Gregory Caldwell Beier
Susarb LLC, Cambridge, Massachusetts
March 2026
From a forthcoming book by Gregory Caldwell Beier.
(c) 2026 Gregory Caldwell Beier. Licensed under CC BY-NC-ND 4.0.
Grossman and Stiglitz (1980) proved that informationally efficient markets are impossible because efficiency destroys the incentive to produce information. Their proof rests on an assumption so foundational that the subsequent literature has never examined it: that trading profit is the sole return to information production. This paper relaxes that assumption. When economic agents can publish structured, timestamped, attributed judgments and accumulate track record capital - a portable professional asset whose value does not depend on whether the price has already moved - information flows into prices as a byproduct of career capital formation rather than trading. The contradiction falls away because the assumption that generated it turns out to be a modeling choice, not a logical necessity. A CARA-normal (constant absolute risk aversion, normally distributed signals) general equilibrium model with two markets and three agent types formalizes the resolution. In the augmented economy, a judgment market operates alongside the asset market, compensating agents for demonstrated calibration quality. The central result (Proposition 1) is that information production cannot fall below the disclosure channel's contribution regardless of how informative prices become: noise trading can collapse the trading channel entirely without disturbing the disclosure channel. Proposition 2 establishes a surprising equivalence - uninformed agents receive the same total scalar precision as in the standard Grossman-Stiglitz equilibrium, but the composition changes, with a portion now entering as structured public reasoning rather than through the noisy price signal. The augmented equilibrium weakly Pareto-dominates the original (Proposition 3), and the judgment market does not generate its own reflexive paradox because track record returns depend on supply and demand for calibration rather than on price informativeness (Proposition 4). Beyond the paradox resolution, the two-channel structure makes visible a relationship between competition and cooperation that the original framing concealed. Disclosers cooperate by sharing reasoning publicly; traders compete by transmitting that reasoning into prices. Neither channel functions without the other - together they produce a coordination system where information production and price efficiency reinforce each other instead of trading off. This competition-cooperation synthesis has a structural parallel in the open-source development model, a game-theoretic restatement as an equilibrium shift from Nash toward Pareto, and a suggestive thermodynamic analogy linking information preservation to reduced reconstruction cost. The paper develops the economic argument in full, specifies the formal model, identifies the transmission mechanism, presents the synthesis across four disciplines at different levels of formality, and derives testable predictions with identification strategies. This paper is the first demonstration that a single economic mechanism manifests simultaneously across economics, computer science, mathematics, and physics - a concrete instance of the unification that the Prolegomena to the Unification of Economics, Computer Science, Mathematics, and Physics proposes.
Keywords: information economics, Grossman-Stiglitz paradox, track records, disclosure, competition-cooperation synthesis, unification, open source, game theory, thermodynamics, information architecture
JEL Codes: D82, D83, G14, C72, D47
The impossibility result that Sanford Grossman and Joseph Stiglitz published in 1980 remains, forty-six years later, among the most consequential in financial economics. The logic is compact. If prices already reflect available information, paying to acquire that information yields no return - the price has already moved. But if nobody acquires information, there is nothing for prices to reflect. No equilibrium exists in which prices are both fully efficient and supported by costly information production.
What followed was a large literature exploring how markets manage this tension without resolving it. The concentration of informed and discretionary liquidity trading in the same periods, producing the intraday clustering of volume and volatility, was formalized by Admati and Pfleiderer (1988). Kyle (1985) worked out how a single informed trader optimally exploits private signals through strategic order sizing, and Vives (2008) developed the broader microeconomics of how competitive markets aggregate diverse information. The concept of noise trading - Black's (1986) term for the uninformed liquidity that sustains informed traders' incentive to acquire information - became central to the literature's resolution strategy. On the disclosure side, the unraveling logic of Grossman (1981) and Milgrom (1981) showed why firms might voluntarily disclose, and Milgrom and Roberts (1986) extended this to strategic settings where competition among senders can force full revelation even when each would prefer to conceal bad news. (The Disclosure Incentive operates on a different margin: unraveling explains why agents reveal what they already know, while the mechanism proposed here explains why agents would produce new information in the first place. The two are complementary - once a critical mass of participants adopts the disclosure framework, Milgrom-Roberts unraveling pressure accelerates further adoption.) Verrecchia (1983) and Dye (1985) formalized the conditions under which voluntary disclosure is partial. The link between disclosure and financing costs was established by Diamond and Verrecchia (1991), who showed that firms making more information public narrow the gap between insider and outsider knowledge, reducing adverse selection and hence the cost of capital. Crawford and Sobel's (1982) foundational model of strategic communication is also relevant here, though the Disclosure Incentive differs from cheap talk in two respects: proper scoring aligns the sender's payoff with honest reporting, and disclosures are verified against outcomes rather than taken on trust.
One assumption has survived every proposed resolution. The original paper built it into the model's structure rather than stating it, and no subsequent work has extracted it for examination: that the return to information production about asset values is captured exclusively through trading on those assets. The entire literature takes this for granted. It functions as a background condition of the research program, not as a proposition anyone has thought to test.
This paper questions that assumption by identifying a second incentive channel. Under the Disclosure Incentive, the return to information production accrues not through trading profit but through track record capital - a portable, compounding professional asset built by publishing structured judgments that are verified against outcomes over time. Because the track record measures judgment quality rather than trading timing, its value does not depend on whether the price has already adjusted. Information production becomes decoupled from trading, and information flows into prices as a byproduct of career capital formation.
What the paradox concealed, by limiting the model to competitive agents, is a structural relationship between competition and cooperation. The Grossman-Stiglitz framework contains only traders seeking private profit from private information; in that world, efficiency and information production necessarily trade off. Adding a cooperative channel - agents who share reasoning publicly and are compensated through demonstrated quality rather than secrecy - changes the equilibrium. Disclosers produce information and traders transmit it into prices, with each group compensated through a different mechanism. The two channels depend on each other in a way that the original framing, by excluding one of them, made impossible to observe.
The same synthesis of competition and cooperation appears, at different levels of formality, in computer science (the open-source development model), in mathematics (a game-theoretic equilibrium shift), and in physics (a thermodynamic analogy linking signal compression to reconstruction cost). The paper develops each manifestation and argues that they reflect a single structural pattern visible from four disciplinary directions.
