Players 1,2, and 3 play the following game. Each player starts with a pile containing one coin in front of him. In turn, each player says either 'stop' si or 'continue' ci . If a player says 'stop,' then the game ends and each player receives his pile of coins. If a player says 'continue,' then his pile looses one coin, while the other two piles gain one coin each. The players play in the order that they are numbered. (Of course, a player gets to play only if all players before him say 'continue.') If all the players say 'continue,' then after the coins are adjusted following player 3's statement, the game ends and each receives all coins in his pile.

(a) Draw the extensive form of this game. (Be sure to label each branch with the associated action, and remember that actions at different information sets cannot have the same label.)

(b) Find all Subgame Perfect Nash Equilibria.