4.3. a. Specify a pooling perfect Bayesian equilibrium in which both Sender types play R in the following signaling game. 1,2 น น 0,1 L t₁ R 2,00 d d .5 3,0 Receiver Nature Receiver 0,0 น .5 | u 1,0 L t₂ R d 3,1 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. 1,1u 1,00 2,1 0,00 1,1 0,0 น 0,1 L t₁ R (1/3) d P 0,0 Receiver Receiver I u 1,1 = น L R (1/3) I d P $1,0 I Receiver Receiver | น 0,0 " t3 L R (1/3) 2,1