{"id":"https://openalex.org/W7134909818","doi":"https://doi.org/10.1109/tmc.2026.3672522","title":"Two-Dimensional Stackelberg Game-Based Incentive Mechanism for Differential Private Federated Learning With Non-IID Data","display_name":"Two-Dimensional Stackelberg Game-Based Incentive Mechanism for Differential Private Federated Learning With Non-IID Data","publication_year":2026,"publication_date":"2026-03-10","ids":{"openalex":"https://openalex.org/W7134909818","doi":"https://doi.org/10.1109/tmc.2026.3672522"},"language":null,"primary_location":{"id":"doi:10.1109/tmc.2026.3672522","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tmc.2026.3672522","pdf_url":null,"source":{"id":"https://openalex.org/S69141925","display_name":"IEEE Transactions on Mobile Computing","issn_l":"1536-1233","issn":["1536-1233","1558-0660","2161-9875"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320439","host_organization_name":"IEEE Computer Society","host_organization_lineage":["https://openalex.org/P4310320439","https://openalex.org/P4310319808"],"host_organization_lineage_names":["IEEE Computer Society","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 Mobile Computing","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/A5128793069","display_name":"Dan Wang","orcid":null},"institutions":[{"id":"https://openalex.org/I173759888","display_name":"Hunan Normal University","ror":"https://ror.org/053w1zy07","country_code":"CN","type":"education","lineage":["https://openalex.org/I173759888"]},{"id":"https://openalex.org/I3130607311","display_name":"Changsha Normal University","ror":"https://ror.org/02sqk3z62","country_code":"CN","type":"education","lineage":["https://openalex.org/I3130607311"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Dan Wang","raw_affiliation_strings":["College of Information Science and Engineering, Hunan Normal University, Changsha, China"],"raw_orcid":"https://orcid.org/0000-0002-8132-9785","affiliations":[{"raw_affiliation_string":"College of Information Science and Engineering, Hunan Normal University, Changsha, China","institution_ids":["https://openalex.org/I173759888","https://openalex.org/I3130607311"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5083836256","display_name":"Xiaoyi Pang","orcid":"https://orcid.org/0000-0002-2763-2695"},"institutions":[{"id":"https://openalex.org/I76130692","display_name":"Zhejiang University","ror":"https://ror.org/00a2xv884","country_code":"CN","type":"education","lineage":["https://openalex.org/I76130692"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xiaoyi Pang","raw_affiliation_strings":["State Key Laboratory of Blockchain and Data Security, Zhejiang University, Hangzhou, China"],"raw_orcid":"https://orcid.org/0000-0002-2763-2695","affiliations":[{"raw_affiliation_string":"State Key Laboratory of Blockchain and Data Security, Zhejiang University, Hangzhou, China","institution_ids":["https://openalex.org/I76130692"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5128756018","display_name":"Jiahui Hu","orcid":null},"institutions":[{"id":"https://openalex.org/I141649914","display_name":"Nanchang University","ror":"https://ror.org/042v6xz23","country_code":"CN","type":"education","lineage":["https://openalex.org/I141649914"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jiahui Hu","raw_affiliation_strings":["School of Artificial Intelligence, Nanchang University, Nanchang, China"],"raw_orcid":"https://orcid.org/0000-0001-8771-7474","affiliations":[{"raw_affiliation_string":"School of Artificial Intelligence, Nanchang University, Nanchang, China","institution_ids":["https://openalex.org/I141649914"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101752867","display_name":"Sheng Yue","orcid":"https://orcid.org/0009-0001-3416-8181"},"institutions":[{"id":"https://openalex.org/I157773358","display_name":"Sun Yat-sen University","ror":"https://ror.org/0064kty71","country_code":"CN","type":"education","lineage":["https://openalex.org/I157773358"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Sheng Yue","raw_affiliation_strings":["School of Cyber Science and Technology, Sun Yat-sen University, Shenzhen, China"],"raw_orcid":"https://orcid.org/0009-0001-3416-8181","affiliations":[{"raw_affiliation_string":"School of Cyber Science and Technology, Sun Yat-sen University, Shenzhen, China","institution_ids":["https://openalex.org/I157773358"]}]},{"author_position":"last","author":{"id":null,"display_name":"Ju Ren","orcid":"https://orcid.org/0000-0003-2782-183X"},"institutions":[{"id":"https://openalex.org/I99065089","display_name":"Tsinghua