The Price of Competitive Information Disclosure
Pith reviewed 2026-05-22 20:51 UTC · model grok-4.3
The pith
When agents strategically disclose quality information, the resulting inefficiency stays bounded by a constant under independent distributions.
A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.
Core claim
In the competitive Bayesian persuasion model, multiple agents selectively disclose information about their qualities to a principal selecting the highest-quality candidates. When agents' quality distributions are independent, the price of anarchy of the resulting game is at most a constant, even with heterogeneous utility functions. This establishes the first theoretical limit on inefficiency in such strategic disclosure settings.
What carries the argument
Price-of-anarchy analysis of the game induced by competitive Bayesian persuasion, which bounds the ratio of the principal's expected utility under truthful full disclosure versus under any Nash equilibrium of the disclosure game.
If this is right
- The principal obtains expected utility within a constant factor of the full-information benchmark under any equilibrium disclosure strategies.
- The constant bound continues to hold when agents have completely heterogeneous preferences over selection outcomes.
- Independence of quality distributions is sufficient to rule out arbitrarily severe inefficiency from strategic disclosure.
- No additional coordination or regulation on what agents reveal is required to keep losses bounded.
Where Pith is reading between the lines
- If quality distributions become correlated, the price of anarchy could grow without bound, though the paper provides no analysis of that case.
- The existence of a constant suggests that the principal could post a simple menu of selection probabilities to induce near-optimal disclosure without needing to observe full signals.
- The bound may extend to repeated or dynamic versions of the game in which agents can condition disclosures on past outcomes.
Load-bearing premise
The agents' quality distributions are independent of one another.
What would settle it
An explicit collection of independent quality distributions together with utility functions for which the ratio between the principal's full-information expected utility and the equilibrium utility grows unboundedly with the number of agents.
read the original 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.
Editorial analysis
A structured set of objections, weighed in public.
Referee Report
Summary. The paper studies a competitive Bayesian persuasion model in which multiple agents strategically disclose information about their private qualities to a principal who selects the highest-quality candidates. It applies the price-of-anarchy framework to quantify the resulting inefficiency and proves that the PoA is bounded by a constant when the agents' quality distributions are independent, even when their utility functions are heterogeneous. The result is presented as the first theoretical guarantee that strategic disclosure cannot produce unbounded inefficiency in this setting.
Significance. If the central derivation holds, the result is significant: it supplies the first constant PoA bound for competitive information disclosure under independent qualities and handles heterogeneous utilities. The paper should be credited for using the product-measure structure induced by independence to decouple signaling strategies and bound the principal's selection error, yielding a parameter-free guarantee. This provides a concrete theoretical limit on welfare loss in Bayesian persuasion with competition.
major comments (1)
- [Section 4] Main theorem (Section 4): The constant PoA bound is derived under the assumption of independent quality distributions. The proof technique relies on product measures to bound selection error; the manuscript should state explicitly whether any step fails under correlation and, if possible, supply a simple counter-example showing that positive or negative correlation can produce PoA growing with the number of agents. This would clarify the necessity of the independence assumption for the claimed constant bound.
minor comments (2)
- [Abstract] Abstract: the statement that the result is 'the first theoretical guarantee' would be strengthened by a brief comparison sentence distinguishing the present constant bound from prior PoA results in non-competitive or non-Bayesian settings.
- [Section 2] Notation: the definition of the principal's selection rule and the agents' disclosure strategies should be collected in a single preliminary section to avoid forward references in the proof.
Simulated Author's Rebuttal
We thank the referee for the constructive comment on the role of the independence assumption. We will revise the manuscript to explicitly address this point.
read point-by-point responses
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Referee: [Section 4] Main theorem (Section 4): The constant PoA bound is derived under the assumption of independent quality distributions. The proof technique relies on product measures to bound selection error; the manuscript should state explicitly whether any step fails under correlation and, if possible, supply a simple counter-example showing that positive or negative correlation can produce PoA growing with the number of agents. This would clarify the necessity of the independence assumption for the claimed constant bound.
Authors: We agree that the constant PoA bound in Theorem 4 relies on the independence of the agents' quality distributions. The proof in Section 4 uses the product-measure structure to decouple the signaling strategies across agents and to bound the principal's selection error. Several steps, including the application of concentration inequalities that treat the agents' posterior beliefs as independent, fail to hold under arbitrary correlations. We will revise Section 4 to state this explicitly and to clarify that the constant bound is specific to the independent case. While we expect that suitable positive or negative correlations can produce PoA that grows with the number of agents, constructing a simple, rigorous counter-example requires additional technical development beyond the scope of the present manuscript. We will therefore add the requested discussion of the assumption's necessity but will not include an explicit counter-example in this revision. revision: partial
- Supplying a simple counter-example showing that positive or negative correlation can produce PoA growing with the number of agents
Circularity Check
Derivation of constant PoA bound is self-contained under stated independence assumption
full rationale
The paper presents a mathematical upper bound on price of anarchy for the competitive Bayesian persuasion setting. The bound is derived from the model primitives (agent quality distributions, heterogeneous utilities, principal selection) using the independence assumption to decouple signaling strategies and bound selection error. No step reduces a fitted parameter to a prediction, renames a known result, or relies on a self-citation chain for the core claim; the result is a theorem proved from the game definition rather than tautological or constructed by construction. The independence assumption is explicitly load-bearing but external to the derivation itself.
discussion (0)
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