论文标题
竞标组合游戏的建设性比较
Constructive comparison in bidding combinatorial games
论文作者
论文摘要
康德，拉尔森，Rai和Upasany（2022）介绍了一类离散的竞标组合游戏，这些概括了正常比赛。有关最佳结果的主要问题已解决。通过概括来自正常游戏的标准游戏比较技术，我们提出了一种算法游戏解决方案，以解决竞标游戏的游戏比较问题。我们证明了这种结果的一些后果，可以将经典结果推广到交替的比赛中（从1982年的获胜方式以及1976年的数字和游戏）。特别是，整数，二元组和数字具有许多不错的属性，例如组结构，但另一方面，游戏 *是不可变的。我们陈述了一些激动人心的猜想和开放问题，供读者潜入这一有希望的竞标组合游戏的道路上。
A class of discrete Bidding Combinatorial Games that generalize alternating normal play was introduced by Kant, Larsson, Rai, and Upasany (2022). The major questions concerning optimal outcomes were resolved. By generalizing standard game comparison techniques from alternating normal play, we propose an algorithmic play-solution to the problem of game comparison for bidding games. We demonstrate some consequences of this result that generalize classical results in alternating play (from Winning Ways 1982 and On Numbers and Games 1976). In particular, integers, dyadics and numbers have many nice properties, such as group structures, but on the other hand the game * is non-invertible. We state a couple of thrilling conjectures and open problems for readers to dive into this promising path of bidding combinatorial games.