The paper proceeds as follows. Section 2 restates the paradox and isolates its core assumption. Section 3 introduces track record capital and the Disclosure Incentive. The formal model occupies Section 4, which proves four propositions characterizing the augmented equilibrium in a CARA-normal framework with two markets and three agent types. Section 5 addresses the transmission mechanism - how disclosed information enters prices when the discloser does not trade. The competition-cooperation synthesis is developed in Section 6 and traced across four disciplines in Section 7. Section 8 applies the framework to externality pricing. Testable predictions with identification strategies appear in Section 9. Limitations are discussed in Section 10, and Section 11 concludes.
Consider a market with two types of agents: informed agents who pay cost c to observe a signal s about the asset's fundamental value v, and uninformed agents who observe only the market price p. If the price is fully revealing - if p is a sufficient statistic for s - then informed agents cannot earn returns in excess of c. Their expected profit from trading on their information is zero net of acquisition costs. But if the expected profit is zero, no rational agent will pay c to become informed. And if no agent becomes informed, the price carries no information about v.
Grossman and Stiglitz (1980) showed that for any positive cost c > 0, there exists no equilibrium in which prices are fully informationally efficient. The result struck directly at the efficient markets hypothesis (Fama, 1970), transforming it from a maintained assumption into a proposition requiring defense (LeRoy, 1989). Grossman (1976) had already shown that competitive markets with diverse information produce fully-revealing rational expectations equilibria; the 1980 paper demonstrated that this conclusion is inconsistent with costly information acquisition. The market settles into a noisy rational expectations equilibrium (Radner, 1979; Hellwig, 1980) in which prices are partially but never fully revealing, and a fraction of agents find it profitable to become informed because the noise in prices preserves their informational advantage.
The assumption this paper isolates is:
Assumption GS: The return to information production is captured exclusively through trading profit in the asset whose value the information concerns.
This assumption is never stated in the original paper because it is built into the model's structure. Agents have two choices: pay c and trade on the signal, or do not pay c and trade on the price. There is no third option. The model contains no mechanism through which an agent could profit from producing information other than by trading on it.
Every subsequent resolution has preserved Assumption GS. Black's (1986) noise trader resolution works because noise traders provide the liquidity against which informed traders extract profit. Kyle's (1985) strategic trading model studies how informed agents optimally exploit their information through trading. Sims's (2003) rational inattention framework reconceptualized the problem of information processing: economic agents have finite cognitive bandwidth, and the decision of what to attend to is itself shaped by the expected return to attention. Sims applied this to consumption and macroeconomic decisions rather than financial trading, but the implication for the Grossman-Stiglitz literature is direct: even when information is available, agents cannot process all of it, and the allocation of attention is itself an economic choice shaped by returns. The literature has treated those returns as trading returns.
The claim that the literature has never examined non-trading returns to information production requires careful engagement, because several bodies of prior work have considered them. The deepest challenge comes from Hirshleifer (1971), who showed - nine years before Grossman-Stiglitz - that the private value of information captured through trading diverges sharply from its social value. Trading profits transfer wealth between participants rather than creating it, which means trading profit was never the socially optimal way to compensate information production. The Disclosure Incentive addresses this deeper problem, not just the narrower one that trading profit approaches zero under efficiency. Among the partial decouplings already in the literature, Admati and Pfleiderer (1986) come closest to the present paper's territory: they model agents who profit from selling information rather than trading on it, demonstrating that information markets and asset markets can coexist. Their seller, however, maximizes revenue by degrading signal quality before sale to prevent buyers from free-riding. Real-world institutions have long compensated information production outside the trading channel - sell-side research analysts earn fees, credit rating agencies earn subscription revenue, financial data providers sell access - but all of these compress the judgment they carry into institutionally filtered outputs. The career-concerns literature is also relevant. Hong and Kubik (2003) found that analysts producing more accurate forecasts receive better career outcomes, a mechanism strikingly close to track record capital, and Ottaviani and Sorensen (2006) formalized how the desire to appear well-informed distorts forecast behavior. The most direct predecessor to the two-channel architecture proposed here is Garcia and Sangiorgi (2011), who analyze a market where information selling and strategic trading coexist in equilibrium, with distinct effects on price informativeness; their model admits multiple compensation channels but treats the information sold as a raw signal rather than structured judgment with a track record mechanism. For the broader landscape, Goldstein and Yang (2017) survey the feedback between price informativeness, real decisions, and information production. What distinguishes the present paper from all of these is developed in Section 3, after the formal structure of the Disclosure Incentive has been specified.
Track record capital is the cumulative, publicly observable record of an agent's structured judgments verified against outcomes over time.
An agent i publishes a sequence of structured judgments {J_i1, J_i2, ..., J_iT} at times t = 1, 2, ..., T. Each judgment contains: the evidence consulted (Input), the analytical method employed (Method), the conclusion reached (Output), the identity of the agent (Identity), and the agent's assessment of what happens when the relevant conditions change at scale (Scaling). At some subsequent time t + k, the outcome is observable. The agent's calibration - the correspondence between stated confidence levels and observed frequencies (Dawid, 1982) - is measured using a proper scoring rule (Brier, 1950; Gneiting and Raftery, 2007), a scoring function with the property that an agent maximizes their expected score by reporting their true beliefs. The track record is the cumulative calibration score across all published judgments.
The five-field structure requires justification. Input, Method, and Output formalize the epistemic content of any analytical judgment - they are the standard decomposition of an inference into evidence, reasoning, and conclusion. Removing any of the three leaves a disclosure that cannot be meaningfully evaluated. An output without method is bare assertion; method without input amounts to speculation; and input that leads to no stated conclusion is raw data with no analytical content. Identity enables verification and track record accumulation - without attribution, no scoring is possible, and the incentive mechanism collapses. These four fields are individually necessary for the Disclosure Incentive to function. Scaling is the non-obvious addition. It forces the discloser to articulate interaction effects across agents and across time - the dimension most likely to contain information that scalar prices compress away. A fund manager's assessment of a single firm's water usage is Input-Method-Output. The same manager's assessment of what happens to aquifer levels when five operators in the same watershed simultaneously increase extraction at the rates their current trajectories imply is Scaling. It is the field that captures the constraint reasoning that the price system structurally cannot carry, because prices aggregate individual transactions without preserving the interaction structure among them. Whether a sixth field would add something essential is an empirical question this paper does not foreclose - the schema is open by design - but these five are jointly sufficient to preserve the information that the price signal destroys and individually necessary for the track record mechanism to operate.
