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- Title
Competitive Equilibrium and Trading Networks: A Network Flow Approach.
- Authors
Candogan, Ozan; Epitropou, Markos; Vohra, Rakesh V.
- Abstract
This paper considers a network of agents who trade indivisible goods or services via bilateral contracts. Under a substitutability assumption on preferences, it is known that a competitive equilibrium exists. In "Competitive Equilibrium and Trading Networks: A Network Flow Approach," Candogan, Epitropou, and Vohra show how to determine equilibrium outcomes as a generalized submodular flow problem. Existence of a competitive equilibrium and its equivalence to seemingly weaker notions of stability follow directly from the optimality conditions of the flow problem. The formulation enables the authors to perform comparative statics with respect to the number of buyers, sellers, and trades. In particular, they are able to shed light on the impact of new trading opportunities on the equilibrium trades, prices, and surpluses. In addition, they present algorithms for finding competitive equilibria in trading networks and testing stability. 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. Funding: O. Candogan gratefully acknowledges financial support from the University of Chicago Booth School of Business. M. Epitropou gratefully acknowledges financial support from the Department of Electrical and Systems Engineering, University of Pennsylvania. The research of R.V. Vohra was supported in part by the National Science Foundation [Grant AST-1343381].
- Subjects
UNIVERSITY of Pennsylvania; UNIVERSITY of Chicago. Booth School of Business; POLYNOMIAL time algorithms; EQUILIBRIUM; PURCHASING agents; STATICS; SYSTEMS engineering
- Publication
Operations Research, 2021, Vol 69, Issue 1, p114
- ISSN
0030-364X
- Publication type
Article
- DOI
10.1287/opre.2020.1997