Advance Microeconomics, Game Theory (Bayesian Equilibrium)

A committee of experts must advise the government on a policy to take. There are two states of nature , with . The government's belief is that states of nature occur with equal probability. The committee, having done its studies and thus learned the true state of nature, makes a policy recommendation to the government. After receiving the recommendation, the government must choose the policy to follow. To land ideas, suppose that the policy is represented by a number in (thus, both the recommendation and the government's decision are in ). The preferences of the expert committee and the government are represented, respectively, by:

with , where respents the policy adopted. Both maximize expected utility.

Let us consider the possibility of a separating equilibrium.

Show that if then there exists a separating equilibrium evaluation whose beliefs:

For this, provide the strategies and show that together with these beliefs they make up a Perfect Bayesian Equilibrium.

Note: separating equilibrium refers that the actions taken by the committee, upon receiving another information, are different.

{-, w 0 ue(0,a) = -(@+b-a) = a ug(0,a) = -(0-a) (at - = aER 6 P(@= wla= ) = 1 - 1 P(@= wla+ a) = 0 #a = = {-, w 0 ue(0,a) = -(@+b-a) = a ug(0,a) = -(0-a) (at - = aER 6 P(@= wla= ) = 1 - 1 P(@= wla+ a) = 0 #a = =