We consider an exchange network with stochastic matching between the pairs of players and analyze the dynamics of bargaining in such a market. The cases of homogeneous expectations, heterogeneous expectations and social preferences are studied. The results show that, in all three cases, the dynamics converge to the solution concept of balanced outcome or Nash bargaining solution, which is an equilibrium concept that combines notions of stability and fairness. In the two first scenarios, the numerical simulations reveal that the convergence toward a fixed point is achieved at the value of the outside option. In the third scenario, the fixed point converges to the value of the outside option supplemented by the surplus share.