Tournament games and positive tournaments
Tournament games and positive tournaments
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锦标赛游戏和积极的锦标赛
DOI：
10.1002/jgt.3190190208
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发表时间：
1995
期刊：
影响因子：
--
通讯作者：
J. Ryan
中科院分区：
文献类型：
--
作者：
David C. Fisher;J. Ryan
给定一个竞赛图T，T上的竞赛图博弈如下：两个局中人独立地选择T的一个节点。如果双方都选择了相同的节点，游戏就打成平手。否则，节点位于连接两个节点的弧的尾部的玩家获胜。我们证明了这个博弈的最优混合策略是唯一的，并且使用奇数个节点。
一个锦标赛是积极的，如果它的锦标赛游戏的最优策略使用它的所有节点。最优策略的唯一性给出了新的锦标赛分解：任何锦标赛都可以唯一地划分为正子锦标赛P1、P2、Pk，因此对于所有1 ≤ i > j ≤ k，Pi“击败”Pj。我们计算了n个节点的正竞赛图的数量，并列出了它们，其中n ≤ 7。John Wiley & Sons，Inc.
Given a tournament T, the tournament game on T is as follows: Two players independently pick a node of T. If both pick the same node, the game is tied. Otherwise, the player whose node is at the tail of the arc connecting the two nodes wins. We show that the optimal mixed strategy for this game is unique and uses an odd number of nodes.
A tournament is positive if the optimal strategy for its tournament game uses all of its nodes. The uniqueness of the optimal strategy then gives a new tournament decomposition: any tournament can be uniquely partitioned into positive subtournaments P1, P2, ,Pk, so Pi “beats” Pj for all 1 ≤ i > j ≤ k. We count the number of n node positive tournaments and list them for n ≤ 7. © 1995 John Wiley & Sons, Inc.