{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,3,31]],"date-time":"2022-03-31T07:26:49Z","timestamp":1648711609177},"reference-count":7,"publisher":"World Scientific Pub Co Pte Lt","issue":"01","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. Game Theory Rev."],"published-print":{"date-parts":[[2005,3]]},"abstract":"<jats:p> A two-person general-sum repeated game with vanishing actions is an infinitely repeated game where the players face the following restrictions. Each action must be used by player k \u2208 {1,2} at least once in every r<jats:sup>k<\/jats:sup> \u2208 \u2115 consecutive stages, otherwise the action vanishes for the remaining play. We assume that the players wish to maximize their limiting average rewards over the entire time-horizon. <\/jats:p><jats:p> A strategy-pair is jointly convergent if for each action pair a number exists to which the relative frequency with which this action pair is chosen, converges with probability one. A pair of feasible rewards is called individually rational if each player receives at least the threat-point reward, i.e., the amount which he can guarantee himself regardless of what the opponent does given r<jats:sup>1<\/jats:sup>, r<jats:sup>2<\/jats:sup> and the actions available in the long run. In a repeated game with vanishing actions, there may exist multiple threat points which are endogenous to the play. <\/jats:p><jats:p> We prove that all individually-rational jointly-convergent pure-strategy rewards can be supported by an equilibrium. Furthermore, each convex combination of individually-rational jointly-convergent pure-strategy rewards, can be supported by an equilibrium for m \u00d7 n-games provided r<jats:sup>1<\/jats:sup> &gt; m \u2265 2, r<jats:sup>2<\/jats:sup> &gt; n \u2265 2. <\/jats:p>","DOI":"10.1142\/s0219198905000430","type":"journal-article","created":{"date-parts":[[2005,4,1]],"date-time":"2005-04-01T06:19:37Z","timestamp":1112336377000},"page":"107-115","source":"Crossref","is-referenced-by-count":5,"title":["A NOTE ON REPEATED GAMES WITH VANISHING ACTIONS"],"prefix":"10.1142","volume":"07","author":[{"given":"REINOUD","family":"JOOSTEN","sequence":"first","affiliation":[{"name":"School of Business, Public Administration and Technology &amp; Financial Engineering Laboratory, University of Twente, POB 217, 7500 AE Enschede, The Netherlands"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf1","volume-title":"Repeated Games of Incomplete Information","author":"Aumann R. J.","year":"1995"},{"key":"rf2","volume-title":"Probability and Measure","author":"Billingsley P.","year":"1986"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.2307\/1914304"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1287\/moor.10.1.117"},{"key":"rf7","first-page":"1","volume":"6","author":"Joosten R.","journal-title":"Games and Economic Behavior"},{"key":"rf8","volume-title":"A Course in Game Theory","author":"Peters H.","year":"1992"},{"key":"rf9","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-58242-4"}],"container-title":["International Game Theory Review"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0219198905000430","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T18:02:25Z","timestamp":1565114545000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0219198905000430"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2005,3]]},"references-count":7,"journal-issue":{"issue":"01","published-online":{"date-parts":[[2011,11,20]]},"published-print":{"date-parts":[[2005,3]]}},"alternative-id":["10.1142\/S0219198905000430"],"URL":"https:\/\/doi.org\/10.1142\/s0219198905000430","relation":{},"ISSN":["0219-1989","1793-6675"],"issn-type":[{"value":"0219-1989","type":"print"},{"value":"1793-6675","type":"electronic"}],"subject":[],"published":{"date-parts":[[2005,3]]}}}