{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,19]],"date-time":"2025-09-19T07:46:26Z","timestamp":1758267986861},"reference-count":15,"publisher":"Wiley","issue":"4-5","license":[{"start":{"date-parts":[[2014,8,1]],"date-time":"2014-08-01T00:00:00Z","timestamp":1406851200000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Mathematical Logic Qtrly"],"published-print":{"date-parts":[[2014,8]]},"abstract":"<jats:p>Game theory is usually considered applied mathematics, but a few game\u2010theoretic results, such as Borel determinacy, were developed by mathematicians for mathematics in a broad sense. These results usually state determinacy, i.e., the existence of a winning strategy in games that involve two players and two outcomes saying who wins. In a multi\u2010outcome setting, the notion of winning strategy is irrelevant yet usually replaced faithfully with the notion of (pure) Nash equilibrium. This article shows that every determinacy result over an arbitrary game structure, e.g., a tree, is transferable into existence of multi\u2010outcome (pure) Nash equilibrium over the same game structure. The equilibrium\u2010transfer theorem requires cardinal or order\u2010theoretic conditions on the strategy sets and the preferences, respectively, whereas counter\u2010examples show that every requirement is relevant, albeit possibly improvable. When the outcomes are finitely many, the proof provides an algorithm computing a Nash equilibrium without significant complexity loss compared to the two\u2010outcome case. As examples of application, this article generalises Borel determinacy, positional determinacy of parity games, and finite\u2010memory determinacy of Muller games.<\/jats:p>","DOI":"10.1002\/malq.201300034","type":"journal-article","created":{"date-parts":[[2014,8,1]],"date-time":"2014-08-01T07:59:32Z","timestamp":1406879972000},"page":"354-371","source":"Crossref","is-referenced-by-count":5,"title":["From winning strategy to Nash equilibrium"],"prefix":"10.1002","volume":"60","author":[{"given":"St\u00e9phane","family":"Le Roux","sequence":"first","affiliation":[{"name":"Viktoriastra\u00dfe 78  64293 Darmstadt Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2014,8]]},"reference":[{"key":"e_1_2_7_2_1","first-page":"1304","article-title":"La th\u00e9orie du jeu et les equations int\u00e9grales \u00e0 noyau sym\u00e9trique","volume":"173","author":"Borel E.","year":"1921","journal-title":"C. R. Hebdom. S\u00e9ances Acad. 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