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Based on the theory of stochastic analysis, a countably infinite set of coupled generalized algebraic Riccati equations are solved and a necessary and sufficient condition for the existence of Nash equilibrium points is obtained. From a new perspective, the finite horizon mixed robust H2\/H\u221e control is investigated, and summarize the relationship between Nash game and H2\/H\u221e control problem. Moreover, the feasibility and validity of the proposed method has been proved by applying it to a numerical example.<\/jats:p>","DOI":"10.3390\/axioms12090882","type":"journal-article","created":{"date-parts":[[2023,9,15]],"date-time":"2023-09-15T04:06:13Z","timestamp":1694750773000},"page":"882","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Non-Zero Sum Nash Game for Discrete-Time Infinite Markov Jump Stochastic Systems with Applications"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6268-8160","authenticated-orcid":false,"given":"Yueying","family":"Liu","sequence":"first","affiliation":[{"name":"College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1487-5089","authenticated-orcid":false,"given":"Zhen","family":"Wang","sequence":"additional","affiliation":[{"name":"College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xiangyun","family":"Lin","sequence":"additional","affiliation":[{"name":"College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2023,9,15]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"987","DOI":"10.1137\/15M1008476","article-title":"Rationally inattentive control of Markov processes","volume":"54","author":"Shafieepoorfard","year":"2016","journal-title":"SIAM J. 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