Optimal Policy Learning with Strategic Agents under Capacity Constraints

Grunnleggende konsepter

The decision maker aims to learn a treatment assignment policy that maximizes the equilibrium policy value in the presence of strategic behavior and capacity constraints.

Sammendrag

The content describes a dynamic model for capacity-constrained treatment assignment where human agents can respond strategically to the decision maker's policy. The key insights are:

Agents are heterogeneous in their raw covariates and ability to modify their covariates. They myopically best respond to the previous treatment assignment policy.

In the mean-field regime with an infinite population of agents, the threshold for receiving treatment under a given policy converges to the policy's mean-field equilibrium threshold. This result enables the development of a consistent estimator for the policy gradient.

In the finite regime with a large but finite number of agents, the system converges to the mean-field equilibrium in a stochastic version of fixed-point iteration.

The policy gradient can be estimated via a unit-level randomized experiment that applies symmetric, mean-zero perturbations to the policy parameters. This allows learning optimal policies in the presence of strategic behavior and capacity constraints.

The authors demonstrate the effectiveness of the policy gradient estimator in a semi-synthetic experiment using data from the National Education Longitudinal Study of 1988.

Statistikk

The content does not provide any specific numerical data or statistics. It focuses on the theoretical model and estimation framework.

Sitater

The content does not contain any striking quotes.

Viktige innsikter hentet fra

Policy Learning with Competing Agents

by Roshni Sahoo... klokken arxiv.org 04-18-2024

https://arxiv.org/pdf/2204.01884.pdf

Dypere Spørsmål

How would the results change if the agents had forward-looking, rather than myopic, behavior

If the agents had forward-looking behavior instead of myopic behavior, the results would likely change significantly. With forward-looking behavior, agents would consider the potential future consequences of their actions when making decisions. This could lead to more strategic behavior, as agents may anticipate how their actions could influence future policies and outcomes.
In the context of the policy learning framework described in the text, forward-looking agents may take into account not only the current policy and threshold but also how their actions could impact future policies and thresholds. This could introduce additional complexity into the model, as agents would need to consider a broader range of potential outcomes and strategies.

What are the implications of relaxing the assumption that agents can only respond to the previous policy threshold, and instead consider the full history of thresholds

Relaxing the assumption that agents can only respond to the previous policy threshold and considering the full history of thresholds would introduce a new level of complexity to the model. Agents would need to take into account how past thresholds have influenced their behavior and outcomes, leading to potentially more nuanced and strategic responses.
By considering the full history of thresholds, agents could adapt their behavior based on patterns and trends in the decision maker's policies. This could result in more sophisticated strategies and potentially different equilibrium outcomes. Additionally, analyzing the impact of historical thresholds on agent behavior could provide insights into the long-term effects of policy decisions.

How could the proposed framework be extended to settings with multiple, interacting decision makers who each control a subset of the treatment assignments

Extending the proposed framework to settings with multiple interacting decision makers controlling different subsets of treatment assignments would require a more sophisticated modeling approach. In this multi-agent setting, decision makers would need to consider not only their own policies and thresholds but also the strategies and behaviors of other decision makers.
One approach could be to incorporate game theory concepts, such as Nash equilibria, to analyze how multiple decision makers interact and make decisions in a strategic environment. Each decision maker's actions would influence the outcomes for all decision makers, leading to a complex interplay of strategies and policies.
Analyzing the interactions between multiple decision makers could provide valuable insights into how competition and cooperation among decision makers impact the overall system. By studying the equilibrium outcomes in these multi-agent settings, researchers could better understand the dynamics of policy learning with competing agents.