  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.
