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Information Design in the Principal-Agent Problem

Yakov Babichenko, Inbal Talgam-Cohen, Haifeng Xu, Konstantin Zabarnyi

TL;DR

The paper develops a framework where a regulator designs the information structure about a principal's agent actions in a principal–agent setting with unobserved effort. It provides a complete threshold-based characterization of implementable utility profiles and actions for both risk-neutral and risk-averse agents under limited liability, using a universal two-signal signaling scheme. It further analyzes constrained information structures with bounded noise, showing a precise condition for $d$-implementability and proving NP-hardness for broader constrained signaling regimes. The results illuminate how information design can shape welfare, outline systematic methods to realize desired outcomes, and identify computational boundaries for signaling under constraints, with implications for contract design and regulatory monitoring. Practically, the findings inform how regulators can craft monitoring policies to achieve targeted incentives while quantifying welfare losses as information becomes noisier or signaling constraints tighten.

Abstract

We study a variant of the principal-agent problem in which the principal does not directly observe the agent's effort outcome; rather, she gets a signal about the agent's action according to a variable information structure designed by a regulator. We consider both the case of a risk-neutral and of a risk-averse agent, focusing mainly on a setting with a limited liability assumption. We provide a clean characterization for implementability of actions and utility profiles by any information structure, which turns out to be simple thresholds on the utilities. We further study naturally constrained information structures in which the signal emitted from any action is either the action itself or some actions nearby. We show that the worst implementable welfare deteriorates gracefully as the information structure becomes noisier. Finally, we show that our clean characterization does not generalize to a larger class of signaling constraints. In fact, even deciding whether a certain action is implementable by some constrained information structure from this class is NP-complete in the general setting.

Information Design in the Principal-Agent Problem

TL;DR

The paper develops a framework where a regulator designs the information structure about a principal's agent actions in a principal–agent setting with unobserved effort. It provides a complete threshold-based characterization of implementable utility profiles and actions for both risk-neutral and risk-averse agents under limited liability, using a universal two-signal signaling scheme. It further analyzes constrained information structures with bounded noise, showing a precise condition for -implementability and proving NP-hardness for broader constrained signaling regimes. The results illuminate how information design can shape welfare, outline systematic methods to realize desired outcomes, and identify computational boundaries for signaling under constraints, with implications for contract design and regulatory monitoring. Practically, the findings inform how regulators can craft monitoring policies to achieve targeted incentives while quantifying welfare losses as information becomes noisier or signaling constraints tighten.

Abstract

We study a variant of the principal-agent problem in which the principal does not directly observe the agent's effort outcome; rather, she gets a signal about the agent's action according to a variable information structure designed by a regulator. We consider both the case of a risk-neutral and of a risk-averse agent, focusing mainly on a setting with a limited liability assumption. We provide a clean characterization for implementability of actions and utility profiles by any information structure, which turns out to be simple thresholds on the utilities. We further study naturally constrained information structures in which the signal emitted from any action is either the action itself or some actions nearby. We show that the worst implementable welfare deteriorates gracefully as the information structure becomes noisier. Finally, we show that our clean characterization does not generalize to a larger class of signaling constraints. In fact, even deciding whether a certain action is implementable by some constrained information structure from this class is NP-complete in the general setting.
Paper Structure (19 sections, 6 theorems, 15 equations, 4 figures, 1 table)

This paper contains 19 sections, 6 theorems, 15 equations, 4 figures, 1 table.

Table of Contents

  1. Introduction
  2. The principal-agent problem.
  3. Information in the Principal-Agent Problem
  4. Outcomes versus signals.
  5. Designing the Information
  6. Information design for moral hazard versus adverse selection.
  7. Applications
  8. Our Results
  9. Paper Organization
  10. Model
  11. Implementability.
  12. Risk-Neutral Agent
  13. Risk-Averse Agent
  14. Limiting the Misinformation of the Principal
  15. A Computational Hardness Result
  16. ...and 4 more sections

Key Result

Theorem 3.1

A utility profile $(*){x,y}\in F$ is implementable if and only if $x\geq \max\{*\}{w_0 ,w_1}$ and $y\geq 0$. Moreover, an action $i\in [*]{n}$ is implementable (for some expected transfer) if and only if $w_a\geq \max\{*\}{w_0,w_1}$. If action $a\in [*]{n}$ is implementable, then the set of implemen

Figures (4)

  • Figure 1: The union of all $n$ lines is the set $F$. In this figure, $w_1\geq 0$, $r_0=0$, and the bold parts of the lines are the implementable utility profiles. The index $i$ denotes the social welfare-maximizing action.
  • Figure 2: The expected principal's (blue) and agent's (red) utilities as a function of $\alpha$.
  • Figure 3: The function $v$ appears in (a). The set $F_i$ appears in (b).
  • Figure 4: The area below the solid line is the set $F$. The blue area is the set of implementable utility profiles.

Theorems & Definitions (14)

  • Theorem 3.1
  • Example 3.2
  • Example 3.3
  • proof : Proof of Theorem \ref{['thm:utility_neutral']}
  • Theorem 4.1
  • proof
  • Theorem 5.1
  • proof
  • Proposition 5.2
  • proof
  • ...and 4 more