4.5 Find all the pure-strategy perfect Bayesian equilibria in Problem 4.3 (a) and (b)

V4.3. a. Specify a pooling perfect Bayesian equilibrium in which both Sender types play R in the following signaling game. 1,2 0 u u 0, 1 L t1 R 2,00 d - - d 5 3,0 Receiver Nature Receiver 0,0 0 u .5 u 1,0 L tz R 3,1 d d 2,2 b. The following three-type signaling game begins with a move by nature, not shown in the tree, that yields one of the three types with equal probability. Specify a pooling perfect Bayesian equilib rium in which all three Sender types play L. 1, 1 Q u u 0,1 R (1/3) d 1,0 0 d 0,0 Receiver Receiver 2, 1 1, 1 - u t2 R (1/3) d d 0,0 1,0 Receiver Receiver 1, 1 u - u 0,0 L t3 R (1/3) d 0,0 . d 2, 1