An existence result on partitioning of a measurable space: Pareto optimality and core

Nobusumi Sagara

Kybernetika (2006)

  • Volume: 42, Issue: 4, page 475-481
  • ISSN: 0023-5954

Abstract

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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.

How to cite

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Sagara, Nobusumi. "An existence result on partitioning of a measurable space: Pareto optimality and core." Kybernetika 42.4 (2006): 475-481. <http://eudml.org/doc/33819>.

@article{Sagara2006,
abstract = {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.},
author = {Sagara, Nobusumi},
journal = {Kybernetika},
keywords = {optimal partitioning; nonatomic finite measure; nonadditive set function; Pareto optimality; core; optimal partitioning; nonatomic finite measure; nonadditive set function; Pareto optimality; core},
language = {eng},
number = {4},
pages = {475-481},
publisher = {Institute of Information Theory and Automation AS CR},
title = {An existence result on partitioning of a measurable space: Pareto optimality and core},
url = {http://eudml.org/doc/33819},
volume = {42},
year = {2006},
}

TY - JOUR
AU - Sagara, Nobusumi
TI - An existence result on partitioning of a measurable space: Pareto optimality and core
JO - Kybernetika
PY - 2006
PB - Institute of Information Theory and Automation AS CR
VL - 42
IS - 4
SP - 475
EP - 481
AB - 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.
LA - eng
KW - optimal partitioning; nonatomic finite measure; nonadditive set function; Pareto optimality; core; optimal partitioning; nonatomic finite measure; nonadditive set function; Pareto optimality; core
UR - http://eudml.org/doc/33819
ER -

References

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  4. Legut J., 10.1007/BF01769272, Internat. J. Game Theory 15 (1986), 1–7 (1986) Zbl0651.90099MR0839092DOI10.1007/BF01769272
  5. Sagara N., An Existence Result on Partitioning of a Measurable Space: Equity and Efficiency, Faculty of Economics, Hosei University 2006, mimeo 
  6. Sagara N., Vlach M., Representation of Convex Preferences in a Nonatomic Measure Space: ε -Pareto Optimality and ε -Core in Cake Division, Faculty of Economics, Hosei University 2006, mimeo 
  7. Scarf H. E., 10.2307/1909383, Econometrica 35 (1967), 50–69 (1967) Zbl0183.24003MR0234735DOI10.2307/1909383
  8. Shapley L., 10.1002/nav.3800140404, Naval Res. Logist. 14 (1967), 453–460 (1967) DOI10.1002/nav.3800140404

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