Risk dynamics in trade networks

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 con-cept of risk measures from finance, and introduce a class of trade dynamics which allow agents to trade contracts contin-gent upon the future outcome. We then show that these trade dynamics exactly correspond to a variant of randomized coor-dinate 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 dy-namics, showing that the market or network converges to a unique steady state. Applying these results to prediction mar-kets, 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 interac-tions on a scale-free network.