{"id":"https://openalex.org/W2594875618","doi":"https://doi.org/10.1109/tie.2017.2674625","title":"Nash Equilibrium Topology of Multi-Agent Systems With Competitive Groups","display_name":"Nash Equilibrium Topology of Multi-Agent Systems With Competitive Groups","publication_year":2017,"publication_date":"2017-03-01","ids":{"openalex":"https://openalex.org/W2594875618","doi":"https://doi.org/10.1109/tie.2017.2674625","mag":"2594875618"},"language":"en","primary_location":{"id":"doi:10.1109/tie.2017.2674625","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tie.2017.2674625","pdf_url":null,"source":{"id":"https://openalex.org/S58031724","display_name":"IEEE Transactions on Industrial Electronics","issn_l":"0278-0046","issn":["0278-0046","1557-9948"],"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 Industrial Electronics","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/A5072171789","display_name":"Jingying Ma","orcid":"https://orcid.org/0000-0003-2014-5509"},"institutions":[{"id":"https://openalex.org/I149594827","display_name":"Xidian University","ror":"https://ror.org/05s92vm98","country_code":"CN","type":"education","lineage":["https://openalex.org/I149594827"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Jingying Ma","raw_affiliation_strings":["Center for Complex Systems, Xidian University, Xi'an, China"],"affiliations":[{"raw_affiliation_string":"Center for Complex Systems, Xidian University, Xi'an, China","institution_ids":["https://openalex.org/I149594827"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5011899531","display_name":"Yuanshi Zheng","orcid":"https://orcid.org/0000-0002-1143-2509"},"institutions":[{"id":"https://openalex.org/I149594827","display_name":"Xidian University","ror":"https://ror.org/05s92vm98","country_code":"CN","type":"education","lineage":["https://openalex.org/I149594827"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yuanshi Zheng","raw_affiliation_strings":["Center for Complex Systems, Xidian University, Xi'an, China"],"affiliations":[{"raw_affiliation_string":"Center for Complex Systems, Xidian University, Xi'an, China","institution_ids":["https://openalex.org/I149594827"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100447536","display_name":"Long Wang","orcid":"https://orcid.org/0000-0001-5600-8157"},"institutions":[{"id":"https://openalex.org/I20231570","display_name":"Peking University","ror":"https://ror.org/02v51f717","country_code":"CN","type":"education","lineage":["https://openalex.org/I20231570"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Long Wang","raw_affiliation_strings":["Center for Systems and Control, Peking University, Beijing, China"],"affiliations":[{"raw_affiliation_string":"Center for Systems and Control, Peking University, Beijing, China","institution_ids":["https://openalex.org/I20231570"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5072171789"],"corresponding_institution_ids":["https://openalex.org/I149594827"],"apc_list":null,"apc_paid":null,"fwci":3.9368,"has_fulltext":false,"cited_by_count":39,"citation_normalized_percentile":{"value":0.94351968,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"64","issue":"6","first_page":"4956","last_page":"4966"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10249","display_name":"Distributed Control Multi-Agent Systems","score":0.9998999834060669,"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":0.9998999834060669,"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/T11031","display_name":"Game Theory and Applications","score":0.9941999912261963,"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/T10482","display_name":"Mathematical and Theoretical Epidemiology and Ecology Models","score":0.9918000102043152,"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":0.7687402963638306},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.6750474572181702},{"id":"https://openalex.org/keywords/extension-topology","display_name":"Extension topology","score":0.4688604474067688},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4678889811038971},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.45238637924194336},{"id":"https://openalex.org/keywords/network-topology","display_name":"Network topology","score":0.44358229637145996},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3933827579021454},{"id":"https://openalex.org/keywords/general-topology","display_name":"General topology","score":0.3307499885559082},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.28503289818763733},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.2679985761642456},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.2432156503200531},{"id":"https://openalex.org/keywords/computer-network","display_name":"Computer network","score":0.06530645489692688}],"concepts":[{"id":"https://openalex.org/C46814582","wikidata":"https://www.wikidata.org/wiki/Q23389","display_name":"Nash equilibrium","level":2,"score":0.7687402963638306},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.6750474572181702},{"id":"https://openalex.org/C143913944","wikidata":"https://www.wikidata.org/wiki/Q5421952","display_name":"Extension topology","level":4,"score":0.4688604474067688},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4678889811038971},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.45238637924194336},{"id":"https://openalex.org/C199845137","wikidata":"https://www.wikidata.org/wiki/Q145490","display_name":"Network topology","level":2,"score":0.44358229637145996},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3933827579021454},{"id":"https://openalex.org/C129089157","wikidata":"https://www.wikidata.org/wiki/Q621550","display_name":"General