Competitive Equilibrium and Trading Networks: A Network Flow Approach

Ozan Candogan (), Markos Epitropou () and Rakesh V. Vohra ()
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Ozan Candogan: Booth School of Business, University of Chicago, Chicago, Illlinois 60637
Markos Epitropou: Department of Electrical and Systems Engineering, University of Pennsylvania, Philadelphia, Pennsylvania 19104
Rakesh V. Vohra: Department of Economics and Department of Electrical and Systems Engineering, University of Pennsylvania, Philadelphia, Pennsylvania 19104

Operations Research, 2021, vol. 69, issue 1, 114-147

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 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.

Keywords: trading networks; competitive equilibrium; submodular flow problems; discrete convexity; comparative statics (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (1)

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