{"id":"https://openalex.org/W4206117711","doi":"https://doi.org/10.1109/tcsii.2021.3137339","title":"Distributed Nash Equilibrium Seeking in a Multi-Coalition Noncooperative Game Under Incomplete Decision Information","display_name":"Distributed Nash Equilibrium Seeking in a Multi-Coalition Noncooperative Game Under Incomplete Decision Information","publication_year":2021,"publication_date":"2021-12-22","ids":{"openalex":"https://openalex.org/W4206117711","doi":"https://doi.org/10.1109/tcsii.2021.3137339"},"language":"en","primary_location":{"id":"doi:10.1109/tcsii.2021.3137339","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tcsii.2021.3137339","pdf_url":null,"source":{"id":"https://openalex.org/S93916849","display_name":"IEEE Transactions on Circuits & Systems II Express Briefs","issn_l":"1549-7747","issn":["1549-7747","1558-3791"],"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 Circuits and Systems II: Express Briefs","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/A5100650688","display_name":"Yamei Li","orcid":"https://orcid.org/0000-0002-2277-0511"},"institutions":[{"id":"https://openalex.org/I200845125","display_name":"Nanjing University of Information Science and Technology","ror":"https://ror.org/02y0rxk19","country_code":"CN","type":"education","lineage":["https://openalex.org/I200845125"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Yamei Li","raw_affiliation_strings":["School of Automation, Nanjing University of Information Science and Technology, Nanjing, China"],"raw_orcid":"https://orcid.org/0000-0002-2277-0511","affiliations":[{"raw_affiliation_string":"School of Automation, Nanjing University of Information Science and Technology, Nanjing, China","institution_ids":["https://openalex.org/I200845125"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5020521560","display_name":"Yanan Zhu","orcid":"https://orcid.org/0000-0001-7980-6282"},"institutions":[{"id":"https://openalex.org/I200845125","display_name":"Nanjing University of Information Science and Technology","ror":"https://ror.org/02y0rxk19","country_code":"CN","type":"education","lineage":["https://openalex.org/I200845125"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yanan Zhu","raw_affiliation_strings":["School of Automation, Nanjing University of Information Science and Technology, Nanjing, China"],"raw_orcid":"https://orcid.org/0000-0001-7980-6282","affiliations":[{"raw_affiliation_string":"School of Automation, Nanjing University of Information Science and Technology, Nanjing, China","institution_ids":["https://openalex.org/I200845125"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100721510","display_name":"Tao Li","orcid":"https://orcid.org/0000-0002-9190-0199"},"institutions":[{"id":"https://openalex.org/I200845125","display_name":"Nanjing University of Information Science and Technology","ror":"https://ror.org/02y0rxk19","country_code":"CN","type":"education","lineage":["https://openalex.org/I200845125"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Tao Li","raw_affiliation_strings":["School of Automation, Nanjing University of Information Science and Technology, Nanjing, China"],"raw_orcid":"https://orcid.org/0000-0002-9190-0199","affiliations":[{"raw_affiliation_string":"School of Automation, Nanjing University of Information Science and Technology, Nanjing, China","institution_ids":["https://openalex.org/I200845125"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5074697668","display_name":"Bo\u2010Chao Zheng","orcid":"https://orcid.org/0000-0001-6142-6580"},"institutions":[{"id":"https://openalex.org/I200845125","display_name":"Nanjing University of Information Science and Technology","ror":"https://ror.org/02y0rxk19","country_code":"CN","type":"education","lineage":["https://openalex.org/I200845125"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Bo-Chao Zheng","raw_affiliation_strings":["School of Automation, Nanjing University of Information Science and Technology, Nanjing, China"],"raw_orcid":"https://orcid.org/0000-0001-6142-6580","affiliations":[{"raw_affiliation_string":"School of Automation, Nanjing University of Information Science and Technology, Nanjing, China","institution_ids":["https://openalex.org/I200845125"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5100650688"],"corresponding_institution_ids":["https://openalex.org/I200845125"],"apc_list":null,"apc_paid":null,"fwci":1.9219,"has_fulltext":false,"cited_by_count":17,"citation_normalized_percentile":{"value":0.86933786,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":96,"max":99},"biblio":{"volume":"69","issue":"8","first_page":"3400","last_page":"3404"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10249","display_name":"Distributed Control Multi-Agent