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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 ...
Informally, an Eval query asks an agent to specify his/her value to a given piece of the cake, and a Cut query (also called a Mark query) asks an agent to specify a piece of cake with a given value. Despite the simplicity of the model, many classic cake-cutting algorithms can be described only by these two queries.
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 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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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 ...
A microwave oven or simply microwave is an electric oven that heats and cooks food by exposing it to electromagnetic radiation in the microwave frequency range. [1] This induces polar molecules in the food to rotate and produce thermal energy in a process known as dielectric heating .
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 ...