The track record is portable - it belongs to the agent rather than to any employer - and it compounds, since each verified judgment adds precision to the calibration estimate. It is also non-replicable retroactively: an agent who begins building a record at time t holds a permanent advantage over one who begins at t + 1, a compounding dynamic Merton (1968) named the Matthew Effect - building on his earlier work on scientific priority (Merton, 1957) - in which early advantage in demonstrated quality attracts further opportunities that reinforce the advantage. Tetlock (2005) and Tetlock and Gardner (2015) established that expert judgment quality varies enormously and is measurable through track records, but did not formalize the economic incentive structure that would cause agents to voluntarily build such records. This paper provides that formalization.
With the five-field structure now specified, what distinguishes this paper from the prior work surveyed in Section 2 can be stated precisely. The point is not that non-trading incentives for information production have never been considered - they have. The point is that every existing partial decoupling operates within an institutional structure that compresses the judgment it carries, and none identifies a mechanism through which disclosure improves judgment quality over time. Admati-Pfleiderer's information seller degrades signal quality before sale. Sell-side analysts produce reports filtered through institutional conflicts of interest and compressed into price targets; rating agencies compress multidimensional assessment into letter grades. The career reward Hong and Kubik documented operates through employer promotion decisions, making it non-portable and institutionally contingent rather than publicly verifiable. Against all of these, the Disclosure Incentive differs in five respects that are now concrete rather than abstract. The disclosure carries the full five-field structure (Input, Method, Output, Identity, Scaling) rather than being compressed into a price target or letter grade. Scoring is proper in the technical sense - it rewards calibration rather than consensus, aligning the discloser's payoff with honest reporting. The record belongs to the agent across institutional affiliations, making it portable in a way that Hong and Kubik's career reward, which operates through employer promotion decisions, is not. The ontology is open: the discloser defines the domain of analysis rather than inheriting it from an employer's coverage universe. And most importantly, the disclosure discipline improves the judgment itself over time rather than merely making existing quality visible to an audience. Taken together, these properties produce a full decoupling of information production from both trading profit and institutional affiliation - and an improvement mechanism that no prior model contains.
Track record capital accumulation, rather than trading profit, is the return channel that defines the Disclosure Incentive.
To see how the mechanism works, consider an agent who observes signal s about the fundamental value of some economic variable. Under Assumption GS, trading on s is the only way to capture a return on the investment in acquiring it. The Disclosure Incentive opens a second path: the agent publishes a structured judgment based on s, waits for the outcome, and allows the track record to update. Where this return accrues matters. It is captured in the labor market, the consulting market, the capital allocation advisory market - anywhere demonstrated judgment quality commands a premium. Because the track record measures judgment quality rather than trading timing, the return does not depend on the asset price. A well-calibrated judgment published after the price has moved is worth exactly as much to the track record as one published before, so long as it was timestamped before the outcome was known. This independence from price efficiency is the property that breaks the paradox.
The crowding-out concern raised by Benabou and Tirole (2006) deserves engagement here. Their framework identifies two channels through which external rewards can backfire: the reward may be read as evidence that the task is unpleasant, undermining intrinsic motivation; and when effort has multiple dimensions, agents may redirect energy toward whichever dimension is measured. The Disclosure Incentive is less exposed to these channels than standard performance pay. Calibration quality - the correspondence between stated confidence and outcomes - is not a proxy for the intrinsic objective of good analytical reasoning; it is that objective, directly measured. And because the reward accrues through a public record rather than a private bonus, it engages reputational motivation, which Benabou and Tirole's own analysis identifies as less susceptible to crowding-out than purely pecuniary incentives. The concern nonetheless has force at the margin: agents might optimize for narrow calibration metrics while neglecting broader analytical depth. The five-field format limits this by scoring the reasoning path, not just the conclusion. Whether that limitation is complete remains an empirical question.
This independence from price efficiency is what resolves the paradox. Under Assumption GS, information production becomes worthless as the price approaches full efficiency. The Disclosure Incentive decouples the return from price efficiency entirely, because the return accrues in a different market - the judgment market - where the relevant variable is calibration quality, not trading timing.
Several existing concepts in economics might appear to capture what track record capital does, but none of them does. Becker's (1964) human capital is accumulated through training and experience; track record capital is not. Two analysts with identical education and experience can have dramatically different track records, because the record measures calibration - the correspondence between stated confidence and observed outcomes - which is a property of the agent's judgment process rather than of their credentials. The distinction from Spence's (1973) signaling is equally sharp. A costly signal communicates an unobservable type indirectly; a track record is a direct, verified measurement of the variable that matters. The agent does not invest in an expensive credential to signal competence - the track record is the credential, verified against reality rather than against an institutional standard.
The relationship to reputation requires more careful treatment. In the Kreps-Wilson (1982) and Holmstrom (1999; circulated as a working paper from 1982) frameworks, reputation is inferred from noisy behavioral signals, and career concerns distort behavior in predictable ways. Scharfstein and Stein (1990), building on his framework, showed that these concerns create incentives to conform - the career cost of an independent judgment that turns out wrong exceeds the career benefit of an independent judgment that turns out right, so managers gravitate toward consensus positions regardless of their private signals. Chevalier and Ellison (1999) documented the empirical counterpart: the shape of the flow-performance relationship facing mutual fund managers distorts their portfolio decisions, with underperforming managers tilting toward higher-variance strategies because the career payoff is convex in recent returns. Their finding confirms that career incentives shape information production behavior in precisely the way the Disclosure Incentive proposes to redirect - but through institutional promotion decisions rather than a portable public record, which means the incentive is for institutional conformity rather than calibration quality. Trueman (1994) formalized the complementary distortion among sell-side analysts: analysts issue forecasts to signal private information, but the career reward is for appearing well-informed rather than for being well-calibrated, which produces herding toward consensus even when the analyst's private signal diverges. The proper scoring rule in the Disclosure Incentive is designed precisely to break this herding - it rewards the correspondence between stated confidence and outcomes, not proximity to consensus. Under track record scoring with proper scoring rules, agents have incentive to be well-calibrated rather than conformist. Honest assessment is the dominant long-run strategy under standard conditions - a single agent reporting forecasts scored by a proper scoring rule without selection over which forecasts to publicize and without information about others' reports (DeGroot and Fienberg, 1983). The practical qualifications to this result, including strategic selection and coordinated manipulation, are addressed in Section 10. The foundational results on proper scoring rules trace to Good (1952), who derived them from rationality axioms, and Savage (1971), who provided the axiomatic characterization connecting scoring rules to subjective probability elicitation. Fama (1980) originated the career-concerns framework that Holmstrom formalized, arguing that the labor market itself constrains managerial behavior because managers know their current performance shapes their future employment terms - the logic that track record capital specifies and makes verifiable.
