In the game of Centipede there are two players. Player 1 moves first, player 2 moves second. After at most two moves, the game ends. The game begins with $1 sitting on a table. Player 1 can either take the $1 or wait. If player 1 takes the $1 the game is over, and player 1 gets to keep the $1. If player 1 waits the $1 quadruples to $4. Now it is player 2's turn. Player 2 can either take the entire $4 or split the $4 evenly with player 1.

a. Draw the extensive form for the game of Centipede.

b. What is the equilibrium to this game? Can player 2's strategy of splitting the money ever be a part of an equilibrium outcome to the game?