Cake-Cutting: Fair Division of Divisible Goods

Abstract

Everyone knows that whenever there is a party, there is also a variety of tastes. Each to his own, you may say—but what if you are the host? Wishing to keep everyone happy and to avoid arguments amongst the guests, a good host would offer a wide choice of food. But what if there is only a single wedding cake? Well, even a single cake may serve well to account for all the different tastes. There may be several layers of delicious sponge, tasty fresh strawberries, and even loads of cream and chocolate splits. It is easy to see that this cake would offer something for everyone—the fruit lover as well as the chocolate fanatic. The crucial bit, though, is that the host will have to divide the cake such that each guest receives a piece she is satisfied with. Even though this may sound easy at a first glance, it will soon become apparent that this is not necessarily the case. It can actually be quite a challenge to cut a single cake in a way such that everyone is happy with the piece received and does not envy anyone else for their portion.