{"id":"https://openalex.org/W2275030070","doi":"https://doi.org/10.1109/tac.2015.2504962","title":"Nash Equilibrium Computation in Subnetwork Zero-Sum Games With Switching Communications","display_name":"Nash Equilibrium Computation in Subnetwork Zero-Sum Games With Switching Communications","publication_year":2015,"publication_date":"2015-12-03","ids":{"openalex":"https://openalex.org/W2275030070","doi":"https://doi.org/10.1109/tac.2015.2504962","mag":"2275030070"},"language":"en","primary_location":{"id":"doi:10.1109/tac.2015.2504962","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2015.2504962","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/A5087956848","display_name":"Youcheng Lou","orcid":"https://orcid.org/0000-0002-1112-4100"},"institutions":[{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"government","lineage":["https://openalex.org/I19820366"]},{"id":"https://openalex.org/I4210120485","display_name":"Academy of Mathematics and Systems Science","ror":"https://ror.org/02jkmyk67","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210120485"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Youcheng Lou","raw_affiliation_strings":["Department of Systems Engineering and Engineering Management, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Systems Engineering and Engineering Management, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China","institution_ids":["https://openalex.org/I4210120485","https://openalex.org/I19820366"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100359415","display_name":"Yiguang Hong","orcid":"https://orcid.org/0000-0001-9505-8739"},"institutions":[{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"government","lineage":["https://openalex.org/I19820366"]},{"id":"https://openalex.org/I4210120485","display_name":"Academy of Mathematics and Systems Science","ror":"https://ror.org/02jkmyk67","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210120485"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yiguang Hong","raw_affiliation_strings":["Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China","institution_ids":["https://openalex.org/I4210120485","https://openalex.org/I19820366"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100365448","display_name":"Lihua Xie","orcid":"https://orcid.org/0000-0002-7137-4136"},"institutions":[{"id":"https://openalex.org/I172675005","display_name":"Nanyang Technological University","ror":"https://ror.org/02e7b5302","country_code":"SG","type":"education","lineage":["https://openalex.org/I172675005"]}],"countries":["SG"],"is_corresponding":false,"raw_author_name":"Lihua Xie","raw_affiliation_strings":["School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore","institution_ids":["https://openalex.org/I172675005"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101779749","display_name":"Guodong Shi","orcid":"https://orcid.org/0000-0002-5929-9655"},"institutions":[{"id":"https://openalex.org/I118347636","display_name":"Australian National University","ror":"https://ror.org/019wvm592","country_code":"AU","type":"education","lineage":["https://openalex.org/I118347636"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Guodong Shi","raw_affiliation_strings":["College of Engineering and Computer Science, The Australian National University, Canberra, ACT, Australia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Engineering and Computer Science, The Australian National University, Canberra, ACT, Australia","institution_ids":["https://openalex.org/I118347636"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5045975901","display_name":"Karl Henrik Johansson","orcid":"https://orcid.org/0000-0001-9940-5929"},"institutions":[{"id":"https://openalex.org/I86987016","display_name":"KTH Royal Institute of Technology","ror":"https://ror.org/026vcq606","country_code":"SE","type":"education","lineage":["https://openalex.org/I86987016"]}],"countries":["SE"],"is_corresponding":false,"raw_author_name":"Karl Henrik Johansson","raw_affiliation_strings":["ACCESS Linnaeus Centre, School of Electrical Engineering, Royal Institute of Technology, Stockholm, Sweden"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"ACCESS Linnaeus Centre, School of Electrical Engineering, Royal Institute of Technology, Stockholm, Sweden","institution_ids":["https://openalex.org/I86987016"]}]}],"institutions":[],"countries_distinct_count":4,"institutions_distinct_count":5,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":10.8319,"has_fulltext":false,"cited_by_count":170,"citation_normalized_percentile":{"value":0.98527966,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":100},"biblio":{"volume":"61","issue":"10","first_page":"2920","last_page":"2935"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10249","display_name":"Distributed Control Multi-Agent Systems","score":1.0,"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":1.0,"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/T10796","display_name":"Cooperative Communication and Network