Dewatripont, Jewitt, and Tirole (1999) showed that career concerns in multitask settings distort effort allocation: agents channel disproportionate effort toward activities whose results are observable to evaluators, starving activities whose outcomes are harder to attribute. The Disclosure Incentive introduces a new visible task - structured judgment disclosure - alongside the existing tasks of portfolio management, client service, and internal reporting. The concern is that agents will reallocate effort toward disclosure at the expense of these other functions. Two features of the framework limit this distortion. The track record scores outcomes, not effort - an agent who produces disclosures of low calibration quality loses rather than gains from the additional visibility. And the five-field structure requires articulation of reasoning, not merely prediction, which constrains agents from treating disclosure as a performative exercise detached from their analytical process. The multitask distortion is real in principle, and monitoring for it is part of the institutional design challenge that accompanies adoption.
The most important property of track record capital - and the one that distinguishes the Disclosure Incentive from all prior models of reputation, career concerns, and information selling - is that the act of structured disclosure improves the quality of the discloser's judgment over time. The mechanism is not signaling in any conventional sense; it does not reveal existing quality to an audience. Rather, the discipline of articulation, verification, and iterative learning generates better quality as a consequence of the disclosure process itself.
Consider a fund manager who begins disclosing structured sustainability reasoning with every capital allocation decision. The first disclosure forces articulation of reasoning that was previously implicit - assumptions about resource constraints, scaling trajectories, and interaction effects that informed the decision but were never stated. The act of stating them exposes gaps. The verification against outcomes reveals which reasoning patterns predict well and which do not. The public record creates accountability that private reasoning does not. Over successive cycles, the manager's sustainability reasoning improves because the disclosure discipline - articulate, publish, score, learn, repeat - is itself a training process for better judgment.
What results is not merely a stronger reputation but a genuinely more skilled investor. After five years of disclosing and being scored on sustainability reasoning, the fund manager makes better capital allocation decisions than a manager of equivalent experience who has not gone through that process, because the disclosure cycle trained the judgment driving the decisions. The track record reflects improved quality rather than simply revealed quality, and capital flows toward this manager for that reason - the track record was the mechanism through which the ability developed, not a window onto ability that existed independently.
This creates a positive externality that compounds. Better-informed capital allocation produces better outcomes for the companies funded, the communities affected, and the constraint environment - aquifers, grids, ecosystems - that the sustainability reasoning addresses. The disclosure discipline generates a better risk-reward profile for the capital under management, and the improved allocation produces benefits extending far beyond the manager's portfolio. Dasgupta and David (1994) showed that the scientific priority system produces a similar externality: scientists disclose findings to build reputational capital, and the disclosed knowledge generates social returns that vastly exceed the private career benefit. Stephan (1996) surveyed the economics of this system comprehensively, documenting how scientists are compensated through recognition and priority rather than market returns. The Disclosure Incentive proposes to engineer the same structure in financial markets, with the additional property that the private benefit includes improved judgment quality alongside improved reputation - a feature the scientific priority system lacks because publication does not formally score the scientist's predictions against outcomes.
This improvement mechanism extends to every domain where structured disclosure is practiced. A teacher who discloses pedagogical reasoning and is scored against student outcomes develops sharper instructional judgment over time. The same logic applies to engineers disclosing infrastructure assessments that are later checked against structural performance, or to farmers whose aquifer observations are scored against depletion measurements - in each case the disclosure is generating better judgment through the discipline of articulation and verification, not extracting value from judgment the practitioner already possessed.
The improvement claim requires a qualification rooted in the conditions under which feedback actually works. Kahneman and Klein (2009) established that feedback improves judgment reliably only in what they termed "high-validity environments" - domains where the relationship between observable cues and eventual outcomes is regular enough that a practitioner can learn to read the cues correctly through repeated exposure. In low-validity environments, where outcome feedback is noisy, delayed, or decoupled from the judgment, feedback produces confident but uncalibrated practitioners rather than genuine expertise. Long-horizon financial judgment - constraint reasoning about aquifers, atmospheric carbon budgets, infrastructure resilience - is precisely the kind of domain where natural feedback is delayed and noisy. The Disclosure Incentive's structured timestamping, proper scoring, and explicit confidence levels are designed to engineer a high-validity feedback environment in a domain where the natural environment lacks one. This is the mechanism through which disclosure can improve judgment quality even in domains where unstructured experience does not - and it explains why decades of institutional experience in financial services have not produced the calibration improvements that the Disclosure Incentive predicts, consistent with Einhorn's (1980) finding that experience without structured outcome feedback does not improve and may worsen judgment through confirmation bias and selective memory.
The experimental evidence that structured probabilistic feedback does improve calibration is established. Lichtenstein and Fischhoff (1980) showed that subjects who received explicit feedback comparing their stated confidence levels to observed outcome frequencies became measurably better calibrated in subsequent tasks - the direct experimental demonstration of the improvement mechanism proposed here. The cognitive science framework explaining why this works is Ericsson, Krampe, and Tesch-Romer's (1993) theory of deliberate practice, which identifies the conditions under which repeated performance produces genuine skill improvement rather than mere experience accumulation. The theory predicts that improvement occurs when the practitioner faces a structured task, receives unambiguous outcome feedback, and encounters enough iterations to detect and correct systematic errors. The Disclosure Incentive's institutional design maps onto each of these conditions: the five-field structure imposes task structure on what would otherwise be unstructured analytical reasoning; proper scoring delivers outcome feedback that is unambiguous by construction; the rolling disclosure cadence generates the iteration frequency; and the public record creates accountability for error correction that private reasoning cannot provide. The improvement mechanism, then, is a specific institutional implementation of deliberate practice applied to probabilistic judgment in financial markets - a domain where the natural conditions for deliberate practice are absent and must be engineered - rather than a metaphorical appeal to the practice literature.
