{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,12]],"date-time":"2026-02-12T12:36:03Z","timestamp":1770899763910,"version":"3.50.1"},"reference-count":39,"publisher":"Institution of Engineering and Technology (IET)","issue":"1","license":[{"start":{"date-parts":[[2026,2,12]],"date-time":"2026-02-12T00:00:00Z","timestamp":1770854400000},"content-version":"vor","delay-in-days":42,"URL":"http:\/\/creativecommons.org\/licenses\/by-nc-nd\/4.0\/"},{"start":{"date-parts":[[2026,1,1]],"date-time":"2026-01-01T00:00:00Z","timestamp":1767225600000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/doi.wiley.com\/10.1002\/tdm_license_1.1"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["92367302"],"award-info":[{"award-number":["92367302"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["ietresearch.onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["IET Communications"],"published-print":{"date-parts":[[2026,1]]},"abstract":"<jats:title>ABSTRACT<\/jats:title>\n                  <jats:p>In federated learning (FL)\u2010assisted Internet of Things (IoT) systems, FL trains models using datasets on various client devices without sending the datasets to a centralized server. This approach enhances the accuracy and reliability of models while preserving the privacy of client devices. However, FL implementations face challenges, such as single point of server failure and lack of incentives. To address the server failure issue, a backup server can be added. Meanwhile, each FL client has varying data quality and motivations to participate, leading to differences in the quality of local models uploaded to the server. To motivate clients to contribute more, we designed a novel incentive mechanism based on the Stackelberg game. This mechanism allocates rewards based on the quality of the models each client uploads, rather than the amount of data trained. We separately modelled the utilities of the server and the clients, allowing the server to rationally allocate rewards based on each client's contribution to model training. After analysing the utilities, we transform the game into two optimization problems and develop an algorithm whose per\u2010round complexity scales linearly with the number of clients under fixed numerical tolerances. The obtained equilibrium matches exhaustive search within numerical precision while significantly reducing\u00a0computation.<\/jats:p>","DOI":"10.1049\/cmu2.70139","type":"journal-article","created":{"date-parts":[[2026,2,12]],"date-time":"2026-02-12T11:56:23Z","timestamp":1770897383000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Enhancing Federated Learning in IoT: A Quality\u2010Based Incentive Mechanism With Stackelberg Game Modelling"],"prefix":"10.1049","volume":"20","author":[{"ORCID":"https:\/\/orcid.org\/0009-0000-0548-3468","authenticated-orcid":false,"given":"Qinchi","family":"Li","sequence":"first","affiliation":[{"name":"The Engineering Research Center of Health Service System Based on Ubiquitous Wireless Networks Nanjing University of Posts and Telecommunications Nanjing China"}]},{"given":"Haitao","family":"Zhao","sequence":"additional","affiliation":[{"name":"The Engineering Research Center of Health Service System Based on Ubiquitous Wireless Networks Nanjing University of Posts and Telecommunications Nanjing China"}]},{"given":"Qin","family":"Wang","sequence":"additional","affiliation":[{"name":"The Engineering Research Center of Health Service System Based on Ubiquitous Wireless Networks Nanjing University of Posts and Telecommunications Nanjing China"}]},{"given":"Weicong","family":"Zhang","sequence":"additional","affiliation":[{"name":"Huawei Institute of Nanjing Nanjing