Coding","score":0.9846000075340271,"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":0.9837999939918518,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/nash-equilibrium","display_name":"Nash equilibrium","score":0.8989801406860352},{"id":"https://openalex.org/keywords/best-response","display_name":"Best response","score":0.6560566425323486},{"id":"https://openalex.org/keywords/subgradient-method","display_name":"Subgradient method","score":0.6079541444778442},{"id":"https://openalex.org/keywords/epsilon-equilibrium","display_name":"Epsilon-equilibrium","score":0.5928381085395813},{"id":"https://openalex.org/keywords/correlated-equilibrium","display_name":"Correlated equilibrium","score":0.5458006858825684},{"id":"https://openalex.org/keywords/subnetwork","display_name":"Subnetwork","score":0.5346288681030273},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5064646005630493},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.49138274788856506},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4836198389530182},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.4660766124725342},{"id":"https://openalex.org/keywords/game-theory","display_name":"Game theory","score":0.4616599678993225},{"id":"https://openalex.org/keywords/transitive-reduction","display_name":"Transitive reduction","score":0.4447602331638336},{"id":"https://openalex.org/keywords/zero-sum-game","display_name":"Zero-sum game","score":0.43822211027145386},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.41698142886161804},{"id":"https://openalex.org/keywords/equilibrium-selection","display_name":"Equilibrium selection","score":0.332242488861084},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.2839754819869995},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.27894240617752075},{"id":"https://openalex.org/keywords/repeated-game","display_name":"Repeated game","score":0.23901906609535217},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.14727997779846191},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.130048006772995}],"concepts":[{"id":"https://openalex.org/C46814582","wikidata":"https://www.wikidata.org/wiki/Q23389","display_name":"Nash equilibrium","level":2,"score":0.8989801406860352},{"id":"https://openalex.org/C32407928","wikidata":"https://www.wikidata.org/wiki/Q2733833","display_name":"Best response","level":3,"score":0.6560566425323486},{"id":"https://openalex.org/C158968445","wikidata":"https://www.wikidata.org/wiki/Q7631150","display_name":"Subgradient method","level":2,"score":0.6079541444778442},{"id":"https://openalex.org/C141824439","wikidata":"https://www.wikidata.org/wiki/Q307521","display_name":"Epsilon-equilibrium","level":4,"score":0.5928381085395813},{"id":"https://openalex.org/C163630976","wikidata":"https://www.wikidata.org/wiki/Q964667","display_name":"Correlated equilibrium","level":5,"score":0.5458006858825684},{"id":"https://openalex.org/C2780186347","wikidata":"https://www.wikidata.org/wiki/Q11414","display_name":"Subnetwork","level":2,"score":0.5346288681030273},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5064646005630493},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.49138274788856506},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4836198389530182},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.4660766124725342},{"id":"https://openalex.org/C177142836","wikidata":"https://www.wikidata.org/wiki/Q44455","display_name":"Game theory","level":2,"score":0.4616599678993225},{"id":"https://openalex.org/C129691609","wikidata":"https://www.wikidata.org/wiki/Q3088151","display_name":"Transitive reduction","level":5,"score":0.4447602331638336},{"id":"https://openalex.org/C136356330","wikidata":"https://www.wikidata.org/wiki/Q156612","display_name":"Zero-sum game","level":3,"score":0.43822211027145386},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.41698142886161804},{"id":"https://openalex.org/C164407509","wikidata":"https://www.wikidata.org/wiki/Q5384490","display_name":"Equilibrium selection","level":4,"score":0.332242488861084},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.2839754819869995},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.27894240617752075},{"id":"https://openalex.org/C202556891","wikidata":"https://www.wikidata.org/wiki/Q1584646","display_name":"Repeated game","level":3,"score":0.23901906609535217},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.14727997779846191},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.130048006772995},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.0},{"id":"https://openalex.org/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","level":1,"score":0.0},{"id":"https://openalex.org/C22149727","wikidata":"https://www.wikidata.org/wiki/Q7940747","display_name":"Voltage graph","level":4,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tac.2015.2504962","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2015.2504962","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":[],"awards":[{"id":"https://openalex.org/G3251294079","display_name":"\u5206\u5e03\u5f0f\u4f18\u5316\u7b97\u6cd5\u53ca\u5176\u9690\u79c1\u4fdd\u62a4\u7b56\u7565\u7814\u7a76","funder_award_id":"71401163","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3703776900","display_name":null,"funder_award_id":"NRF-CRP8-2011-03","funder_id":"https://openalex.org/F4320320709","funder_display_name":"National