Answer Happy

2. (40 points) Consider the following sequential game. The first move is one of chance. Player 1 observes the move by Nature, but Player 2 does not. Player 1 is Type I with probability and Type II with probability Nature (1) B A B UR NA 2 21-A 2 1-UB C D C D C D C D 4,1 2,3 3,2 1,5 6,4 0,2 5,7 2,1 (a) Does this game have any separating perfect Bayesian equilibria? Show your analysis, and if there is such an equilibrium, report it. In searching for perfect Bayesian equilibria, check directly by (1) checking each possible separating strategy by player 1, (2) update player 2's beliefs HA and up by Bayes Rule when possible and formulate beliefs when it is not), (3) determine player 2's best response to player 1, given the updated beliefs, and (4) check if player 1 would stay with the specified strategy. (b) Does this game have any pooling perfect Bayesian equilibria? Show your analysis, and if there is such an equilibrium, report it. In searching for the perfect Bayesian equilibria, follow the same procedure for (a), except of course check each possible pooling strategy by player 1.