{"id":"https://openalex.org/W3041493239","doi":"https://doi.org/10.1109/tac.2020.3008113","title":"Distributed Nash Equilibrium Seeking in an Aggregative Game on a Directed Graph","display_name":"Distributed Nash Equilibrium Seeking in an Aggregative Game on a Directed Graph","publication_year":2020,"publication_date":"2020-07-09","ids":{"openalex":"https://openalex.org/W3041493239","doi":"https://doi.org/10.1109/tac.2020.3008113","mag":"3041493239"},"language":"en","primary_location":{"id":"doi:10.1109/tac.2020.3008113","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2020.3008113","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/A5020521560","display_name":"Yanan Zhu","orcid":"https://orcid.org/0000-0001-7980-6282"},"institutions":[{"id":"https://openalex.org/I76569877","display_name":"Southeast University","ror":"https://ror.org/04ct4d772","country_code":"CN","type":"education","lineage":["https://openalex.org/I76569877"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yanan Zhu","raw_affiliation_strings":["School of Mathematics, Southeast University, Nanjing, China"],"raw_orcid":"https://orcid.org/0000-0001-7980-6282","affiliations":[{"raw_affiliation_string":"School of Mathematics, Southeast University, Nanjing, China","institution_ids":["https://openalex.org/I76569877"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100627758","display_name":"Wenwu Yu","orcid":"https://orcid.org/0000-0003-3755-179X"},"institutions":[{"id":"https://openalex.org/I76569877","display_name":"Southeast University","ror":"https://ror.org/04ct4d772","country_code":"CN","type":"education","lineage":["https://openalex.org/I76569877"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Wenwu Yu","raw_affiliation_strings":["School of Mathematics and the School of Automation, Southeast University, Nanjing, China"],"raw_orcid":"https://orcid.org/0000-0003-3755-179X","affiliations":[{"raw_affiliation_string":"School of Mathematics and the School of Automation, Southeast University, Nanjing, China","institution_ids":["https://openalex.org/I76569877"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5040088510","display_name":"Guanghui Wen","orcid":"https://orcid.org/0000-0003-0070-8597"},"institutions":[{"id":"https://openalex.org/I76569877","display_name":"Southeast University","ror":"https://ror.org/04ct4d772","country_code":"CN","type":"education","lineage":["https://openalex.org/I76569877"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Guanghui Wen","raw_affiliation_strings":["School of Mathematics, Southeast University, Nanjing, China"],"raw_orcid":"https://orcid.org/0000-0003-0070-8597","affiliations":[{"raw_affiliation_string":"School of Mathematics, Southeast University, Nanjing, China","institution_ids":["https://openalex.org/I76569877"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5024633466","display_name":"Guanrong Chen","orcid":"https://orcid.org/0000-0003-1381-7418"},"institutions":[{"id":"https://openalex.org/I168719708","display_name":"City University of Hong Kong","ror":"https://ror.org/03q8dnn23","country_code":"HK","type":"education","lineage":["https://openalex.org/I168719708"]}],"countries":["HK"],"is_corresponding":false,"raw_author_name":"Guanrong Chen","raw_affiliation_strings":["Department of Electrical Engineering, City University of Hong Kong, Kowloon, Hong Kong"],"raw_orcid":"https://orcid.org/0000-0003-1381-7418","affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, City University of Hong Kong, Kowloon, Hong Kong","institution_ids":["https://openalex.org/I168719708"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":5.9048,"has_fulltext":false,"cited_by_count":102,"citation_normalized_percentile":{"value":0.96243486,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":98,"max":100},"biblio":{"volume":"66","issue":"6","first_page":"2746","last_page":"2753"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10249","display_name":"Distributed Control Multi-Agent Systems","score":0.9991000294685364,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10249","display_name":"Distributed Control Multi-Agent Systems","score":0.9991000294685364,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12794","display_name":"Adaptive Dynamic Programming Control","score":0.9961000084877014,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10482","display_name":"Mathematical and Theoretical Epidemiology and Ecology