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Policy Learning with Competing Agents

Roshni SahooStefan Wager
摘要
Decision makers often aim to learn a treatment assignment policy under acapacity constraint on the number of agents that they can treat. When agentscan respond strategically to such policies, competition arises, complicatingthe estimation of the effect of the policy. In this paper, we studycapacity-constrained treatment assignment in the presence of such interference.We consider a dynamic model where heterogeneous agents myopically best respondto the previous treatment assignment policy. When the number of agents is largebut finite, we show that the threshold for receiving treatment under a givenpolicy converges to the policy's mean-field equilibrium threshold. Based onthis result, we develop a consistent estimator for the policy effect anddemonstrate in simulations that it can be used for learning optimalcapacity-constrained policies in the presence of strategic behavior.
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