This is game theory.

I need this explained detailed as possible.

A simple signaling game: Consider the following signaling game. Here, 1,0 ,0,0 Sender 01 U [P] L R [9] D D P() = 3,1 2,1 Receiver 0 Receiver 0,1 P(02 = 1,1 L 1 -p] R 02 (1-9) Sender D D 2,0 3,0 nature (player 0) first selects the type of the sender: with probability { the type is 01 and with probability the type is 62. Each type of the sender can then send either message or message R. The receiver observes the message, but does not observe the type of the sender. At each of her two information sets, the receiver has to decide between U and D. The notation for the beliefs of the receiver is indicated in brackets [:). The payoffs of the sender at terminal nodes are the first entries; the ones of the receiver are the second entries. Please answer the following questions: (a) What are the pure strategies of the sender? (b) What are the pure strategies of the receiver? (c) Describe all pure-strategy pooling and separating weak perfect Bayesian equilibria in this game. A simple signaling game: Consider the following signaling game. Here, 1,0 ,0,0 Sender 01 U [P] L R [9] D D P() = 3,1 2,1 Receiver 0 Receiver 0,1 P(02 = 1,1 L 1 -p] R 02 (1-9) Sender D D 2,0 3,0 nature (player 0) first selects the type of the sender: with probability { the type is 01 and with probability the type is 62. Each type of the sender can then send either message or message R. The receiver observes the message, but does not observe the type of the sender. At each of her two information sets, the receiver has to decide between U and D. The notation for the beliefs of the receiver is indicated in brackets [:). The payoffs of the sender at terminal nodes are the first entries; the ones of the receiver are the second entries. Please answer the following questions: (a) What are the pure strategies of the sender? (b) What are the pure strategies of the receiver? (c) Describe all pure-strategy pooling and separating weak perfect Bayesian equilibria in this game