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Multi-Sender Disclosure with Costs

Navin Kartik, Frances Xu Lee, Wing Suen

TL;DR

The paper investigates voluntary disclosure with multiple biased senders who can reveal or conceal private information at a cost, using a reduced-form model with conditionally independent signals to derive threshold-based disclosure strategies. A key contribution is showing that, absent costs, the two-sender benchmark matches the single-sender case, but with concealment costs disclosures are strategic complements while with disclosure costs they are strategic substitutes, with the direction driven by disagreement between the sender’s threshold type and the DM’s nondisclosure belief. The analysis leverages the IVP theorem from KLS21-IVP to explain how others’ disclosures systematically shift a sender’s incentives, and extends the results to many senders, sequential reporting, and changes in signal precision, yielding nuanced welfare implications. The main takeaway is that additional information sources can improve or hurt DM welfare depending on the underlying cost structure, implying careful consideration of institutional design when promoting disclosure or suppression regimes in legal and financial contexts.

Abstract

We study voluntary disclosure with multiple biased senders who may bear costs for disclosing or concealing their private information. Under relevant assumptions, disclosures are strategic substitutes under a disclosure cost but complements under a concealment cost. Additional senders thus impede any sender's disclosure under a disclosure cost but promote it under a concealment cost. In the former case, a decision maker can be harmed by additional senders, even when senders have opposing interests. The effects under both kinds of message costs turn on how a sender, when concealing his information, expects others' messages to systematically sway the decision maker's belief.

Multi-Sender Disclosure with Costs

TL;DR

The paper investigates voluntary disclosure with multiple biased senders who can reveal or conceal private information at a cost, using a reduced-form model with conditionally independent signals to derive threshold-based disclosure strategies. A key contribution is showing that, absent costs, the two-sender benchmark matches the single-sender case, but with concealment costs disclosures are strategic complements while with disclosure costs they are strategic substitutes, with the direction driven by disagreement between the sender’s threshold type and the DM’s nondisclosure belief. The analysis leverages the IVP theorem from KLS21-IVP to explain how others’ disclosures systematically shift a sender’s incentives, and extends the results to many senders, sequential reporting, and changes in signal precision, yielding nuanced welfare implications. The main takeaway is that additional information sources can improve or hurt DM welfare depending on the underlying cost structure, implying careful consideration of institutional design when promoting disclosure or suppression regimes in legal and financial contexts.

Abstract

We study voluntary disclosure with multiple biased senders who may bear costs for disclosing or concealing their private information. Under relevant assumptions, disclosures are strategic substitutes under a disclosure cost but complements under a concealment cost. Additional senders thus impede any sender's disclosure under a disclosure cost but promote it under a concealment cost. In the former case, a decision maker can be harmed by additional senders, even when senders have opposing interests. The effects under both kinds of message costs turn on how a sender, when concealing his information, expects others' messages to systematically sway the decision maker's belief.
Paper Structure (27 sections, 13 theorems, 16 equations, 2 figures)

This paper contains 27 sections, 13 theorems, 16 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Results.
  3. Implications.
  4. Other related literature.
  5. Outline.
  6. Model
  7. Players.
  8. Information.
  9. Communication.
  10. Message costs.
  11. Timing.
  12. A Single-Sender Benchmark
  13. Strategic Substitutes and Complements
  14. Discussion.
  15. Extensions
  16. ...and 12 more sections

Key Result

Lemma 1

The nondisclosure belief function $\eta(\hat{s},p,\pi)$ has the following properties:

Figures (2)

  • Figure 1: The single-sender game with an upward-biased sender, illustrated with $c>0>c'$ and $p'_i>p_i$. Equilibrium thresholds are given by intersections of $\eta(s_i,\cdot)$ and $s_i-c$ or $s_i-c'$.
  • Figure 2: Sender $i$'s "best response" to sender $j$ (both upward biased), illustrated with $c>0>c'$, $p'_j>p_j$, and $\hat{s}'_j<\hat{s}_j<\overline s$.

Theorems & Definitions (20)

  • Lemma 1
  • Proposition 1
  • Proposition 2
  • Lemma 2
  • Lemma 3
  • Proposition 3
  • Proposition 4
  • Corollary 1
  • Proposition 5
  • Remark 1
  • ...and 10 more