[Paper Review] Costly Evidence and Discretionary Disclosure

Mark Whitmeyer, Kun Zhang|arXiv (Cornell University)|Aug 9, 2022

Law, Economics, and Judicial Systems4 citations

TL;DR

This paper studies a sender who endogenously acquires costly evidence and chooses whether to certify it for disclosure to a receiver. It shows that transparency in evidence acquisition harms the receiver by enabling sender commitment to withhold information, and that even tiny evidence costs lead to coarse information acquisition—converging to the Pareto-worst free-learning equilibrium. A strictly positive certification fee can also improve receiver welfare under covert acquisition.

ABSTRACT

A sender flexibly acquires evidence--which she may pay a third party to certify--to disclose to a receiver. When evidence acquisition is overt, the receiver observes the evidence gathering process irrespective of whether its outcome is certified. When acquisition is covert, the receiver does not. In contrast to the case with exogenous evidence, the receiver prefers a strictly positive certification cost. As acquisition costs vanish, equilibria converge to the Pareto-worst free-learning equilibrium. The receiver always prefers covert to overt evidence acquisition.

Motivation & Objective

• To analyze how transparency in evidence acquisition affects equilibrium outcomes and receiver welfare.
• To examine the role of evidence acquisition costs and certification fees in shaping sender incentives and information disclosure.
• To investigate the limit behavior of equilibria as evidence acquisition costs vanish, contrasting 'cheap' vs. 'free' information.
• To compare covert versus overt evidence acquisition settings and their implications for information aggregation and welfare.
• To explore how certification fees affect receiver preferences and equilibrium outcomes under endogenous information acquisition.

Proposed method

• Models a sender who flexibly acquires costly evidence about a state and chooses whether to pay a third party to certify it.
• Uses a Bayesian persuasion framework with a receiver who takes an action based on the sender's message, affecting both players' payoffs.
• Analyzes equilibria under two regimes: overt (public) and covert (hidden) evidence acquisition.
• Employs a value function approach to characterize sender incentives, showing that for small costs, the sender acquires only coarse evidence.
• Derives conditions under which equilibria are monotone partitional, with binary posterior distributions over high and low states.
• Uses a limit analysis as acquisition cost κ → 0 to show convergence to the Pareto-worst free-learning equilibrium under covert acquisition.

Experimental results

Research questions

• RQ1 How does transparency in evidence acquisition affect the receiver’s welfare and equilibrium outcomes?
• RQ2 What is the impact of a strictly positive certification fee when evidence acquisition is covert?
• RQ3 How do equilibria change as evidence acquisition costs approach zero, and what is the limiting equilibrium?
• RQ4 Why does the receiver prefer covert over overt evidence acquisition, and under what conditions is this strict?
• RQ5 How does endogenous evidence acquisition differ from exogenous evidence in terms of equilibrium efficiency and information precision?

Key findings

• The receiver always prefers covert to overt evidence acquisition, and strictly prefers it when the sender acquires information in equilibrium.
• A strictly positive certification fee can strictly improve receiver welfare under covert acquisition, contrary to findings in models with exogenous evidence.
• As evidence acquisition costs vanish (κ → 0), equilibria converge to the Pareto-worst free-learning equilibrium under covert acquisition.
• Even with vanishingly small costs, the sender acquires only coarse evidence—focusing on high or low states—due to cost-minimization incentives.
• Under overt acquisition, the limit as κ → 0 results in no information acquisition, regardless of whether evidence is free or cheap.
• The limiting equilibrium under covert, cheap evidence is the same as the Pareto-worst equilibrium in the free-information benchmark, highlighting a key distinction between 'cheap' and 'free' information.