How to Cut a Cake Fairly: A Generalization to Groups

Cutting a Cake Fairly for Groups Revisited

Cake cutting is a classic fair division problem, with the cake serving as a metaphor for a heterogeneous divisible resource. Recently, it was shown that for any number of players with arbitrary preferences over a cake, it is possible to partition the players into groups of any desired size and divide the cake among the groups so that each group receives a single contiguous piece and every player is envy-free. For two groups, we characterize the group sizes for which such an assignment can be computed by a finite algorithm, showing that the task is possible exactly when one of the groups is a s…

Fairness and Efficiency in Cake-Cutting with Single-Peaked Preferences

We study the cake-cutting problem when agents have single-peaked preferences over the cake. We show that a recently proposed mechanism by Wang-Wu (2019) to obtain envy-free allocations can yield large welfare losses. Using a simplifying assumption, we characterize all Pareto optimal allocations, which have a simple structure: are peak-preserving and non-wasteful. Finally, we provide simple alternative mechanisms that Pareto dominate that of Wang-Wu, and which achieve envy-freeness or Pareto optimality.

Obvious Manipulations in Cake-Cutting

In cake-cutting, strategy-proofness is a very costly requirement in terms of fairness: for n=2 it implies a dictatorial allocation, whereas for n > 2 it requires that one agent receives no cake. We show that a weaker version of this property recently suggested by Troyan and Morril, called non-obvious manipulability, is compatible with the strong fairness property of proportionality, which guarantees that each agent receives 1/n of the cake. Both properties are satisfied by the leftmost leaves mechanism, an adaptation of the Dubins - Spanier moving knife procedure. Most other classical proporti…

甜点上的对决，掌握重复切蛋糕的艺术

Dueling Over Dessert, Mastering the Art of Repeated Cake Cutting

研究两人在重复切蛋糕中的公平分配问题，提出利用类似二分搜索策略和Blackwell approachability理论，证明参与者可在极限下实现(1/2, 1/2)的公平效用配置，并证明fictitious play以 $O(1/\sqrt{T})$ 速率收敛。