Competitive Equilibrium and Trading Networks: A Network Flow Approach

• 成果类型: Article
• 署名作者: Candogan, Ozan; Epitropou, Markos; Vohra, Rakesh V.
• 署名单位: University of Chicago; University of Pennsylvania; University of Pennsylvania
• 刊物名称: OPERATIONS RESEARCH
• ISSN/ISSBN: 0030-364X
• DOI: 10.1287/opre.2020.1997
• 发表日期: 2021
• 页码: 114-147
• 关键词: capacity scaling algorithm; Discrete convexity; gross substitutes; dynamic auction; STABILITY; efficient

摘要

Under full substitutability of preferences, it is known that a competitive equilibrium exists in trading networks and is equivalent to (chain) stable outcomes. In this paper, we formulate the problem of finding an efficient set of trades as a generalized submodular flow problem in a suitable network. Existence of a competitive equilibrium and its equivalence with the seemingly weaker notion of stability follow directly from the optimality conditions of the flow problem. Our formulation enables us to perform comparative statics with respect to the number of buyers, sellers, and trades. For instance, we establish that if a new buyer is added to the economy, at an equilibrium the prices of all existing trades increase. In addition, we give a polynomial time algorithm for finding competitive equilibria in trading networks and testing (chain) stability.