Consider a cheap talk game in which Nature moves by choosing a sender's type, where the type space has five elements: -3, -2, 1, 2, and 3, each occurring with equal probability of 1/5. The sender learns his type and chooses one of three possible messages: bumpy, smooth, and slick. The receiver observes the sender's message and then chooses one of three actions: 0, 2, and 4. The sender's payoff equals his type multiplied by the receiver's action. The receiver's payoff equals the sender's type multiplied by twice the receiver's action. Remember you must specify strategies for both players and the beliefs of the receiver to be a perfect Bayes-Nash eq. Remember to not only find it but show me how you checked to make sure it was a PBNE.

a) Find a separating perfect Bayes-Nash eq.

b) Find a semi-separating perfect Bayes-Nash eq.