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\u043c\u043d\u043e\u0436\u0435\u0441\u0442\u0432\u0435\u043d\u043d\u044b\u0445 \u0441\u0442\u0440\u0443\u043a\u0442\u0443\u0440 \u0438\u043d\u0444\u043e\u0440\u043c\u0438\u0440\u043e\u0432\u0430\u043d\u043d\u043e\u0441\u0442\u0438 (\u041e\u041c\u0421\u0418) \u0434\u043e\u043f\u0443\u0441\u043a\u0430\u0435\u0442 \u0440\u0430\u0437\u043b\u0438\u0447\u043d\u043e\u0435 \u043a\u043e\u043b\u0438\u0447\u0435\u0441\u0442\u0432\u043e \u0443\u0447\u0430\u0441\u0442\u043d\u0438\u043a\u043e\u0432 \u0432 \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u043b\u0435\u043d\u0438\u044f\u0445 \u0430\u0433\u0435\u043d\u0442\u043e\u0432 \u043e \u0441\u0438\u0442\u0443\u0430\u0446\u0438\u0438  \u0421 \u043f\u043e\u043c\u043e\u0449\u044c\u044e \u041e\u041c\u0421\u0418 \u043a\u0430\u043a \u043e\u0431\u043e\u0431\u0449\u0435\u043d\u0438\u044f \u043c\u043d\u043e\u0436\u0435\u0441\u0442\u0432\u0435\u043d\u043d\u044b\u0445 \u0441\u0442\u0440\u0443\u043a\u0442\u0443\u0440 \u0438\u043d\u0444\u043e\u0440\u043c\u0438\u0440\u043e\u0432\u0430\u043d\u043d\u043e\u0441\u0442\u0438 (\u043e\u0431\u043e\u0431\u0449\u0430\u044e\u0449\u0438\u0445 \u0432 \u0441\u0432\u043e\u044e \u043e\u0447\u0435\u0440\u0435\u0434\u044c \u0442\u043e\u0447\u0435\u0447\u043d\u044b\u0435 \u0441\u0442\u0440\u0443\u043a\u0442\u0443\u0440\u044b \u0438\u043d\u0444\u043e\u0440\u043c\u0438\u0440\u043e\u0432\u0430\u043d\u043d\u043e\u0441\u0442\u0438) \u043c\u043e\u0436\u043d\u043e \u043e\u043f\u0438\u0441\u044b\u0432\u0430\u0442\u044c \u0441\u0438\u0442\u0443\u0430\u0446\u0438\u0438, \u043a\u043e\u0433\u0434\u0430 \u0430\u0433\u0435\u043d\u0442\u044b \u043d\u0435 \u0437\u043d\u0430\u044e\u0442 \u0442\u043e\u0447\u043d\u043e\u0433\u043e \u0441\u043e\u0441\u0442\u043e\u044f\u043d\u0438\u044f \u0441\u0438\u0441\u0442\u0435\u043c\u044b \u0438 \u0432\u044b\u043d\u0443\u0436\u0434\u0435\u043d\u044b \u043f\u0440\u0438\u043d\u0438\u043c\u0430\u0442\u044c \u0440\u0435\u0448\u0435\u043d\u0438\u044f \u0432 \u0443\u0441\u043b\u043e\u0432\u0438\u044f\u0445 \u043d\u0435\u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u043d\u043e\u0441\u0442\u0438. \u0422\u0430\u043a\u043e\u0433\u043e \u0440\u043e\u0434\u0430 \u0441\u0442\u0440\u0443\u043a\u0442\u0443\u0440\u044b \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u044e\u0442\u0441\u044f \u0434\u043b\u044f \u043f\u043e\u0441\u0442\u0440\u043e\u0435\u043d\u0438\u044f \u0438\u043d\u0444\u043e\u0440\u043c\u0430\u0446\u0438\u043e\u043d\u043d\u043e\u0433\u043e \u0443\u043f\u0440\u0430\u0432\u043b\u0435\u043d\u0438\u044f \u0438 \u043c\u043e\u0433\u0443\u0442 \u0431\u044b\u0442\u044c \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u043e\u0432\u0430\u043d\u044b \u0434\u043b\u044f \u0443\u043f\u0440\u0430\u0432\u043b\u0435\u043d\u0438\u044f \u0434\u0438\u043d\u0430\u043c\u0438\u043a\u043e\u0439 \u043c\u043d\u0435\u043d\u0438\u0439 \u0432\u00a0\u0441\u043e\u0446\u0438\u0430\u043b\u044c\u043d\u044b\u0445 \u0441\u0435\u0442\u044f\u0445 \u0438 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\u0434\u0435\u0439\u0441\u0442\u0432\u0438\u0439 \u0430\u0433\u0435\u043d\u0442\u0430\u043c\u0438 \u0438 \u0432 \u0440\u0435\u0437\u0443\u043b\u044c\u0442\u0430\u0442\u0435 \u043f\u043e\u043b\u0443\u0447\u0435\u043d\u0438\u044f \u0438\u043c\u0438 \u0441\u043e\u043e\u0431\u0449\u0435\u043d\u0438\u044f.