Risk Dynamics in Trade Networks

TL;DR

This paper introduces a novel framework for modeling trade interactions among agents aiming to minimize risk, linking trade dynamics to coordinate descent methods, and demonstrating convergence to a unique steady state in various network settings.

Contribution

It develops a new risk-based trade dynamic framework, connects it to coordinate descent algorithms, and proves convergence in complex network scenarios including prediction markets.

Findings

Trade dynamics correspond to a variant of randomized coordinate descent.

The market converges to a unique steady state under general conditions.

The framework applies to scale-free networks and prediction markets.

Abstract

We introduce a new framework to model interactions among agents which seek to trade to minimize their risk with respect to some future outcome. We quantify this risk using the concept of risk measures from finance, and introduce a class of trade dynamics which allow agents to trade contracts contingent upon the future outcome. We then show that these trade dynamics exactly correspond to a variant of randomized coordinate descent. By extending the analysis of these coordinate descent methods to account for our more organic setting, we are able to show convergence rates for very general trade dynamics, showing that the market or network converges to a unique steady state. Applying these results to prediction markets, we expand on recent results by adding convergence rates and general aggregation properties. Finally, we illustrate the generality of our framework by applying it to agent interactions on a scale-free network.