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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.
There is a generalization of the cake-cutting problem in which there are several cakes, and each agent needs to get a piece in each cake. Cloutier, Nyman and Su [17] study two-player envy-free multi-cake division. For two cakes, they prove that an EF allocation may not exist when there are 2 agents and each cake is cut into 2 pieces.
The classic divide and choose procedure for cake-cutting is not truthful: if the cutter knows the chooser's preferences, they can get much more than 1/2 by acting strategically. For example, suppose the cutter values a piece by its size while the chooser values a piece by the amount of chocolate in it.
An RF switch or microwave switch is a device to route high frequency signals through transmission paths. RF (radio frequency) and microwave switches are used extensively in microwave test systems for signal routing between instruments and devices under test (DUT). Incorporating a switch into a switch matrix system enables you to route signals ...
Zeng [10] presented an algorithm for approximate envy-free cake-cutting with different entitlements. Dall'Aglio and MacCheroni [11]: Thm.3 proved the existence of proportional cake-cutting with different entitlements even when agents' preferences are described by non-additive preference relations, as long as they satisfy certain axioms.
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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 ...