Exchange Networks with Stochastic Matching

This paper tries to prove that the outcomes stemming from interactions on assignment markets bring about coordination in case of a stochastic matching subject to various forms of expectations. 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 convergent expectations, divergent expectations and of social preferences are studied. The extension of earlier works lies in the consideration of a stochastic matching on a graph dependent on the weights of edges. The results show that, in all three cases, the dynamics converges rapidly to the generalized Nash bargaining solution, which is an equilibrium that combines notions of stability and fairness. In the first two scenarios, the numerical simulations reveal that the convergence toward a fixed point is speedily achieved at the value of the outside option. In the third scenario, the fixed point promptly converges to the value of the outside option supplemented by the surplus share.