topology","level":3,"score":0.3307499885559082},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.28503289818763733},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.2679985761642456},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.2432156503200531},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.06530645489692688},{"id":"https://openalex.org/C81332173","wikidata":"https://www.wikidata.org/wiki/Q179899","display_name":"Topological space","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tie.2017.2674625","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tie.2017.2674625","pdf_url":null,"source":{"id":"https://openalex.org/S58031724","display_name":"IEEE Transactions on Industrial Electronics","issn_l":"0278-0046","issn":["0278-0046","1557-9948"],"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 Industrial Electronics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3029348492","display_name":null,"funder_award_id":"61533001","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4177694624","display_name":null,"funder_award_id":"JB160419","funder_id":"https://openalex.org/F4320335787","funder_display_name":"Fundamental Research Funds for the Central Universities"},{"id":"https://openalex.org/G6850143148","display_name":null,"funder_award_id":"61375120","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8125030641","display_name":null,"funder_award_id":"61304160","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8676284154","display_name":null,"funder_award_id":"61563043","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"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":39,"referenced_works":["https://openalex.org/W170560239","https://openalex.org/W1578630563","https://openalex.org/W1673091696","https://openalex.org/W1983523909","https://openalex.org/W1989408492","https://openalex.org/W1993811387","https://openalex.org/W2015410655","https://openalex.org/W2032218247","https://openalex.org/W2033545621","https://openalex.org/W2033800890","https://openalex.org/W2038739174","https://openalex.org/W2056226204","https://openalex.org/W2067664905","https://openalex.org/W2068060907","https://openalex.org/W2075469757","https://openalex.org/W2089947584","https://openalex.org/W2092215165","https://openalex.org/W2099175737","https://openalex.org/W2107306424","https://openalex.org/W2108383324","https://openalex.org/W2117854200","https://openalex.org/W2122375213","https://openalex.org/W2122787820","https://openalex.org/W2123876595","https://openalex.org/W2135097535","https://openalex.org/W2160141417","https://openalex.org/W2165744313","https://openalex.org/W2172143163","https://openalex.org/W2248946215","https://openalex.org/W2249859651","https://openalex.org/W2332287806","https://openalex.org/W2515039113","https://openalex.org/W2517050798","https://openalex.org/W2529002166","https://openalex.org/W2560289364","https://openalex.org/W3121562466","https://openalex.org/W4238591275","https://openalex.org/W4240790602","https://openalex.org/W4302033101"],"related_works":["https://openalex.org/W4378422247","https://openalex.org/W1963725260","https://openalex.org/W2257096812","https://openalex.org/W4256394076","https://openalex.org/W2096666603","https://openalex.org/W437370296","https://openalex.org/W2375866554","https://openalex.org/W1980603880","https://openalex.org/W2122295425","https://openalex.org/W2974428018"],"abstract_inverted_index":{"Competition":[0],"is":[1,76,105,119,157,164,173,185],"ubiquitous":[2],"in":[3,50],"nature.":[4],"This":[5],"paper":[6],"studies":[7],"competition":[8,45],"phenomena":[9],"of":[10,14,17,73,91,98,139],"multi-agent":[11],"systems":[12],"consisting":[13],"three":[15],"groups":[16,30,57],"agents.":[18],"In":[19],"order":[20],"to":[21,33,39,135],"achieve":[22],"maximal":[23],"influence,":[24],"the":[25,28,34,52,55,70,74,84,92,95,99,102,111,114,137,140,147,152,159,167,177,180],"first":[26,53],"and":[27,54,66,161],"second":[29,56],"send":[31,65],"information":[32],"third":[35,115,141,153,181],"group,":[36],"which":[37,51],"leads":[38],"competition.":[40],"First,":[41],"we":[42,82],"formulate":[43],"this":[44],"as":[46,94],"a":[47,120,124,186],"noncooperative":[48],"game":[49,93],"are":[58,131],"two":[59],"players.":[60],"Players":[61],"decide":[62],"agents":[63,138],"who":[64],"receive":[67],"information.":[68],"Consequently,":[69],"interaction":[71,85,117,155,183],"topology":[72,86,97,172],"system":[75],"generated":[77],"from":[78],"players'":[79],"strategies.":[80],"Therefore,":[81],"define":[83],"decided":[87],"by":[88],"Nash":[89,128],"equilibrium":[90,96,108,129,148,168,171],"system.":[100],"Second,":[101],"necessary":[103,160],"condition":[104,163],"established":[106],"for":[107,166,176],"topology.":[109,149,169],"For":[110],"case":[112],"that":[113],"group's":[116,154,182],"graph":[118,156,184],"tree":[121],"or":[122],"has":[123],"center":[125],"vertex,":[126],"interchangeable":[127],"solutions":[130],"obtained.":[132],"Moreover,":[133],"due":[134],"competition,":[136],"group":[142],"might":[143],"reach":[144],"consensus":[145],"under":[146],"Finally,":[150],"when":[151],"bidirected,":[158],"sufficient":[162],"given":[165],"The":[170],"also":[174],"presented":[175],"scenario":[178],"where":[179],"bidirected":[187],"circulant":[188],"graph.":[189]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":6},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":5},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":11}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
