Vilfredo Pareto cuts the cake
Article Abstract:
The classic 'cake division' problem can be solved using an extension of the concept of allocation. In this solution, the n-person 'cake division' problem is reduced to a normal form that lies in the unit simplex of Euclidean n-space. Assuming canonical utility functions, it is possible, using this reduction approach, to provide geometric and analytic characterizations of all Pareto optimum solutions.
Publication Name: The Journal of Mathematical Economics
Subject: Mathematics
ISSN: 0304-4068
Year: 1995
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Partition ratios, Pareto optimal cake division, and related notions
Article Abstract:
The equitable division of pieces of cake among a group of n players is studied. Partition ratios are represented by certain real numbers, and various products of these numbers reveal information about trades and transfers.
Publication Name: The Journal of Mathematical Economics
Subject: Mathematics
ISSN: 0304-4068
Year: 1999
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On the structure of Pareto optimal cake partitions
Article Abstract:
Pareto optimal partitions of a cake amongst n players were studied.
Publication Name: The Journal of Mathematical Economics
Subject: Mathematics
ISSN: 0304-4068
Year: 2000
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