Dynamic Network Formation in Two-Sided Economies

We study the dynamic stability of 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 function, the peak being greater for men than for women. We propose two stochastic Markov processes in which self-interested agents form and sever links over time, but may also take actions that do not increase their utility with small probability. In the first process, an agent who invests more time in a relationship signals commitment to his/her partner, whereas in the second, such an agent is perceived as having a weaker position. We prove that only egalitarian pairwise stable networks (in which all agents have the same number of partners) form in the long run under the first process, while under the second, only anti-egalitarian pairwise stable networks (in which all women are matched to a small number of men) arise. This latter outcome is also consistent with the presence of "herd externality" or "informational cascade", leading to a pattern of a one-sided thin market. Applying these results to communication shows that the diffusion of a given piece of information can widely vary across identical economies, and that information concentrates more in women than in men. The model sheds light on patterns of network formation in several two-sided markets, including employer-employee, dating, buyer-seller, and faculty-student relationships.