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Specifically, we consider bi-matrix games where the payoffs are fuzzy random variables. Using probability and possibility measures, we formulate related fuzzy chance-constrained games. Then, we introduce Nash equilibrium for these games. Next, we establish sufficient conditions for the existence of this equilibrium. Further, the problem of its computing is formulated as a nonlinear complementarity problem. Finally, examples of market competition games and pollution management are given to illustrate the application potential of the proposed approach. The novelty and advantage of this work are that it grants the players the freedom to choose the probability and possibility confidence\/satisfaction levels at which they want Nash equilibrium to be, and equilibrium computation is simpler compared to existing approaches to fuzzy random bi-matrix games. <\/jats:p>","DOI":"10.1142\/s0218488523500459","type":"journal-article","created":{"date-parts":[[2023,12,21]],"date-time":"2023-12-21T05:48:14Z","timestamp":1703137694000},"page":"1005-1031","source":"Crossref","is-referenced-by-count":3,"title":["Nash Equilibrium in Fuzzy Random Bi-Matrix Games"],"prefix":"10.1142","volume":"31","author":[{"given":"Farida","family":"Achemine","sequence":"first","affiliation":[{"name":"Laboratoire de Math\u00e9matiques Pures et Appliqu\u00e9es, Facult\u00e9 des Sciences, Universit\u00e9 Mouloud Mammeri de Tizi Ouzou, 15000 Tizi-Ouzou, Algeria"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Moussa","family":"Larbani","sequence":"additional","affiliation":[{"name":"Ecole Nationale Sup\u00e9rieure de Statistique, et d\u2019Economie Appliqu\u00e9e (ENSSEA), Kol\u00e9a, Algeria"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2023,12,20]]},"reference":[{"key":"S0218488523500459BIB002","first-page":"81","volume":"8","author":"Bigdeli H.","year":"2018","journal-title":"Iranian Journal of Numerical Analysis and Optimization"},{"key":"S0218488523500459BIB003","doi-asserted-by":"publisher","DOI":"10.1007\/BF02836676"},{"key":"S0218488523500459BIB004","volume-title":"A General Theory of Equilibrium Selection in Games","author":"Harsanyi J. 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