Consider the following signaling game. Nature rst determines player 1's type, either high

or low, with equal probabilities. Then player 1, observing his own type, decides whether to

choose left (L) or Right (R). If he chooses left, the game ends and players' payos become

(u1, u2) = (2, 0), regardless of player 1's type. The gure below depicts these payos in

the left-hand side of the tree. If, instead, player 1 chooses Right, player 2 is called on to

move. In particular, without observing whether player 1's type is high or low, player 2

must respond by either selecting Up (U) or Down (D). As indicated by the payos in the

right-hand side of the tree, when player 1's type is high, player 2 prefers to play Up. The

opposite preference ranking applies when player 1's type is low.

a) Describe all the pure-strategy pooling Bayesian Equilibria.

b) Describe all the pure-strategy separating Bayesian Equilibria.