China"}]},{"given":"Yangzhi","family":"Chen","sequence":"additional","affiliation":[{"name":"The Engineering Research Center of Health Service System Based on Ubiquitous Wireless Networks Nanjing University of Posts and Telecommunications Nanjing China"}]},{"given":"Zhixiang","family":"Hu","sequence":"additional","affiliation":[{"name":"The Engineering Research Center of Health Service System Based on Ubiquitous Wireless Networks Nanjing University of Posts and Telecommunications Nanjing China"}]}],"member":"265","published-online":{"date-parts":[[2026,2,12]]},"reference":[{"issue":"3","key":"e_1_2_10_2_1","doi-asserted-by":"crossref","first-page":"510","DOI":"10.1109\/TNNLS.2015.2512838","article-title":"Machine Learning Capabilities of a Simulated Cerebellum","volume":"28","author":"Hausknecht M.","year":"2017","journal-title":"IEEE Transactions on Neural Networks and Learning Systems"},{"issue":"7","key":"e_1_2_10_3_1","doi-asserted-by":"crossref","first-page":"5864","DOI":"10.1109\/TIE.2017.2767551","article-title":"Prognosis of Bearing Acoustic Emission Signals Using Supervised Machine Learning","volume":"65","author":"Elforjani M.","year":"2018","journal-title":"IEEE Transactions on Industrial Electronics"},{"issue":"3","key":"e_1_2_10_4_1","doi-asserted-by":"crossref","first-page":"2115","DOI":"10.1109\/TII.2019.2936825","article-title":"Correlated Differential Privacy: Feature Selection in Machine Learning","volume":"16","author":"Zhang T.","year":"2020","journal-title":"IEEE Transactions on Industrial Informatics"},{"issue":"4","key":"e_1_2_10_5_1","doi-asserted-by":"crossref","first-page":"2468","DOI":"10.1109\/TNSE.2020.2972602","article-title":"On Virtual Resource Allocation of Heterogeneous Networks in Virtualization Environment: A Service Oriented Perspective","volume":"7","author":"Cao H.","year":"2020","journal-title":"IEEE Transactions on Network Science and Engineering"},{"issue":"4","key":"e_1_2_10_6_1","doi-asserted-by":"crossref","first-page":"3846","DOI":"10.1109\/TVT.2021.3065967","article-title":"Resource\u2010Ability Assisted Service Function Chain Embedding and Scheduling for 6G Networks With Virtualization","volume":"70","author":"Cao H.","year":"2021","journal-title":"IEEE Transactions on Vehicular Technology"},{"issue":"7","key":"e_1_2_10_7_1","doi-asserted-by":"crossref","first-page":"5986","DOI":"10.1109\/JIOT.2019.2956615","article-title":"Communication\u2010Efficient Federated Learning for Wireless Edge Intelligence in IoT","volume":"7","author":"Mills J.","year":"2020","journal-title":"IEEE Internet of Things Journal"},{"issue":"12","key":"e_1_2_10_8_1","doi-asserted-by":"crossref","first-page":"8475","DOI":"10.1109\/TII.2021.3064351","article-title":"Deep Reinforcement Learning Assisted Federated Learning Algorithm for Data Management of IIoT","volume":"17","author":"Zhang P.","year":"2021","journal-title":"IEEE Transactions on Industrial Informatics"},{"key":"e_1_2_10_9_1","doi-asserted-by":"crossref","unstructured":"S.Wu L.Zhang Y.Wang andZ.Han \u201cSpectrum Allocation and Device Association in Federated Learning\u2010Enabled Industrial IoT via Hypergraph Matching \u201dpreprint TechRxiv 2021 https:\/\/www.techrxiv.org\/users\/680888\/articles\/677333\u2010spectrum\u2010allocation\u2010and\u2010device\u2010association\u2010in\u2010federated\u2010learning\u2010enabled\u2010industrial\u2010iot\u2010via\u2010hypergraph\u2010matching.","DOI":"10.36227\/techrxiv.15074076"},{"issue":"6","key":"e_1_2_10_10_1","doi-asserted-by":"crossref","first-page":"6798","DOI":"10.1109\/TVT.2020.2984369","article-title":"Improving TCP Performance Over WiFi for Internet of Vehicles: A Federated Learning Approach","volume":"69","author":"Pokhrel