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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 division is the problem in game theory of dividing a set of resources among several people who have an entitlement to them so that each person receives their due share. . That problem arises in various real-world settings such as division of inheritance, partnership dissolutions, divorce settlements, electronic frequency allocation, airport traffic management, and exploitation of Earth ...
In case the "cake" is a 1-dimensional interval, this translates to the requirement that each piece is also an interval. In case the cake is a 1-dimensional circle ("pie"), this translates to the requirement that each piece be an arc; see fair pie-cutting. Another constraint is adjacency. This constraint applies to the case when the "cake" is a ...
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.
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The following algorithms can be used to find an envy-free cake-cutting with maximum sum-of-utilities, for a cake which is a 1-dimensional interval, when each person may receive disconnected pieces and the value functions are additive: [6] For partners with piecewise-constant valuations: divide the cake into m totally-constant regions.
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Meunier and Su [5] show that there always exists an envy-free cake-cutting among any number of agents, when there is a single secretive agent. Frick, Houston-Edwards and Meunier [6] show that there always exists an envy-free allocation of rooms and rent (also called rental harmony) when there is a single secretive agent. The result holds for ...