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Policy Learning with Competing Agents

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  • Roshni Sahoo
  • Stefan Wager

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 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.

Suggested Citation

  • Roshni Sahoo & Stefan Wager, 2022. "Policy Learning with Competing Agents," Papers 2204.01884, arXiv.org, revised Apr 2024.
    • Handle: RePEc:arx:papers:2204.01884
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    References listed on IDEAS

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    Cited by:

    1. Luofeng Liao & Christian Kroer, 2023. "Statistical Inference and A/B Testing for First-Price Pacing Equilibria," Papers 2301.02276, arXiv.org, revised Jun 2023.
    2. Daido Kido, 2023. "Incorporating Preferences Into Treatment Assignment Problems," Papers 2311.08963, arXiv.org.
    3. Luofeng Liao & Yuan Gao & Christian Kroer, 2022. "Statistical Inference for Fisher Market Equilibrium," Papers 2209.15422, arXiv.org.

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