S. R.","year":"2020","journal-title":"IEEE Transactions on Vehicular Technology"},{"issue":"4","key":"e_1_2_10_11_1","doi-asserted-by":"crossref","first-page":"4298","DOI":"10.1109\/TVT.2020.2973651","article-title":"Blockchain Empowered Asynchronous Federated Learning for Secure Data Sharing in Internet of Vehicles","volume":"69","author":"Lu Y.","year":"2020","journal-title":"IEEE Transactions on Vehicular Technology"},{"issue":"12","key":"e_1_2_10_12_1","doi-asserted-by":"crossref","first-page":"24561","DOI":"10.1109\/TITS.2022.3205596","article-title":"Mobile Charging Station Placements in Internet of Electric Vehicles: A Federated Learning Approach","volume":"23","author":"Liu L.","year":"2022","journal-title":"IEEE Transactions on Intelligent Transportation Systems"},{"issue":"11","key":"e_1_2_10_13_1","doi-asserted-by":"crossref","first-page":"5596","DOI":"10.1109\/JBHI.2022.3198440","article-title":"Customized Federated Learning for Multi\u2010Source Decentralized Medical Image Classification","volume":"26","author":"Wicaksana J.","year":"2022","journal-title":"IEEE Journal of Biomedical and Health Informatics"},{"issue":"12","key":"e_1_2_10_14_1","doi-asserted-by":"crossref","first-page":"5805","DOI":"10.1109\/JBHI.2022.3192648","article-title":"Edge Intelligence: Federated Learning\u2010Based Privacy Protection Framework for Smart Healthcare Systems","volume":"26","author":"Akter M.","year":"2022","journal-title":"IEEE Journal of Biomedical and Health Informatics"},{"issue":"7","key":"e_1_2_10_15_1","doi-asserted-by":"crossref","first-page":"2615","DOI":"10.1109\/JBHI.2020.3040015","article-title":"Variation\u2010Aware Federated Learning With Multi\u2010Source Decentralized Medical Image Data","volume":"25","author":"Yan Z.","year":"2021","journal-title":"IEEE Journal of Biomedical and Health Informatics"},{"issue":"11","key":"e_1_2_10_16_1","doi-asserted-by":"crossref","first-page":"7108","DOI":"10.1109\/TWC.2020.3008091","article-title":"Multi\u2010Armed Bandit\u2010Based Client Scheduling for Federated Learning","volume":"19","author":"Xia W.","year":"2020","journal-title":"IEEE Transactions on Wireless Communications"},{"issue":"1","key":"e_1_2_10_17_1","doi-asserted-by":"crossref","first-page":"269","DOI":"10.1109\/TWC.2020.3024629","article-title":"A Joint Learning and Communications Framework for Federated Learning Over Wireless Networks","volume":"20","author":"Chen M.","year":"2021","journal-title":"IEEE Transactions on Wireless Communications"},{"issue":"1","key":"e_1_2_10_18_1","doi-asserted-by":"crossref","first-page":"86","DOI":"10.1109\/TCCN.2021.3089738","article-title":"Federated Learning for Automatic Modulation Classification Under Class Imbalance and Varying Noise Condition","volume":"8","author":"Wang Y.","year":"2022","journal-title":"IEEE Transactions on Cognitive Communications and Networking"},{"issue":"6","key":"e_1_2_10_19_1","doi-asserted-by":"crossref","first-page":"310","DOI":"10.1109\/MNET.011.2000286","article-title":"Internet of Things Intrusion Detection: Centralized, On\u2010Device, or Federated Learning?","volume":"34","author":"Rahman S. A.","year":"2020","journal-title":"IEEE Network"},{"issue":"8","key":"e_1_2_10_20_1","doi-asserted-by":"crossref","first-page":"6178","DOI":"10.1109\/JIOT.2020.3022911","article-title":"Privacy\u2010Preserving Federated Learning Framework Based on Chained Secure Multiparty Computing","volume":"8","author":"Li Y.","year":"2021","journal-title":"IEEE Internet of Things Journal"},{"issue":"11","key":"e_1_2_10_21_1","doi-asserted-by":"crossref","first-page":"10782","DOI":"10.1109\/JIOT.2020.2987958","article-title":"Privacy\u2010Preserving Federated Learning in Fog Computing","volume":"7","author":"Zhou