Abstract
Consider a situation in which n players divide a cake. Each player has a preference expressed by a measure on the cake. Given a positive number ∈, a cake division is said to be ∈-envy-free, if every player measures his/her piece not smaller than the largest piece by ∈. This paper first forms an ∈-envy-free procedure for such an approximate envy-free division, based on a known idea of Brams and Taylor (1996), then presents another completely new procedure. The first procedure does not work for chore division but the second one works well. The number of necessary cuts of each procedure is bounded. Furthermore, the new procedure is generalized for ∈-multi-fair division. Finally, this paper gives procedures for ∈-envy-free division in unequal ratios.
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Zeng, DZ. (2000). Approximate Envy-Free Procedures. In: Patrone, F., García-Jurado, I., Tijs, S. (eds) Game Practice: Contributions from Applied Game Theory. Theory and Decision Library, vol 23. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-4627-6_17
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DOI: https://doi.org/10.1007/978-1-4615-4627-6_17
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