1. (19 points) Consider the following game based on the Trust Game (which is often used to measure the level of trust in a society). An \"investor\" (player 1) can decide whether to send $20 to an \"entrepreneur\" (player 2). If she keeps the money, the game ends with the investor getting $20 and the entrepreneur getting $0. If the investor sends the money, it gets tripled to $60, and the entrepreneur decides whether to keep all the $60 to herself, or to split it evenly with the investor. (a) (3 pts) Draw a game tree (similar to one that we have seen in class) that represents the possible outcomes and choices in this game. Make sure to label which player makes a decision at each node. (b) (2 pts) First, let's suppose both players are purely self-interested, and they both know that the other is purely self-interested. What will Player 2 do, if Player 1 chooses to send the money to her? (c) (2 pts) What will Player 1 do, knowing that Player 2 will make the choice found above? (d) (4 pts) Now, suppose the two players have distributional preferences as introduced in class: if $1 and :32 are the amounts of money players 1 and 2 end up with, respectively, then player 1's utility is 1 5331 + 7372 if $1 2 332 U1($1,$2) : a1 + 332 if .131