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Competitive Equilibrium and Trading Networks: A Network Flow Approach

Published: 21 July 2016 Publication History

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.

References

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Faruk Gul and Ennio Stacchetti. 1999. Walrasian Equilibrium with Gross Substitutes. Journal of Economic Theory 87, 1 (1999), 95--124.
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John W Hatfield, Scott D Kominers, Alexandru Nichifor, Michael Ostrovsky, and Alexander Westkamp. 2013. Stability and Competitive Equilibrium in Trading Networks. Journal of Political Economy 121, 5 (2013), 966--1005.
[3]
John W Hatfield, Scott D Kominers, Alexandru Nichifor, Michael Ostrovsky, and Alexander Westkamp. 2015a. Chain Stability in Trading Networks. Working Paper (2015).
[4]
John W Hatfield, Scott D Kominers, Alexandru Nichifor, Michael Ostrovsky, and Alexander Westkamp. 2015b. Full Substitutability. In Proc. of the 16th ACM Conference on Electronic Commerce (EC '15). ACM, 39--40.
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Alexander S Kelso and Vincent Crawford. 1982. Job Matching, Coalition Formation, and Gross Substitutes. Econometrica 50, 6 (1982), 1483--1504.
[6]
Michael Ostrovsky. 2008. Stability in Supply Chain Networks. American Economic Review 98, 3 (2008), 897--923.
[7]
Lloyd S Shapley and Martin Shubik. 1971. The assignment game I: The core. International Journal of game theory 1, 1 (1971), 111--130.
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Ning Sun and Zaifu Yang. 2006. Equilibria and Indivisibilities: Gross Substitutes and Complements. Econometrica 74, 5 (2006), 1385--1402.

Cited By

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  • (2024)Maximum Flow is Fair: A Network Flow Approach to Committee VotingProceedings of the 25th ACM Conference on Economics and Computation10.1145/3670865.3673603(964-983)Online publication date: 8-Jul-2024
  • (2023)Equivalence between substitutability and M$$^\natural $$-concavity for set functions under discrete transfersJapan Journal of Industrial and Applied Mathematics10.1007/s13160-023-00564-z40:2(965-983)Online publication date: 30-Jan-2023
  • (2023)Complexity of stability in trading networksInternational Journal of Game Theory10.1007/s00182-022-00833-052:3(629-648)Online publication date: 8-Apr-2023
  • Show More Cited By

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cover image ACM Conferences
EC '16: Proceedings of the 2016 ACM Conference on Economics and Computation
July 2016
874 pages
ISBN:9781450339360
DOI:10.1145/2940716
Permission to make digital or hard copies of part or all of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for third-party components of this work must be honored. For all other uses, contact the Owner/Author.

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 21 July 2016

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Author Tags

  1. competitive equilibrium
  2. discrete convexity
  3. stability
  4. submodular flow problems
  5. trading networks

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EC '16
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EC '16: ACM Conference on Economics and Computation
July 24 - 28, 2016
Maastricht, The Netherlands

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EC '16 Paper Acceptance Rate 80 of 242 submissions, 33%;
Overall Acceptance Rate 664 of 2,389 submissions, 28%

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Cited By

View all
  • (2024)Maximum Flow is Fair: A Network Flow Approach to Committee VotingProceedings of the 25th ACM Conference on Economics and Computation10.1145/3670865.3673603(964-983)Online publication date: 8-Jul-2024
  • (2023)Equivalence between substitutability and M$$^\natural $$-concavity for set functions under discrete transfersJapan Journal of Industrial and Applied Mathematics10.1007/s13160-023-00564-z40:2(965-983)Online publication date: 30-Jan-2023
  • (2023)Complexity of stability in trading networksInternational Journal of Game Theory10.1007/s00182-022-00833-052:3(629-648)Online publication date: 8-Apr-2023
  • (2021)Consistency of the doctor-optimal equilibrium price vector in job-matching marketsJournal of Economic Theory10.1016/j.jet.2021.105346(105346)Online publication date: Aug-2021
  • (2020)Matching With Complementary ContractsEconometrica10.3982/ECTA1668688:5(1793-1827)Online publication date: 2020
  • (2019)Full substitutabilityTheoretical Economics10.3982/TE324014:4(1535-1590)Online publication date: 2019
  • (2018)Evolution of the global coal trade network: A complex network analysisResources Policy10.1016/j.resourpol.2018.10.005Online publication date: Nov-2018
  • (undefined)Matching with Complementary ContractsSSRN Electronic Journal10.2139/ssrn.3234080

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