# Policy Learning with Competing Agents

arXiv: https://arxiv.org/abs/2204.01884 · HTML: https://mlsanity.com/paper/2204.01884/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 49 references that are in the map.
- First posted on arXiv 4 Apr 2022.

## Builds on (most cited first, 10 of 10)

- [Strategic Classification](https://mlsanity.com/paper/1506.06980/) (2015)
- [Strategic Classification from Revealed Preferences](https://mlsanity.com/paper/1710.07887/) (2017)
- [Alternative Microfoundations for Strategic Classification](https://mlsanity.com/paper/2106.12705/) (2021)
- [The Role of Randomness and Noise in Strategic Classification](https://mlsanity.com/paper/2005.08377/) (2020)
- [Experimental Design in Two-Sided Platforms: An Analysis of Bias](https://mlsanity.com/paper/2002.05670/) (2020)
- [Generalized Strategic Classification and the Case of Aligned Incentives](https://mlsanity.com/paper/2202.04357/) (2022)
- [On classification of strategic agents who can both game and improve](https://mlsanity.com/paper/2203.00124/) (2022)
- [Manipulation-Proof Machine Learning](https://mlsanity.com/paper/2004.03865/) (2020)
- [Experimenting in Equilibrium](https://mlsanity.com/paper/1903.02124/) (2019)
- [Treatment Effects in Market Equilibrium](https://mlsanity.com/paper/2109.11647/) (2021)

## Built on by (most cited first, 2 of 2)

- [Practical Performative Policy Learning with Strategic Agents](https://mlsanity.com/paper/2412.01344/) (2024)
- [Operationalizing Counterfactual Metrics: Incentives, Ranking, and Information Asymmetry](https://mlsanity.com/paper/2305.14595/) (2023)

## Abstract (arXiv)

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.