Single-Stage Causal Incentive Design via Optimal Interventions.

Area of Science:

• Economics
• Computer Science
• Causal Inference
• Mechanism Design

Background:

• Principal-agent problems (PAPs) involve optimizing incentives under bilateral private information.
• Existing frameworks often struggle with the complexities of private information and causal relationships.
• Causal graphical models (CGMs) offer a formal way to represent these relationships.

Purpose of the Study:

• To introduce Causal Incentive Design (CID), a novel framework integrating causal inference with PAPs.
• To formalize PAPs using CGMs and model incentives as interventions.
• To develop methods for estimating and selecting optimal incentive policies from observational data.

Main Methods:

• Formalized PAPs using additive-noise CGMs.
• Modeled incentives as interventions on a function space variable (Γ).
• Developed a Functional Causal Bayesian Optimization (FCBO) algorithm for policy selection, utilizing functional Gaussian processes and UCB acquisition functions.

Main Results:

• Defined a causal estimand V(Γ) representing the principal's expected utility under intervention.
• Developed efficient estimation techniques using Gauss-Hermite quadrature and kernel reweighting.
• Established high-probability cumulative-regret bounds for the FCBO algorithm.

Conclusions:

• CID provides a causal decision-making pipeline for selecting high-performing incentives in single-shot games.
• The framework enables offline policy selection, suitable for scenarios where adaptive deployment is impractical.
• This work pioneers the application of CGMs and causal reasoning to incentive design and PAPs.