音乐椅
Musical chairs
摘要：
在{ \em Musical Chairs}游戏$MC(n,m)$中，一队$n$玩家与敌对的{ \em调度程序}进行比赛。如果游戏无限期地进行，则调度器获胜，而在有限数量的回合后终止则被宣布为团队获胜。在游戏的每一轮，每个玩家{ \em占据}一个可用的$m$ { \em椅子}。终止（和一个团队的胜利）是宣布尽快每个球员占据一个独特的椅子。同时占据同一张椅子的两个玩家被称为{ \em in conflict}。换句话说，只要没有冲突，就可以终止（以及团队的胜利）。整个游戏中唯一的通信方式是这样的：在游戏的每一轮，调度程序选择一个任意的非空的当前冲突的玩家集合，并分别通知他们每个人必须移动。一个被通知的玩家根据它的确定性程序改变它的椅子。正如我们所展示的，对于$m\ge 2n-1$椅子，团队有一个获胜的策略。此外，使用拓扑参数，我们表明，这个界是紧的。对于$m\leq 2n-2$，调度程序有一个策略，可以保证游戏无限期地继续下去，从而获胜。我们还就其他有趣的问题得出了一些结果。例如，如果$m \ge 2n-1$（这样球队才能赢），他们多快才能取得胜利？
英文摘要：
In the {\em Musical Chairs} game $MC(n,m)$ a team of $n$ players plays against an adversarial {\em scheduler}. The scheduler wins if the game proceeds indefinitely, while termination after a finite number of rounds is declared a win of the team. At each round of the game each player {\em occupies} one of the $m$ available {\em chairs}. Termination (and a win of the team) is declared as soon as each player occupies a unique chair. Two players that simultaneously occupy the same chair are said to be {\em in conflict}. In other words, termination (and a win for the team) is reached as soon as there are no conflicts. The only means of communication throughout the game is this: At every round of the game, the scheduler selects an arbitrary nonempty set of players who are currently in conflict, and notifies each of them separately that it must move. A player who is thus notified changes its chair according to its deterministic program. As we show, for $m\ge 2n-1$ chairs the team has a winning strategy. Moreover, using topological arguments we show that this bound is tight. For $m\leq 2n-2$ the scheduler has a strategy that is guaranteed to make the game continue indefinitely and thus win. We also have some results on additional interesting questions. For example, if $m \ge 2n-1$ (so that the team can win), how quickly can they achieve victory?
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。
