Volume of trade and dynamic network formation in two-sided economies

We study the long-run stability of trade networks in a two-sided economy of agents labelled men and women. Each agent desires relationships with the other type, but having multiple partners is costly. This cost-benefit trade-off results in each agent having a single-peaked utility over the number of partners - the volume of trade - , the peak being greater for men than for women. We propose a stochastic matching process in which self-interested agents form and sever links over time. Links can be added or deleted, sometimes simultaneously by a single agent. While the unperturbed process yields each pairwise stable network as an absorbing state, stochastic stability in two perturbed processes provides a signficant refinement, leading respectively to egalitarian and anti-egalitarian pairwise stable networks. This has implications for the concentration on each side of the market of a random information shock. The analysis captures stylized facts, related to market fragmentation, concentration and contagion asymmetry, in several two-sided economies.