Consider an economy with a single risky asset paying terminal value v at date 2, where v is drawn from N(v-bar, tau_v^{-1}), with tau_v denoting the precision of the prior. A riskless asset has zero net return. The total supply of the risky asset is normalized to zero. The setup extends the CARA-normal noisy rational expectations framework of Grossman and Stiglitz (1980) and Diamond and Verrecchia (1981) by adding a third agent type - the discloser - alongside the informed traders and uninformed agents of the standard model.
A continuum of agents indexed on [0,1] have CARA utility with common risk aversion coefficient gamma. Noise traders submit random demand u drawn from N(0, tau_u^{-1}), independent of v and all other random variables.
At date 0, each agent i chooses one of three types:
Uninformed (U): pays no cost, observes no signal.
Trader (T): pays cost c > 0, privately observes signal s_i = v + epsilon_i, where epsilon_i is drawn from N(0, tau_epsilon^{-1}), independent across agents. Trades on private information.
Discloser (D): pays cost c > 0, observes signal s_i = v + epsilon_i, publishes s_i immediately, and earns track record return from the judgment market. The discloser's signal becomes public upon publication.
Let lambda_T and lambda_D denote the fractions choosing T and D respectively, with lambda_T, lambda_D >= 0 and lambda_T + lambda_D <= 1.
The timing is:
Date 0: Agents choose type.
Date 1: Disclosers simultaneously publish their signals. All agents observe the aggregate disclosure. The asset market clears and price p is determined. Disclosers receive their track record return.
Date 2: Asset pays v.
When lambda_D > 0, the published signals {s_j : j in D} are publicly observable. In the continuum, the aggregate disclosure statistic
d-bar = (1/lambda_D) integral_{j in D} s_j dj = v + eta
where eta is drawn from N(0, (lambda_D * tau_epsilon)^{-1}), provides a sufficient statistic for the disclosed signals with precision tau_D = lambda_D * tau_epsilon.
After disclosure, the public precision (prior plus disclosure) is:
tau_pub = tau_v + tau_D = tau_v + lambda_D * tau_epsilon
This is the precision available to every agent - uninformed, trader, and discloser - before the price is observed. It exceeds the prior precision tau_v whenever lambda_D > 0.
Given the public information, the economy reduces to a standard Grossman-Stiglitz problem with effective prior precision tau_pub and fraction lambda_T of informed traders.
Each trader's private information, conditional on the public disclosure, has precision tau_epsilon (the trader's individual signal adds tau_epsilon beyond the public set). Each discloser's own signal is already in the public set, so disclosers have no residual private information for trading purposes.
Following Grossman and Stiglitz (1980) and Hellwig (1980), we conjecture a linear rational expectations equilibrium in which the price is a linear function of the aggregate informed demand and the noise:
p = P(lambda_T * (aggregate trader signal) + u; tau_pub)
The price signal provides uninformed agents with precision tau_p(lambda_T) about v beyond what tau_pub already reveals. The standard properties hold: tau_p(0) = 0, tau_p is strictly increasing in lambda_T, and tau_p is increasing in tau_u. The convention throughout is that tau_u denotes the precision of noise trading: higher tau_u means lower noise variance, which makes prices more informative and increases tau_p.
The posterior precision for each agent type is:
Trader: tau_T = tau_pub + tau_p(lambda_T) + tau_epsilon
Uninformed/Discloser: tau_U = tau_pub + tau_p(lambda_T)
In the CARA-normal framework, the certainty-equivalent benefit of becoming an informed trader (the trading profit) is determined by the ratio of posterior precisions. The indifference condition for the marginal trader is:
Phi(lambda_T, tau_pub) = exp(2 * gamma * c)
where Phi(lambda_T, tau_pub) = (tau_pub + tau_p(lambda_T) + tau_epsilon) / (tau_pub + tau_p(lambda_T))
This is the Grossman-Stiglitz indifference condition, modified only in that tau_pub replaces tau_v. The function Phi is strictly decreasing in lambda_T (more traders make the price more informative, reducing the marginal trader's advantage) and strictly decreasing in tau_pub (better public information reduces the marginal value of a private signal).
The track record return captures the market value of demonstrated judgment quality. A judgment market operates alongside the asset market: principals (employers, capital allocators, institutional clients) hire or allocate capital to agents based on demonstrated calibration.
Let r-bar_D(lambda_D) denote the expected track record return per discloser when the fraction of disclosers is lambda_D. We impose four assumptions:
(J1) r-bar_D is continuous and strictly decreasing on [0,1]: more disclosers increases supply in the judgment market, reducing the per-discloser premium.
(J2) r-bar_D(0) > c: when no agent is disclosing, the first entrant earns a return exceeding information cost. This holds whenever demonstrated calibration commands any premium in a world where calibration is unobserved. The condition is empirically grounded: global spending on financial market data and news alone reached a record $44.3 billion in 2024 (Burton Taylor Consulting, 2025), confirming that capital markets already pay at scale for information about asset values. The Disclosure Incentive predicts that a fraction of this expenditure will shift from reconstructed information to disclosed judgment as track record infrastructure develops.
(J3) r-bar_D(1) < c: if all agents disclose, the judgment market premium is competed below cost. This rules out corner solutions and is the natural analog of diminishing returns.
(J4) r-bar_D(lambda_D) is independent of price efficiency: the judgment market compensates calibration quality, not trading timing. Whether the asset price has already adjusted to reflect the discloser's signal is irrelevant to the track record score.
Assumption J4 is the crux of the resolution. It formalizes the paper's central insight: that the return to disclosure operates in a different market from the return to trading, and the reflexive structure that generates the Grossman-Stiglitz paradox - information production improves price efficiency, which destroys the return to information production - does not apply to the judgment market.
By J1-J3 and the intermediate value theorem, there exists a unique lambda_D* in (0,1) such that:
r-bar_D(lambda_D*) = c
This is the judgment market equilibrium. Agents with calibration quality above the marginal cutoff disclose; those below do not.
