Envy-Free Mechanisms with Minimum Number of Cuts
نویسندگان
چکیده
We study the problem of fair division of a heterogeneous resource among strategic players. Given a divisible heterogeneous cake, we wish to divide the cake among n players in a way that meets the following criteria: (I) every player (weakly) prefers his allocated cake to any other player’s share (such notion is known as envy-freeness), (II) the mechanism is strategy-proof (truthful), and (III) the number of cuts made on the cake is minimal. We provide methods, namely expansion process and expansion process with unlocking, for dividing the cake under different assumptions on the valuation functions of the players.
منابع مشابه
The Query Complexity of Cake Cutting
We study the query complexity of cake cutting and give lower bounds for computing approximately envy-free, perfect, and equitable allocations with the minimum number of cuts. These lower bounds are tight for three players in the case of envy-free allocations and for two players in the case of perfect and equitable allocations. We also formalize moving knife procedures and show that a large subc...
متن کاملCake division with minimal cuts: envy-free procedures for three persons, four persons, and beyond
The minimal number of parallel cuts required to divide a cake into n pieces is n 1. A new 3person procedure, requiring two parallel cuts, is given that produces an envy-free division, whereby each person thinks he or she receives at least a tied-for-largest piece. An extension of this procedure leads to a 4-person division, using three parallel cuts, which makes at most one person envious. Fina...
متن کاملEnvy-free two-player mm-cake and three-player two-cake divisions
Cloutier, Nyman, and Su (Mathematical Social Sciences 59 (2005), 26–37) initiated the study of envy-free cake-cutting problems involving several cakes. The classical result in this area is that when there are q players and one cake, an envy-free cake-division requiring only q − 1 cuts exists under weak and natural assumptions. Among other results, Cloutier, Nyman, and Su showed that when there ...
متن کاملAlgorithmic Solutions for Envy-Free Cake Cutting
We study the problem of finding an envy-free allocation of a cake to d+1 players using d cuts. Two models are considered, namely, the oracle-function model and the polynomial-time function model. In the oracle-function model, we are interested in the number of times an algorithm has to query the players about their preferences to find an allocation with the envy less than . We derive a matchin...
متن کاملBetter Ways to Cut a Cake - Revisited
Procedures to divide a cake among n people with n-1 cuts (the minimum number) are analyzed and compared. For 2 persons, cut-and-choose, while envy-free and efficient, limits the cutter to exactly 50% if he or she is ignorant of the chooser’s preferences, whereas the chooser can generally obtain more. By comparison, a new 2person surplus procedure (SP’), which induces the players to be truthful ...
متن کامل