Misère死胡同的研究进展：博弈比较、标准形和共轭逆
Progress on misère dead ends: game comparison, canonical form, and conjugate inverses
摘要：
本文讨论了限制性吝啬游戏理论（Plambeck，Siegel 2008）中的几个重大缺陷，主要是在研究充分的死胡同游戏领域$\mathcal{E}$（Milley，Renault 2013）中;如果一个玩家在$X\in \mathcal E$中用完了移动，那么他们在$X$的任何追随者中都不能再移动。一个对策论域是一类在选言和下封闭的对策，它具有选择性和共轭性。我们使用来自绝对组合对策论的新结果（Larsson，Nowakowski，Santos 2017）来证明$\mathcal{E}$和双子叶植物博弈的宇宙$\mathcal{D}\subset \mathcal{E}$（要么两者都可以移动，要么没有一个玩家可以移动）具有用于比较博弈的“仅选项”测试，这反过来又用于定义$\mathcal{E}$中的唯一简化博弈（规范形式）。我们通过扩展$\mathcal{D}$的类似工作，特别是通过解决更大宇宙中的两端的可逆性问题，来发展$\mathcal{E}$的约化。最后，利用$\mathcal{E}$和$\mathcal{D}$中定义的标准型，证明了这两个论域以及公平对策的子论域都具有共轭性质：每个逆对策都是通过对换局中人的边而得到的.
英文摘要：
This paper addresses several significant gaps in the theory of restricted misère play (Plambeck, Siegel 2008), primarily in the well-studied universe of dead-ending games, $\mathcal{E}$ (Milley, Renault 2013); if a player run out of moves in $X\in \mathcal E$, then they can never move again in any follower of $X$. A universe of games is a class of games which is closed under disjunctive sum, taking options and conjugates. We use novel results from absolute combinatorial game theory (Larsson, Nowakowski, Santos 2017) to show that $\mathcal{E}$ and the universe $\mathcal{D}\subset \mathcal{E}$ of dicot games (either both, or none of the players can move) have 'options only' test for comparison of games, and this in turn is used to define unique reduced games (canonical forms) in $\mathcal{E}$. We develop the reductions for $\mathcal{E}$ by extending analogous work for $\mathcal{D}$, in particular by solving the problem of reversibility through ends in the larger universe. Finally, by using the defined canonical forms in $\mathcal{E}$ and $\mathcal{D}$, we prove that both of these universes, as well as the subuniverse of impartial games, have the conjugate property: every inverse game is obtained by swapping sides of the players.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
