The convergence of the core of a fuzzy exchange economy

Xia Zhang; Hao Sun; Moses Olabhele Esangbedo; Xuanzhu Jin

Kybernetika (2021)

  • Volume: 57, Issue: 4, page 671-687
  • ISSN: 0023-5954

Abstract

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This paper focuses on a new model called fuzzy exchange economy (FXE), which integrates fuzzy consumption, fuzzy initial endowment and the agent’s fuzzy preference (vague attitude) in the fuzzy consumption set. Also, the existence of the fuzzy competitive equilibrium for the FXE is verified through a related pure exchange economy. We define a core-like concept (called weak fuzzy core) of the FXE and prove that any fuzzy competitive allocation belongs to the weak fuzzy core. The fuzzy replica economy, which is the -fold repetition of the FXE, is considered. Finally, we show that the weak fuzzy core of the -fold fuzzy replica economy, i. e., the set of all fuzzy allocations which cannot be blocked by any coalition of agents, converges to the set of fuzzy competitive allocations of the FXE as becomes large.

How to cite

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Zhang, Xia, et al. "The convergence of the core of a fuzzy exchange economy." Kybernetika 57.4 (2021): 671-687. <http://eudml.org/doc/297851>.

@article{Zhang2021,
abstract = {This paper focuses on a new model called fuzzy exchange economy (FXE), which integrates fuzzy consumption, fuzzy initial endowment and the agent’s fuzzy preference (vague attitude) in the fuzzy consumption set. Also, the existence of the fuzzy competitive equilibrium for the FXE is verified through a related pure exchange economy. We define a core-like concept (called weak fuzzy core) of the FXE and prove that any fuzzy competitive allocation belongs to the weak fuzzy core. The fuzzy replica economy, which is the $r$-fold repetition of the FXE, is considered. Finally, we show that the weak fuzzy core of the $r$-fold fuzzy replica economy, i. e., the set of all fuzzy allocations which cannot be blocked by any coalition of agents, converges to the set of fuzzy competitive allocations of the FXE as $r$ becomes large.},
author = {Zhang, Xia, Sun, Hao, Esangbedo, Moses Olabhele, Jin, Xuanzhu},
journal = {Kybernetika},
keywords = {pure exchange economy; fuzzy competitive equilibrium; fuzzy replica economy; weak fuzzy core; fuzzy Edgeworth equilibrium},
language = {eng},
number = {4},
pages = {671-687},
publisher = {Institute of Information Theory and Automation AS CR},
title = {The convergence of the core of a fuzzy exchange economy},
url = {http://eudml.org/doc/297851},
volume = {57},
year = {2021},
}

TY - JOUR
AU - Zhang, Xia
AU - Sun, Hao
AU - Esangbedo, Moses Olabhele
AU - Jin, Xuanzhu
TI - The convergence of the core of a fuzzy exchange economy
JO - Kybernetika
PY - 2021
PB - Institute of Information Theory and Automation AS CR
VL - 57
IS - 4
SP - 671
EP - 687
AB - This paper focuses on a new model called fuzzy exchange economy (FXE), which integrates fuzzy consumption, fuzzy initial endowment and the agent’s fuzzy preference (vague attitude) in the fuzzy consumption set. Also, the existence of the fuzzy competitive equilibrium for the FXE is verified through a related pure exchange economy. We define a core-like concept (called weak fuzzy core) of the FXE and prove that any fuzzy competitive allocation belongs to the weak fuzzy core. The fuzzy replica economy, which is the $r$-fold repetition of the FXE, is considered. Finally, we show that the weak fuzzy core of the $r$-fold fuzzy replica economy, i. e., the set of all fuzzy allocations which cannot be blocked by any coalition of agents, converges to the set of fuzzy competitive allocations of the FXE as $r$ becomes large.
LA - eng
KW - pure exchange economy; fuzzy competitive equilibrium; fuzzy replica economy; weak fuzzy core; fuzzy Edgeworth equilibrium
UR - http://eudml.org/doc/297851
ER -

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