\u041f\u0440\u0435\u0434\u043b\u043e\u0436\u0435\u043d\u044b \u0444\u043e\u0440\u043c\u0430\u043b\u044c\u043d\u044b\u0435 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f \u0438\u043d\u0444\u043e\u0440\u043c\u0430\u0446\u0438\u043e\u043d\u043d\u043e\u0433\u043e \u0440\u0430\u0432\u043d\u043e\u0432\u0435\u0441\u0438\u044f \u0434\u043b\u044f \u043e\u0431\u043e\u0438\u0445 \u0442\u0438\u043f\u043e\u0432 \u041e\u041c\u0421\u0418, \u043f\u0440\u0438\u0447\u0435\u043c \u0438\u043d\u0444\u043e\u0440\u043c\u0430\u0446\u0438\u043e\u043d\u043d\u043e\u0435 \u0440\u0430\u0432\u043d\u043e\u0432\u0435\u0441\u0438\u0435 \u0434\u043b\u044f \u0432\u0435\u0440\u043e\u044f\u0442\u043d\u043e\u0441\u0442\u043d\u043e\u0439 \u041e\u041c\u0421\u0418 \u0441\u0444\u043e\u043c\u0443\u043b\u0438\u0440\u043e\u0432\u0430\u043d\u043d\u043e \u0442\u0430\u043a\u0438\u043c \u043e\u0431\u0440\u0430\u0437\u043e\u043c, \u0447\u0442\u043e \u043f\u043e\u0437\u0432\u043e\u043b\u044f\u0435\u0442 \u043d\u0430\u0445\u043e\u0434\u0438\u0442\u044c \u0440\u0430\u0432\u043d\u043e\u0432\u0435\u0441\u0438\u044f \u0411\u0430\u0439\u0435\u0441\u0430\u00a0\u2013\u00a0\u041d\u044d\u0448\u0430.<\/jats:p>\n                                                                                            <jats:p>A new model for describing agents' awareness is proposed that generalizes the known reflexion models in the following sense: the proposed model of generalized multiple awareness structures (GMAS) allows for different numbers of participants in agents' perceptions of the situation. Such structures are used to construct information control and can be used to control the dynamics of opinions in social networks and to improve safety in transportation systems even when agents do not know the total number of agents in the system, which is very common in real life but rarely considered in game theory and epistemic logic. In the article, a formal description of probabilistic and interval GMAS is given, and cases of their transformation as a result of observing the choice of actions by agents and as a result of receiving a message by them are considered. Formal definitions of information equilibrium for both types of GMAS are proposed, and the information equilibrium for probabilistic GMAS is formulated in such a way that it allows us to find Bayes\u00a0\u2013Nash equilibria.