我想求一下这本书的答案可以么...太强大了好么 答案都有的...

我只确定第一问:
for finite number of generations, 只看最后一个generation的young people.
这个YP不可能给老人任何数量的巧克力，因为他知道他是最后一代，没有人在他老的时候会给他东西...
所以了.......by definition...X=1is the only NE as no one will have an incentive to deviate for all generations.

第二个么:我猜是用trigger strategy...一般TS肯定会有一个parto improvement跟之前的那个比起来......
eg:smoothing the consumption plan

第三个么…既然都知道X=0.5了 还是很好推的…
By given X=1 and X=0.5
The only deviation is from 0.5 to 1.
And since the barbarians only will steal all the goods at the end of period t, then the consumption for that period has already been implemented.
People will deviate if and only if the deviation can improve their consumption/utility.
Then the utility (no deviation, ie: X=0.5 by given the probability of losing all the remaining goods q) : 0.5+(1−q)0.5+q(−1) = 1−1.5q
Each term: get 0.5+ get o.5 Pr (no barbarians) + get (-1) Pr(Barbarians)

Compared with the payoff of, deviate ie: X=1.
Utility= 1-1=0
This is because; they consumed all the goods at one period, then definitely will receive a negative utility regardless whether barbarians will come)  

Then assume people will choose X=0.5 when indifferent:
set two equations equal: q=2/3, if q>2/3 then will deviate to X=1

题目里有些要考虑discounting么?折现是discounting么?
如果考虑discounting的话
个人认为就要分情况讨论
如果discounting rate=0...........肯定全都X=1.
或者discounting rate=1....或者无限接近1.......

如果第三问中考虑参与人的行为只考虑当期，即第t期。那他的期望也应该是(1-q)0.5+q(-1)=0，因为本期消费的0.5不算数啊。
第二问中无所谓冷酷策略，因为每个参与人只生存两期。题目里说了。
答案在1楼附件，如果是拉氏此书的答案，在rasmusen.org/gi

说实话我没看懂你说的是什么...冷酷策略我不知道是什么
但是第二问题里看你中文翻译的 什么都没说 只说是无限次

但是为什么本期的不算...?算payoff是for the whole periods...
我只是对比了两个strategies的expected payoff.
.