{"id":"https://openalex.org/W2065949826","doi":"https://doi.org/10.1109/cdc.2011.6161425","title":"Mean Field (NCE) stochastic control: Populations of major and egoist-altruist agents","display_name":"Mean Field (NCE) stochastic control: Populations of major and egoist-altruist agents","publication_year":2011,"publication_date":"2011-12-01","ids":{"openalex":"https://openalex.org/W2065949826","doi":"https://doi.org/10.1109/cdc.2011.6161425","mag":"2065949826"},"language":"en","primary_location":{"id":"doi:10.1109/cdc.2011.6161425","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2011.6161425","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Conference on Decision and Control and European Control Conference","raw_type":"proceedings-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/A5010058546","display_name":"Arman C. Kizilkale","orcid":"https://orcid.org/0000-0001-6324-5951"},"institutions":[{"id":"https://openalex.org/I5023651","display_name":"McGill University","ror":"https://ror.org/01pxwe438","country_code":"CA","type":"education","lineage":["https://openalex.org/I5023651"]}],"countries":["CA"],"is_corresponding":true,"raw_author_name":"Arman C. Kizilkale","raw_affiliation_strings":["Department of Electrical and Computer Engineering and the Centre for Intelligent Machines, McGill University, Montreal, Canada","Department of Electrical and Computer Engineering, and the Centre for Intelligent Machines, McGill University, Montr\u00e9al, Canada#TAB#"],"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering and the Centre for Intelligent Machines, McGill University, Montreal, Canada","institution_ids":["https://openalex.org/I5023651"]},{"raw_affiliation_string":"Department of Electrical and Computer Engineering, and the Centre for Intelligent Machines, McGill University, Montr\u00e9al, Canada#TAB#","institution_ids":["https://openalex.org/I5023651"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5044187847","display_name":"Peter E. Caines","orcid":"https://orcid.org/0000-0002-5248-9456"},"institutions":[{"id":"https://openalex.org/I5023651","display_name":"McGill University","ror":"https://ror.org/01pxwe438","country_code":"CA","type":"education","lineage":["https://openalex.org/I5023651"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Peter E. Caines","raw_affiliation_strings":["Department of Electrical and Computer Engineering and the Centre for Intelligent Machines, McGill University, Montreal, Canada","Department of Electrical and Computer Engineering, and the Centre for Intelligent Machines, McGill University, Montr\u00e9al, Canada#TAB#"],"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering and the Centre for Intelligent Machines, McGill University, Montreal, Canada","institution_ids":["https://openalex.org/I5023651"]},{"raw_affiliation_string":"Department of Electrical and Computer Engineering, and the Centre for Intelligent Machines, McGill University, Montr\u00e9al, Canada#TAB#","institution_ids":["https://openalex.org/I5023651"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5010058546"],"corresponding_institution_ids":["https://openalex.org/I5023651"],"apc_list":null,"apc_paid":null,"fwci":1.6335,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.89261837,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":null,"issue":null,"first_page":"5547","last_page":"5552"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12137","display_name":"Economic theories and models","score":0.9976000189781189,"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"}},"topics":[{"id":"https://openalex.org/T12137","display_name":"Economic theories and models","score":0.9976000189781189,"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"}},{"id":"https://openalex.org/T11031","display_name":"Game Theory and Applications","score":0.9911999702453613,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T10067","display_name":"Stochastic processes and financial applications","score":0.9904000163078308,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/minor","display_name":"Minor (academic)","score":0.7893402576446533},{"id":"https://openalex.org/keywords/nash-equilibrium","display_name":"Nash equilibrium","score":0.7135443091392517},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.6297953128814697},{"id":"https://openalex.org/keywords/population","display_name":"Population","score":0.5858653783798218},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4750549793243408},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4718701243400574},{"id":"https://openalex.org/keywords/social-cost","display_name":"Social cost","score":0.43069350719451904},{"id":"https://openalex.org/keywords/game-theory","display_name":"Game theory","score":0.41778892278671265},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.34002748131752014},{"id":"https://openalex.org/keywords/economics","display_name":"Economics","score":0.2719374895095825},{"id":"https://openalex.org/keywords/microeconomics","display_name":"Microeconomics","score":0.14054036140441895}],"concepts":[{"id":"https://openalex.org/C2779760435","wikidata":"https://www.wikidata.org/wiki/Q5396169","display_name":"Minor (academic)","level":2,"score":0.7893402576446533},{"id":"https://openalex.org/C46814582","wikidata":"https://www.wikidata.org/wiki/Q23389","display_name":"Nash