Diffusion and protection across a random graph

<jats:title>Abstract</jats:title><jats:p>We study the interplay between the diffusion of a harmful state in a network of contacts and the possibility of individual agents to undertake costly investment to protect themselves against infection. We characterize how equilibrium diffusion outcomes, such as the immunization rate, total prevalence and welfare, respond to changes in the architecture of the network, and show that these responses depend on the details of the diffusion process.</jats:p>