  Given an algorithmic predictor that is accurate on some source population
consisting of strategic human decision subjects, will it remain accurate if the
population respond to it? In our setting, an agent or a user corresponds to a
sample $(X,Y)$ drawn from a distribution $\cal{D}$ and will face a model $h$
and its classification result $h(X)$. Agents can modify $X$ to adapt to $h$,
which will incur a distribution shift on $(X,Y)$. Our formulation is motivated
by applications where the deployed machine learning models are subjected to
human agents, and will ultimately face responsive and interactive data
distributions. We formalize the discussions of the transferability of a model
by studying how the performance of the model trained on the available source
distribution (data) would translate to the performance on its induced domain.
We provide both upper bounds for the performance gap due to the induced domain
shift, as well as lower bounds for the trade-offs that a classifier has to
suffer on either the source training distribution or the induced target
distribution. We provide further instantiated analysis for two popular domain
adaptation settings, including covariate shift and target shift.