C.","year":"2020","journal-title":"IEEE Internet of Things Journal"},{"issue":"2","key":"e_1_2_10_22_1","first-page":"1035","article-title":"A Survey of Incentive Mechanism Design for Federated Learning","volume":"10","author":"Zhan Y.","year":"2022","journal-title":"IEEE Transactions on Emerging Topics in Computing"},{"issue":"7","key":"e_1_2_10_23_1","doi-asserted-by":"crossref","first-page":"6360","DOI":"10.1109\/JIOT.2020.2967772","article-title":"A Learning\u2010Based Incentive Mechanism for Federated Learning","volume":"7","author":"Zhan Y.","year":"2020","journal-title":"IEEE Internet of Things Journal"},{"issue":"3","key":"e_1_2_10_24_1","doi-asserted-by":"crossref","first-page":"2588","DOI":"10.1109\/TNSE.2021.3100096","article-title":"Privacy\u2010Preserving Incentive Mechanism Design for Federated Cloud\u2010Edge Learning","volume":"8","author":"Liu T.","year":"2021","journal-title":"IEEE Transactions on Network Science and Engineering"},{"issue":"4","key":"e_1_2_10_25_1","doi-asserted-by":"crossref","first-page":"880","DOI":"10.1109\/JSAC.2017.2680798","article-title":"Incentive Mechanism for Mobile Crowdsourcing Using an Optimized Tournament Model","volume":"35","author":"Zhang Y.","year":"2017","journal-title":"IEEE Journal on Selected Areas in Communications"},{"issue":"9","key":"e_1_2_10_26_1","doi-asserted-by":"crossref","first-page":"4203","DOI":"10.1109\/TVT.2014.2363842","article-title":"Quality\u2010Driven Auction\u2010Based Incentive Mechanism for Mobile Crowd Sensing","volume":"64","author":"Wen Y.","year":"2015","journal-title":"IEEE Transactions on Vehicular Technology"},{"key":"e_1_2_10_27_1","doi-asserted-by":"crossref","unstructured":"Y.Wei Y.Zhu H.Zhu Q.Zhang andG.Xue \u201cTruthful Online Double Auctions for Dynamic Mobile Crowdsourcing \u201d in2015 IEEE Conference on Computer Communications (INFOCOM)(IEEE 2015) 2074\u20132082.","DOI":"10.1109\/INFOCOM.2015.7218592"},{"key":"e_1_2_10_28_1","doi-asserted-by":"crossref","unstructured":"Q.Wang W.Wang S.Jin H.Zhu andN. T.Zhang \u201cSmart Media Pricing (SMP): Non\u2010Uniform Packet Pricing Game for Wireless Multimedia Communications \u201d in2016 IEEE Conference on Computer Communications Workshops (INFOCOM WKSHPS)(IEEE 2016) 27\u201332.","DOI":"10.1109\/INFCOMW.2016.7562040"},{"issue":"12","key":"e_1_2_10_29_1","doi-asserted-by":"crossref","first-page":"3358","DOI":"10.1109\/JSAC.2022.3213345","article-title":"A Fast Blockchain\u2010Based Federated Learning Framework With Compressed Communications","volume":"40","author":"Cui L.","year":"2022","journal-title":"IEEE Journal on Selected Areas in Communications"},{"issue":"1","key":"e_1_2_10_30_1","doi-asserted-by":"crossref","first-page":"173","DOI":"10.1109\/TNSE.2021.3050781","article-title":"VFChain: Enabling Verifiable and Auditable Federated Learning via Blockchain Systems","volume":"9","author":"Peng Z.","year":"2022","journal-title":"IEEE Transactions on Network Science and Engineering"},{"issue":"16","key":"e_1_2_10_31_1","doi-asserted-by":"crossref","first-page":"12806","DOI":"10.1109\/JIOT.2021.3072611","article-title":"Federated Learning Meets Blockchain in Edge Computing: Opportunities and Challenges","volume":"8","author":"Nguyen D. C.","year":"2021","journal-title":"IEEE Internet of Things Journal"},{"issue":"5","key":"e_1_2_10_32_1","doi-asserted-by":"crossref","first-page":"1536","DOI":"10.1109\/TPDS.2023.3253604","article-title":"Incentive Mechanism Design for Joint Resource Allocation in Blockchain\u2010Based Federated Learning","volume":"34","author":"Wang Z.","year":"2023","journal-title":"IEEE Transactions on Parallel and Distributed