  We consider a one-sided assignment market or exchange network with
transferable utility and propose a model for the dynamics of bargaining in such
a market. Our dynamical model is local, involving iterative updates of 'offers'
based on estimated best alternative matches, in the spirit of pairwise Nash
bargaining. We establish that when a balanced outcome (a generalization of the
pairwise Nash bargaining solution to networks) exists, our dynamics converges
rapidly to such an outcome. We extend our results to the cases of (i) general
agent 'capacity constraints', i.e., an agent may be allowed to participate in
multiple matches, and (ii) 'unequal bargaining powers' (where we also find a
surprising change in rate of convergence).