Models","score":0.9887999892234802,"subfield":{"id":"https://openalex.org/subfields/2739","display_name":"Public Health, Environmental and Occupational Health"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/nash-equilibrium","display_name":"Nash equilibrium","score":0.8006792068481445},{"id":"https://openalex.org/keywords/best-response","display_name":"Best response","score":0.6871162056922913},{"id":"https://openalex.org/keywords/lyapunov-function","display_name":"Lyapunov function","score":0.6388392448425293},{"id":"https://openalex.org/keywords/risk-dominance","display_name":"Risk dominance","score":0.5794201493263245},{"id":"https://openalex.org/keywords/game-theory","display_name":"Game theory","score":0.546235203742981},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5132893919944763},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.48465782403945923},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.48185431957244873},{"id":"https://openalex.org/keywords/graph-theory","display_name":"Graph theory","score":0.46273526549339294},{"id":"https://openalex.org/keywords/epsilon-equilibrium","display_name":"Epsilon-equilibrium","score":0.45536935329437256},{"id":"https://openalex.org/keywords/constraint","display_name":"Constraint (computer-aided design)","score":0.4530654549598694},{"id":"https://openalex.org/keywords/potential-game","display_name":"Potential game","score":0.437055379152298},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.4352220892906189},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.42457833886146545},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.2489105463027954},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.23530274629592896},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.0687817633152008}],"concepts":[{"id":"https://openalex.org/C46814582","wikidata":"https://www.wikidata.org/wiki/Q23389","display_name":"Nash equilibrium","level":2,"score":0.8006792068481445},{"id":"https://openalex.org/C32407928","wikidata":"https://www.wikidata.org/wiki/Q2733833","display_name":"Best response","level":3,"score":0.6871162056922913},{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.6388392448425293},{"id":"https://openalex.org/C22349654","wikidata":"https://www.wikidata.org/wiki/Q2039354","display_name":"Risk dominance","level":5,"score":0.5794201493263245},{"id":"https://openalex.org/C177142836","wikidata":"https://www.wikidata.org/wiki/Q44455","display_name":"Game theory","level":2,"score":0.546235203742981},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5132893919944763},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.48465782403945923},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.48185431957244873},{"id":"https://openalex.org/C88230418","wikidata":"https://www.wikidata.org/wiki/Q131476","display_name":"Graph theory","level":2,"score":0.46273526549339294},{"id":"https://openalex.org/C141824439","wikidata":"https://www.wikidata.org/wiki/Q307521","display_name":"Epsilon-equilibrium","level":4,"score":0.45536935329437256},{"id":"https://openalex.org/C2776036281","wikidata":"https://www.wikidata.org/wiki/Q48769818","display_name":"Constraint (computer-aided design)","level":2,"score":0.4530654549598694},{"id":"https://openalex.org/C2778079155","wikidata":"https://www.wikidata.org/wiki/Q288500","display_name":"Potential game","level":3,"score":0.437055379152298},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.4352220892906189},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.42457833886146545},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.2489105463027954},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.23530274629592896},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.0687817633152008},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tac.2020.3008113","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2020.3008113","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"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Reduced inequalities","score":0.46000000834465027,"id":"https://metadata.un.org/sdg/10"}],"awards":[{"id":"https://openalex.org/G4741143070","display_name":null,"funder_award_id":"61673104","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6315690620","display_name":null,"funder_award_id":"61673107","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7504887357","display_name":null,"funder_award_id":"3207012001A3","funder_id":"https://openalex.org/F4320335787","funder_display_name":"Fundamental