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

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• 作者：Yoshiko T. Ikebe ; Yosuke Sekiguchi…
• 关键词：Stability ; Competitive equilibria ; Efficiency ; Lattice ; Twisted $$\hbox {M}^{\natural }$$ M ?concave functions ; Generalized full substitutes condition ; 91B50 ; 91B68
• 刊名：Japan Journal of Industrial and Applied Mathematics
• 出版年：2015
• 出版时间：July 2015
• 年：2015
• 卷：32
• 期：2
• 页码：373-410
• 全文大小：681 KB
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• 作者单位：Yoshiko T. Ikebe (1)
  Yosuke Sekiguchi (2)
  Akiyoshi Shioura (3)
  Akihisa Tamura (2)
  
  1. Department of Management Science, Tokyo University of Science, Tokyo, 162-8601, Japan
  2. Department of Mathematics, Keio University, Yokohama, 223-8522, Japan
  3. Graduate School of Information Sciences, Tohoku University, Sendai, 980-8579, Japan
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Applications of Mathematics
  Computational Mathematics and Numerical Analysis
  
• 出版者：Springer Japan
• ISSN：1868-937X

文摘

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 \(\hbox {M}^{\natural }\)-concave functions. We show that a valuation function of an agent is twisted \(\hbox {M}^{\natural }\)-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 \(\hbox {M}^{\natural }\)-concave.