{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,5]],"date-time":"2025-10-05T04:34:30Z","timestamp":1759638870270,"version":"3.41.2"},"reference-count":19,"publisher":"Centre pour la Communication Scientifique Directe (CCSD)","license":[{"start":{"date-parts":[[2011,9,1]],"date-time":"2011-09-01T00:00:00Z","timestamp":1314835200000},"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>Using coalgebraic methods, we extend Conway's theory of games to possibly\nnon-terminating, i.e. non-wellfounded games (hypergames). We take the view that\na play which goes on forever is a draw, and hence rather than focussing on\nwinning strategies, we focus on non-losing strategies. Hypergames are a\nfruitful metaphor for non-terminating processes, Conway's sum being similar to\nshuffling. We develop a theory of hypergames, which extends in a non-trivial\nway Conway's theory; in particular, we generalize Conway's results on game\ndeterminacy and characterization of strategies. Hypergames have a rather\ninteresting theory, already in the case of impartial hypergames, for which we\ngive a compositional semantics, in terms of a generalized Grundy-Sprague\nfunction and a system of generalized Nim games. Equivalences and congruences on\ngames and hypergames are discussed. We indicate a number of intriguing\ndirections for future work. We briefly compare hypergames with other notions of\ngames used in computer science.<\/jats:p>","DOI":"10.2168\/lmcs-7(3:8)2011","type":"journal-article","created":{"date-parts":[[2014,11,14]],"date-time":"2014-11-14T13:45:24Z","timestamp":1415972724000},"source":"Crossref","is-referenced-by-count":4,"title":["Conway games, algebraically and coalgebraically"],"prefix":"10.46298","volume":"Volume 7, Issue 3","author":[{"given":"Furio","family":"Honsell","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Marina","family":"Lenisa","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"25203","published-online":{"date-parts":[[2011,9,1]]},"reference":[{"key":"10.2168\/LMCS-7(3:8)2011_AGMO03","first-page":"421","volume":"2988","author":"S. Abramsky, D.R. Ghica, A.S. Murawski","year":"2004,","journal-title":"Springer LNCS"},{"key":"10.2168\/LMCS-7(3:8)2011_Acz88","unstructured":"P. Aczel. Non-wellfounded sets, CSLI Lecture Notes 14, Stanford 1988."},{"key":"10.2168\/LMCS-7(3:8)2011_BM96","unstructured":"J. Barwise, L. Moss. Vicious Circles, CSLI Lecture Notes 60, Stanford 1996."},{"key":"10.2168\/LMCS-7(3:8)2011_BCG82","unstructured":"E. Berlekamp, J. Conway, R. Guy. Winning Ways, Academic Press, 1982."},{"key":"10.2168\/LMCS-7(3:8)2011_Con76","unstructured":"J.H. Conway. On Numbers and Games, second edition, A K Peters Ltd, 2001 (first edition by Academic Press, 1976)."},{"key":"10.2168\/LMCS-7(3:8)2011_FH83","unstructured":"M. Forti, F. Honsell. Set-theory with free construction principles,Ann. Scuola Norm. Sup. Pisa, Cl. Sci. (4) 10, 1983, 493-522."},{"key":"10.2168\/LMCS-7(3:8)2011_FR01","doi-asserted-by":"crossref","first-page":"13","DOI":"10.1016\/S0304-3975(00)00074-8","volume":"252","author":"A. Fraenkel, O. 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Equivalences and Congruences on Infinite Conway's Games, submitted for publication, 2011.","DOI":"10.1051\/ita\/2012001"},{"key":"10.2168\/LMCS-7(3:8)2011_HLR11a","unstructured":"F. Honsell, M. Lenisa, R. Redamalla. A General Framework for Games, submitted for publication, 2011."},{"key":"10.2168\/LMCS-7(3:8)2011_Jech03","unstructured":"T. Jech. Set Theory, third edition, Springer, 2003."},{"key":"10.2168\/LMCS-7(3:8)2011_Joy77","unstructured":"A. Joyal. Remarques sur la Theorie des Jeux a deux personnes, Gazette des sciences mathematiques du Quebec 1(4), 1977 (English translation by R. Houston, 2003). R.J. Nowakowski ed.. More Games of No Chance,MSRI42, 2002."},{"key":"10.2168\/LMCS-7(3:8)2011_San02","doi-asserted-by":"publisher","DOI":"10.1016\/S0022-4049(01)00098-6"},{"key":"10.2168\/LMCS-7(3:8)2011_San02a","doi-asserted-by":"publisher","DOI":"10.1051\/ita:2002010"},{"key":"10.2168\/LMCS-7(3:8)2011_Smi66","doi-asserted-by":"publisher","DOI":"10.1016\/S0021-9800(66)80005-4"},{"key":"10.2168\/LMCS-7(3:8)2011_Spra35","unstructured":"R.P. Sprague. \u00dcber mathematische Kampfspiele,Tohoku Math. J.41, 1935-6, 438-444."},{"key":"10.2168\/LMCS-7(3:8)2011_Tho02","doi-asserted-by":"crossref","unstructured":"W. Thomas. Infinite games and verification, Proc. ofCAV'02, Springer LNCS 2404, 2002, 58-64.","DOI":"10.1007\/3-540-45657-0_5"}],"container-title":["Logical Methods in Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/lmcs.episciences.org\/703\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/lmcs.episciences.org\/703\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,4,11]],"date-time":"2023-04-11T19:54:10Z","timestamp":1681242850000},"score":1,"resource":{"primary":{"URL":"https:\/\/lmcs.episciences.org\/703"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,9,1]]},"references-count":19,"URL":"https:\/\/doi.org\/10.2168\/lmcs-7(3:8)2011","relation":{"is-same-as":[{"id-type":"arxiv","id":"1107.1351","asserted-by":"subject"},{"id-type":"doi","id":"10.48550\/arXiv.1107.1351","asserted-by":"subject"}]},"ISSN":["1860-5974"],"issn-type":[{"type":"electronic","value":"1860-5974"}],"subject":[],"published":{"date-parts":[[2011,9,1]]},"article-number":"703"}}