A Dynamic Theory of Fidelity Networks with an Application to the Spread of HIV/AIDS

We study the dynamic stability of delity networks, which are networks that form in a mating economy of agents of two types (say men and women), where each agent desires direct links with opposite type agents, while engaging in multiple partnerships is considered an act of in delity. In delity is punished more severely for women than for men. We consider two stochastic processes in which agents form and sever links over time based on the reward from doing so, but may also take non-bene cial actions with small probability. In the rst process, an agent who invests more time in a relationship makes it stronger and harder to break by his/her partner; in the second, such an agent is perceived as weak. Under the rst process, only egalitarian pairwise stable networks (in which all agents have the same number of partners) are visited in the long run, while under the second, only anti-egalitarian pairwise stable networks (in which all women are matched to a small number of men) are. Next, we apply these results to nd that under the rst process, HIV/AIDS is equally prevalent among men and women, while under the second, women bear a greater burden. The key message is that anti-female discrimination does not necessarily lead to higher HIV/AIDS prevalence among women in the short run, but it does in the long run. JEL classi cation numbers: A14, C7, I12, J00