<\/jats:p>","DOI":"10.25728\/ubs.2024.109.1","type":"journal-article","created":{"date-parts":[[2024,10,30]],"date-time":"2024-10-30T12:33:06Z","timestamp":1730291586000},"page":"6-20","source":"Crossref","is-referenced-by-count":0,"title":["\u041e\u0431\u043e\u0431\u0449\u0435\u043d\u043d\u0430\u044f \u043c\u043d\u043e\u0436\u0435\u0441\u0442\u0432\u0435\u043d\u043d\u0430\u044f \u0441\u0442\u0440\u0443\u043a\u0442\u0443\u0440\u0430 \u0438\u043d\u0444\u043e\u0440\u043c\u0438\u0440\u043e\u0432\u0430\u043d\u043d\u043e\u0441\u0442\u0438"],"prefix":"10.25728","author":[{"given":"\u0424\u0435\u0434\u044f\u043d\u0438\u043d","family":"\u0414\u0435\u043d\u0438\u0441 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\u043f\u0440\u043e\u0438\u0437\u0432\u043e\u043b\u044c\u043d\u044b\u043c \u0447\u0438\u0441\u043b\u043e\u043c \u043b\u0438\u0434\u0435\u0440\u043e\u0432 \/\/ \u0418\u043d\u0444\u043e\u0440\u043c\u0430\u0442\u0438\u043a\u0430 \u0438 \u0430\u0432\u0442\u043e\u043c\u0430-\u0442\u0438\u0437\u0430\u0446\u0438\u044f. \u2013 2022. \u2013 \u211621(2). \u2013 \u0421. 339\u2013375."},{"key":"2","unstructured":"\u041d\u041e\u0412\u0418\u041a\u041e\u0412 \u0414.\u0410. \u0422\u0435\u043e\u0440\u0438\u044f \u0443\u043f\u0440\u0430\u0432\u043b\u0435\u043d\u0438\u044f \u043e\u0440\u0433\u0430\u043d\u0438\u0437\u0430\u0446\u0438\u043e\u043d\u043d\u044b\u043c\u0438 \u0441\u0438\u0441\u0442\u0435\u043c\u0430\u043c\u0438. \u2013 \u041c.: \u041b\u0415\u041d\u0410\u041d\u0414, 2022. \u2013 500 \u0441."},{"key":"3","unstructured":"\u041d\u041e\u0412\u0418\u041a\u041e\u0412 \u0414.\u0410., \u0427\u0425\u0410\u0420\u0422\u0418\u0428\u0412\u0418\u041b\u0418 \u0410.\u0413. \u0420\u0435\u0444\u043b\u0435\u043a\u0441\u0438\u0432\u043d\u044b\u0435 \u0438\u0433\u0440\u044b. \u2013 \u041c.: \u0421\u0438\u043d\u0442\u0435\u0433, 2003. \u2013 160 \u0441."},{"key":"4","unstructured":"\u041d\u041e\u0412\u0418\u041a\u041e\u0412 \u0414.\u0410., \u0427\u0425\u0410\u0420\u0422\u0418\u0428\u0412\u0418\u041b\u0418 \u0410.\u0413. \u0420\u0435\u0444\u043b\u0435\u043a\u0441\u0438\u044f \u0438 \u0443\u043f\u0440\u0430\u0432\u043b\u0435\u043d\u0438\u0435: \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u0447\u0435\u0441\u043a\u0438\u0435 \u043c\u043e\u0434\u0435\u043b\u0438. \u2013 \u041c.: \u0418\u0437\u0434-\u0432\u043e \u0444\u0438\u0437\u044e-\u043c\u0430\u0442. \u043b\u0438\u0442-\u0440\u044b, 2013. \u2013 412 \u0441."},{"key":"5","unstructured":"\u0427\u0425\u0410\u0420\u0422\u0418\u0428\u0412\u0418\u041b\u0418 \u0410.\u0413. \u041e\u0431 \u043e\u0434\u043d\u043e\u0439 \u0440\u0435\u0444\u043b\u0435\u043a\u0441\u0438\u0432\u043d\u043e\u0439 \u0438\u0433\u0440\u0435 \u043f\u043e-\u0438\u0441\u043a\u0430 \/\/ \u0423\u043f\u0440\u0430\u0432\u043b\u0435\u043d\u0438\u0435 \u0431\u043e\u043b\u044c\u0448\u0438\u043c\u0438 \u0441\u0438\u0441\u0442\u0435\u043c\u0430\u043c\u0438: \u0441\u0431\u043e\u0440\u043d\u0438\u043a \u0442\u0440\u0443-\u0434\u043e\u0432. \u2013 2003. \u0412\u044b\u043f. 5. \u2013 \u0421. 123\u2013128."},{"key":"6","unstructured":"\u0427\u0425\u0410\u0420\u0422\u0418\u0428\u0412\u0418\u041b\u0418 \u0410.\u0413. \u0420\u0435\u0444\u043b\u0435\u043a\u0441\u0438\u0432\u043d\u044b\u0435 \u0438\u0433\u0440\u044b: \u0442\u0440\u0430\u043d\u0441\u0444\u043e\u0440-\u043c\u0430\u0446\u0438\u044f \u0441\u0442\u0440\u0443\u043a\u0442\u0443\u0440 \u0438\u043d\u0444\u043e\u0440\u043c\u0438\u0440\u043e\u0432\u0430\u043d\u043d\u043e\u0441\u0442\u0438 \/\/ \u041f\u0440\u043e\u0431\u043b\u0435\u043c\u044b \u0443\u043f\u0440\u0430\u0432\u043b\u0435\u043d\u0438\u044f. \u2013 2008. \u2013 \u21165. \u2013 \u0421. 