1. Consider the following situation.

Maipo and Pisco need to decide how to divide a cake between the two of them. Both like cake and want to get as much cake as they can. They decide to let Maipo cut the cake first and then Pisco gets to pick which piece he wants.

For simplicity, assume that Maipo can only cut the cake in two ways: He can either divide it into two pieces that are equal size (i.e., both will get half the cake) or he can divide the cake into two pieces where one piece is twice the size of the other (i.e., one will get a piece that is two-thirds of the cake and the other will get a piece that is one-third of the cake).

1. Set up this game as a sequential game and draw the game tree that represents it

Note: You can either draw the game tree by hand and then photograph/scan the tree and paste it into the assignment or use the drawing tool in Word to draw the tree.

2. Find the sub-game perfect Nash Equilibria to this game. Underline the strategies or highlight the game tree path to show what the Nash Equilibria is/are.

3. Is/are the sub-game perfect Nash Equilibrium efficient? EXPLAIN.