The equilibrium of the augmented economy is a pair (lambda_T*, lambda_D*) satisfying:
Condition 1 (Judgment market clearing): r-bar_D(lambda_D*) = c
Condition 2 (Trader indifference): Phi(lambda_T*, tau_v + lambda_D* * tau_epsilon) = exp(2 * gamma * c)
The equilibrium is determined sequentially. Condition 1 pins down lambda_D* independently of the asset market (by J4, the track record return does not depend on lambda_T or on price informativeness). Given lambda_D*, Condition 2 determines lambda_T* as in the standard Grossman-Stiglitz framework, but with the augmented public precision tau_pub = tau_v + lambda_D* * tau_epsilon.
The sequential structure is a direct consequence of J4: the judgment market clears first, and the asset market adjusts to the information environment that the judgment market creates.
Existence and uniqueness. Under J1-J4 and the standard regularity conditions of the Grossman-Stiglitz framework (CARA utility, normal distributions), existence and uniqueness follow from: (a) the intermediate value theorem guarantees a unique lambda_D* satisfying Condition 1; (b) given lambda_D*, the standard Grossman-Stiglitz existence argument (their Theorem 1) guarantees a unique lambda_T* satisfying Condition 2 for the effective prior tau_pub.
We now state and prove the central result.
Proposition 1 (Resolution). In the augmented economy, information production is bounded below by lambda_D* > 0 regardless of noise trading intensity. The Grossman-Stiglitz impossibility - that fully efficient prices are inconsistent with costly information production - does not hold.
Proof. The Grossman-Stiglitz paradox proceeds as follows. In the pure-trading economy (lambda_D = 0), the trader indifference condition Phi(lambda_T, tau_v) = exp(2 * gamma * c) determines lambda_T*. As tau_u increases (noise variance decreases), the price becomes more informative for any given lambda_T, which reduces the trading advantage. In the limit, tau_p(lambda_T) grows large even for small lambda_T, so Phi approaches 1 from above for any lambda_T > 0. Since exp(2 * gamma * c) > 1 for c > 0, the indifference condition forces lambda_T* toward zero. Information production collapses as the price becomes more efficient. This is the paradox.
In the augmented economy, lambda_D* is determined by Condition 1 independently of tau_u. As tau_u increases and tau_p grows large, the same logic pushes lambda_T* toward zero. But lambda_D* is unaffected. Total information production lambda_T* + lambda_D* >= lambda_D* > 0 for all values of tau_u.
Moreover, the disclosure channel transmits information into the public domain without reliance on noise trading. The public precision tau_pub = tau_v + lambda_D* * tau_epsilon exceeds the prior tau_v regardless of whether any traders participate. Information enters the price system through the public channel (disclosure) even when the private channel (trading) is unprofitable.
The paradox required that the sole incentive for information production (trading profit) vanishes as prices become efficient. With a second incentive (track record return) that is independent of price efficiency (J4), the sole-incentive premise fails, and the contradiction does not arise. QED.
Proposition 2 (Informational equivalence and compositional improvement). The augmented equilibrium has the same total information available to uninformed agents as the standard Grossman-Stiglitz equilibrium, but the composition of information differs in a way that is economically significant.
Proof. In both equilibria, the trader indifference condition equates the same ratio. In the standard economy:
Phi(lambda_GS*, tau_v) = exp(2 * gamma * c)
In the augmented economy:
Phi(lambda_T*, tau_v + lambda_D* * tau_epsilon) = exp(2 * gamma * c)
Both conditions require:
tau_epsilon / (tau_pub + tau_p) = exp(2 * gamma * c) - 1
where the right side is the same constant. Therefore:
tau_v + tau_p(lambda_GS*) = tau_v + lambda_D* * tau_epsilon + tau_p(lambda_T*)
which gives:
tau_p(lambda_GS*) = lambda_D* * tau_epsilon + tau_p(lambda_T*)
Total uninformed precision is the same: tau_v + tau_p(lambda_GS*) = tau_v + lambda_D* * tau_epsilon + tau_p(lambda_T*). The trader indifference condition endogenously adjusts lambda_T* downward to maintain the marginal trader's informational advantage.
The compositional difference is: in the augmented economy, a portion lambda_D* * tau_epsilon of the total information enters the public domain directly as structured reasoning, while in the standard economy, all information enters through the noisy price channel. The disclosed information is observable in its full dimensionality - Input, Method, Output, Identity, Scaling - while the price signal is a scalar compression. QED.
The compositional difference has three consequences that fall outside the CARA-normal framework but are economically material. First, structured disclosure preserves reasoning that the price compresses away - an agent who reads the disclosed judgment learns not only the conclusion but the analytical path, enabling evaluation and learning that the price does not support. Second, disclosed information is available immediately upon publication, while trading transmits information into prices with the delay inherent in the noisy aggregation process. Third, the disclosed information is attributed, which enables the track record scoring that sustains the judgment market. None of these properties appears in the scalar precision comparison, but all three matter for the quality of the information environment.
Proposition 3 (Pareto improvement). The augmented equilibrium weakly Pareto-dominates the Grossman-Stiglitz equilibrium, and strictly dominates for disclosers.
Proof sketch. Uninformed agents achieve the same posterior precision in both equilibria (Proposition 2) and therefore the same expected utility from trading. Traders achieve the same expected utility by indifference (their trading profit net of cost is equalized in equilibrium). Disclosers achieve expected utility equal to that of traders (both types are indifferent at the margin), but through the track record channel rather than the trading channel - and disclosers who are inframarginal (with calibration quality above the cutoff) earn strictly positive rents. Additionally, all agents benefit from the compositional improvement (access to structured reasoning rather than only the price signal), though this benefit is not captured in the CARA-normal welfare calculation. QED.
There is a potential objection rooted in the public information literature. Morris and Shin (2002) showed that increasing the precision of public information can reduce welfare when agents have coordination motives, because the public signal becomes a focal point that agents follow at the expense of their own private assessments - even when those private assessments are collectively more informative. If disclosed information functions as a public signal in their sense, then increased disclosure precision (higher tau_pub) could induce the overweighting pathology and reverse the Pareto improvement. The Morris-Shin result does not apply here for two reasons. First, in the CARA-normal framework of Section 4, agents are price-takers with no coordination motive - they maximize individual expected utility against the price, not against each other's actions. The Morris-Shin pathology requires a beauty-contest payoff structure where agents want to match each other's actions, which is absent from the Grossman-Stiglitz setting. Second, the compositional improvement identified in Proposition 2 works against the overweighting concern rather than reinforcing it: the five-field disclosure structure preserves the analytical reasoning behind the conclusion, which enables agents to evaluate and critically assess the public signal rather than treating it as a focal point for coordination. Compressed public signals invite overweighting precisely because they provide no basis for independent evaluation. Structured disclosures provide that basis. The Morris-Shin concern is real in settings with coordination motives and compressed public signals; the Disclosure Incentive's institutional design addresses both conditions.
