帽子的机制设计和证明

Sorry I did not see the condition: at the same time. If this is the case, then it is mixed strategy. There is 50% chance.

I am stupid.

怎么还搞什么英汉结合。。。

5# 猫爪

回复猫同学：

你仔细看了我13楼的帖子就不会有疑问了。这样一种策略是存在的。这就是1号说与2号的帽子颜色相同的颜色，2号说与1号帽子颜色相反的颜色。

6# 猫爪

回复猫同学：

采取说多数人的帽子的颜色的策略是不成功的。因为如果给N个人带上红帽子，N个人带上蓝帽子，那么采取这种策略就会导致没有一个人猜对的结果。

Yes, you are right. If both them wear red, which means (red, red). A says red and B says blue, then A is right and B is wrong. If both them wear blue, which means (blue, blue). A says blue and B says red, then A is right again and B is wrong again. If A wears blue and B wears red, which means (blue, red). A says red and B says red. This time A is wrong but B is right. If A wears red and B wears blue, which means (red, blue). A says blue and B says red. Once again, A is wrong and B is right. Therefore, there is alway N person right.

18# defeniks

well, technically, if there is 2N players, you first divide them into N groups with 2 players in each group. then you can repeat what i did when if there's only 2 players.

imp555 发表于 2009-6-24 13:47
5# 猫爪

回复猫同学：

你仔细看了我13楼的帖子就不会有疑问了。这样一种策略是存在的。这就是1号说与2号的帽子颜色相同的颜色，2号说与1号帽子颜色相反的颜色。

恩，有道理。

利用颜色的有限性，双方有意识的选择与对方选择相反的另一种选择（1或者和2相同，或者相反，这是完备的），这样就解决了。

本质上，牺牲了都答对的可能性，来保证至少有一人答对。

不错。

imp555 发表于 2009-6-24 13:57
6# 猫爪

回复猫同学：

采取说多数人的帽子的颜色的策略是不成功的。因为如果给N个人带上红帽子，N个人带上蓝帽子，那么采取这种策略就会导致没有一个人猜对的结果。

我当时想的是：

如果自己的颜色不影响整个帽子多少的比例时，可以按多的来。

如果能够影响比例，就没办法选择了。