{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,2]],"date-time":"2022-04-02T04:26:33Z","timestamp":1648873593625},"reference-count":8,"publisher":"World Scientific Pub Co Pte Lt","issue":"04","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. Game Theory Rev."],"published-print":{"date-parts":[[2020,12]]},"abstract":"<jats:p> It is a classical and interesting problem to find a Nash equilibrium of noncooperative games in the strategic form. It is well known that the game always has a mixed-strategy Nash equilibrium, but it does not necessarily have a pure-strategy Nash equilibrium. Takeshita and Kawasaki proved that every noncooperative partially monotone game has a pure-strategy Nash equilibrium, that is, the partial monotonicity is a sufficient condition for a noncooperative game to have a pure-strategy Nash equilibrium. In this paper, we prove the necessary and sufficient condition for a noncooperative [Formula: see text]-person game with [Formula: see text] to be partially monotone. This result is an improvement of Takeshita and Kawasaki\u2019s result. <\/jats:p>","DOI":"10.1142\/s0219198920500061","type":"journal-article","created":{"date-parts":[[2020,2,4]],"date-time":"2020-02-04T07:34:45Z","timestamp":1580801685000},"page":"2050006","source":"Crossref","is-referenced-by-count":0,"title":["A Necessary and Sufficient Condition for Partial Monotonicity of Noncooperative Games"],"prefix":"10.1142","volume":"22","author":[{"given":"Naoki","family":"Matsumoto","sequence":"first","affiliation":[{"name":"Research Institute for Digital Media and Content, Keio University, Hiyoshi Campus West Annex 1, 2-1-1 Hiyoshihoncho, Kouhoku-ku, Yokohama, Kanagawa 223-8523, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2020,7,14]]},"reference":[{"key":"S0219198920500061BIB001","doi-asserted-by":"crossref","first-page":"689","DOI":"10.1016\/j.aml.2008.08.005","volume":"5","author":"Hou J. C.","year":"2009","journal-title":"Appl. Math. Lett."},{"key":"S0219198920500061BIB002","doi-asserted-by":"crossref","first-page":"457","DOI":"10.1215\/S0012-7094-41-00838-4","volume":"8","author":"Kakutani S.","year":"1941","journal-title":"Duke Math. J."},{"key":"S0219198920500061BIB003","doi-asserted-by":"crossref","first-page":"48","DOI":"10.1073\/pnas.36.1.48","volume":"36","author":"Nash J. F.","year":"1950","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"S0219198920500061BIB004","doi-asserted-by":"crossref","first-page":"286","DOI":"10.2307\/1969529","volume":"54","author":"Nash J. F.","year":"1951","journal-title":"Ann. Math."},{"key":"S0219198920500061BIB005","doi-asserted-by":"crossref","first-page":"51","DOI":"10.5109\/21046","volume":"41","author":"Sato J.","year":"2009","journal-title":"Bull. Inform. Cybernet."},{"key":"S0219198920500061BIB006","doi-asserted-by":"crossref","first-page":"431","DOI":"10.11650\/twjm\/1500405347","volume":"13","author":"Sato J.","year":"2009","journal-title":"Taiwanese J. Math."},{"key":"S0219198920500061BIB007","first-page":"192","volume":"55","author":"Takeshita J.","year":"2012","journal-title":"Oper. Res. Soc. Japan"},{"key":"S0219198920500061BIB008","doi-asserted-by":"crossref","first-page":"285","DOI":"10.2140\/pjm.1955.5.285","volume":"5","author":"Tarski A.","year":"1955","journal-title":"Pacific J. Math."}],"container-title":["International Game Theory Review"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0219198920500061","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,1,18]],"date-time":"2021-01-18T10:02:05Z","timestamp":1610964125000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0219198920500061"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,7,14]]},"references-count":8,"journal-issue":{"issue":"04","published-print":{"date-parts":[[2020,12]]}},"alternative-id":["10.1142\/S0219198920500061"],"URL":"https:\/\/doi.org\/10.1142\/s0219198920500061","relation":{},"ISSN":["0219-1989","1793-6675"],"issn-type":[{"value":"0219-1989","type":"print"},{"value":"1793-6675","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,7,14]]}}}