| Title:
|
An existence result on partitioning of a measurable space: Pareto optimality and core (English) |
| Author:
|
Sagara, Nobusumi |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 |
| Volume:
|
42 |
| Issue:
|
4 |
| Year:
|
2006 |
| Pages:
|
475-481 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
This paper investigates the problem of optimal partitioning of a measurable space among a finite number of individuals. We demonstrate the sufficient conditions for the existence of weakly Pareto optimal partitions and for the equivalence between weak Pareto optimality and Pareto optimality. We demonstrate that every weakly Pareto optimal partition is a solution to the problem of maximizing a weighted sum of individual utilities. We also provide sufficient conditions for the existence of core partitions with non- transferable and transferable utility. (English) |
| Keyword:
|
optimal partitioning |
| Keyword:
|
nonatomic finite measure |
| Keyword:
|
nonadditive set function |
| Keyword:
|
Pareto optimality |
| Keyword:
|
core |
| MSC:
|
28A10 |
| MSC:
|
28B05 |
| MSC:
|
90C29 |
| MSC:
|
91B32 |
| idZBL:
|
Zbl 1249.90241 |
| idMR:
|
MR2275349 |
| . |
| Date available:
|
2009-09-24T20:17:55Z |
| Last updated:
|
2015-03-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/135729 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
[3] Dubins L. E., Spanier E. H.: How to cut a cake fairly.Amer. Math. Monthly 68 (1961), 1–17 Zbl 0108.31601, MR 0129031, 10.2307/2311357 |
| Reference:
|
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| Reference:
|
[5] Sagara N.: An Existence Result on Partitioning of a Measurable Space: Equity and Efficiency.Faculty of Economics, Hosei University 2006, mimeo |
| Reference:
|
[6] Sagara N., Vlach M.: Representation of Convex Preferences in a Nonatomic Measure Space: $\varepsilon $-Pareto Optimality and $\varepsilon $-Core in Cake Division.Faculty of Economics, Hosei University 2006, mimeo |
| Reference:
|
[7] Scarf H. E.: The core of an $N$ person game.Econometrica 35 (1967), 50–69 Zbl 0183.24003, MR 0234735, 10.2307/1909383 |
| Reference:
|
[8] Shapley L.: On balanced sets and cores.Naval Res. Logist. 14 (1967), 453–460 10.1002/nav.3800140404 |
| . |
