Stability and competitive equilibria in multi-unit trading networks with discrete concave utility functions

Yoshiko T. Ikebe, Yosuke Sekiguchi, Akiyoshi Shioura, Akihisa Tamura

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

Hatfield, Kominers, Nichifor, Ostrovsky, and Westkamp showed the existence of stable outcomes and competitive equilibria in a model of trading networks under the assumption that all agents’ preferences satisfy a condition called the full substitutes condition. In this paper, we extend their model by using discrete concave utility functions called twisted $$\hbox {M}^{\natural }$$<sup>M♮</sup>-concave functions. We show that a valuation function of an agent is twisted $$\hbox {M}^{\natural }$$<sup>M♮</sup>-concave if and only if the agent’s preference satisfies the generalized variant of the full substitutes condition. We also show that under the generalized full substitutes condition, there exist stable outcomes and competitive equilibria in the extended model and the set of competitive equilibrium price vectors forms a lattice. In addition, we discuss the connection among competitive equilibria, stability, and efficiency. Finally, we investigate the relationship among stability, strong group stability, and chain stability and verify these three stability concepts are equivalent as long as valuation functions of all agents are twisted $$\hbox {M}^{\natural }$$<sup>M♮</sup>-concave.

Original languageEnglish
Pages (from-to)373-410
Number of pages38
JournalJapan Journal of Industrial and Applied Mathematics
Volume32
Issue number2
DOIs
Publication statusPublished - 2015 Jul 28

    Fingerprint

Keywords

  • Competitive equilibria
  • Efficiency
  • Generalized full substitutes condition
  • Lattice
  • Stability
  • Twisted <sup>♮</sup>-concave functions

ASJC Scopus subject areas

  • Applied Mathematics
  • Engineering(all)

Cite this