Systems","score":0.9983999729156494,"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":0.9983999729156494,"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/T10482","display_name":"Mathematical and Theoretical Epidemiology and Ecology Models","score":0.9858999848365784,"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"}},{"id":"https://openalex.org/T12794","display_name":"Adaptive Dynamic Programming Control","score":0.9796000123023987,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/nash-equilibrium","display_name":"Nash equilibrium","score":0.7198714017868042},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5820804834365845},{"id":"https://openalex.org/keywords/complete-information","display_name":"Complete information","score":0.5426353812217712},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5347470641136169},{"id":"https://openalex.org/keywords/game-theory","display_name":"Game theory","score":0.5220520496368408},{"id":"https://openalex.org/keywords/lyapunov-function","display_name":"Lyapunov function","score":0.5033835768699646},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.49369606375694275},{"id":"https://openalex.org/keywords/potential-game","display_name":"Potential game","score":0.4853860139846802},{"id":"https://openalex.org/keywords/best-response","display_name":"Best response","score":0.4720607399940491},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.4505711495876312},{"id":"https://openalex.org/keywords/strategy","display_name":"Strategy","score":0.4449220299720764},{"id":"https://openalex.org/keywords/replicator-equation","display_name":"Replicator equation","score":0.43452808260917664},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.42970675230026245},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.23163339495658875},{"id":"https://openalex.org/keywords/economics","display_name":"Economics","score":0.2176879644393921},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.1413973867893219},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.1173863410949707}],"concepts":[{"id":"https://openalex.org/C46814582","wikidata":"https://www.wikidata.org/wiki/Q23389","display_name":"Nash equilibrium","level":2,"score":0.7198714017868042},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5820804834365845},{"id":"https://openalex.org/C113336015","wikidata":"https://www.wikidata.org/wiki/Q574010","display_name":"Complete information","level":2,"score":0.5426353812217712},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5347470641136169},{"id":"https://openalex.org/C177142836","wikidata":"https://www.wikidata.org/wiki/Q44455","display_name":"Game theory","level":2,"score":0.5220520496368408},{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.5033835768699646},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.49369606375694275},{"id":"https://openalex.org/C2778079155","wikidata":"https://www.wikidata.org/wiki/Q288500","display_name":"Potential game","level":3,"score":0.4853860139846802},{"id":"https://openalex.org/C32407928","wikidata":"https://www.wikidata.org/wiki/Q2733833","display_name":"Best response","level":3,"score":0.4720607399940491},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.4505711495876312},{"id":"https://openalex.org/C88959737","wikidata":"https://www.wikidata.org/wiki/Q1546627","display_name":"Strategy","level":3,"score":0.4449220299720764},{"id":"https://openalex.org/C50318809","wikidata":"https://www.wikidata.org/wiki/Q2145081","display_name":"Replicator equation","level":3,"score":0.43452808260917664},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.42970675230026245},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.23163339495658875},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.2176879644393921},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.1413973867893219},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.1173863410949707},{"id":"https://openalex.org/C2908647359","wikidata":"https://www.wikidata.org/wiki/Q2625603","display_name":"Population","level":2,"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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","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/tcsii.2021.3137339","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tcsii.2021.3137339","pdf_url":null,"source":{"id":"https://openalex.org/S93916849","display_name":"IEEE Transactions on Circuits & Systems II Express Briefs","issn_l":"1549-7747","issn":["1549-7747","1558-3791"],"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 Circuits and Systems II: Express Briefs","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.7200000286102295,"display_name":"Peace, Justice and strong