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.

Mathematical analysis

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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.

United States, Economics, Research and Development in the Social Sciences and Humanities, Analysis, Partition, Partition (Property), Pareto, Vilfredo

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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.

Usage, Mathematical logic, Division, Division (Mathematics)

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