合作无妒忌师
Cooperative envy-free division
摘要：
借助位形空间和等变拓扑，研究了一般的“合作无嫉妒分割问题”。一群玩家想切一块“蛋糕”$I=[0,1]$，然后以一种没有嫉妒的方式在他们之间分蛋糕。一旦蛋糕被切好，放在圆桌上的盘子里（每盘最多一块），每个玩家通过指向一个（或几个）她喜欢的盘子来做出选择。新颖之处在于，她的选择可能取决于整个“分配配置”。特别是，玩家可以选择一个空盘子（可能更喜欢其中一个空盘子），并且不仅考虑她喜欢的盘子的内容，还考虑相邻盘子的内容。我们表明，如果玩家的数量是一个主要的权力，在这种设置下，存在一个嫉妒的免费部门在标准的假设下，偏好是封闭的。
英文摘要：
Relying on configuration spaces and equivariant topology, we study a general "cooperative envy-free division problem". A group of players want to cut a "cake" $I=[0,1]$ and divide among themselves the pieces in an envy-free manner. Once the cake is cut and served in plates on a round table (at most one piece per plate), each player makes her choice by pointing at one (or several) plates she prefers. The novelty is that her choice may depend on the whole "allocation configuration". In particular, a player may choose an empty plate (possibly preferring one of the empty plates over the other), and take into account not only the content of her preferred plate, but also the content of the neighbouring plates. We show that if the number of players is a prime power, in this setting an envy-free division exists under standard assumptions that the preferences are closed.
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。
