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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. However, an EF allocation exists when there are 2 agents and one cake is cut into 3 pieces (the least-wanted piece is discarded), or when there are 3 agents and each cake is cut into 2 pieces (one agent is ignored; the ...
Anonymous fair cake-cutting requires that not only the values be equal, but also the pieces themselves be equal. [2] This implies symmeric fairness, but it is stronger . For example, it is not satisfied by the symmetric-divide-and-choose above, since in the case that a = g , the first agent always gets the leftmost piece and the second agent ...
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).
So the cutter can cut the cake into two pieces with almost the same amount of chocolate, such that the smaller piece has slightly more chocolate. Then, the chooser will take the smaller piece and the cutter will win the larger piece, which may be worth much more than 1/2 (depending on how the chocolate is distributed).
Alice cuts the cake to 6 pieces with valuation-ratios 5:3:2:1:1:1. George marks the pieces that have for him at least the value mentioned by Alice. Now there are two "good" cases - cases in which we can use these pieces to attain a weighted-proportional division respecting the different entitlements:
An envy-free cake-cutting is a kind of fair cake-cutting.It is a division of a heterogeneous resource ("cake") that satisfies the envy-free criterion, namely, that every partner feels that their allocated share is at least as good as any other share, according to their own subjective valuation.
The RW model specifies two kinds of queries that a fair division algorithm may ask the agents: Eval and Cut. 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.
In the problem of envy-free cake-cutting, there is a cake modeled as an interval, and agents with different value measures over the cake. The value measures are accessible only via queries of the form "evaluate a given piece of cake" or "mark a piece of cake with a given value".