4. [(a)=10,(b)=10,(c)=10] Consider the following simple signaling model with two players N={1,2}. The game's timeline is given as: i. Nature draws a type ti for player 1 from a set of feasible types T={t1,t2} where Pr(t1)=0.4. ii. Player 1 observes ti and then chooses a message mj from a set of feasible messages M={L,R}. iii. Player 2 observes mj (but not ti ) and then chooses an action ak from a set of feasible actions A={u,d}. iv. Payoffs are given as follows: When player 1 's type is t1, if player 1 chooses L and player 2 chooses u, then (3,1), if player 1 chooses L and player 2 chooses d, then (1,0), if player 1 chooses R and player 2 chooses u, then (1,0), if player 1 chooses R and player 2 chooses d, then (0,1). When player 1 's type is t2, if player 1 chooses L and player 2 chooses u, then (1,0), if player 1 chooses L and player 2 chooses d, then (3,1), if player 1 chooses R and player 2 chooses u, then (0,1), if player 1 chooses R and player 2 chooses d, then (2,0). The first number is player 1's payoff. (a) Draw a game tree. (b) Find a set of pooling Perfect Bayesian equilibria (show your procedure). (c) Explain what the off-the-equilibrium beliefs mean and why you cannot apply a Bayes rule for it. 4. [(a)=10,(b)=10,(c)=10] Consider the following simple signaling model with two players N={1,2}. The game's timeline is given as: i. Nature draws a type ti for player 1 from a set of feasible types T={t1,t2} where Pr(t1)=0.4. ii. Player 1 observes ti and then chooses a message mj from a set of feasible messages M={L,R}. iii. Player 2 observes mj (but not ti ) and then chooses an action ak from a set of feasible actions A={u,d}. iv. Payoffs are given as follows: When player 1 's type is t1, if player 1 chooses L and player 2 chooses u, then (3,1), if player 1 chooses L and player 2 chooses d, then (1,0), if player 1 chooses R and player 2 chooses u, then (1,0), if player 1 chooses R and player 2 chooses d, then (0,1). When player 1 's type is t2, if player 1 chooses L and player 2 chooses u, then (1,0), if player 1 chooses L and player 2 chooses d, then (3,1), if player 1 chooses R and player 2 chooses u, then (0,1), if player 1 chooses R and player 2 chooses d, then (2,0). The first number is player 1's payoff. (a) Draw a game tree. (b) Find a set of pooling Perfect Bayesian equilibria (show your procedure). (c) Explain what the off-the-equilibrium beliefs mean and why you cannot apply a Bayes rule for it