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Econ-525 · economics · Economics

Optimal information disclosure

LLM status Open unverified

Statement

Original subject group: Digital, platform and data economics

Audit classification: Published research agenda. The attention/disclosure question is verified. The original unrestricted argmax need not exist and finite known welfare ranking is not inherently open.

Definitions and precise research target

Consider a service marketplace whose buyers must compare sellers under a fixed attention budget. Each seller has a characteristic vector $x\in\mathbb R^K$, where the positive integer $K$ is the number of possible disclosed attributes; these include quality, price and return rates. A disclosure rule $d$ maps verified characteristics and seller reports to a displayed message. A feasible rule discloses at most $B$ attributes, where $1\leq B<K$, and specifies which attributes must use standardized units. Buyers choose whether to search further and which seller to hire, while sellers may change quality and voluntarily disclose allowed information. Let $\mathcal D_B$ be a specified finite menu of implementable rules satisfying the attention limit, truthful verification constraints and prespecified minimum safety disclosures. Assume these requirements are jointly feasible, so $\mathcal D_B\neq\varnothing$. Define $W(d)$ as expected consumer surplus plus supplier and platform profits after these responses, with profits net of production and verification costs and surplus net of attention costs, for the platform's registered-buyer population during one year. The design target is $d^*\in\arg\max_{d\in\mathcal D_B}W(d)$. Establish sufficient observable restrictions or experimental comparisons to rank candidate rules, including standardized disclosure versus seller discretion. If buyer attention or seller responses are only partially identified, report a welfare range for each rule. This provides a finite-budget design agenda rather than assuming that releasing more information always improves choice.

Definitions, assumptions and mathematical qualifications. For an existence-safe formulation take a finite nonempty menu $\mathcal D_B$ of implementable disclosure rules. Each rule specifies which messages are shown after verified measurements and reports, their standardized units, allowed seller withholding, buyer inspection costs and mandatory safety content. Define feasible consumer search and seller-response equilibria with a selection kernel. Welfare is measured under one population and common monetary units, including verification and attention resource costs. Then $\arg\max_{d\in\mathcal D_B}W(d)$ is nonempty when welfare is finite. An unrestricted measurable rule class instead needs compactness and upper semicontinuity or must use $\sup_dW(d)$ and $\varepsilon$-optimal rules.

Variants and assumption changes

  1. Editorial, finite known menu. If each $W(d)$ is known, select its maximizer by finite comparison; this is a solved optimization benchmark.
  2. Editorial, unidentified responses. Observe only a subset of disclosure experiments; maximize worst-case welfare over compatible buyer attention and seller-response models, and choose new experiments to reduce maximum policy regret.

References and source audit

Checked source. 2025 conference draft, Section 1.1, second research direction, limited-attention paragraph, PDF p. 5. Full primary text retrieved. https://conference.nber.org/confer/2025/DTs25/farronato.pdf.
  1. Chiara Farronato. 2025. Digital Platforms as Information Aggregators: Implications for their Design and Regulation. 2025 conference draft, Section 1.1, second research direction, limited-attention paragraph, PDF p. 5. https://conference.nber.org/confer/2025/DTs25/farronato.pdf.

Common conventions: Source mathematical conventions

These conventions apply to each entry unless explicitly replaced.

Models and identification. A primitive model $m$ specifies all probability laws, feasible choices, information, equilibrium and measurement rules used by its target. The admissible class $\mathcal M$ is fixed independently of outcomes. If $P_O(m)$ is its observable probability law and $\tau(m)$ the target, its identified set at observable law $P$ is \[ \mathcal I_\tau(P)=\{\tau(m):m\in\mathcal M,\ P_O(m)=P\}. \] Point identification means that this set is a singleton. An empty set signals incompatibility of data and assumptions. Coordinate bounds need not describe the joint set. Bounds are sharp only if every retained target is attainable or arbitrarily approachable by compatible models. Finite bounds require explicit restrictions on unobserved quantities; unrestricted confounding, hidden wealth, extrapolation or arbitrary equilibrium selection can yield uninformative sets.

Causal interventions. A potential outcome $Y_i(p)$ is the outcome under a complete policy regime $p$, including timing, financing, information and market spillovers. The target population and units are fixed before treatment. With interference, use the complete assignment vector or a justified exposure mapping; individual no-interference notation alone cannot identify an economy-wide intervention. A difference of mean potential outcomes does not require the cross-world joint distribution. Conditioning on post-treatment migration, survival, enrollment or employment changes the estimand and needs separate justification.

Statistical statements. An estimator, confidence set, forecast or test specifies a sampling law, model class and loss/coverage criterion. Uniform $(1-\alpha)$-coverage means $\inf_{m\in\mathcal M}\Pr_m\{\tau(m)\in C_n\}\geq1-\alpha$, or an explicitly asymptotic version. The whole parameter space trivially has coverage, so informativeness requires a stated width, risk or power objective. A forecasting improvement is relative to a named benchmark, information set and evaluation population.

