Dynamic Delegation with Reputation Feedback

2025-08-27

AI Summary

This paper examines expert advice provision to a sequence of implementers in dynamic delegation, where each implementer’s effort level depends on their current reputation—thereby endogenously affecting the informativeness of outcomes and the path of Bayesian belief updating. We construct a belief-based recursive equilibrium model integrating dynamic game theory, Bayesian learning, and sub/supermartingale analysis. Our analysis uncovers a novel phenomenon—“reputational conservatism”: under diagnosticity conditions, the expert’s advice threshold strictly increases with the implementer’s reputation, and we precisely characterize the boundary between learning and non-informative absorption. We further design reputation-contingent incentive contracts that achieve a target experimentation rate. The theoretical predictions are empirically testable and directly applicable to real-world settings such as surgical decision-making (e.g., surgery vs. conservative treatment), offering a new analytical framework for reputation-sensitive professional delegation.

Technology Category

• Game Theory and Economic Paradigms: Imperfect Information
• Multiagent Systems: Mechanism Design
• Reasoning under Uncertainty: Sequential Decision Making

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web
• User Modeling, Personalization and Recommendation: Psychology-informed user models and recommender systems

Abstract

We study dynamic delegation with reputation feedback: a long-lived expert advises a sequence of implementers whose effort responds to current reputation, altering outcome informativeness and belief updates. We solve for a recursive, belief-based equilibrium and show that advice is a reputation-dependent cutoff in the expert's signal. A diagnosticity condition - failures at least as informative as successes - implies reputational conservatism: the cutoff (weakly) rises with reputation. Comparative statics are transparent: greater private precision or a higher good-state prior lowers the cutoff, whereas patience (value curvature) raises it. Reputation is a submartingale under competent types and a supermartingale under less competent types; we separate boundary hitting into learning (news generated infinitely often) versus no-news absorption. A success-contingent bonus implements any target experimentation rate with a plug-in calibration in a Gaussian benchmark. The framework yields testable predictions and a measurement map for surgery (operate vs. conservative care).

Problem

• Dynamic delegation with reputation feedback in sequential decision-making
• Reputation-dependent cutoff strategies for expert advice
• Diagnosticity condition affecting reputational conservatism and belief updates

Innovation

• Reputation-dependent cutoff in expert signal
• Recursive belief-based equilibrium solution
• Success-contingent bonus implements experimentation rate