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Fair cake-cutting algorithms: Ortega, Kyropoulou and Segal-Halevi [29] tested algorithms such as Divide and choose, Last diminisher, Even–Paz and Selfridge–Conway between laboratory subjects. It is known that these procedures are not strategyproof , and indeed, they found that subjects often manipulate them.
The first published algorithm for proportional division of a cake was the last diminisher algorithm, published in 1948. Its run-time complexity was O(n^2). in 1984, Shimon Even and Azaria Paz published their improved algorithm, whose run-time complexity is only O(n log n).
Average-proportional cake-cutting (i.e., an allocation between n families, such that for each family, the average value is at least 1/n of the total) cannot be computed using finitely-many RW queries, even when there are 2 families with 2 members in each family. The proof is by reduction from equitable cake-cutting.
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 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.
In the envy-free cake-cutting problem, a "cake" (a heterogeneous divisible resource) has to be divided among n partners with different preferences over parts of the cake. . The cake has to be divided to n pieces such that: (a) each partner receives a single connected piece, and (b) each partner believes that his piece is (weakly) better than all other pie
The Robertson–Webb rotating-knife procedure is a procedure for envy-free cake-cutting of a two-dimensional cake among three partners. [1]: 77–78 It makes only two cuts, so each partner receives a single connected piece.
In 1988, prior to the discovery of the BTP, Sol Garfunkel contended that the problem solved by the theorem, namely n-person envy-free cake-cutting, was among the most important problems in 20th century mathematics. [2] The BTP was discovered by Steven Brams and Alan D. Taylor.