{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,3]],"date-time":"2025-11-03T09:16:58Z","timestamp":1762161418054,"version":"3.37.3"},"reference-count":14,"publisher":"World Scientific Pub Co Pte Ltd","issue":"03","funder":[{"DOI":"10.13039\/501100001691","name":"Japan Society for the Promotion of Science KAKENHI","doi-asserted-by":"crossref","award":["15K03481","18K01594"],"award-info":[{"award-number":["15K03481","18K01594"]}],"id":[{"id":"10.13039\/501100001691","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. Game Theory Rev."],"published-print":{"date-parts":[[2019,9]]},"abstract":"<jats:p> We consider a two-person zero-sum game with two sets of strategic variables which are related by invertible functions. They are denoted by [Formula: see text] and [Formula: see text] for players A and B. The payoff function of Player A is [Formula: see text]. Then, the payoff function of Player B is [Formula: see text]. [Formula: see text] is upper semi-continuous and quasi-concave on [Formula: see text] for each [Formula: see text] (or each [Formula: see text]), upper semi-continuous and quasi-concave on [Formula: see text] for each [Formula: see text] (or each [Formula: see text]), lower semi-continuous and quasi-convex on [Formula: see text] for each [Formula: see text] (or each [Formula: see text], and lower semi-continuous and quasi-convex on [Formula: see text] for each [Formula: see text] (or each [Formula: see text]). <\/jats:p><jats:p> We will show that the following four patterns of competition are equivalent, that is, they yield the same outcome. <\/jats:p><jats:p> (1) Players A and B choose [Formula: see text] and [Formula: see text] (competition by [Formula: see text]). <\/jats:p><jats:p> (2) Players A and B choose [Formula: see text] and [Formula: see text] (competition by [Formula: see text]). <\/jats:p><jats:p> (3) Players A and B choose [Formula: see text] and [Formula: see text] (competition by [Formula: see text]). <\/jats:p><jats:p> (4) Players A and B choose [Formula: see text] and [Formula: see text] (competition by [Formula: see text]). <\/jats:p>","DOI":"10.1142\/s0219198918500147","type":"journal-article","created":{"date-parts":[[2018,9,25]],"date-time":"2018-09-25T08:46:16Z","timestamp":1537865176000},"page":"1850014","source":"Crossref","is-referenced-by-count":2,"title":["Two Person Zero-Sum Game with Two Sets of Strategic Variables"],"prefix":"10.1142","volume":"21","author":[{"given":"Atsuhiro","family":"Satoh","sequence":"first","affiliation":[{"name":"Faculty of Economics, Hokkai-Gakuen University, Toyohira-ku, Sapporo, Hokkaido, 062-8605, Japan"}]},{"given":"Yasuhito","family":"Tanaka","sequence":"additional","affiliation":[{"name":"Faculty of Economics, Doshisha University, Kamigyo-ku, Kyoto, 602-8580, Japan"}]}],"member":"219","published-online":{"date-parts":[[2019,10,30]]},"reference":[{"key":"S0219198918500147BIB001","doi-asserted-by":"publisher","DOI":"10.1080\/00029890.2005.11920204"},{"key":"S0219198918500147BIB002","doi-asserted-by":"publisher","DOI":"10.2996\/kmj\/1138038812"},{"key":"S0219198918500147BIB003","doi-asserted-by":"publisher","DOI":"10.1016\/j.econmod.2012.12.016"},{"key":"S0219198918500147BIB004","doi-asserted-by":"publisher","DOI":"10.1515\/bejte-2017-0012"},{"key":"S0219198918500147BIB005","doi-asserted-by":"publisher","DOI":"10.17811\/ebl.2.3.2013.134-139"},{"key":"S0219198918500147BIB006","first-page":"1653","volume":"34","author":"Satoh A.","year":"2014","journal-title":"Econ. 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