两个玩家的树搜索游戏
The tree search game for two players
摘要：
我们考虑一个两人在树$T$上的搜索博弈。随机选择一个顶点（玩家未知）作为目标。玩家轮流猜测顶点。如果猜测$v$不是目标，则通知两个参与者目标位于$T \smallsetminus v$的哪个子树中。猜对目标的玩家获胜。当两个球员发挥最佳，我们表明，他们每个人都赢得了概率约为$1/2$。当一个玩家玩最佳和其他随机播放，我们表明，最优策略的球员赢得之间的概率$9/16$和$2/3$（渐近）。当两个球员随机发挥，我们表明，每个赢得概率之间的$13/30$和$17/30$（渐近）。
英文摘要：
We consider a two-player search game on a tree $T$. One vertex (unknown to the players) is randomly selected as the target. The players alternately guess vertices. If a guess $v$ is not the target, then both players are informed in which subtree of $T \smallsetminus v$ the target lies. The winner is the player who guesses the target. When both players play optimally, we show that each of them wins with probability approximately $1/2$. When one player plays optimally and the other plays randomly, we show that the player with the optimal strategy wins with probability between $9/16$ and $2/3$ (asymptotically). When both players play randomly, we show that each wins with probability between $13/30$ and $17/30$ (asymptotically).
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。
