Your little twin sisters (whom you lovingly refer to as Thing 1 and Thing 2) are driving you crazy! You've baked them a lovely birthday cake, but they won't stop fighting over who gets the biggest slice. To settle the dispute, you draw on a time- honored ritual: You ask Thing I to cut the cake and Thing 2 to choose which piece she wants. On your own, draw the extensive form Of this game. Let Thing 1 's strategies be "Cut Evenly" or "Cut Unevenly"; depending on what's on the platter, Thing 2's strategies might include "Take Big Slice," "Take Small Slice," or ' 'Take Equal Slice." Assign payoffs to Thing 1 and Thing 2 that grow with the size of the slice they receive.

The equilibrium outcome for this game is :