可计算简单对策的Nakamura数
The Nakamura numbers for computable simple games
摘要：
简单博弈的Nakamura数在偏好聚合（或多标准排序）中起着关键作用：参与者可以理性处理的替代品的数量总是小于这个数字。我们全面研究了一个简单的游戏的各种性质强加给它的Nakamura数的限制。我们发现，一个可计算的游戏有一个有限的Nakamura数大于3，只有当它是适当的，非强，非弱，无论它是否是单调的，或者它是否有一个有限的载体。缺乏强性通常会导致无法严格排名的替代方案。
英文摘要：
The Nakamura number of a simple game plays a critical role in preference aggregation (or multi-criterion ranking): the number of alternatives that the players can always deal with rationally is less than this number. We comprehensively study the restrictions that various properties for a simple game impose on its Nakamura number. We find that a computable game has a finite Nakamura number greater than three only if it is proper, nonstrong, and nonweak, regardless of whether it is monotonic or whether it has a finite carrier. The lack of strongness often results in alternatives that cannot be strictly ranked.
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。
