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to train federated models while complying with their privacy, data security, and government regulations. Due to federated model training, an accurate model should be trained, and all federated players should actively participate. Therefore, it is crucial to design an incentive mechanism; however, there is a conflict between fairness and Pareto efficiency in the incentive mechanism. In this paper, we propose an incentive mechanism via the combination of the Shapley value and Pareto efficiency optimization, in which a third party is introduced to supervise the federated payoff allocation. If the payoff can reach Pareto optimality, the federated payoff is allocated by the Shapley value method; otherwise, the relevant federated players are punished. Numerical and simulation experiments show that the mechanism can achieve fair payoff allocation and Pareto optimality payoff allocation. The Nash equilibrium of this mechanism is formed when Pareto optimality payoff allocation is achieved.<\/jats:p>","DOI":"10.3390\/axioms12070636","type":"journal-article","created":{"date-parts":[[2023,6,28]],"date-time":"2023-06-28T00:50:52Z","timestamp":1687913452000},"page":"636","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":11,"title":["Federated Learning Incentive Mechanism Design via Shapley Value and Pareto Optimality"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5335-963X","authenticated-orcid":false,"given":"Xun","family":"Yang","sequence":"first","affiliation":[{"name":"School of Mathematics and Statistics, Guizhou University, Guiyang 550025, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8724-6449","authenticated-orcid":false,"given":"Shuwen","family":"Xiang","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Guizhou University, Guiyang 550025, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8733-4596","authenticated-orcid":false,"given":"Changgen","family":"Peng","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Public Big Data, College of Computer Science and Technology, Guizhou University, Guiyang 550025, China"},{"name":"Guizhou Big Data Academy, Guizhou University, Guiyang 550025, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6590-5757","authenticated-orcid":false,"given":"Weijie","family":"Tan","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Public Big Data, College of Computer Science and Technology, Guizhou University, Guiyang 550025, China"},{"name":"Guizhou Big Data Academy, Guizhou University, Guiyang 550025, China"},{"name":"Key Laboratory of Advanced Manufacturing Technology, Ministry of Education, Guizhou University, Guiyang 550025, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1691-3384","authenticated-orcid":false,"given":"Zhen","family":"Li","sequence":"additional","affiliation":[{"name":"College of Big Data and Information Engineering, Guizhou University, Guiyang 550025, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0403-8834","authenticated-orcid":false,"given":"Ningbo","family":"Wu","sequence":"additional","affiliation":[{"name":"School of Information, Guizhou University of Finance and Economics, Guiyang 550025, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1289-9343","authenticated-orcid":false,"given":"Yan","family":"Zhou","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Public Big Data, College of Computer Science and Technology, Guizhou University, Guiyang 550025, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2023,6,27]]},"reference":[{"key":"ref_1","unstructured":"Kone\u010dn\u1ef3, J., McMahan, H.B., Ramage, D., and Richt\u00e1rik, P. 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