博弈论~又见博弈论~跪求一道题目希望大家给出详细解答-经管之家官网！

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~~~~
这次题目看着好像比较复杂，多给点悬赏，嫌少跟咱要，只要拿到这十分，给多少钱都行啊~5555
下面是从PDF直接复制来的，看不方便的话麻烦下载帖子下面的"homework 3.pdf"，或者这里给纳米盘下载链接：http://d.namipan.com/d/b67b943c0ec4f92b394d3b8ae00d56defdb6daacf2600000


Homework III
1. Consider a market for loans to finance investment projects. All investment
projects require an outlay of 1 dollar. There are two types of projects: good
and bad. A good projects has a probability of pG of yielding profits of  > 0
and a probability (1 − pG) of yielding profits of zero. For a bad project, the
relative probabilities are pB and (1 − pB), respectively, where pG > pB. The
fraction of projects that are good is  2 (0, 1).
Entrepreneurs go to banks to borrow the cash to make the initial outlay
(assume for now that they borrow the entire amount). A loan contract specifies
an amount R that is supposed to be repaid to the bank. Entrepreneurs
know the type of project they have, but the banks do not. In the event that
a project yields profits of zero, the entrepreneur default on her loan contract,
and the bank receives nothing. Banks are competitive and risk neutral. The
risk-free rate of interest (the rate the banks pay to borrow funds) is r. Assume
that
pG − (1 + r) > 0 > pB − (1 + r).
(a) Find the equilibrium level of R and the set of projects financed. How
does this depend on pG, pB, , , and r?
(b) Now suppose that the entrepreneur can off to contribute some fraction
x of the 1 dollar initial outlay from her own funds (x 2 [0, 1]). The
entrepreneur is liquidity constrained, however, so that the effective cost
of doing so is (1 + )x, where  > r.
(i) What is an entrepreneur’s payoff as a function of her project type,
her loan-repayment amount R, and her contribution x?
(ii) Describe the best (from a welfare perspective) separating perfect
Bayesian equilibrium of a game in which the entrepreneur first
makes an offer that specifies the level of x she is willing to put
into a project, banks then respond by making offers specifying the
level of R they would require, and finally the entrepreneur accepts
a bank’s offer or decides not to go ahead with the project. How
1
does the amount contributed by entrepreneurs with good projects
change with small changes in pB, pG, , , and r?
(iii) How do the two types of entrepreneurs do in the separating equilibrium
of (b) (ii) compared with the equilibrium in (a)?