Game Theory, Thank you so much!

Question 3: Three players move sequentially, one by one, such that player 1 moves rst, then after observing player 1's choice, player 2 moves and nally, after observing player 2's choice, player 3 moves. Each player can choose whether to contribute (C) or not contribute (N) towards the construction of a public good. If there are a total of 2 or 3 contributors, then the benet of the public good to each person is 4. If there are a total of U or 1 contributors, then the benet of the public good to each person is 2. Contributing costs 1, and if a player does not contribute, the cost is U. The payoC to a player is benet minus cost. (a) (6 points) Draw the extensive form (or game tree) for this game. How many proper sub games are there? (b) (6' points) Write down all possible strategies of players 1 and 2. How many strategies does player 3 have? (c) (8 points) What is the subgame perfect equilibrium of this game