  Decision makers often aim to learn a treatment assignment policy under a
capacity constraint on the number of agents that they can treat. When agents
can respond strategically to such policies, competition arises, complicating
estimation of the optimal policy. In this paper, we study capacity-constrained
treatment assignment in the presence of such interference. We consider a
dynamic model where the decision maker allocates treatments at each time step
and heterogeneous agents myopically best respond to the previous treatment
assignment policy. When the number of agents is large but finite, we show that
the threshold for receiving treatment under a given policy converges to the
policy's mean-field equilibrium threshold. Based on this result, we develop a
consistent estimator for the policy gradient. In a semi-synthetic experiment
with data from the National Education Longitudinal Study of 1988, we
demonstrate that this estimator can be used for learning capacity-constrained
policies in the presence of strategic behavior.
