neighbors at $t - 2$, and so forth. Such a process will result in violations of the NTR assumption, and many other assumptions that would make analysis tractable. @manski_identification_2013 shows how some, quite specific, models of simultaneous endogenous choice can produce some restrictions on $f_i(\cdot)$.[^9]

Since many appealing CTR assumptions are violated by the very theories that motivate the expectation of interference, it is useful to evaluate the performance of available design and analysis methods — including estimators that would be motivated by these assumptions — under outcome generating processes consistent with these theories. In particular, we now consider outcome generating processes in which vertices respond to their own treatment and the prior behavior of their neighbors. That is, peer behavior fully mediates the effects of the assignments of an ego’s peers on the ego. This is notably different from @aronow_estimating_2011 and @ugander_graph_2013, where ego response is specified in terms of peer assignments without being mediated through peer behavior.[^10]

We consider a dynamical model with discrete time steps in which a vertex’s behavior at time $t$, denoted by the vector $Y_{i,t}$, is a function $h$ of ego treatment assignment and it and its neighbors’ prior behaviors $Y_{\delta{(i)},t-1}$, such that $$h_{i,t} 