6. Pooling Perfect Bayesian Nash Equilibrium Consider the following dynamic signaling game that begins by nature drawing one of three types for Player 1 with equal probability. Player 1 knows their type, but Player 2 does not. Player 1's action space is {Left, Right}, and Player 2's action space is {Up, Down}. Specify the conditions under which a pooling perfect Bayesian equilibrium exists where all three Player 1 types play L. Player 2 Player 1 Player 2 1,1 0,1 L ti R (1/3) d !d P 1,0 2,1 0,0 1,1 0,0 7 t2 R L (1/3) P 1,0 0,0 10 L t3 R (1/3) d d 0,0 2,1 1,1