equilibrium","level":2,"score":0.7135443091392517},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.6297953128814697},{"id":"https://openalex.org/C2908647359","wikidata":"https://www.wikidata.org/wiki/Q2625603","display_name":"Population","level":2,"score":0.5858653783798218},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4750549793243408},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4718701243400574},{"id":"https://openalex.org/C2777644927","wikidata":"https://www.wikidata.org/wiki/Q2300947","display_name":"Social cost","level":2,"score":0.43069350719451904},{"id":"https://openalex.org/C177142836","wikidata":"https://www.wikidata.org/wiki/Q44455","display_name":"Game theory","level":2,"score":0.41778892278671265},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.34002748131752014},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.2719374895095825},{"id":"https://openalex.org/C175444787","wikidata":"https://www.wikidata.org/wiki/Q39072","display_name":"Microeconomics","level":1,"score":0.14054036140441895},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C144024400","wikidata":"https://www.wikidata.org/wiki/Q21201","display_name":"Sociology","level":0,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C149923435","wikidata":"https://www.wikidata.org/wiki/Q37732","display_name":"Demography","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/cdc.2011.6161425","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2011.6161425","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Conference on Decision and Control and European Control Conference","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities","score":0.4000000059604645}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":22,"referenced_works":["https://openalex.org/W46545661","https://openalex.org/W1512235915","https://openalex.org/W1576577548","https://openalex.org/W1888172398","https://openalex.org/W1983321045","https://openalex.org/W1983997656","https://openalex.org/W2011000015","https://openalex.org/W2038686546","https://openalex.org/W2054616847","https://openalex.org/W2074598069","https://openalex.org/W2077787105","https://openalex.org/W2109874145","https://openalex.org/W2123807026","https://openalex.org/W2124776038","https://openalex.org/W2147324680","https://openalex.org/W2151627108","https://openalex.org/W2415746836","https://openalex.org/W2949885533","https://openalex.org/W3023995834","https://openalex.org/W6634723149","https://openalex.org/W6716490778","https://openalex.org/W6735652139"],"related_works":["https://openalex.org/W2803931294","https://openalex.org/W2282604764","https://openalex.org/W2500870930","https://openalex.org/W2218535193","https://openalex.org/W2470927734","https://openalex.org/W2468739564","https://openalex.org/W2171981925","https://openalex.org/W2501065092","https://openalex.org/W1554758635","https://openalex.org/W3018272572"],"abstract_inverted_index":{"For":[0],"noncooperative":[1],"games":[2],"the":[3,72,75,100,115,119,124,145,164,182,186,190,194,203,215,222],"Nash":[4,21],"Certainty":[5],"Equivalence":[6],"(NCE),":[7],"or":[8,58],"Mean":[9],"Field":[10],"(MF)":[11],"methodology":[12],"[1],":[13],"[2]":[14],"provides":[15],"decentralized":[16],"strategies":[17],"which":[18,138],"asymptotically":[19],"yield":[20],"equilibria.":[22],"An":[23],"extension":[24],"of":[25,30,53,78,94,110,118,166],"this":[26,68],"theory":[27,50],"to":[28,40,149,219,226],"populations":[29,42,52],"altruistic":[31],"agents":[32,55,62,143,155],"(defined":[33],"with":[34],"so-called":[35,60],"social":[36,116,187,204,216],"cost":[37,101,113,117,195,205,217],"functions)":[38],"and":[39,48,56,74,90,98,114,130,175,201],"mixed":[41,95],"was":[43,63],"carried":[44],"out":[45],"in":[46,65,144,181],"[3],":[47],"a":[49,86,91,107,132,211],"treating":[51],"egoistic":[54],"one":[57],"more":[59],"major":[61,88],"developed":[64],"[4].":[66],"In":[67],"paper":[69],"we":[70],"study":[71],"equilibria":[73],"overall":[76],"stability":[77],"dynamic":[79],"LQG":[80],"games,":[81],"where":[82,152],"(i)":[83,153,193],"there":[84],"is":[85,106],"single":[87],"agent":[89,105,180,200],"large":[92],"population":[93,223],"minor":[96,104,120,179,199],"agents,":[97],"(ii)":[99,163,202],"for":[102,172],"each":[103,178,198],"convex":[108],"combination":[109],"its":[111],"own":[112],"agents.":[121],"We":[122],"analyse":[123],"resulting":[125],"equilibria,":[126],"provide":[127],"experimental":[128],"results,":[129],"present":[131],"mean":[133],"field":[134],"stochastic":[135],"control":[136],"algorithm,":[137],"when":[139],"applied":[140],"by":[141,197],"all":[142,154,173],"system,":[146],"gives":[147],"rise":[148],"system":[150,183],"behaviour":[151],"systems":[156],"are":[157],"L":[158],"<sup":[159],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[160],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">2</sup>":[161],"stable,":[162],"set":[165],"controls":[167],"yields":[168],"an":[169],"\u03b5-Nash":[170],"equilibrium":[171],"\u03b5,":[174],"(iii)":[176],"if":[177,210],"only":[184],"considers":[185],"cost,":[188],"then":[189],"difference":[191],"between":[192],"observed":[196,209],"that":[206],"would":[207],"be":[208],"centralized":[212],"controller":[213],"minimizes":[214],"tends":[218],"zero":[220],"as":[221],"size":[224],"grows":[225],"infinity.":[227]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2012,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}