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A Statistical Test of Walrasian Equilibrium by Means of Complex Networks Theory

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  • Leonardo Bargigli
  • Andrea Lionetto
  • Stefano Viaggiu

Abstract

We represent an exchange economy in terms of statistical ensembles for complex networks by introducing the concept of market configuration. This is defined as a sequence of nonnegative discrete random variables $\{w_{ij}\}$ describing the flow of a given commodity from agent $i$ to agent $j$. This sequence can be arranged in a nonnegative matrix $W$ which we can regard as the representation of a weighted and directed network or digraph $G$. Our main result consists in showing that general equilibrium theory imposes highly restrictive conditions upon market configurations, which are in most cases not fulfilled by real markets. An explicit example with reference to the e-MID interbank credit market is provided.

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  • Leonardo Bargigli & Andrea Lionetto & Stefano Viaggiu, 2013. "A Statistical Test of Walrasian Equilibrium by Means of Complex Networks Theory," Papers 1307.0817, arXiv.org, revised Sep 2016.
    • Handle: RePEc:arx:papers:1307.0817
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    1. Garibaldi,Ubaldo & Scalas,Enrico, 2010. "Finitary Probabilistic Methods in Econophysics," Cambridge Books, Cambridge University Press, number 9780521515597.
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    1. Di Vece, Marzio & Garlaschelli, Diego & Squartini, Tiziano, 2023. "Reconciling econometrics with continuous maximum-entropy network models," Chaos, Solitons & Fractals, Elsevier, vol. 166(C).
    2. George Judge, 2015. "Entropy Maximization as a Basis for Information Recovery in Dynamic Economic Behavioral Systems," Econometrics, MDPI, vol. 3(1), pages 1-10, February.

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