywords/bellman-equation","display_name":"Bellman equation","score":0.5118862390518188},{"id":"https://openalex.org/keywords/field","display_name":"Field (mathematics)","score":0.472557008266449},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.43496188521385193},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3721214234828949},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.30506432056427},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.1476755142211914},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.14250344038009644}],"concepts":[{"id":"https://openalex.org/C196978813","wikidata":"https://www.wikidata.org/wiki/Q3302775","display_name":"Hamilton\u2013Jacobi\u2013Bellman equation","level":3,"score":0.8685070276260376},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7459069490432739},{"id":"https://openalex.org/C51955184","wikidata":"https://www.wikidata.org/wiki/Q1545585","display_name":"Stochastic differential equation","level":2,"score":0.6598545908927917},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5814070701599121},{"id":"https://openalex.org/C92757383","wikidata":"https://www.wikidata.org/wiki/Q382497","display_name":"Affine transformation","level":2,"score":0.547424852848053},{"id":"https://openalex.org/C202213908","wikidata":"https://www.wikidata.org/wiki/Q626011","display_name":"Mean field theory","level":2,"score":0.5140413045883179},{"id":"https://openalex.org/C14646407","wikidata":"https://www.wikidata.org/wiki/Q1430750","display_name":"Bellman equation","level":2,"score":0.5118862390518188},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.472557008266449},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.43496188521385193},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3721214234828949},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.30506432056427},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.1476755142211914},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.14250344038009644},{"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:10.1109/tac.2013.2289711","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2013.2289711","pdf_url":null,"source":{"id":"https://openalex.org/S184954342","display_name":"IEEE Transactions on Automatic Control","issn_l":"0018-9286","issn":["0018-9286","1558-2523","2334-3303"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Automatic Control","raw_type":"journal-article"},{"id":"pmh:oai:repository.kaust.edu.sa:10754/563474","is_oa":false,"landing_page_url":"http://hdl.handle.net/10754/563474","pdf_url":null,"source":{"id":"https://openalex.org/S4306401596","display_name":"King Abdullah University of Science and Technology Repository (King Abdullah University of Science and Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I71920554","host_organization_name":"King Abdullah University of Science and Technology","host_organization_lineage":["https://openalex.org/I71920554"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1523888516","display_name":null,"funder_award_id":"FA9550-","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"},{"id":"https://openalex.org/G4603001257","display_name":null,"funder_award_id":"FA9550-10-1-0573","funder_id":"https://openalex.org/F4320333591","funder_display_name":"Multidisciplinary University Research Initiative"},{"id":"https://openalex.org/G5341545339","display_name":null,"funder_award_id":"FA9550-10-1-057","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"},{"id":"https://openalex.org/G5809100787","display_name":null,"funder_award_id":"FA9550","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"},{"id":"https://openalex.org/G6520717675","display_name":null,"funder_award_id":"FA9550-10-1-0573","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"},{"id":"https://openalex.org/G7090116110","display_name":null,"funder_award_id":"FA9550","funder_id":"https://openalex.org/F4320332467","funder_display_name":"U.S. Air Force"},{"id":"https://openalex.org/G7758152977","display_name":null,"funder_award_id":"support","funder_id":"https://openalex.org/F4320322892","funder_display_name":"Centre National de la Recherche Scientifique"},{"id":"https://openalex.org/G8521281903","display_name":null,"funder_award_id":"AFOSR","funder_id":"https://openalex.org/F4320332467","funder_display_name":"U.S. Air