Research Funds for the Central Universities"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320335787","display_name":"Fundamental Research Funds for the Central Universities","ror":null}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":54,"referenced_works":["https://openalex.org/W1486118835","https://openalex.org/W1516681311","https://openalex.org/W1543439990","https://openalex.org/W1923997169","https://openalex.org/W1985348591","https://openalex.org/W1997949764","https://openalex.org/W2007926026","https://openalex.org/W2022745069","https://openalex.org/W2024006515","https://openalex.org/W2026509976","https://openalex.org/W2053497389","https://openalex.org/W2056226204","https://openalex.org/W2058626062","https://openalex.org/W2067050450","https://openalex.org/W2070291355","https://openalex.org/W2073515808","https://openalex.org/W2088077079","https://openalex.org/W2139197149","https://openalex.org/W2275030070","https://openalex.org/W2289072378","https://openalex.org/W2345998142","https://openalex.org/W2487747673","https://openalex.org/W2501656778","https://openalex.org/W2519129141","https://openalex.org/W2521320587","https://openalex.org/W2570191885","https://openalex.org/W2584256285","https://openalex.org/W2591158312","https://openalex.org/W2594659080","https://openalex.org/W2604292427","https://openalex.org/W2611964096","https://openalex.org/W2690123879","https://openalex.org/W2734684603","https://openalex.org/W2766719770","https://openalex.org/W2769121376","https://openalex.org/W2782789197","https://openalex.org/W2782978807","https://openalex.org/W2783096200","https://openalex.org/W2801481166","https://openalex.org/W2811183536","https://openalex.org/W2884713680","https://openalex.org/W2890467898","https://openalex.org/W2899989669","https://openalex.org/W2914412030","https://openalex.org/W2949161887","https://openalex.org/W2962910407","https://openalex.org/W3104002866","https://openalex.org/W3124789100","https://openalex.org/W3140720497","https://openalex.org/W4231611411","https://openalex.org/W4241879758","https://openalex.org/W4301791716","https://openalex.org/W6732632707","https://openalex.org/W6746328129"],"related_works":["https://openalex.org/W1853631319","https://openalex.org/W3192122086","https://openalex.org/W4301347782","https://openalex.org/W1554758635","https://openalex.org/W1667857601","https://openalex.org/W1976009178","https://openalex.org/W2013767790","https://openalex.org/W2092374696","https://openalex.org/W2077964199","https://openalex.org/W157961742"],"abstract_inverted_index":{"An":[0],"aggregative":[1],"game":[2,38],"with":[3,47,64,75,95],"local":[4,65],"constraint":[5],"sets":[6],"is":[7,17,24,126],"studied":[8],"in":[9,39],"this":[10],"article,":[11],"where":[12],"each":[13],"player's":[14],"cost":[15],"function":[16,22,59],"dependent":[18],"on":[19,67],"the":[20,31,37,43,57,72,90,109,130],"aggregation":[21,58],"that":[23,52],"unavailable":[25],"to":[26,55,104,107,128],"all":[27],"players.":[28],"To":[29],"compute":[30],"Nash":[32],"equilibrium":[33],"(NE)":[34],"point":[35,111],"of":[36,92],"a":[40,68],"distributed":[41],"manner,":[42],"players":[44],"are":[45,53,87,102],"endowed":[46],"several":[48],"auxiliary":[49],"state":[50],"variables":[51],"used":[54],"estimate":[56],"by":[60,89,112],"exchanging":[61],"their":[62],"estimates":[63],"neighbors":[66],"directed":[69,81],"graph.":[70],"In":[71],"two":[73],"cases":[74],"strongly":[76],"connected":[77],"weight-balanced":[78],"and":[79,119],"weight-unbalanced":[80],"graphs,":[82],"respectively,":[83],"NE":[84,110],"seeking":[85],"strategies":[86],"proposed":[88,100],"interconnection":[91],"projected":[93],"gradient-play":[94],"average":[96],"consensus":[97],"dynamics.":[98],"The":[99],"algorithms":[101],"proved":[103],"be":[105],"able":[106],"reach":[108],"using":[113],"tools":[114],"from":[115],"variational":[116],"inequality":[117],"theory":[118],"Lyapunov":[120],"stability":[121],"theory.":[122],"Finally,":[123],"an":[124],"example":[125],"simulated":[127],"demonstrate":[129],"theoretical":[131],"results.":[132]},"counts_by_year":[{"year":2026,"cited_by_count":7},{"year":2025,"cited_by_count":27},{"year":2024,"cited_by_count":24},{"year":2023,"cited_by_count":15},{"year":2022,"cited_by_count":23},{"year":2021,"cited_by_count":6}],"updated_date":"2026-07-22T07:51:19.307946","created_date":"2025-10-10T00:00:00"}