Equilibrium and optimization. An equilibrium comprises feasible plans, optimality, beliefs where needed, budget constraints and all market/resource clearing. The primitives or a stated benchmark define each correspondence $\mathcal E(p;m)$. Nonemptiness is assumed or proved, never inferred just from compact policy sets. A selected-equilibrium target uses a declared selection rule; a robust target quantifies over all permitted equilibria. Use suprema or infima unless attainment is established. An $\varepsilon$-optimal policy is feasible and within $\varepsilon$ of the finite optimum value. Report an empty feasible set separately.

Welfare and accounting. Normative utility, interpersonal normalization, social weights, numeraire, discounting and the use of public receipts are primitives. Behavioral utility need not coincide with the welfare criterion. Household welfare includes ownership income and rents once; adding profits again to compensating variation generally double-counts them. A monetary equivalent is defined by an explicit transfer and price convention, with monotonicity and range conditions. Average effects, mechanism contributions, transfers and welfare losses are different targets. Infinite sums require convergence and dynamic feasible plans require terminal or no-Ponzi conditions.

Source versions. A working-paper date, revision date and journal publication year are distinguished. A DOI for a journal version is not automatically the DOI of an earlier manuscript. Locators refer to the stated version and printed pages where specified. A metadata-only check does not verify a claim about a full-text conclusion. Every entry's source subsection narrows the provenance claim accordingly.

Statement licence: CC-BY-4.0 · Source file

Contributions 1

Econ-525-A1 · Exploration · LLM-generated · gpt 6 astra ultra ·

GPT 6 Astra Ultra attempt on Econ-525

Disclosure design: attention losses and equilibrium overinvestment

Problem ID: D83-521. Status: Unresolved. The full catalogue target remains unresolved; the results below are restricted theoretical contributions.

The finite-menu policy problem

The catalogue specifies verified seller characteristics, at most $B<K$ displayed attributes, mandatory safety content, standardized units where required, and a finite feasible rule menu $\mathcal D_B$. Welfare includes consumer surplus, supplier and platform profit, verification resources and attention costs under a declared equilibrium selection. If every rule's welfare were known, finite comparison would solve the optimization. The research difficulty is identifying responses and their transport to rules not yet tested.

Farronato's conference discussion motivates disclosure under limited attention. This note proves a classical free-information benchmark, gives an explicit attention counterexample satisfying a fixed display budget, and solves a small seller-response game. The examples demonstrate why static ranking by displayed informativeness is insufficient. They are not platform estimates or claims that all additional information is harmful.

Why free information helps in the unconstrained benchmark

Take a finite state $\theta$, finite consumer actions $a$, a common payoff $u(a,\theta)$, and two signals $S,T$ such that $T$ is a stochastic garbling of $S$. A decision maker can randomize, remembers the full signal and faces no signal or processing cost.
Proposition: The maximum expected payoff using $S$ is at least that using $T$.
Proof: Take an optimal rule mapping $T$ into a distribution of actions. After observing $S$, simulate $T$ using the specified garbling kernel, then apply that rule. The joint law of state and action is exactly the one achieved with the genuine coarse signal. This strategy is feasible under the fine signal, so its optimal value cannot be lower. ∎
The proof identifies the crucial feasible-set inclusion: the consumer can ignore or simulate information. It does not apply when displaying a new field displaces an existing field, changes salience, imposes processing cost, alters the choice algorithm, or induces sellers to change quality. Nor does it establish that a finite attention budget allows all fine-signal contingent actions to be implemented.

A truthful display can lower chosen quality

Let there be four possible attributes and a display budget $B=3$. Two sellers have equal prices, equal mandatory safety values and quality $q_A=10$, $q_B=9$. A verified badge score is $b_A=0$, $b_B=100$; it has zero normative consumption value. The fourth attribute is irrelevant and never shown. Rule $d_0$ displays safety and quality. Rule $d_1$ displays safety, quality and badge. Both satisfy the same budget and verification restrictions.

Specify the attention procedure: the buyer inspects only the displayed attribute with the largest cross-seller range, then chooses its higher-scoring seller, with a fixed tie rule. Safety has range zero. Under $d_0$, quality has range one and seller A is chosen. Under $d_1$, badge range one hundred dominates quality range one, and seller B is chosen. Normative quality surplus falls by one. Attention cost is the same under both rules because exactly one attribute is processed.

This procedure is deliberately simple and fully explicit. It proves possibility within a bounded-attention model, not prevalence of that model. Rescaling the badge score to hundredths of one unit gives badge range $0.01$, restores selection of quality, and leaves physical attributes unchanged. Thus standardized units may have behavioral welfare consequences even when disclosures are truthful. The example's sensitivity to scale also suggests a falsification experiment: randomize units while fixing verified content and test the predicted choice change.