Research Foundation Singapore"},{"id":"https://openalex.org/G444015423","display_name":null,"funder_award_id":"61333001","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5947242638","display_name":null,"funder_award_id":"4152057","funder_id":"https://openalex.org/F4320322919","funder_display_name":"Natural Science Foundation of Beijing Municipality"}],"funders":[{"id":"https://openalex.org/F4320320709","display_name":"National Research Foundation Singapore","ror":"https://ror.org/03cpyc314"},{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320322327","display_name":"Knut och Alice Wallenbergs Stiftelse","ror":"https://ror.org/004hzzk67"},{"id":"https://openalex.org/F4320322581","display_name":"Vetenskapsr\u00e5det","ror":"https://ror.org/03zttf063"},{"id":"https://openalex.org/F4320322919","display_name":"Natural Science Foundation of Beijing Municipality","ror":null}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":43,"referenced_works":["https://openalex.org/W391578156","https://openalex.org/W1544734049","https://openalex.org/W1568288633","https://openalex.org/W1583497301","https://openalex.org/W1588593629","https://openalex.org/W1893117846","https://openalex.org/W1971980754","https://openalex.org/W1973754217","https://openalex.org/W1982722567","https://openalex.org/W1982993533","https://openalex.org/W2019312235","https://openalex.org/W2020123437","https://openalex.org/W2022948311","https://openalex.org/W2026018281","https://openalex.org/W2026509976","https://openalex.org/W2029080014","https://openalex.org/W2044212084","https://openalex.org/W2049659086","https://openalex.org/W2056182476","https://openalex.org/W2056226204","https://openalex.org/W2092079425","https://openalex.org/W2100994411","https://openalex.org/W2110100895","https://openalex.org/W2114791779","https://openalex.org/W2117412539","https://openalex.org/W2119682789","https://openalex.org/W2122304153","https://openalex.org/W2124351843","https://openalex.org/W2128658178","https://openalex.org/W2135674292","https://openalex.org/W2137435346","https://openalex.org/W2142184324","https://openalex.org/W2145374086","https://openalex.org/W2163525955","https://openalex.org/W2163841953","https://openalex.org/W2164642931","https://openalex.org/W2172813797","https://openalex.org/W2797302609","https://openalex.org/W2963156126","https://openalex.org/W3016074254","https://openalex.org/W4238591275","https://openalex.org/W4250589301","https://openalex.org/W4297953140"],"related_works":["https://openalex.org/W4301347782","https://openalex.org/W1667857601","https://openalex.org/W3004964213","https://openalex.org/W4287871712","https://openalex.org/W3011680666","https://openalex.org/W3006995042","https://openalex.org/W2128266000","https://openalex.org/W1518504063","https://openalex.org/W4233209381","https://openalex.org/W1971187086"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3,72,126],"investigate":[4],"a":[5,12,32,41,45,57,78,111,131],"distributed":[6,34],"Nash":[7,42,58,79,112,132],"equilibrium":[8,43,59,80,113,133],"computation":[9],"problem":[10],"for":[11,75,104,117],"time-varying":[13],"multi-agent":[14],"network":[15],"consisting":[16],"of":[17,44],"two":[18,22,122],"subnetworks,":[19],"where":[20],"the":[21,25,52,92,105,128,137,141,145],"subnetworks":[23],"share":[24],"same":[26],"objective":[27,93],"function.":[28],"We":[29,48,96],"first":[30],"propose":[31],"subgradient-based":[33],"algorithm":[35,54,107],"with":[36,68,85,140],"heterogeneous":[37,102],"stepsizes":[38,87,103,138],"to":[39,108,130],"compute":[40],"zero-sum":[46],"game.":[47],"then":[49],"prove":[50],"that":[51,74,98,110],"proposed":[53,106,146],"can":[55,114],"achieve":[56],"under":[60],"uniformly":[61],"jointly":[62],"strongly":[63],"connected":[64],"(UJSC)":[65],"weight-balanced":[66],"digraphs":[67],"homogenous":[69,86],"stepsizes.":[70],"Moreover,":[71],"demonstrate":[73],"weighted-unbalanced":[76],"graphs":[77],"may":[81],"not":[82],"be":[83,115],"achieved":[84,116],"unless":[88],"certain":[89],"conditions":[90],"on":[91],"function":[94],"hold.":[95],"show":[97],"there":[99],"always":[100],"exist":[101],"guarantee":[109],"UJSC":[118],"digraphs.":[119],"Finally,":[120],"in":[121,144],"standard":[123],"weight-unbalanced":[124],"cases,":[125],"verify":[127],"convergence":[129],"by":[134],"adaptively":[135],"updating":[136],"along":[139],"arc":[142],"weights":[143],"algorithm.":[147]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":13},{"year":2024,"cited_by_count":22},{"year":2023,"cited_by_count":24},{"year":2022,"cited_by_count":21},{"year":2021,"cited_by_count":24},{"year":2020,"cited_by_count":17},{"year":2019,"cited_by_count":15},{"year":2018,"cited_by_count":12},{"year":2017,"cited_by_count":16},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}