Decentralized Pure Exchange Processes on Networks

TL;DR

This paper introduces a class of decentralized exchange processes on networks, analyzing their convergence to stable allocations and how network topology influences trade dynamics and final distributions.

Contribution

It characterizes a class of exchange processes, defines a fair trading process, and links network structure to the final allocation outcomes.

Findings

Processes converge to stable allocation sets

Network topology influences utility gain distribution

Existence of a one-to-one map between networks and limit points

Abstract

We define a class of pure exchange Edgeworth trading processes that under minimal assumptions converge to a stable set in the space of allocations, and characterise the Pareto set of these processes. Choosing a specific process belonging to this class, that we define fair trading, we analyse the trade dynamics between agents located on a weighted network. We determine the conditions under which there always exists a one-to-one map between the set of networks and the set of limit points of the dynamics. This result is used to understand what is the effect of the network topology on the trade dynamics and on the final allocation. We find that the positions in the network affect the distribution of the utility gains, given the initial allocations