43\u201348."},{"key":"7","doi-asserted-by":"crossref","unstructured":"AGHASSI M., BERTSIMAS D. Robust game theory \/\/ Math-ematical programming. \u2013 2006. \u2013 Vol. 107(1\u20132). \u2013 P. 231\u2013273.","DOI":"10.1007\/s10107-005-0686-0"},{"key":"8","doi-asserted-by":"crossref","unstructured":"AUMANN R.J., HEIFETZ A. Incomplete information \/\/ Handbook of game theory with economic applications. \u2013 2002. \u2013 P. 1665\u20131686.","DOI":"10.1016\/S1574-0005(02)03006-0"},{"key":"9","doi-asserted-by":"crossref","unstructured":"FEDYANIN D.N. Threshold and Network generalizations of Muddy Faces Puzzle \/\/ Proc. of the 11th IEEE Int. Conf. on Application of Information and Communication Technolo-gies (AICT2017, Moscow). \u2013 M.: IEEE, 2017. \u2013 Vol. 1. \u2013 P. 256\u2013260.","DOI":"10.1109\/ICAICT.2017.8686956"},{"key":"10","unstructured":"FEDYANIN D.N. Logic for Chkhartishvili-Novikov Struc-tures of Beliefs \/\/ Int. Journal of Unconventional Computing. \u2013 2020. \u2013 Vol. 15, Iss. 4. \u2013 P. 259\u2013273."},{"key":"11","doi-asserted-by":"crossref","unstructured":"GALEAZZI P., LORINI E. Epistemic logic meets epistemic game theory: A comparison between multi-agent Kripke models and type spaces \/\/ Synthese. \u2013 2016. \u2013 Vol. 193. \u2013 P. 2097\u20132127.","DOI":"10.1007\/s11229-015-0834-x"},{"key":"12","unstructured":"HARSANYI J.C. Games with incomplete information \/\/ The American Economic Review. \u2013 1995. \u2013 Vol. 85(3). \u2013 P. 291\u2013303."},{"key":"13","doi-asserted-by":"crossref","unstructured":"JACKSON M.O., SIMON L.K., SWINKELS J.M., ZA-ME W.R. Communication and equilibrium in discontinuous games of incomplete information \/\/ Econometrica. \u2013 2002. \u2013 Vol. 70(5). \u2013 P. 1711\u20131740.","DOI":"10.1111\/1468-0262.00351"},{"key":"14","doi-asserted-by":"crossref","unstructured":"PEREA A. Epistemic Game Theory: Reasoning and Choice. Universiteit Maastricht, 2012. \u2013 580 p.","DOI":"10.1017\/CBO9780511844072"}],"container-title":["\u0423\u043f\u0440\u0430\u0432\u043b\u0435\u043d\u0438\u0435 \u0431\u043e\u043b\u044c\u0448\u0438\u043c\u0438 \u0441\u0438\u0441\u0442\u0435\u043c\u0430\u043c\u0438: \u0441\u0431\u043e\u0440\u043d\u0438\u043a \u0442\u0440\u0443\u0434\u043e\u0432"],"original-title":[],"language":"ru","deposited":{"date-parts":[[2024,10,30]],"date-time":"2024-10-30T12:33:14Z","timestamp":1730291594000},"score":1,"resource":{"primary":{"URL":"http:\/\/ubs.mtas.ru\/archive\/search_results_new.php?publication_id=23208"}},"subtitle":["Generalized multiple information structure"],"short-title":[],"issued":{"date-parts":[[2024,5,31]]},"references-count":14,"journal-issue":{"issue":"109","published-online":{"date-parts":[[2024,5,31]]}},"URL":"https:\/\/doi.org\/10.25728\/ubs.2024.109.1","relation":{},"ISSN":["1819-2440"],"issn-type":[{"value":"1819-2440","type":"print"}],"subject":[],"published":{"date-parts":[[2024,5,31]]}}}