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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 ...
Symmetric fair cake-cutting is a variant of the fair cake-cutting problem, in which fairness is applied not only to the final outcome, but also to the assignment of roles in the division procedure. As an example, consider a birthday cake that has to be divided between two children with different tastes, such that each child feels that his/her ...
Truthful cake-cutting is the design of truthful mechanisms for fair cake-cutting. The currently known algorithms and impossibility results are shown here. The main cases in which it is unknown whether a deterministic truthful fair mechanism exists are: [10]
It was the first example of a continuous procedure in fair division. The knife is passed over the cake from the left end to the right. Any player may say stop when they think / of the cake is to the left of the knife, the cake is cut and the player who spoke gets that piece. Repeat with the remaining cake and players, the last player gets the ...
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.
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.
In the above example, the order would be: Lemon (0), Chocolate (1), Vanilla+Cherries (4). Start at the point where all cake is given to George (0,30). Move each piece-of-cake in order from George to Alice; draw a line whose slope is the corresponding utility-ratio. Finish at the point where all cake is given to Alice (30,0).
Despite the simplicity of the model, many classic cake-cutting algorithms can be described only by these two queries. On the other hand, there are fair cake-cutting problems that provably cannot be solved in the RW model using finitely many queries. The Eval and Cut queries were first described in the book of Jack M. Robertson and William A ...