Graphical Economies with Resale

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.