Stability and competitive equilibria in multi-unit trading networks with discrete concave utility functions
type: Item
instance of: scholarly article
title: Stability and competitive equilibria in multi-unit trading networks with discrete concave utility functions
zbMATH Open document ID: 1330.91130
author: Yoshiko T. Ikebe
author: Yosuke Sekiguchi
author: Akiyoshi Shioura
author: Akihisa Tamura
published in: Japan Journal of Industrial and Applied Mathematics
publication date: 2015-09-15T00:00:00Z
review text: The authors introduce the multi-unit trading network model and study its stability properties and competitive equilibria. In this model, valuation functions of each agent are twisted \(M^{\natural}\)-concave functions defined on the set of integer vectors. The generalized full substitutes condition is introduced and the authors show that this condition is equivalent to twisted \(M^{\natural}\)-concavity. Furthermore, they show that there exists a competitive equilibrium under the generalized full substitutes condition and that the set of competitive equilibrium price vectors forms a lattice. The relationship between competitive equilibria, stability, and efficiency is considered. It is proved that a competitive equilibrium is stable, and a competitive equilibrium trade vector is efficient. The relation between the three stability concepts stability, strong group stability and chain stability is discussed and it is shown that these concepts are equivalent under the generalized full substitutes condition.
reviewed by: Aleksandr D. Borisenko
Mathematics Subject Classification ID: 91B50
Mathematics Subject Classification ID: 91B16
Mathematics Subject Classification ID: 91B68
zbMATH DE Number: 6482430
zbMATH Keywords: two-sided market model
zbMATH Keywords: multi-unit trading network model
zbMATH Keywords: stability
zbMATH Keywords: competitive equilibria
zbMATH Keywords: efficiency
zbMATH Keywords: lattice
zbMATH Keywords: twisted \(M^{\natural}\)-concave functions
zbMATH Keywords: generalized full substitutes condition
MaRDI profile type: Publication
full work available at URL: s13160-015-0175-7
OpenAlex ID: W790680491
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DOI: 10.1007/S13160-015-0175-7
description: scientific article; zbMATH DE number 6482430