University","ror":"https://ror.org/03cve4549","country_code":"CN","type":"education","lineage":["https://openalex.org/I99065089"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Ju Ren","raw_affiliation_strings":["Department of Computer Science and Technology, BNRist, Tsinghua University, Beijing, China"],"raw_orcid":"https://orcid.org/0000-0003-2782-183X","affiliations":[{"raw_affiliation_string":"Department of Computer Science and Technology, BNRist, Tsinghua University, Beijing, China","institution_ids":["https://openalex.org/I99065089"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":6,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":9.7964,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.96915497,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":97},"biblio":{"volume":"25","issue":"8","first_page":"12688","last_page":"12703"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10764","display_name":"Privacy-Preserving Technologies in Data","score":0.9732999801635742,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T10764","display_name":"Privacy-Preserving Technologies in Data","score":0.9732999801635742,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.009200000204145908,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T11704","display_name":"Mobile Crowdsensing and Crowdsourcing","score":0.002199999988079071,"subfield":{"id":"https://openalex.org/subfields/1706","display_name":"Computer Science Applications"},"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/stackelberg-competition","display_name":"Stackelberg competition","score":0.982200026512146},{"id":"https://openalex.org/keywords/incentive","display_name":"Incentive","score":0.7247999906539917},{"id":"https://openalex.org/keywords/private-information-retrieval","display_name":"Private information retrieval","score":0.598800003528595},{"id":"https://openalex.org/keywords/differential-privacy","display_name":"Differential privacy","score":0.5605000257492065},{"id":"https://openalex.org/keywords/mechanism-design","display_name":"Mechanism design","score":0.5267000198364258},{"id":"https://openalex.org/keywords/nash-equilibrium","display_name":"Nash equilibrium","score":0.45080000162124634},{"id":"https://openalex.org/keywords/boosting","display_name":"Boosting (machine learning)","score":0.4343000054359436}],"concepts":[{"id":"https://openalex.org/C199510392","wikidata":"https://www.wikidata.org/wiki/Q1184602","display_name":"Stackelberg competition","level":2,"score":0.982200026512146},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.8206999897956848},{"id":"https://openalex.org/C29122968","wikidata":"https://www.wikidata.org/wiki/Q1414816","display_name":"Incentive","level":2,"score":0.7247999906539917},{"id":"https://openalex.org/C99221444","wikidata":"https://www.wikidata.org/wiki/Q1532069","display_name":"Private information retrieval","level":2,"score":0.598800003528595},{"id":"https://openalex.org/C23130292","wikidata":"https://www.wikidata.org/wiki/Q5275358","display_name":"Differential privacy","level":2,"score":0.5605000257492065},{"id":"https://openalex.org/C153517567","wikidata":"https://www.wikidata.org/wiki/Q26090","display_name":"Mechanism design","level":2,"score":0.5267000198364258},{"id":"https://openalex.org/C46814582","wikidata":"https://www.wikidata.org/wiki/Q23389","display_name":"Nash equilibrium","level":2,"score":0.45080000162124634},{"id":"https://openalex.org/C46686674","wikidata":"https://www.wikidata.org/wiki/Q466303","display_name":"Boosting (machine learning)","level":2,"score":0.4343000054359436},{"id":"https://openalex.org/C141513077","wikidata":"https://www.wikidata.org/wiki/Q378542","display_name":"Independent and identically distributed random variables","level":3,"score":0.42989999055862427},{"id":"https://openalex.org/C93996380","wikidata":"https://www.wikidata.org/wiki/Q44127","display_name":"Server","level":2,"score":0.4185999929904938},{"id":"https://openalex.org/C2992525071","wikidata":"https://www.wikidata.org/wiki/Q50818671","display_name":"Federated learning","level":2,"score":0.36629998683929443},{"id":"https://openalex.org/C89611455","wikidata":"https://www.wikidata.org/wiki/Q6804646","display_name":"Mechanism (biology)","level":2,"score":0.3637000024318695},{"id":"https://openalex.org/C177142836","wikidata":"https://www.wikidata.org/wiki/Q44455","display_name":"Game theory","level":2,"score":0.36000001430511475},{"id":"https://openalex.org/C91810955","wikidata":"https://www.wikidata.org/wiki/Q7731670","display_name":"Incentive