Delegation without Priors

2026-09-28

AI Summary

This study addresses the challenge of minimizing worst-case regret when delegating decisions to a biased agent in the absence of a prior distribution. To this end, it proposes a discretionary interval rule that integrates default actions, fixed gaps, and stochastic boundaries, effectively decoupling decision deviations from degrees of freedom. By introducing randomized boundary strategies to hedge against potential worst-case scenarios, the approach achieves an optimal balance between constraining over-adjustment and preserving flexibility. Furthermore, this work establishes the optimality of the proposed mechanism structure among all stochastically incentive-compatible mechanisms, thereby providing a novel theoretical framework for robust delegated decision-making.

Abstract

A principal relies on information held by a biased agent in decision-making. Without a prior over the circumstances that may arise, she designs a delegation rule to minimize the worst-case regret. Optimal delegation combines a default action, a fixed gap above it, and a higher discretionary interval with random boundaries. This structure separates two margins: whether the decision departs from the default and how much discretion the agent receives conditional on doing so. The default and gap limit excessive adjustment when little adaptation is warranted, while the higher interval preserves flexibility when larger adjustments are needed. Randomizing the discretionary interval's floor and ceiling hedges the principal's exposure across potential worst-case states. This rule is optimal among all stochastic incentive-compatible mechanisms.

Problem

• delegation
• prior-free
• regret minimization
• biased agent
• mechanism design

Innovation

• Delegation without priors
• Minimax regret
• Stochastic mechanisms
• Incentive compatibility
• Randomized discretionary interval