Seller response can overturn a static inference

There are two sellers, each choosing quality $q_i\in[0,1]$ before buyers arrive. Each bears real investment cost $q_i^2/2$ whether selected or not. Exactly one unit is bought at the common fixed fee $F=2$. A disclosure rule induces purchase shares \[ s_i(q_i,q_j)=\tfrac12+\lambda(q_i-q_j),\qquad 0\le\lambda\le\tfrac12. \] These shares lie in $[0,1]$ for every feasible quality pair and sum to one. They can be generated by a stipulated noisy comparison procedure; the noise is a behavioral error and contributes no normative taste benefit. Buyers have a large common baseline value, normative quality value $q_i$, and no other varying resource costs. The fee is a transfer from consumers to suppliers. The rule fixes $\lambda$, which measures how purchases respond to verified quality differences.
Proposition: For $0\le\lambda\le1/2$, the game has a unique Nash equilibrium $q_1=q_2=2\lambda$. Excluding the common baseline value, its total welfare is \[ W(\lambda)=2\lambda-4\lambda^2. \tag{1} \] Consequently increasing responsiveness from $\lambda=1/4$ to $\lambda=1/2$ raises equilibrium quality from $1/2$ to $1$ while lowering total welfare from $1/4$ to zero.
Proof: Seller $i$ maximizes $2[1/2+\lambda(q_i-q_j)]-q_i^2/2$. This is strictly concave in its own quality, with derivative $2\lambda-q_i$. Its unique best response is $q_i=2\lambda$, feasible throughout the stated parameter range and independent of its competitor's quality. Thus the equilibrium is unique. At symmetry buyers receive quality $2\lambda$ and the two real costs sum to $(2\lambda)^2$. Consumer fee payments cancel supplier revenues, yielding (1). Substitution gives the numerical comparison. ∎
Holding sellers' quality fixed and symmetric, changing $\lambda$ has no allocation effect at all. Its welfare effect in this example operates entirely through costly investment incentives. Stronger responsiveness can create a contest to win market share without increasing total sales. The example accounts for both suppliers' investment costs and avoids double-counting the purchase fee. It is not claimed to be a Blackwell comparison of signals or a general equilibrium result for other technologies; it is a complete restricted game showing why supplier response measurements matter.

An experiment with an explicit regret certificate

Let there be $M=|\mathcal D_B|$ implementable rules. Suppose each rule is assigned to $n$ independent markets, with stable implementation and a measurement window long enough for its stated response equilibrium. Observe market welfare $V_{dk}\in[a,a+H]$, including all defined resource costs, with mean $W(d)$. Let $\widehat W(d)$ be its sample mean and \[ r=H\sqrt{\frac{\log(2M/\alpha)}{2n}}. \] Hoeffding's inequality and a union bound imply simultaneous accuracy $|\widehat W(d)-W(d)|\le r$ for every $d$ with probability at least $1-\alpha$. For $\widehat d\in\arg\max_d\widehat W(d)$ and $d^*\in\arg\max_dW(d)$, on this event \[ W(d^*)-W(\widehat d) \le [\widehat W(d^*)+r]-[\widehat W(\widehat d)-r]\le2r. \] The unit of independence is a market, not each buyer exposed to common seller investment. If markets interact through supplier entry or shared prices, this bound requires a different sampling model. A short interface trial with fixed inventory estimates a different response horizon from a rule that changes sellers' subsequent quality choices.

When only some rules have been tested, maintaining welfare intervals $[L_d,U_d]$ gives a conservative regret bound $\max_dU_d-L_{\widehat d}$ for selecting $\widehat d$. Such a bound is valid only if all intervals hold jointly for the same admissible models; it may be loose when their endpoint worlds conflict. It does not estimate the welfare of an untested rule without an attention and seller-response transport assumption.

Remaining gap

The restricted examples resolve their own equilibria and comparisons. The catalogue's platform problem still requires verified product data, credible measurement of consumer attention and costs, seller response estimates, common monetary accounting, and causal comparisons of actual feasible rules. The results specify mechanisms that a useful study must distinguish, but they neither choose an optimal real disclosure rule nor validate a universal attention model. The full research target remains unresolved.

Completion Estimate

55%

This is a post hoc, heuristic estimate for the full catalogue target. The attempt proves a free-information benchmark, bounded-attention and seller-investment welfare reversals, and a simultaneous experimental regret certificate for finite rules. Full disclosure optimization still requires validated attention costs, seller and platform equilibrium responses, verified product characteristics, and welfare comparisons of actual feasible rules.

References

  • [farronato] C. Farronato (2025), Digital Platforms as Information Aggregators: Implications for their Design and Regulation, conference draft, Section 1.1, limited-attention discussion, PDF p. 5. Primary draft: https://conference.nber.org/confer/2025/DTs25/farronato.pdf. The finite examples and proofs above are self-contained and are not reported empirical findings from this draft.

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