Combinatorial Game Theory typically studies sequential rulesets with perfect information where two players alternate moves. There are rulesets with {\em entailing moves} that break the alternating play axiom and/or restrict the other player's options within the disjunctive sum components. Although some examples have been analyzed in the classical work Winning Ways, such rulesets usually fall outside the scope of the established normal play mathematical theory. At the first Combinatorial Games Workshop at MSRI, John H. Conway proposed that an effort should be made to devise some nontrivial ruleset with entailing moves that had a complete analysis. Recently, Larsson, Nowakowski, and Santos proposed a more general theory, {\em affine impartial}, which facilitates the mathematical analysis of impartial rulesets with entailing moves. Here, by using this theory, we present a complete solution for a nontrivial ruleset with entailing moves.
翻译:组合博弈论通常研究具有完美信息且双方交替对弈的序贯规则集。存在一些具有{\em 蕴含移动}的规则集,它们打破了交替对弈公理,或者在析取和的组成部分中限制对手的选择。尽管在经典著作《制胜之道》中分析了一些例子,但这类规则集通常超出了已建立的正常对局数学理论的范畴。在MSRI举办的第一次组合博弈研讨会上,约翰·H·康威提议应致力于设计一个具有蕴含移动且可被完整分析的非平凡规则集。最近,拉尔森、诺瓦科夫斯基和桑托斯提出了一种更一般的理论——{\em 仿射无偏博弈},该理论促进了具有蕴含移动的无偏规则集的数学分析。本文利用该理论,给出了一个具有蕴含移动的非平凡规则集的完整解。