  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
