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Managing Persuasion Robustly: The Optimality of Quota Rules

Dirk Bergemann, Tan Gan, Yingkai Li

TL;DR

The paper studies a robust sender–receiver persuasion problem where both players have commitment power and the receiver faces uncertainty about the sender’s preferences and feasible information structures. It develops a unifying regret framework, showing that the receiver’s best robust response is a quota rule that matches the marginal action distribution to a fixed quota, thereby aligning incentives and protecting against sender manipulation. The analysis decomposes regret into decision and agency losses, proving quota rules minimize worst-case regret and are best-in-class even under binary-action simplifications and general mechanism extensions. The results cover max-min, min-max regret, and competitive-ratio styles, with implications for corporate, judicial, and regulatory settings where commitment and information frictions prevail.

Abstract

We study a sender-receiver model in which the receiver can commit to a decision rule before the sender determines the information policy. The decision rule can depend on the information structure chosen by the sender and the realized signals. This framework captures applications where a decision-maker (the receiver) seeks advice from an interested party (the sender). In these applications, the receiver frequently faces uncertainty regarding the sender's preferences and the set of feasible information structures. Consequently, we adopt a unified robust analysis framework that includes the max-min utility, the min-max regret, and the min-max competitive ratio as special cases. We show that the optimal decision rule is always a quota rule.

Managing Persuasion Robustly: The Optimality of Quota Rules

TL;DR

The paper studies a robust sender–receiver persuasion problem where both players have commitment power and the receiver faces uncertainty about the sender’s preferences and feasible information structures. It develops a unifying regret framework, showing that the receiver’s best robust response is a quota rule that matches the marginal action distribution to a fixed quota, thereby aligning incentives and protecting against sender manipulation. The analysis decomposes regret into decision and agency losses, proving quota rules minimize worst-case regret and are best-in-class even under binary-action simplifications and general mechanism extensions. The results cover max-min, min-max regret, and competitive-ratio styles, with implications for corporate, judicial, and regulatory settings where commitment and information frictions prevail.

Abstract

We study a sender-receiver model in which the receiver can commit to a decision rule before the sender determines the information policy. The decision rule can depend on the information structure chosen by the sender and the realized signals. This framework captures applications where a decision-maker (the receiver) seeks advice from an interested party (the sender). In these applications, the receiver frequently faces uncertainty regarding the sender's preferences and the set of feasible information structures. Consequently, we adopt a unified robust analysis framework that includes the max-min utility, the min-max regret, and the min-max competitive ratio as special cases. We show that the optimal decision rule is always a quota rule.
Paper Structure (25 sections, 15 theorems, 123 equations, 3 figures)

This paper contains 25 sections, 15 theorems, 123 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Motivation
  3. Related Work
  4. Model
  5. Payoff Environment
  6. Robustness and Regret
  7. Generalized Regret
  8. General Decision Rules
  9. Managing Persuasion With Known Sender
  10. Regret Minimizing Decision Rule
  11. Decision Loss and Agency Loss
  12. Optimal Quota Rules
  13. The Optimality of the Quota Rule
  14. Binary Actions
  15. Binary States
  16. ...and 10 more sections

Key Result

Proposition 1

Under the "shoot the agent" decision rule $\alpha_S$, it is optimal for the sender to choose the second-best information structure $\pi^*$:

Figures (3)

  • Figure 1: The timeline of the model.
  • Figure 2: The above figures illustrate the optimal quota $q$ for action $a=1$ in the binary-action and binary-state environment.
  • Figure 3: An illustration of binary monotone partition with two types of errors.

Theorems & Definitions (35)

  • Proposition 1: Punitive Decision Rule
  • proof : Proof of Proposition \ref{['lemma_shoottheagent']}
  • Definition 1: Quota Constraints
  • Definition 2: Quota Rules
  • Lemma 1: Sender-Optimal Information Structure under Quota Rules
  • proof : Proof of Lemma \ref{['trivial_lemma']}
  • Proposition 2: Second-Best Implementation
  • Lemma 2: Lipschitz Continuity
  • Lemma 3: Local Optimality
  • Theorem 1: Optimality of Quota Rules
  • ...and 25 more