assignment and its neighbors’ assignments. This *neighborhood treatment response* (NTR) assumption has that, for any two global assignments $z_0, z_1 \in \mathbb{Z}^N$ and any stochastic component $U \in \mathbb{U}^N$, $$z_{1,i} = z_{0,i} \text{ and } z_{1,\delta(i)} = z_{0,\delta(i)} \Rightarrow f_i(z_{1}, U) = f_i(z_{0}, U),$$ where $\delta(i)$ are the neighbors of vertex $i$. @aronow_estimating_2011 and @ugander_graph_2013 consider further restrictions, such as that a vertex’s response only depends on the number of treated neighbors.

### Implausibility of tractable treatment response assumptions {#sec:implausibility}

How should we select an exposure model? @aronow_estimating_2011 [Section 3] suggest that we “must use substantive judgment to fix a model somewhere between the traditional randomized experiment and arbitrary exposure models”. However, it is unclear how substantive judgement can directly inform the selection of an exposure model for experiments in networks — at least when the vast majority of vertices are in a single connected component. Interference is often expected because of peer effects: in discrete time, then the behavior of a vertex at $t$ is affected by the behavior of its neighbors at $t - 1$; if this is the case, then the behavior of a vertex at $t$ would also be affected by the behavior of its neighbors’ 