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Competitive Equilibrium and Trading Networks: A Network Flow Approach

Author

Listed:
  • 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)

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.

Suggested Citation

  • Ozan Candogan & Markos Epitropou & Rakesh V. Vohra, 2021. "Competitive Equilibrium and Trading Networks: A Network Flow Approach," Operations Research, INFORMS, vol. 69(1), pages 114-147, January.
    • Handle: RePEc:inm:oropre:v:69:y:2021:i:1:p:114-147
    DOI: 10.1287/opre.2020.1997
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    References listed on IDEAS

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    Cited by:

    1. P. Jean‐Jacques Herings & Yu Zhou, 2022. "Competitive Equilibria In Matching Models With Financial Constraints," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 63(2), pages 777-802, May.

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