论文标题
竞标组合游戏
Bidding combinatorial games
论文作者
论文摘要
组合游戏理论是数学和理论计算机科学的一个分支，它可以使用完美的信息研究顺序的2玩游戏。正常比赛是不能移动失败的球员的惯例。在这里，我们通过离散的Richman Auctions将经典的正常比赛推广到无限的许多游戏家族（Develin等，2010，Larsson等，2021，Lazarus等，1996）。我们概括了完美的娱乐结果的概念，并找到了结果可行性的确切特征。作为主要结果，我们证明了每个这样的结果类别的游戏形式。然后，我们描述他们的晶格结构。通过对一般家庭的限制，例如公正和{\ em对称终止}，我们发现了令人惊讶的类比。
Combinatorial Game Theory is a branch of mathematics and theoretical computer science that studies sequential 2-player games with perfect information. Normal play is the convention where a player who cannot move loses. Here, we generalize the classical alternating normal play to infinitely many game families, by means of discrete Richman auctions (Develin et al. 2010, Larsson et al. 2021, Lazarus et al. 1996). We generalize the notion of a perfect play outcome, and find an exact characterization of outcome feasibility. As a main result, we prove existence of a game form for each such outcome class; then we describe their lattice structures. By imposing restrictions to the general families, such as impartial and {\em symmetric termination}, we find surprising analogies with alternating play.
