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The Price of Competitive Information Disclosure

Siddhartha Banerjee, Kamesh Munagala, Yiheng Shen, Kangning Wang

TL;DR

The paper investigates competitive Bayesian persuasion where multiple agents selectively disclose information about private qualities to a principal selecting up to $k$ candidates. It defines the price of concealment as the ratio between the first-best welfare with full information and the welfare in Nash equilibrium under strategic signaling, and proves a universal constant bound $\mathrm{PoA} \le 11+5\sqrt{5} \approx 22.18$ under independent priors and monotone utilities, with a lower bound of 2 in simple cases. The analysis introduces a novel framework that blends core–tail decomposition, line sweeps over value distributions, and a carefully constructed deviation signal $s^*$ to bound inefficiency, and also provides a warm-up result showing $\mathrm{PoA} \le 4$ for identical priors and single-item selection. The results imply that strategic information disclosure cannot lead to arbitrarily bad societal outcomes, offering theoretical guarantees for information design in hiring-like and selection settings and guiding future work on extending to richer priors, objectives, and multi-dimensional agent values.

Abstract

In many decision-making scenarios, individuals strategically choose what information to disclose to optimize their own outcomes. It is unclear whether such strategic information disclosure can lead to good societal outcomes. To address this question, we consider a competitive Bayesian persuasion model in which multiple agents selectively disclose information about their qualities to a principal, who aims to choose the candidates with the highest qualities. Using the price-of-anarchy framework, we quantify the inefficiency of such strategic disclosure. We show that the price of anarchy is at most a constant when the agents have independent quality distributions, even if their utility functions are heterogeneous. This result provides the first theoretical guarantee on the limits of inefficiency in Bayesian persuasion with competitive information disclosure.

The Price of Competitive Information Disclosure

TL;DR

The paper investigates competitive Bayesian persuasion where multiple agents selectively disclose information about private qualities to a principal selecting up to candidates. It defines the price of concealment as the ratio between the first-best welfare with full information and the welfare in Nash equilibrium under strategic signaling, and proves a universal constant bound under independent priors and monotone utilities, with a lower bound of 2 in simple cases. The analysis introduces a novel framework that blends core–tail decomposition, line sweeps over value distributions, and a carefully constructed deviation signal to bound inefficiency, and also provides a warm-up result showing for identical priors and single-item selection. The results imply that strategic information disclosure cannot lead to arbitrarily bad societal outcomes, offering theoretical guarantees for information design in hiring-like and selection settings and guiding future work on extending to richer priors, objectives, and multi-dimensional agent values.

Abstract

In many decision-making scenarios, individuals strategically choose what information to disclose to optimize their own outcomes. It is unclear whether such strategic information disclosure can lead to good societal outcomes. To address this question, we consider a competitive Bayesian persuasion model in which multiple agents selectively disclose information about their qualities to a principal, who aims to choose the candidates with the highest qualities. Using the price-of-anarchy framework, we quantify the inefficiency of such strategic disclosure. We show that the price of anarchy is at most a constant when the agents have independent quality distributions, even if their utility functions are heterogeneous. This result provides the first theoretical guarantee on the limits of inefficiency in Bayesian persuasion with competitive information disclosure.

Paper Structure

This paper contains 27 sections, 11 theorems, 57 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Voluntary information disclosure and the price of concealment.
  3. Summary of Results
  4. Remarks.
  5. Techniques.
  6. Related Work
  7. Strategic information revelation and Bayesian persuasion.
  8. Competitive Bayesian persuasion games.
  9. Fairness and strategic selection.
  10. Preliminaries
  11. Agent Values and Signaling Schemes
  12. Individual Utilities and Social Welfare
  13. Nash Equilibrium and Price of Anarchy
  14. Lower Bounds on the Price of Anarchy
  15. Warm-up: Identical Priors and Constant Utility of Selection
  16. ...and 12 more sections

Key Result

Theorem 3.1

Consider a setting with $k = 1$, symmetric agents with $\mathcal{F}_i\sim\mathtt{Bernoulli}(\zeta)$ and $N\zeta \leq 1$, and constant utility of selection for all $i \in [N]$. Then the price of anarchy satisfies

Figures (2)

  • Figure 1: An illustration of the final state of the line sweep for an example with $5$ agents. As shown in the figure, agent $2$ and agent $5$ have a mean above the sweep line larger than $E_\mathrm{cut}$, as their quantile cuts satisfy $q_i = 1$.
  • Figure 2: Illustration of construction of deviation signaling scheme $s^*$.

Theorems & Definitions (26)

  • Example 1.1
  • Example 1.2: continued from \ref{['eg:intro']}
  • Example 1.3: continued from \ref{['eg:intro']}
  • Definition 2.1: First-Best Social Welfare
  • Definition 2.2: Nash Equilibrium Signaling
  • Definition 2.3: Price of Anarchy
  • Theorem 3.1
  • proof
  • Theorem 4.1
  • Lemma 4.2
  • ...and 16 more