Graphical Economies with Resale

TL;DR

This paper introduces a new graph-based economic model allowing long-range trade through resale, overcoming local limitations of previous models and unifying Arrow-Debreu and KKO frameworks.

Contribution

The authors propose a resale-enabled model that generalizes existing networked economies, enabling long-range trade and broader equilibrium existence results.

Findings

The model allows for long-range trade via resale.

Equilibria exist under broad conditions, including sparse endowments.

An auction-based algorithm computes approximate equilibria.

Abstract

Kakade, Kearns, and Ortiz (KKO) introduce a graph-theoretic generalization of the classic Arrow--Debreu (AD) exchange economy. Despite its appeal as a networked version of AD, we argue that the KKO model is too local, in the sense that goods cannot travel more than one hop through the network. We introduce an alternative model in which agents may purchase goods on credit in order to resell them. In contrast to KKO, our model allows for long-range trade, and yields equilibria in more settings than KKO, including sparse endowments. Our model smoothly interpolates between the KKO and AD equilibrium concepts: we recover KKO when the resale capacity is zero, and recover AD when it is sufficiently large. We give general equilibrium existence results, and an auction-based algorithm to compute approximate equilibria when agent utilities satisfy the weak gross-substitutes property.