{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,9,15]],"date-time":"2024-09-15T22:32:40Z","timestamp":1726439560861},"reference-count":13,"publisher":"World Scientific Pub Co Pte Ltd","issue":"04","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. Game Theory Rev."],"published-print":{"date-parts":[[2013,12]]},"abstract":"<jats:p> In this paper, we deal with a subclass of two-person finite SeR-SIT (Separable Reward-State Independent Transition) semi-Markov games which can be solved by solving a single matrix\/bimatrix game under discounted as well as limiting average (undiscounted) payoff criteria. A SeR-SIT semi-Markov game does not satisfy the so-called (Archimedean) ordered field property in general. Besides, the ordered field property does not hold even for a SeR-SIT-PT (Separable Reward-State-Independent Transition Probability and Time) semi-Markov game, which is a natural version of a SeR-SIT stochastic (Markov) game. However by using an additional condition, we have shown that a subclass of finite SeR-SIT-PT semi-Markov games have the ordered field property for both discounted and undiscounted semi-Markov games with both players having state-independent stationary optimals. The ordered field property also holds for the nonzero-sum case under the same assumptions. We find a relation between the values of the discounted and the undiscounted zero-sum semi-Markov games for this modified subclass. We propose a more realistic pollution tax model for this subclass of SeR-SIT semi-Markov games than pollution tax model for SeR-SIT stochastic game. Finite step algorithms are given for the discounted and for the zero-sum undiscounted cases. <\/jats:p>","DOI":"10.1142\/s0219198913400264","type":"journal-article","created":{"date-parts":[[2013,7,2]],"date-time":"2013-07-02T04:08:03Z","timestamp":1372738083000},"page":"1340026","source":"Crossref","is-referenced-by-count":7,"title":["ORDERED FIELD PROPERTY IN A SUBCLASS OF FINITE SER-SIT SEMI-MARKOV GAMES"],"prefix":"10.1142","volume":"15","author":[{"given":"PRASENJIT","family":"MONDAL","sequence":"first","affiliation":[{"name":"Mathematics Department, Jadavpur University, Kolkata-700032, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"SAGNIK","family":"SINHA","sequence":"additional","affiliation":[{"name":"Mathematics Department, Jadavpur University, Kolkata-700032, India"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2013,11,18]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1287\/moor.1.3.197"},{"volume-title":"Competitive Markov Decision Processes","year":"1997","author":"Filar J. A.","key":"rf2"},{"key":"rf3","first-page":"833","volume":"21","author":"Ghosh M. K.","journal-title":"Comp. Appl. Math."},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.2307\/1969164"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.2307\/3214791"},{"key":"rf6","doi-asserted-by":"publisher","DOI":"10.1007\/BF01769259"},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.2307\/1969529"},{"key":"rf8","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-45567-4_19"},{"key":"rf9","doi-asserted-by":"publisher","DOI":"10.1007\/BF00935250"},{"volume-title":"Applied Probability Models with Optimization Applications","year":"1970","author":"Ross S. M.","key":"rf10"},{"key":"rf11","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.39.10.1095"},{"key":"rf13","doi-asserted-by":"publisher","DOI":"10.1137\/1103024"},{"key":"rf14","unstructured":"H.\u00a0Weyl, Contributions to the Theory of Games, Ann. Math. Studies\u00a024, eds. H. W.\u00a0Kuhn and A. W.\u00a0Tucker (Princeton University Press, Princeton, NJ, 1950)\u00a0pp. 19\u201325."}],"container-title":["International Game Theory Review"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0219198913400264","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T09:27:49Z","timestamp":1565083669000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0219198913400264"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,11,18]]},"references-count":13,"journal-issue":{"issue":"04","published-online":{"date-parts":[[2013,11,18]]},"published-print":{"date-parts":[[2013,12]]}},"alternative-id":["10.1142\/S0219198913400264"],"URL":"https:\/\/doi.org\/10.1142\/s0219198913400264","relation":{},"ISSN":["0219-1989","1793-6675"],"issn-type":[{"type":"print","value":"0219-1989"},{"type":"electronic","value":"1793-6675"}],"subject":[],"published":{"date-parts":[[2013,11,18]]}}}