In the following game, nature determines Player 1 to be type I (probability = 0.3) or type II (probability = 0.7). Player 2 is unaware of Player 1's type. In this game Player 1 chooses L or R and subsequently Player 2 chooses U or D.

For simplicity, please assume that Player 2 (Receiver) believes they're at the following decision nodes with specified probabilities: Top Right: p Bottom Right: (1-p) Top Left: q Bottom Left: (1-q) Describe all pure-strategy pooling and separating perfect Bayesian equilibria. Justify all answers.

15, 8 20, 16 U U P R N D 10, 5 0.3 Type I D 10, 10 Nature 10, 9 U 0.7 Type II 10, 6 U R NO D D 15, 12 20, 8