Proposition 4 (No judgment market paradox). The judgment market does not generate a reflexive paradox analogous to Grossman-Stiglitz.
Proof. The Grossman-Stiglitz paradox has a specific reflexive structure: information production increases price efficiency, which reduces the return to information production (trading profit), which reduces information production. The feedback loop generates the impossibility.
In the judgment market, the analog would require: disclosure increases the supply of calibrated judgment, which reduces the track record return, which reduces disclosure, which reduces the supply of calibrated judgment. This is a standard supply-demand adjustment, not a paradox. It has a stable interior equilibrium at lambda_D* where r-bar_D(lambda_D*) = c, determined by J1-J3.
The reflexive structure is absent because track record return does not depend on the information content of the price - it depends on the supply and demand for demonstrated calibration in the judgment market. No analog of the efficiency-destroys-incentive loop exists. The judgment market is a conventional labor/reputation market with diminishing returns, not a reflexive information-aggregation market.
An additional consideration strengthens this result. Tetlock (2005) established that calibration quality has large and persistent cross-sectional variance: even among trained forecasters with equivalent access to information, the best-calibrated agents dramatically outperform the median. This means that even when lambda_D is large, top-calibrated disclosers retain a scarce skill premium. The judgment market does not collapse to zero returns for all participants when entry increases - it develops a skill gradient, as labor markets generally do. QED.
Several comparative statics follow directly from the equilibrium conditions.
A decrease in noise trading variance (higher tau_u) pushes lambda_T* toward zero without affecting lambda_D*. This is the comparative static that most directly illustrates the resolution: the limiting case that destroys the trading channel leaves the disclosure channel intact.
An increase in the track record return function (r-bar_D shifts up) raises lambda_D*, which raises tau_pub, which lowers lambda_T*. More disclosure crowds out some trading, but total information production increases and a larger share of information enters the public domain through the cooperative channel.
An increase in information cost c reduces both lambda_D* and lambda_T*. But the relative resilience differs: the trading channel becomes fragile as c approaches the maximum trading profit, while the disclosure channel survives as long as the judgment market premium exceeds c for some agents.
An increase in the demand for demonstrated calibration (the principals' side of the judgment market grows) shifts r-bar_D up, raising lambda_D* and expanding the cooperative channel. The prediction is that growth in the advisory, consulting, and capital allocation sectors - sectors that value demonstrated judgment - will expand the disclosure equilibrium.
If the discloser publishes rather than trades, how does the disclosed information find its way into the price?
Not through the discloser's own trading activity. What the discloser produces is a public good - structured, calibrated reasoning about the constraint environment - and the price moves only when other participants act on it. Traders read the disclosed reasoning, weigh it against their own analysis, and those who find it valuable express that assessment through their order flow. The price adjusts as a consequence of trading activity that the disclosure informed but did not itself generate. Track record capital compensates the discloser for producing the reasoning; trading profit compensates the traders who carried it into the price.
The transmission chain runs from publication through evaluation to trading: a structured judgment enters the public domain, market participants assess it, and the subset that finds it decision-relevant translates it into positions. Section 6 develops the complementarity structure in full. For the transmission mechanism, the essential point is that the two channels divide the labor of information production and price transmission between different agents with different compensation, and neither channel can perform the other's function.
There is a speed problem worth confronting. If a discloser publishes a well-calibrated judgment openly and instantly, algorithmic traders will parse and price it in milliseconds, driving trading profit toward zero for everyone - discloser and human traders alike - before anyone can act on the signal through conventional means. Under that scenario, the entire cost of information production falls on track record return. Section 4.6 establishes that the paradox resolves even in this limiting case, so long as track record return exceeds c for a positive measure of agents. But the limiting case understates the mechanism's practical flexibility.
The structured disclosure format accommodates a rolling timing architecture, drawing on the logic of 13-F filings (quarterly institutional holdings disclosures, due 45 days after quarter end) but operating on a continuous daily basis. A discloser selects a cadence and delay - anywhere from immediate release to whatever horizon suits the analysis. One common structure would release the analytical content (reasoning, confidence level, the security or constraint being assessed) immediately, while holding back the position size or capital allocation for a specified embargo period of 30, 60, or 90 days. Priority for the track record attaches the moment the timestamped signal is published; the embargo simply preserves an informational advantage during the intervening window. Once the delay expires, the full disclosure enters the public domain and enriches the information environment available to all participants.
What matters about this design is that the discloser controls the timing entirely, without regulatory prescription. The track record scores both calibration quality and adherence to the chosen cadence, so an agent who commits to 30-day rolling disclosure and honors it consistently accumulates a qualitatively different record from one operating on a 90-day or immediate-release cycle. The cadence commitment itself carries information - about how time-sensitive the underlying analysis is, how confident the discloser is in it, and how much accountability the discloser is willing to accept. Market forces rather than regulators will determine where the equilibrium embargo length settles. Most participants will likely gravitate toward short delays, 30 days or less, because very little analysis remains genuinely proprietary for longer and the track record benefits of faster disclosure - more scored data points, stronger priority claims, greater contribution to the information network - outweigh whatever trading profit a longer delay might preserve.
Selective disclosure concerns under Regulation FD (SEC, 2000) do not arise in the standard case, because the discloser's structured reasoning about publicly available information, published on a self-determined rolling schedule, constitutes the discloser's own analytical work product rather than material nonpublic information from an issuer. The independent analyst whose reasoning derives entirely from public sources is the clean case; the Reg FD analysis for issuers and for institutional participants with access to material nonpublic information involves different boundaries that require separate treatment. Whether or not the embargo component is adopted, the resolution holds. The cooperative channel functions on track record return alone, and the embargo serves only as a practical accommodation of the competitive channel's need for a temporary informational edge.
