在龙的存在下，
Envy-free division in the presence of a dragon
摘要：
我们证明了几个结果，解决了在不可预测（秘密）的球员，称为“龙”的存在下，嫉妒的免费部门的问题。有两种基本情况。1.有$r-1$玩家和龙。一旦“蛋糕”被分成$r$部分，龙做出他的选择，并抓住其中一块。在那之后，玩家们想以一种没有嫉妒的方式分割剩下的部分。2.有$r+1$玩家将蛋糕分成$r$小块。一条凶猛的龙来了，吞下了一个玩家。玩家们希望提前切蛋糕，这样无论谁是被巨龙吞噬的倒霉玩家，剩下的玩家都可以毫无羡慕地分享瓷砖。在这两种设置中，玩家都可以选择退化的蛋糕。此外，他们事先构建了蛋糕的切割和“决策树“，使他们能够最大限度地减少可以给每个参与者的不确定性。
英文摘要：
We prove several results addressing the envy-free division problem in the presence of an unpredictable (secretive) player, called the "dragon". There are two basic scenarios. 1. There are $r-1$ players and a dragon. Once the "cake" is divided into $r$ parts, the dragon makes his choice and grabs one of the pieces. After that the players want to divide the remaining pieces in an envy-free fashion. 2. There are $r+1$ players who divide the cake into $r$ pieces. A ferocious dragon comes and swallows one of the players. The players want to cut the cake in advance in such a way that no matter who is the unlucky player swallowed by the dragon, the remaining players can share the tiles in an envy-free manner. In both settings the players are allowed to choose degenerate pieces of the cake. Moreover, they construct in advance both a cut of the cake and a "decision tree", allowing them to minimize the uncertainty of what pieces can be given to each 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。
