{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T17:11:11Z","timestamp":1760202671184,"version":"3.41.2"},"reference-count":1,"publisher":"Centre pour la Communication Scientifique Directe (CCSD)","license":[{"start":{"date-parts":[[2013,5,22]],"date-time":"2013-05-22T00:00:00Z","timestamp":1369180800000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/arxiv.org\/licenses\/nonexclusive-distrib\/1.0"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"abstract":"<jats:p>In game theory, the concept of Nash equilibrium reflects the collective\nstability of some individual strategies chosen by selfish agents. The concept\npertains to different classes of games, e.g. the sequential games, where the\nagents play in turn. Two existing results are relevant here: first, all finite\nsuch games have a Nash equilibrium (w.r.t. some given preferences) iff all the\ngiven preferences are acyclic; second, all infinite such games have a Nash\nequilibrium, if they involve two agents who compete for victory and if the\nactual plays making a given agent win (and the opponent lose) form a\nquasi-Borel set. This article generalises these two results via a single\nresult. More generally, under the axiomatic of Zermelo-Fraenkel plus the axiom\nof dependent choice (ZF+DC), it proves a transfer theorem for infinite\nsequential games: if all two-agent win-lose games that are built using a\nwell-behaved class of sets have a Nash equilibrium, then all multi-agent\nmulti-outcome games that are built using the same well-behaved class of sets\nhave a Nash equilibrium, provided that the inverse relations of the agents'\npreferences are strictly well-founded.<\/jats:p>","DOI":"10.2168\/lmcs-9(2:3)2013","type":"journal-article","created":{"date-parts":[[2013,11,29]],"date-time":"2013-11-29T13:39:25Z","timestamp":1385732365000},"source":"Crossref","is-referenced-by-count":8,"title":["Infinite sequential Nash equilibrium"],"prefix":"10.46298","volume":"Volume 9, Issue 2","author":[{"given":"Stephane Le","family":"Roux","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"25203","published-online":{"date-parts":[[2013,5,22]]},"reference":[{"key":"653:not-found"}],"container-title":["Logical Methods in Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/lmcs.episciences.org\/1190\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/lmcs.episciences.org\/1190\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,4,11]],"date-time":"2023-04-11T20:05:39Z","timestamp":1681243539000},"score":1,"resource":{"primary":{"URL":"https:\/\/lmcs.episciences.org\/1190"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,5,22]]},"references-count":1,"URL":"https:\/\/doi.org\/10.2168\/lmcs-9(2:3)2013","relation":{"is-same-as":[{"id-type":"arxiv","id":"1302.3973","asserted-by":"subject"},{"id-type":"doi","id":"10.48550\/arXiv.1302.3973","asserted-by":"subject"}]},"ISSN":["1860-5974"],"issn-type":[{"type":"electronic","value":"1860-5974"}],"subject":[],"published":{"date-parts":[[2013,5,22]]},"article-number":"1190"}}