Making Information More Valuable

Mark Whitmeyer

arxiv: 2210.04418 · v6 · submitted 2022-10-10 · 💰 econ.TH

Making Information More Valuable

Mark Whitmeyer This is my paper

Pith reviewed 2026-05-24 10:46 UTC · model grok-4.3

classification 💰 econ.TH

keywords value of informationconvexity of payoffposterior beliefsdecision theorymonopolistic screeningdelegationinformation acquisition

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The pith

A change makes information more valuable exactly when the agent's reduced-form payoff becomes more convex in her beliefs.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper shows that information becomes more valuable under a change to the decision problem if and only if that change makes the agent's reduced-form payoff more convex as a function of her posterior belief. This matters because the value of information comes from the gains the agent can achieve by tailoring actions to different possible beliefs, and greater convexity directly measures those gains. The result provides an if-and-only-if characterization that applies to any transformation of the problem. It is illustrated by a geometric condition for when adding an action increases information value, with natural extension to multiple actions, and applied to cases where information is sold by a monopolist and where a principal delegates with information acquisition.

Core claim

We prove that information becomes more valuable if and only if the agent's reduced-form payoff in her belief becomes more convex. When the transformation corresponds to the addition of an action, the requisite increase in convexity occurs if and only if a simple geometric condition holds, which extends in a natural way to the addition of multiple actions. We apply these findings to two scenarios: a monopolistic screening problem in which the good is information and delegation with information acquisition.

What carries the argument

The reduced-form payoff function that maps the agent's posterior belief to her expected payoff, with its degree of convexity determining the value of information.

Load-bearing premise

The agent's decision problem can be represented by a payoff that is a function solely of her posterior belief.

What would settle it

An example of a transformation of a decision problem that increases the value of information without making the reduced-form payoff more convex.

read the original abstract

We study what changes to an agent's decision problem increase her value for information. We prove that information becomes more valuable if and only if the agent's reduced-form payoff in her belief becomes more convex. When the transformation corresponds to the addition of an action, the requisite increase in convexity occurs if and only if a simple geometric condition holds, which extends in a natural way to the addition of multiple actions. We apply these findings to two scenarios: a monopolistic screening problem in which the good is information and delegation with information acquisition.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The paper gives a clean iff result: changes raise the value of information exactly when they make the reduced-form payoff more convex, plus a geometric test for adding actions.

read the letter

The main result is that information becomes more valuable if and only if the agent's reduced-form payoff v(μ) becomes more convex. This is an if-and-only-if link that follows from the standard representation of value of information as the expected gain under convex order on posteriors. The paper also gives a geometric condition that tells exactly when adding an action produces the required increase in convexity, and shows how the condition extends to multiple actions. The applications to a screening problem where the good is information and to delegation with information acquisition are direct and do not require extra machinery. These pieces are useful because they turn a comparison that used to be case-by-case into a check on convexity or a simple geometric test. The central assumption is that the decision problem admits a reduced-form payoff that depends only on the posterior belief. That is the usual setup in this literature, so the result applies cleanly inside that frame, but it would not cover transformations that break the representation. The abstract states the claims without visible gaps or circularity, and the stress-test logic on mean-preserving spreads and convex order holds up. This is for readers already working in information economics who need a tool to compare value of information across modified decision problems. A specialist thinking about screening or delegation models will get immediate use from the applications. It deserves a serious referee because the characterization is sharp, the geometric condition looks new, and the applications are relevant without overclaiming.

Referee Report

0 major / 3 minor

Summary. The paper proves that a transformation of an agent's decision problem increases the value of information if and only if the agent's reduced-form payoff function v(μ) over posterior beliefs μ becomes more convex. When the transformation is the addition of an action (or multiple actions), the required increase in convexity holds if and only if a stated geometric condition on the new action's payoffs is satisfied. The result is applied to a monopolistic screening problem in which the good sold is information and to a delegation setting with endogenous information acquisition.

Significance. If the central if-and-only-if characterization holds, the paper supplies a direct, decision-theoretic criterion for ranking the value of information across decision problems that builds on the standard representation v(μ) = max_a ∫ u(a, θ) dμ(θ) and the fact that any mean-preserving spread of posteriors is attainable. The geometric condition for action addition and the two applications to screening and delegation are concrete strengths. The result is parameter-free and derived from primitives without ad-hoc assumptions.

minor comments (3)

[§2] §2 (or wherever the reduced-form payoff is first defined): explicitly state the domain of v(μ) and confirm that the belief simplex remains unchanged after the transformation, as this is required for the convex-order comparison to be well-defined.
[§3] The geometric condition for adding an action (likely in §3) would benefit from a diagram or explicit coordinate example to illustrate the half-space or supporting-hyperplane interpretation.
[Application 1] In the screening application, clarify whether the monopolist's reduced-form payoff is computed before or after the buyer acquires information, to avoid ambiguity in the convexity comparison.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their supportive summary and recommendation of minor revision. No major comments were raised in the report.

Circularity Check

0 steps flagged

No significant circularity

full rationale

The paper's central claim is a standard if-and-only-if characterization: a transformation increases the value of information precisely when it increases the convexity of the reduced-form value function v(μ) = max_a ∫ u(a, θ) dμ(θ). This follows directly from the definition of the value of an information structure as E[v(μ)] − v(μ0) and the fact that any mean-preserving spread of posteriors is attainable; the equivalence to convex order is a direct consequence of these primitives and holds after any well-defined transformation of the decision problem. No load-bearing step reduces to a fitted parameter, self-citation chain, or definitional renaming. The derivation is self-contained against external decision-theoretic benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Based on abstract alone, the result rests on standard decision-theoretic axioms (Bayesian updating, expected utility) and the existence of a reduced-form payoff function; no free parameters, invented entities, or ad-hoc assumptions are mentioned.

axioms (1)

domain assumption The agent's payoff admits a reduced-form representation as a function of her posterior belief only.
Invoked to allow direct comparison of convexity across transformations.

pith-pipeline@v0.9.0 · 5589 in / 1101 out tokens · 17763 ms · 2026-05-24T10:46:07.450995+00:00 · methodology

Making Information More Valuable

Core claim

What carries the argument

Load-bearing premise

What would settle it

discussion (0)