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Competitive Equilibrium and Trading Networks: A Network Flow Approach

Author

Listed:
  • Candogan, Ozan

    (University of Chicago)

  • Epitropou, Markos

    (University of Pennsylvania)

  • Vohra, Rakesh V.

    (University of Pennsylvania)

Abstract

Under full substitutability of preferences, it has been shown that a competitive equilibrium exists in trading networks,and is equivalent (after a restriction to equilibrium trades) 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. Equivalence with seemingly weaker notions of stability follows directly from the optimality conditions, in particular the absence of improvement cycles in the flow problem. Our formulation yields strongly polynomial algorithms for finding competitive equilibria in trading networks, and testing (chain) stability.

Suggested Citation

  • Candogan, Ozan & Epitropou, Markos & Vohra, Rakesh V., 2016. "Competitive Equilibrium and Trading Networks: A Network Flow Approach," Economics Series 323, Institute for Advanced Studies.
    • Handle: RePEc:ihs:ihsesp:323
    as

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    File URL: https://irihs.ihs.ac.at/id/eprint/4027
    File Function: First version, 2016
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    References listed on IDEAS

    as
    1. John William Hatfield & Scott Duke Kominers & Alexandru Nichifor & Michael Ostrovsky & Alexander Westkamp, 2013. "Stability and Competitive Equilibrium in Trading Networks," Journal of Political Economy, University of Chicago Press, vol. 121(5), pages 966-1005.
    2. Gul, Faruk & Stacchetti, Ennio, 1999. "Walrasian Equilibrium with Gross Substitutes," Journal of Economic Theory, Elsevier, vol. 87(1), pages 95-124, July.
    3. Ning Sun & Zaifu Yang, 2006. "Equilibria and Indivisibilities: Gross Substitutes and Complements," Econometrica, Econometric Society, vol. 74(5), pages 1385-1402, September.
    4. Kominers, Scott Duke & Hatfield, John William & Nichifor, Alexandru & Ostrovsky, Michael & Westkamp, Alexander, 2021. "Chain stability in trading networks," Theoretical Economics, Econometric Society, vol. 16(1), January.
    5. Michael Ostrovsky, 2008. "Stability in Supply Chain Networks," American Economic Review, American Economic Association, vol. 98(3), pages 897-923, June.
    6. Danilov, Vladimir & Koshevoy, Gleb & Murota, Kazuo, 2001. "Discrete convexity and equilibria in economies with indivisible goods and money," Mathematical Social Sciences, Elsevier, vol. 41(3), pages 251-273, May.
    7. Kelso, Alexander S, Jr & Crawford, Vincent P, 1982. "Job Matching, Coalition Formation, and Gross Substitutes," Econometrica, Econometric Society, vol. 50(6), pages 1483-1504, November.
    8. Hatfield, John William & Kominers, Scott Duke & Nichifor, Alexandru & Ostrovsky, Michael & Westkamp, Alexander, 2019. "Full substitutability," Theoretical Economics, Econometric Society, vol. 14(4), November.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Wang, Wenya & Li, Zhenfu & Cheng, Xin, 2019. "Evolution of the global coal trade network: A complex network analysis," Resources Policy, Elsevier, vol. 62(C), pages 496-506.
    2. Can Kizilkale & Rakesh Vohra, 2020. "Constrained Trading Networks," Papers 2008.09757, arXiv.org.
    3. Wang, Wenya & Li, Zhenfu, 2019. "The evolution of China’s interregional coal trade network, 1997–2016," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 536(C).
    4. Yokote, Koji, 2021. "Consistency of the doctor-optimal equilibrium price vector in job-matching markets," Journal of Economic Theory, Elsevier, vol. 197(C).
    5. Kominers, Scott Duke & Hatfield, John William & Nichifor, Alexandru & Ostrovsky, Michael & Westkamp, Alexander, 2021. "Chain stability in trading networks," Theoretical Economics, Econometric Society, vol. 16(1), January.
    6. Marzena Rostek & Nathan Yoder, 2020. "Matching With Complementary Contracts," Econometrica, Econometric Society, vol. 88(5), pages 1793-1827, September.
    7. Hafalir, Isa E. & Kojima, Fuhito & Yenmez, M. Bumin, 2022. "Interdistrict school choice: A theory of student assignment," Journal of Economic Theory, Elsevier, vol. 201(C).
    8. Liu, Nairong & An, Haizhong & Hao, Xiaoqing & Feng, Sida, 2017. "The stability of the international heat pump trade pattern based on complex networks analysis," Applied Energy, Elsevier, vol. 196(C), pages 100-117.
    9. Tamás Fleiner & Zsuzsanna Jankó & Ildikó Schlotter & Alexander Teytelboym, 2023. "Complexity of stability in trading networks," International Journal of Game Theory, Springer;Game Theory Society, vol. 52(3), pages 629-648, September.
    10. Kazuo Murota, 2016. "Discrete convex analysis: A tool for economics and game theory," The Journal of Mechanism and Institution Design, Society for the Promotion of Mechanism and Institution Design, University of York, vol. 1(1), pages 151-273, December.
    11. Hatfield, John William & Kominers, Scott Duke & Nichifor, Alexandru & Ostrovsky, Michael & Westkamp, Alexander, 2019. "Full substitutability," Theoretical Economics, Econometric Society, vol. 14(4), November.
    12. Koji Yokote, 2020. "On optimal taxes and subsidies: A discrete saddle-point theorem with application to job matching under constraints," The Journal of Mechanism and Institution Design, Society for the Promotion of Mechanism and Institution Design, University of York, vol. 5(1), pages 37-77, December.

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    More about this item

    Keywords

    Trading networks; competitive equilibrium; stability; submodular flow problems; discrete convexity;
    All these keywords.

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