Force"},{"id":"https://openalex.org/G8726057126","display_name":null,"funder_award_id":"9550-10-1-0573","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"}],"funders":[{"id":"https://openalex.org/F4320322892","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73"},{"id":"https://openalex.org/F4320332467","display_name":"U.S. Air Force","ror":"https://ror.org/006gmme17"},{"id":"https://openalex.org/F4320333591","display_name":"Multidisciplinary University Research Initiative","ror":null},{"id":"https://openalex.org/F4320338279","display_name":"Air Force Office of Scientific Research","ror":"https://ror.org/011e9bt93"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":43,"referenced_works":["https://openalex.org/W111157985","https://openalex.org/W182704713","https://openalex.org/W263845233","https://openalex.org/W1569313452","https://openalex.org/W1576577548","https://openalex.org/W1578630563","https://openalex.org/W1808956822","https://openalex.org/W1821455959","https://openalex.org/W1946156631","https://openalex.org/W1974345218","https://openalex.org/W1983321045","https://openalex.org/W1986522846","https://openalex.org/W1994139361","https://openalex.org/W2008462649","https://openalex.org/W2011000015","https://openalex.org/W2011435133","https://openalex.org/W2018911937","https://openalex.org/W2021321016","https://openalex.org/W2027591506","https://openalex.org/W2038686546","https://openalex.org/W2043295228","https://openalex.org/W2054673836","https://openalex.org/W2058397079","https://openalex.org/W2077437174","https://openalex.org/W2078363504","https://openalex.org/W2082578341","https://openalex.org/W2096035449","https://openalex.org/W2103714988","https://openalex.org/W2107555698","https://openalex.org/W2115684267","https://openalex.org/W2123807026","https://openalex.org/W2132241089","https://openalex.org/W2134665667","https://openalex.org/W2178177313","https://openalex.org/W2274518346","https://openalex.org/W3145429483","https://openalex.org/W4212780424","https://openalex.org/W4238187298","https://openalex.org/W4249667877","https://openalex.org/W6634132281","https://openalex.org/W6647041316","https://openalex.org/W6653398440","https://openalex.org/W6679723688"],"related_works":["https://openalex.org/W2032834442","https://openalex.org/W3153900688","https://openalex.org/W2115544975","https://openalex.org/W2902017027","https://openalex.org/W1654696814","https://openalex.org/W4291598237","https://openalex.org/W4239477580","https://openalex.org/W2766998270","https://openalex.org/W4255265352","https://openalex.org/W3168988147"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3],"study":[4],"a":[5,39],"class":[6],"of":[7,23,55,92],"risk-sensitive":[8],"mean-field":[9,21,57,78,86],"stochastic":[10,25],"differential":[11,26],"games.":[12],"We":[13,50,102],"show":[14],"that":[15],"under":[16],"appropriate":[17],"regularity":[18],"conditions,":[19],"the":[20,24,35,56,61,68,74,84,107],"value":[22,36],"game":[27],"with":[28,34,45],"exponentiated":[29],"integral":[30],"cost":[31,63],"functional":[32],"coincides":[33],"function":[37],"satisfying":[38],"Hamilton":[40],"-Jacobi-":[41],"Bellman":[42],"(HJB)":[43],"equation":[44],"an":[46,52],"additional":[47],"quadratic":[48],"term.":[49],"provide":[51,103],"explicit":[53],"solution":[54],"best":[58],"response":[59],"when":[60],"instantaneous":[62],"functions":[64],"are":[65,71,88],"log-quadratic":[66],"and":[67,83,99,115],"state":[69],"dynamics":[70],"affine":[72],"in":[73,90],"control.":[75],"An":[76],"equivalent":[77],"risk-neutral":[79],"problem":[80],"is":[81],"formulated":[82],"corresponding":[85],"equilibria":[87],"characterized":[89],"terms":[91],"backward-forward":[93],"macroscopic":[94],"McKean-Vlasov":[95,116],"equations,":[96,98],"Fokker-Planck-Kolmogorov":[97],"HJB":[100],"equations.":[101],"numerical":[104],"examples":[105],"on":[106],"mean":[108],"field":[109],"behavior":[110],"to":[111],"illustrate":[112],"both":[113],"linear":[114],"dynamics.":[117]},"counts_by_year":[{"year":2026,"cited_by_count":4},{"year":2025,"cited_by_count":20},{"year":2024,"cited_by_count":10},{"year":2023,"cited_by_count":10},{"year":2022,"cited_by_count":10},{"year":2021,"cited_by_count":7},{"year":2020,"cited_by_count":18},{"year":2019,"cited_by_count":20},{"year":2018,"cited_by_count":25},{"year":2017,"cited_by_count":17},{"year":2016,"cited_by_count":11},{"year":2015,"cited_by_count":22},{"year":2014,"cited_by_count":7},{"year":2013,"cited_by_count":2}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}