Systems"},{"key":"e_1_2_10_33_1","doi-asserted-by":"crossref","first-page":"94","DOI":"10.1016\/j.comcom.2020.07.045","article-title":"Privacy\u2010Preserving Model Training Architecture for Intelligent Edge Computing","volume":"162","author":"Qu X.","year":"2020","journal-title":"Computer Communications"},{"issue":"5","key":"e_1_2_10_34_1","doi-asserted-by":"crossref","first-page":"2019","DOI":"10.1109\/TNET.2018.2840098","article-title":"Incentive Mechanism for Privacy\u2010Aware Data Aggregation in Mobile Crowd Sensing Systems","volume":"26","author":"Jin H.","year":"2018","journal-title":"IEEE\/ACM Transactions on Networking"},{"issue":"5","key":"e_1_2_10_35_1","doi-asserted-by":"crossref","first-page":"993","DOI":"10.1080\/10556788.2017.1298596","article-title":"Semi\u2010Stochastic Coordinate Descent","volume":"32","author":"Kone\u010dn\u00fd J.","year":"2017","journal-title":"Optimization Methods and Software"},{"issue":"10","key":"e_1_2_10_36_1","doi-asserted-by":"crossref","first-page":"2320","DOI":"10.1109\/TMC.2014.2307327","article-title":"Motivating Smartphone Collaboration in Data Acquisition and Distributed Computing","volume":"13","author":"Duan L.","year":"2014","journal-title":"IEEE Transactions on Mobile Computing"},{"key":"e_1_2_10_37_1","doi-asserted-by":"crossref","unstructured":"D.Yang G.Xue X.Fang andJ.Tang \u201cCrowdsourcing to Smartphones: Incentive Mechanism Design for Mobile Phone Sensing \u201d inProceedings of the 18th Annual International Conference on Mobile Computing and Networking(ACM 2012) 173\u2013184.","DOI":"10.1145\/2348543.2348567"},{"issue":"2","key":"e_1_2_10_38_1","doi-asserted-by":"crossref","first-page":"203","DOI":"10.1007\/BF01130406","article-title":"Processor Design for Portable Systems","volume":"13","author":"Burd T. D.","year":"1996","journal-title":"Journal of VLSI Signal Processing Systems for Signal, Image and Video Technology"},{"issue":"5","key":"e_1_2_10_39_1","doi-asserted-by":"crossref","first-page":"3241","DOI":"10.1109\/TWC.2020.2971981","article-title":"A Crowdsourcing Framework for On\u2010Device Federated Learning","volume":"19","author":"Pandey S. R.","year":"2020","journal-title":"IEEE Transactions on Wireless Communications"},{"key":"e_1_2_10_40_1","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9781139171656","volume-title":"Mathematical Analysis: A Straightforward Approach","author":"Binmore K. G.","year":"1982"}],"container-title":["IET Communications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/ietresearch.onlinelibrary.wiley.com\/doi\/pdf\/10.1049\/cmu2.70139","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/ietresearch.onlinelibrary.wiley.com\/doi\/full-xml\/10.1049\/cmu2.70139","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/ietresearch.onlinelibrary.wiley.com\/doi\/pdf\/10.1049\/cmu2.70139","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,2,12]],"date-time":"2026-02-12T11:56:30Z","timestamp":1770897390000},"score":1,"resource":{"primary":{"URL":"https:\/\/ietresearch.onlinelibrary.wiley.com\/doi\/10.1049\/cmu2.70139"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,1]]},"references-count":39,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2026,1]]}},"alternative-id":["10.1049\/cmu2.70139"],"URL":"https:\/\/doi.org\/10.1049\/cmu2.70139","archive":["Portico"],"relation":{},"ISSN":["1751-8628","1751-8636"],"issn-type":[{"value":"1751-8628","type":"print"},{"value":"1751-8636","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,1]]},"assertion":[{"value":"2025-09-30","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2026-01-21","order":2,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2026-02-12","order":3,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}],"article-number":"e70139"}}