institutions","id":"https://metadata.un.org/sdg/16"}],"awards":[{"id":"https://openalex.org/G5674403503","display_name":null,"funder_award_id":"BK20200809","funder_id":"https://openalex.org/F4320322769","funder_display_name":"Natural Science Foundation of Jiangsu Province"},{"id":"https://openalex.org/G6702909607","display_name":null,"funder_award_id":"20KJB120004","funder_id":"https://openalex.org/F4320335440","funder_display_name":"Natural Science Research of Jiangsu Higher Education Institutions of China"},{"id":"https://openalex.org/G7498125188","display_name":null,"funder_award_id":"61973168","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/F4320322769","display_name":"Natural Science Foundation of Jiangsu Province","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320335440","display_name":"Natural Science Research of Jiangsu Higher Education Institutions of China","ror":null}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":30,"referenced_works":["https://openalex.org/W1630241696","https://openalex.org/W1971441460","https://openalex.org/W1985348591","https://openalex.org/W2026018281","https://openalex.org/W2032656479","https://openalex.org/W2100431085","https://openalex.org/W2113702258","https://openalex.org/W2315826754","https://openalex.org/W2568893241","https://openalex.org/W2611964096","https://openalex.org/W2805316908","https://openalex.org/W2899989669","https://openalex.org/W2919725712","https://openalex.org/W2962910407","https://openalex.org/W2999418630","https://openalex.org/W3024828079","https://openalex.org/W3041493239","https://openalex.org/W3104002866","https://openalex.org/W3126629040","https://openalex.org/W3128631749","https://openalex.org/W3135623636","https://openalex.org/W3135910512","https://openalex.org/W3174070171","https://openalex.org/W3185117385","https://openalex.org/W3199400742","https://openalex.org/W4225616414","https://openalex.org/W6777444434","https://openalex.org/W6796941742","https://openalex.org/W6801524147","https://openalex.org/W6810951977"],"related_works":["https://openalex.org/W2365698029","https://openalex.org/W4300514062","https://openalex.org/W2949715110","https://openalex.org/W2787689390","https://openalex.org/W3013584695","https://openalex.org/W1988769349","https://openalex.org/W2141828543","https://openalex.org/W2494067724","https://openalex.org/W1987517087","https://openalex.org/W4298859366"],"abstract_inverted_index":{"This":[0],"brief":[1],"studies":[2],"a":[3,11,55,109,117,144,164,188,213],"distributed":[4,110,193],"Nash":[5],"equilibrium":[6],"(NE)":[7],"seeking":[8,111,195],"strategy":[9,112],"for":[10],"multi-coalition":[12,130],"noncooperative":[13],"game":[14,21],"with":[15,184],"local":[16,40,92],"decision":[17,101],"sets.":[18],"In":[19],"the":[20,36,39,45,48,59,63,66,81,84,99,125,128,150,153,172,175,207],"model,":[22],"each":[23,51,71,87,140,156],"coalition":[24,52,72,88],"consists":[25],"of":[26,38,70,127],"some":[27],"agents":[28,46,64,85,154],"and":[29,58,94],"its":[30,76],"cost":[31,41,69,78],"funciton":[32],"is":[33,73,121,136,168,200,210],"determined":[34],"by":[35,143,181,202],"sum":[37],"functions":[42],"subject":[43],"to":[44,74,123,138,170],"in":[47,65,86,103,155],"coalition,":[49],"where":[50,174],"serves":[53],"as":[54],"virtual":[56],"player":[57],"actual":[60],"decision-makers":[61],"are":[62],"coalition.":[67,157],"The":[68,132,158],"minimize":[75],"own":[77],"function":[79],"under":[80],"case":[82],"that":[83,113,148],"only":[89,183],"know":[90],"their":[91,185],"information":[93,102],"can":[95,114],"not":[96],"directly":[97],"access":[98],"opponent\u2019s":[100],"other":[104,178],"coalitions.":[105],"To":[106],"this":[107,192],"end,":[108],"be":[115],"viewed":[116],"two-time":[118],"scale":[119],"system":[120,135,161],"developed":[122],"search":[124],"NE":[126,194],"formulated":[129],"game.":[131],"fast":[133],"time-scale":[134,160],"used":[137],"estimate":[139,177],"coalition\u2019s":[141],"pseudo-gradient":[142],"connected":[145],"interference":[146],"graph":[147],"illustrates":[149],"interactions":[151],"among":[152],"slow":[159],"based":[162],"on":[163],"projected":[165],"psedudo-gradient":[166],"dynamics":[167],"implemented":[169],"seek":[171],"NE,":[173],"coalitions":[176],"coalitions\u2019":[179],"decisions":[180],"interacting":[182],"neighbors":[186],"via":[187,212],"weight-balanced":[189],"digraph.":[190],"For":[191],"strategy,":[196],"asymptotic":[197],"convergence":[198],"result":[199],"given":[201],"Lyapunov":[203],"stability":[204],"analysis.":[205],"Finally,":[206],"theoretical":[208],"results":[209],"demonstrated":[211],"numerical":[214],"example.":[215]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":7},{"year":2023,"cited_by_count":5}],"updated_date":"2026-05-05T08:41:31.759640","created_date":"2025-10-10T00:00:00"}