compatibility","level":3,"score":0.35740000009536743},{"id":"https://openalex.org/C93226319","wikidata":"https://www.wikidata.org/wiki/Q193137","display_name":"Differential (mechanical device)","level":2,"score":0.3253999948501587},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3246999979019165},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.28690001368522644},{"id":"https://openalex.org/C42475967","wikidata":"https://www.wikidata.org/wiki/Q194292","display_name":"Operations research","level":1,"score":0.2678999900817871},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.26409998536109924},{"id":"https://openalex.org/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","level":1,"score":0.2565000057220459},{"id":"https://openalex.org/C175444787","wikidata":"https://www.wikidata.org/wiki/Q39072","display_name":"Microeconomics","level":1,"score":0.2538999915122986}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tmc.2026.3672522","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tmc.2026.3672522","pdf_url":null,"source":{"id":"https://openalex.org/S69141925","display_name":"IEEE Transactions on Mobile Computing","issn_l":"1536-1233","issn":["1536-1233","1558-0660","2161-9875"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320439","host_organization_name":"IEEE Computer Society","host_organization_lineage":["https://openalex.org/P4310320439","https://openalex.org/P4310319808"],"host_organization_lineage_names":["IEEE Computer Society","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 Mobile Computing","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2520926689","display_name":null,"funder_award_id":"62302164","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6109278019","display_name":null,"funder_award_id":"2023M731071","funder_id":"https://openalex.org/F4320321543","funder_display_name":"China Postdoctoral Science Foundation"},{"id":"https://openalex.org/G8616192000","display_name":null,"funder_award_id":"62572496","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/F4320321543","display_name":"China Postdoctoral Science Foundation","ror":"https://ror.org/0426zh255"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Incentive":[0],"mechanisms":[1,19],"are":[2,25,42],"essential":[3],"for":[4,69,171],"boosting":[5],"client":[6,23],"engagement":[7],"in":[8,57,191],"differential":[9],"private":[10],"federated":[11],"learning":[12,164],"(DP-FL).":[13],"However,":[14],"existing":[15],"Stakelberg":[16],"games-based":[17],"incentive":[18,67],"typically":[20],"assume":[21],"that":[22,28,131,184],"decisions":[24,92,111,130,170],"one-dimension":[26],"and":[27,32,45,54,82,93,107,112,119,146,174,178],"data":[29,40,52],"is":[30],"independent":[31],"identically":[33],"distributed":[34],"(IID)":[35],"across":[36],"clients.":[37,147],"In":[38],"reality,":[39],"distributions":[41],"often":[43],"non-IID":[44,72],"clients":[46,81,108,120,175],"have":[47],"two-dimensional":[48,64,91,110],"resources":[49],"decisions,":[50],"including":[51],"quantity":[53],"privacy.":[55],"Therefore,":[56],"this":[58],"paper,":[59],"we":[60,98,135,158],"present":[61],"a":[62,86,122,141,160],"novel":[63],"Stackelberg":[65,124,142,156],"game-based":[66],"mechanism":[68],"DP-FL":[70],"with":[71],"data,":[73],"aiming":[74],"to":[75,149,152,166],"maximize":[76,132],"the":[77,89,94,101,115,128,138,150,155,168,189],"total":[78,194],"utility":[79,102],"of":[80,104,140,193],"server":[83,106,118,145,173],"by":[84,176],"seeking":[85],"balance":[87],"between":[88,117,144],"clients'":[90],"server's":[95],"payment.":[96],"Specifically,":[97],"first":[99],"formulate":[100],"functions":[103],"both":[105,172],"under":[109],"then":[113],"model":[114],"interactions":[116],"as":[121],"single-leader-multiple-followers":[123],"game.":[125],"To":[126],"derive":[127],"optimal":[129,169],"their":[133],"utilities,":[134],"theoretically":[136],"prove":[137],"existence":[139],"equilibrium":[143],"Due":[148],"difficulty":[151],"directly":[153],"calculate":[154],"equilibrium,":[157],"propose":[159],"bi-level":[161],"multi-agent":[162],"reinforment":[163],"algorithm":[165],"learn":[167],"trial":[177],"error.":[179],"Extensive":[180],"simulation":[181],"results":[182],"demonstrate":[183],"our":[185],"proposed":[186],"method":[187],"outperforms":[188],"baselines":[190],"terms":[192],"utility.":[195]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-07-22T07:51:19.307946","created_date":"2026-03-12T00:00:00"}
