Consider the following game: 3 players can contribute or not to a public good. For the public good to be successfully created, 2 contributions are necessary (a third contribution would not add anything to the public good). These are the payoffs each of the three players assign to all possible outcomes:

3 : I didn't contribute but the public good was created anyway

2 : I did contribute and the public good was created

1 : I didn't contribute and the public good was not created

0 : I did contribute and the public good was not created

The decisions are made sequentially: player 1 moves, then player 2, then player 3.

(a) Find the set of pure strategy Nash equilibria of this game if it is played as a simultaneous move game.

(b) Find the set of subgame perfect Nash equilibria of this game when it is played sequentially.