Question

Your little twin sisters, Charlotte and Emily, 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 Charlotte to cut the cake and then ask Emily to choose which piece she wants.

5.1. Draw the extensive form of this game. Let Charlotte’s strategies be “Cut Evenly” or “Cut Unevenly.” Let Emily’s strategies be “Take Big Slice”, “Take Small Slice” and “Take Equal Slice.” (For Emily, not all three strategies may be possible after each of Charlotte’s strategies.) The payoffs to the girls grow with the size of the slice they receive; so for simplicity, let the payoffs be 1, 2, and 3.

5.2. Find the equilibrium outcome of this game. Show your work.

5.3. After the rules are announced, Emily shouts, “It’s not fair! I want to be the one who cuts the cake, not the one who chooses the slice!” Is Emily’s complaint valid? Answer in terms of mover advantage.

Answer 1