Competitive Equilibrium and Trading Networks: A Network Flow Approach

40 Pages Posted: 28 Feb 2016 Last revised: 23 Jun 2017

See all articles by Ozan Candogan

Ozan Candogan

University of Chicago - Booth School of Business

Markos Epitropou

University of Pennsylvania, Department of Electrical and Systems Engineering

Rakesh Vohra

University of Pennsylvania - Department of Economics

Date Written: February 24, 2016

Abstract

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 outcome as a generalized submodular flow problem on 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. In particular, 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.

Keywords: Trading Networks, Competitive Equilibrium, Stability, Submodular Flow Problems, Discrete Convexity

Suggested Citation

Candogan, Ozan and Epitropou, Markos and Vohra, Rakesh, Competitive Equilibrium and Trading Networks: A Network Flow Approach (February 24, 2016). Available at SSRN: https://ssrn.com/abstract=2738610 or http://dx.doi.org/10.2139/ssrn.2738610

Ozan Candogan (Contact Author)

University of Chicago - Booth School of Business ( email )

5807 S. Woodlawn Avenue
Chicago, IL 60637
United States

HOME PAGE: http://faculty.chicagobooth.edu/ozan.candogan/

Markos Epitropou

University of Pennsylvania, Department of Electrical and Systems Engineering ( email )

Room 306, Moore Bldg, 200 South 33rd Street
Philadelphia, PA 19104
United States

Rakesh Vohra

University of Pennsylvania - Department of Economics ( email )

Ronald O. Perelman Center for Political Science
133 South 36th Street
Philadelphia, PA 19104-6297
United States

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