{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:32:03Z","timestamp":1760239923267,"version":"build-2065373602"},"reference-count":7,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2019,1,29]],"date-time":"2019-01-29T00:00:00Z","timestamp":1548720000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100004281","name":"Narodowe Centrum Nauki","doi-asserted-by":"publisher","award":["2016\/23\/D\/ST1\/01557"],"award-info":[{"award-number":["2016\/23\/D\/ST1\/01557"]}],"id":[{"id":"10.13039\/501100004281","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Games"],"abstract":"<jats:p>The problem of the existence of Berge equilibria in the sense of Zhukovskii in normal-form finite games in pure and in mixed strategies is studied. The example of a three-player game that has Berge equilibrium neither in pure, nor in mixed strategies is given.<\/jats:p>","DOI":"10.3390\/g10010007","type":"journal-article","created":{"date-parts":[[2019,1,29]],"date-time":"2019-01-29T11:27:52Z","timestamp":1548761272000},"page":"7","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Example of a Finite Game with No Berge Equilibria at All"],"prefix":"10.3390","volume":"10","author":[{"given":"Jaros\u0142aw","family":"Pykacz","sequence":"first","affiliation":[{"name":"Institute of Mathematics, Faculty of Mathematics, Physics, and Informatics, University of Gda\u0144sk, 80-308 Gda\u0144sk, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Pawe\u0142","family":"Bytner","sequence":"additional","affiliation":[{"name":"Institute of Mathematics, Faculty of Mathematics, Physics, and Informatics, University of Gda\u0144sk, 80-308 Gda\u0144sk, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0034-9803","authenticated-orcid":false,"given":"Piotr","family":"Fr\u0105ckiewicz","sequence":"additional","affiliation":[{"name":"Institute of Mathematics, Pomeranian University, 76-200 S\u0142upsk, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2019,1,29]]},"reference":[{"key":"ref_1","unstructured":"Berge, C. (1957). Th\u00e9orie G\u00e9n\u00e9rale des Jeux \u00e0 n Personnes, Gauthier-Villars."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"166","DOI":"10.1016\/j.jmp.2011.02.001","article-title":"Mutual support in games: Some properties of Berge equilibria","volume":"55","author":"Colman","year":"2011","journal-title":"J. Math. Psychol."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"80","DOI":"10.20537\/2226-3594-2017-49-04","article-title":"Berge equilibrium in normal form static games: A literature review","volume":"49","author":"Larbani","year":"2017","journal-title":"Izv. Inst. Mat. Inform. Udmurt. Gos. Univ."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"48","DOI":"10.1073\/pnas.36.1.48","article-title":"Equilibrium points in n-person games","volume":"36","author":"Nash","year":"1950","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Peters, H. (2008). Game Theory. A Multi-Leveled Approach, Springer.","DOI":"10.1007\/978-3-540-69291-1"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1250005","DOI":"10.1142\/S0219198912500053","article-title":"A new theorem to find Berge equilibria","volume":"14","author":"Musy","year":"2012","journal-title":"Int. Game Theory Rev."},{"key":"ref_7","unstructured":"Bytner, P. (2016). Berge Equilibria in Pure and Mixed Strategies. [Master\u2019s Thesis, University of Gda\u0144sk]. (In Polish)."}],"container-title":["Games"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-4336\/10\/1\/7\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T12:29:25Z","timestamp":1760185765000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-4336\/10\/1\/7"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,1,29]]},"references-count":7,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2019,3]]}},"alternative-id":["g10010007"],"URL":"https:\/\/doi.org\/10.3390\/g10010007","relation":{},"ISSN":["2073-4336"],"issn-type":[{"type":"electronic","value":"2073-4336"}],"subject":[],"published":{"date-parts":[[2019,1,29]]}}}