这是online quiz 上的一题,关于subgame perfect equilibrium 没有掌握好,有哪位能赐教啊?~~
题目背景:John Nash and his buddy return to the bar in which a few weeks ago
they failed to secure either a blonde or a brunette. This week they have
a new plan. First, John will choose a girl to approach. Then, after
observing the girl that John approaches, his buddy will choose a girl
to approach (he can approach the same girl that John has approached
or either of the other ones). There are still 3 girls: one blonde (B) and
two brunettes (b1, b2) in the bar. Both John and his friend still prefer
blondes to brunettes. They will be successful in approaching any girl,
unless she is approached by both of them, in which case they leave the
bar with nothing. Represent this situation as an extensive form game.
问题:Work out the Subgame Perfect equilibriumia.
题目大概意思就是有两个男生一个叫 john 一个是他的兄弟题目里没给名字,就叫tim好了,两个人都去搭讪女生,
女生一共有3个,分别为金发碧眼的B 和两位深肤色的女孩(b1,b2),john 和他的兄弟tim都喜欢金发碧眼的B 多于两
位深肤色的女孩。如果两个男生搭讪了同一名女生即为搭讪失败,反之即为成功。现在是john先去搭讪,然后根据john
搭讪的女孩的情况,tim再去搭讪。。。
战略一共是有27个,具体的subgame perfect equilibrium 是什么呢?另外题中的纳什平衡又是什么呢?
之后的小题让我更加纠结。。
问题:下面哪一个是纳什平衡但不是SPE?对于tim的战略(。,。,。)表示john选择B,b1,b2后的对应选择
(a) b1; (b2;B;B)
(b) b1; (B;B;B)
(c) b1; (b1;B; b2)
(d) None of the above.