Multiplayer games as extension of misère games
نویسندگان
چکیده
منابع مشابه
Misère Quotients of Impartial Games
The G-values of various games, by R. K. Guy and C. A. B. Smith, introduced a broad class of impartial games and gave complete normalplay solutions for many of them. In this paper, we announce misère-play solutions to many of the games considered by Guy and Smith. They are described in terms of misère quotients—commutative monoids that encode the additive structure of specific misère-play games....
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We announce misère-play solutions to several previously-unsolved combinatorial games. The solutions are described in terms of misère quotients—commutative monoids that encode the additive structure of specific misère-play games. We also introduce several advances in the structure theory of misère quotients, including a connection between the combinatorial structure of normal and misère play.
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We show that partizan games admit canonical forms in misère play. The proof is a synthesis of the canonical form theorems for normal-play partizan games and misère-play impartial games. It is fully constructive, and algorithms readily emerge for comparing misère games and calculating their canonical forms. We use these techniques to show that there are precisely 256 games born by day 2, and to ...
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ژورنال
عنوان ژورنال: International Journal of Game Theory
سال: 2019
ISSN: 0020-7276,1432-1270
DOI: 10.1007/s00182-019-00662-8