Many models for systemic risk in finance and elsewhere suppose a given and fixed network topology. In reality, as conditions change, agents tend to modify the topology in response to the changing conditions.  This talk will describe how these responses can significantly change the dynamics of risk propagation in networks and will provide examples in which agents' individually rational decisions on network connections lead to different forms of equilibrium and effects on systemic risk.  The examples will include financial cross-holdings and the supply chains of industrial firms.