Player 1 is the sender and player 2 is the receiver.

The sender privately observes the state of the world {1,2,3} and sends a message m {1,2,3}. The receiver observes the message and then chooses an action a {1,2,3}. This ends the game.

The common prior belief on state is denoted by P(); assume P( = 1) = 1/4,P( =2) = 1/2,P( = 3) = 1/4.

The sender's payo does not depend on the state and is equal to the action chosen by the receiver.

The receiver's payo is 1 if a = and 0 otherwise.

Let denote the sender's mixed strategy; specically, let (m|) [0,1] denote the probability of sending message m when the sender's type is .

The receiver is restricted to using only pure strategies. Let denote the receiver's (pure) strategy; specically, let (m) {1,2,3} denote the receiver's action after message m.

(a) Show that every perfect Bayesian equilibrium (PBE) results in the receiver choosing a = 2 with probability 1.

(b) Construct a PBE.