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Divide and choose (also Cut and choose or I cut, you choose) is a procedure for fair division of a continuous resource, such as a cake, between two parties. It involves a heterogeneous good or resource ("the cake") and two partners who have different preferences over parts of the cake (both want as much of it as possible). The procedure ...
The main difficulty in designing an envy-free procedure for n > 2 agents is that the problem is not "divisible".I.e., if we divide half of the cake among n/2 agents in an envy-free manner, we cannot just let the other n/2 agents divide the other half in the same manner, because this might cause the first group of n/2 agents to be envious (e.g., it is possible that A and B both believe they got ...
The "cake" is only a metaphor; procedures for fair cake-cutting can be used to divide various kinds of resources, such as land estates, advertisement space or broadcast time. The prototypical procedure for fair cake-cutting is divide and choose, which is mentioned in the book of Genesis to resolve Abraham and Lot's conflict. This procedure ...
The BHS mechanism was extended to any number of agents, but only for a special case of piecewise-uniform valuations, in which each agent desires only a single interval of the form [0, x i]. Ianovsky [14] proves that no truthful mechanism can attain a utilitarian-optimal cake-cutting, even when all agents have piecewise-uniform valuations ...
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When any player shouts "cut", the cake is cut by the sword and by whichever of the players' knives happens to be the central one of the three (that is, the second in order from the sword). Then the cake is divided in the following way: The piece to the left of the sword, which we denote Left, is given to the player who first shouted "cut". We ...
In a hilarious moment captured on camera, the queen was presented the opportunity to cut into a large celebratory sheet cake. Instead of making the first cut into the cake with a standard knife ...
Cake-cutting may refer to: Fair cake-cutting, a mathematical problem of fairly dividing a heterogenous resource among people with different preferences Efficient cake-cutting, a similar division problem in economics and computer science; Wedding-cake cutting, the habit of cutting the wedding cake and distributing it to the guests, as a symbol ...