3. (8pts) In this game, two players 1 and 2 divide $5 between themselves. Player 1 moves first and makes a proposal as to how to divide the $5. Player 1's choices are x = 0, 1, 2, 3, 4, 5, meaning how many dollars he intends to keep, the rest 5x dollars go to Player 2. After Player 1 makes the proposal, Player 2 has two choices: either accept or reject Player 1's offer. If Player 2 accepts the offer, they split the money according to the offer and payoffs are (x, 5 x). If Player 2 rejects Player 1's offer, the $5 will be automatically taken away from them, leaving payoffs (0, 0) for the two players. (a) (2pts) Draw a game tree to illustrate the choices players can make and payoffs they may get. (b) (4pts) Use backward induction to solve the game. Use arrows to indicate players's optimal choices on the game tree. (c) (2pts) Find all subgame perfect equilibria.