There are two firms (an incumbent and an entrant, I and E). The two firms compete in quantity a la Cournot over two periods. The constant marginal cost of I is c
(common knowledge). The constant marginal cost of E is either cL or cH (cL < cH). Only E knows its marginal cost (private information). I initially believes that E’s marginal cost is cL with probability μ1 (common knowledge). The inverse demand function is p = a − Q where a is a positive constrant and Q is industry output.
The game runs as follows. In period 1, given μ1, the firms simultaneously choose output levels, xI and xE. I updates its belief (E’s marginal cost is cL with probability μ2) based on the first period outcome. In period 2, they choose quantities supplied, yI and yE, once again, and the game ends. Each firm’s payoff is the discount sum of profits over two periods. The discount factor is δ (this can be larger than unity if the second period lasts longer than the first). The solution concept is perfect Bayesian equilibrium.

问： Given μ2, solve the second period game. Note that, this is just a one-shot game with onesided incomplete information. Explain how the (second period) equilibrium quantities and the (second period) profits change with an increase in μ2.

英文太长了，翻译一下，方便各位阅读
题目：有2个企业（在位者I和进入者E)。二者在2个时期内进行古诺竞争。在位者I的边际成本为c（共同信息）。进入者E的边际成本为cL或cH（cL<cH)。只有E知道自己的边际成本。I 最初以μ1的概率认为E的边际成本为cL。逆需要方程为p = a − Q
在时期1，μ1给定，二者同时选择产出水平，xI 和 xE。 在时期1的产出基础上， I更新自己的belief(E’s marginal cost is cL with probability μ2)。
在时期2，二者选择供给量，yI and yE
每个企业的收益是在2个时期利润折现之和。折现率是δ。

问题：给定μ2，解出第2时期的博弈。解释在时期2内，如果μ2增加，均衡产量和利润怎样变动？