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Policy Learning with Competing Agents

Roshni Sahoo () and Stefan Wager ()
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Roshni Sahoo: Department of Computer Science, Stanford University, Stanford, California 94305
Stefan Wager: Graduate School of Business, Stanford University, Stanford, California 94305

Operations Research, 2025, vol. 73, issue 5, 2515-2529

Abstract: 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 assignments in the presence of such interference. We consider a dynamic model in which 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 semisynthetic 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.

Keywords: Machine; Learning; and; Data; Science; learning with strategic agents; budget-constrained policies; mean-field model; interference (search for similar items in EconPapers)
Date: 2025
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