Problem 1: [20 pts] Consider the following game involving 4 players. In period 1, player 1 chooses

whether to play action A1 or B1. In period 2 (after player 1's decision has been made), player 2

chooses whether to play action A2 or B2. In period 3, player 3 chooses whether to play action A3

or B3 and in period 4, player 4 chooses whether to play A4 or B4. The payoffs are: if all players

choose A, then every player obtains 0 utils. If at least one player chooses B, then each player who

chose A obtains 2 utils, while every player who chose B obtains 1 util.

Part a: [5 pts] Suppose that all players can observe the actions of all players acting before him/her

before making his/her decision. Draw the game tree of this game.

Part b: [5 pts] How many strategies does player 3 have in the game from part a? Write out all of

player 3's strategies.

Part c: [5 pts] Now suppose instead that each player i = 2; 3; 4 can only observe the action of the

player acting immediately before him/her (action of player i-1). Draw the game tree.

Part c: [5 pts] How many strategies does player 3 have in the game from part c? Write out all of

player 3's strategies.