Consider the following extensive form game. Agent A moves rst and can move either U or D. Agent B moves second and can move either L or R in response to U or D. Agent A can be one of two types: T1 or T2. Agent A knows his own type but Agent B does not know Agent A's type. Agent B's commonly known prior belief is that Agent A is type T1 with probability 0.6 and type 72 with probability 0.4. Thus, while Agent B can tell which move was made by Agent A, she cannot tell which type of agent made that move. 1.1. Prove that there is a Nash equilibrium in which both types of Agent A move U and Agent B responds to move U with L. Note that you must specify how Agent B responds to D. 1.2. Prove that the above Nash equilibrium (NE) is a sequential equilibrium (SE). 1.3. Prove that the above SE does not pass Cho-Kreps Intuitive Criterion. Is this a Divinity equilibrium? 1.4. Prove that another SE is for both 71 and 7'2 to move D and B to respond to D with R. Prove that this SE doesn't pass Cho-Kreps Intuitive Criterion. Is this a Divinity equilibrium? 1.5. Identify the perfectly separating universally divine sequential equilibrium and prove that it is so. (3.5} (0,4) (2.5} (1,5) 0 0 A=T1 (pznfi) A=T2 (1320.4) L} L}