AI summaryⓘ
The authors study how a central planner can influence many decision-makers who have their own goals, by designing payments or incentives to guide their decisions towards what’s best for the group. They introduce a method called RAID that learns about the decision-makers' hidden preferences while adjusting incentives over time. Their approach switches between trying out new incentives and using current estimates to improve outcomes, and it guarantees that their estimates get closer to the truth and the overall system cost gets closer to optimal. They also extend their method to handle cases where observations are noisy in a tricky way, showing consistent performance. Their experiments confirm their theoretical findings.
Incentive designNash equilibriumNonlinear gamesLeast-squares estimationRegret analysisExploration-exploitationParameter estimationError-in-variablesSocial costAdaptive control
Authors
Georgios Vasileiou, Lantian Zhang, Silun Zhang
Abstract
Incentive design studies how a central authority can influence strategic agents through payments, subsidies, or taxes, so that individual objectives align with collective welfare. This paper introduces a No-Regret Adaptive Incentive Design (RAID) framework for nonlinear games with continuous action spaces and private agent costs. In this framework, the authority (planner) designs incentives that regulate the Nash equilibrium toward a socially optimal action profile, while simultaneously learning agents' unknown preferences from repeated strategic responses. We formulate the RAID problem and construct a least-squares estimator whose strong consistency requires only diminishing excitation. Leveraging this weak excitation requirement, we propose a switching incentive policy that alternates between probing (exploration) and estimate-based (exploitation) incentives. The resulting policy achieves an $O(t^{-0.5})$ parameter estimation rate and accumulates $O(t^{0.5}\log t)$ squared social-cost regret, almost surely. We further extend the framework to an endogenous-noise response model, where standard least-squares estimation is biased due to an error-in-variables correlation between the noise and agent responses. We utilize a repeated-sampling estimator and corresponding switching policy that retain the same almost-sure convergence and regret rates. Numerical experiments validate the effectiveness and predicted convergence rates of the method.