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

TL;DR

This paper models exchange economies as complex networks and introduces a statistical test to evaluate if market configurations satisfy Walrasian equilibrium conditions, revealing many real markets do not meet these theoretical criteria.

Contribution

It develops a novel network-based framework for testing Walrasian equilibrium in markets using statistical ensembles and applies it to real interbank market data.

Findings

Market configurations often do not satisfy equilibrium conditions.

The network approach reveals restrictive conditions of equilibrium.

Application to e-MID market illustrates the method's practical relevance.

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.