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A division is called envy-free (EF) if each partner thinks that his piece is at least as valuable as the other piece. An EF division of a pie can always be found using divide and choose: one partner cuts the pie into two sectors he considers equal, and the other partner chooses the sector that he considers better. But for a pie, better ...
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.
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.
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The cutter can cut the cake to two pieces that they consider equal. Then, regardless of what the chooser does, they are left with a piece that is as valuable as the other piece. The chooser can select the piece they consider more valuable. Then, even if the cutter divided the cake to pieces that are unequal (in the chooser's mind), the chooser ...
The cake is cut when either player calls "stop", when he or she perceives the knife to be at the 50-50 point. If stop is called, the player to call stop gets the left-hand side of the cake. This will produce an envy-free division if the caller gets the left piece and the other player gets the right piece. (This procedure is not necessarily ...
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