Divide-and-Conquer: A Proportional, Minimal-Envy Cake-Cutting Procedure

Properties of discrete cake-cutting procedures that use a minimal number of cuts (n-1 if there are n players) are analyzed. None is always envy-free or efficient, but divide-and-conquer (D&C) minimizes the maximum number of players that any single player may envy. It works by asking n ? 2 players successively to place marks on a cake that divide it into equal or approximately equal halves, then halves of these halves, and so on. Among other properties, D&C (i) ensures players of more than 1/n shares if their marks are different and (ii) is strategyproof for risk-averse players. However, D&C may not allow players to obtain proportional, connected pieces if they have unequal entitlements. Possible applications of D&C to land division are briefly discussed

Cake-Cutting is Not a Piece of Cake

Fair cake-cutting is the division of a cake or resource among N users so that each user is content. Users may value a given piece of cake differently, and information about how a user values dierent parts of the cake can only be obtained by requesting users to "cut" pieces of the cake into specified ratios. One of the most interesting open questions is to determine the minimum number of cuts required to divide the cake fairly. It is known that O(N log N) cuts suffices, however, it is not known whether one can do better. We sho