Question

一道博弈论的题目，高分求解

咱想要详细的过程，因为是要交的
大家别怪咱这样作弊，实在因为老师用英文上课听不懂，而上课的都是大三的师兄师姐，他们都是学过高级微观课的，老师都讲给他们听啊，我刚过完大一，悔只在我选错课...
大家麻烦下...
拜托了，学分绩啊~~~~

Suppose there are two types of college students: A (able) and C (challenged).
You, a potential employer, are willing to pay $150,000 a year to a
type A, and $100,000 to a type C (you have to pay this much in a competitive
job market). You cannot directly observe any particular job applicant’s
type. But you know that types differ in their tolerance for taking a tough
course rather than an easy one in college. Suppose that the A types regard
the cost of each tough course as equivalent to $6,000 a year of salary, while
the C types regard it as $9,000 a year of salary.
a) Find first the minimum number of tough courses so that anyone who
has taken that number of tough courses will be regarded as a type A, and
anyone who has taken less than that number will be regarded as a type C.
Then write down your wage function.
b) If the populations of these two types are 50-50, show that both types
are better off under pooling in which you pay all the same salary.

以上不方便看的话，下面链接的图片“未命名.bmp“是原文（PDF）的截图，或者用纳米盘链接下载：http://d.namipan.com/d/b07aa77b32c5e0a91eeab686c50e0a8db529e926e6701b00

再次拜谢~~

咱也不知道这题值多少分，嫌少跟咱提，咱可以提高哈~

Answer 1

A学生 学习难课程的支付是6000每年,毕业后工资150000每年,那么他能接受的极限就是150000/6000=25门难课程,同理C是100000/9000=11.1门难课程(应该不考虑贴现问题),那么C类型的学生必然不会超过11门难课程(超出其支付-收入均衡值),但是如果C说谎,隐瞒自己的类型,招聘方只能从其所上难课的数量来确定其类型,那么C 就可能获得150000的薪水,于是该种情况下150000/9000=16.7门难课,也就是说超过16门难课,C没有将自己伪装成A的动机了,选到17门难课的一定是A.后一个问是在求啥不大确定,A,C的类型已经明确一半一半,雇佣者不知道其底细,本以为它想求混合战略,但是它又说对所有人只付一个工资,变成了线形最优了...但是统一工资亏得一定是A,付高了C占便宜,付低了C无所谓,A吃亏,没懂这个题目不好意思...