What the Grossman-Stiglitz literature assumed for forty-six years was that a single channel - trading - had to handle both the production of information and its transmission into prices. Once the two functions are separated and each is given its own incentive structure, the contradiction that held them together falls away.
Something the Grossman-Stiglitz framing concealed becomes visible once the resolution is in place: competition and cooperation stand in a structural relationship that the original model's architecture made impossible to see. With only competitive agents in the model, information functions as a weapon whose value depends entirely on secrecy, and the paradox follows inescapably - the competitive mechanism erodes the incentive to produce the very information it requires.
Adding the cooperative channel changes the equilibrium's character. Disclosers who share reasoning publicly and accept the reputational exposure of being scored against outcomes are producing a public good, but they do so because the track record asset that results from sustained, well-calibrated disclosure is individually valuable. The motivation is self-interest channeled through cooperation rather than through secrecy - a distinction that matters because it means the cooperative channel does not depend on altruism and will not collapse when participants behave strategically.
What emerges when both channels operate at once is a coordination mechanism that neither could produce in isolation. The competitive channel carries information into prices through trading; the cooperative channel generates the information that gives trading its signal. Strip away cooperation, and traders are left competing on noise because no one has an incentive to produce the underlying analysis. Strip away competition, and disclosed reasoning accumulates without being translated into the price system where capital allocation decisions are made. The reinforcement between information production and price efficiency depends on having both functions active simultaneously, each compensated through its own channel.
The idea that competition and cooperation can function as complementary elements of a single system rather than as opposing forces has substantial precedent, though the specific form it takes here is new. Axelrod's (1984) tournament experiments showed that self-interested agents arrive at cooperative behavior through repeated interaction even without external enforcement - a result whose logic maps directly onto the track record mechanism, where the iteration of disclose-score-learn-repeat generates the cooperative equilibrium. The game-theoretic foundation was established by Kreps, Milgrom, Roberts, and Wilson (1982), whose proof that reputation concerns sustain cooperation in finitely repeated games rests on exactly the type uncertainty that track record capital exploits: each player's doubt about whether the other is a cooperative type makes defection costly in early rounds. In a different literature, the "private-collective" model that Von Hippel and von Krogh (2003) identified in open-source development describes private agents who voluntarily contribute output to a public commons when the reputational return exceeds the contribution cost - a structural parallel to the Disclosure Incentive operating in a different domain. Ostrom's (1990) work on commons governance demonstrated that communities manage collective action through institutional designs that weave competitive and cooperative incentives together, while Brandenburger and Nalebuff (1996) formalized "co-opetition" through the value net framework, showing how firms that are simultaneously customers, suppliers, and competitors sustain both competitive and cooperative relationships within a single game.
The present paper's contribution is narrower and more specific than any of these. Where Brandenburger-Nalebuff describes strategic coexistence across firm roles, and where Ostrom identifies governance institutions that manage shared resources, the competition-cooperation synthesis developed here resolves a specific impossibility result in a specific market setting: structured disclosure complementing trading, with proper scoring rules providing the verification infrastructure that Axelrod's repeated games, von Hippel-von Krogh's open-source communities, and Ostrom's commons governance all require in their respective domains. The synthesis requires both channels operating within a single market on a single information production problem, and the reason it remained invisible for forty-six years is architectural. Assumption GS excluded the cooperative channel from the model. Once that channel is restored, the paradox turns out to have been a consequence of modeling coordination as pure competition rather than a deep fact about information economics.
The competition-cooperation synthesis developed in Section 6 extends beyond the economics of information markets. Four disciplines encounter the same structural pattern - each from a different direction, each at a different level of formality - and the convergence is what makes the pattern worth attending to.
Sections 2 through 6 constitute the economics entrance in full. The Grossman-Stiglitz paradox resolves when a cooperative information production channel operates alongside the competitive transmission channel, and the equilibrium shifts from a constrained Nash outcome toward a Pareto improvement (Proposition 3). Hayek (1945) described prices as aggregators of dispersed knowledge; the Disclosure Incentive addresses the question Hayek left open, which is how the dispersed knowledge enters the aggregator in the first place when the mechanism Grossman and Stiglitz analyzed - trading on private information - proves insufficient on its own. The cooperative channel supplies the missing input.
Open-source software development runs on the same structural logic. Contributors share code publicly, and their compensation takes the form of reputation capital - a demonstrated record of skill, a portfolio of contributions whose quality is observable. Companies then build products on the shared codebase, competing in the market that cooperation made possible. The cooperative layer produces the substrate; the competitive layer carries its value to users. Lerner and Tirole (2002) provided the formal explanation: contributing to an open-source project generates a publicly observable record of skill, and the labor market rewards that record with a wage premium independent of whether the contributor captured any commercial value from the code. Their career-concern model - where public contribution yields a private reputational return sufficient to cover the cost of contributing - is structurally parallel to the Disclosure Incentive. A historical precedent in a very different industry reinforces the point: Allen (1983) documented nineteenth-century iron manufacturers voluntarily sharing blast furnace innovations because the reputation gained among engineers, combined with the cumulative benefits of collective improvement, exceeded whatever advantage secrecy could have preserved. Benkler's (2002) concept of "commons-based peer production" captures the enabling condition: when information goods can be decomposed into fine-grained modules that contributors complete independently, decentralized voluntary production becomes feasible at scale, as a mode distinct from both market exchange and hierarchical organization. Raymond (1999) documented the same phenomenon ethnographically in the Linux community, where decentralized contributors outperformed centralized development teams because the reputational incentive drew a larger and more diverse talent pool than any single firm could assemble.
Three contributions distinguish the present paper from this literature. The first is domain application: the career-concern logic that Lerner and Tirole identified in open source, when instantiated as structured judgment disclosure with proper scoring rules, resolves a foundational paradox in financial economics. The second is a verification apparatus that the open-source literature lacks. Code quality is assessed through use and peer review; the Disclosure Incentive scores predictions against outcomes using proper scoring rules, which requires that disclosed judgments be reliably timestamped to establish priority - the distributed systems problem that Lamport (1978) solved for logical clocks and that cryptographic hash chains now solve for tamper-proof ordering. The third, and the one with the largest downstream implications, is the improvement mechanism. Lerner-Tirole's career-concern model implies that public contribution signals existing quality; the Disclosure Incentive generates better quality through the iterative cycle of articulation, publication, scoring, and learning. The difference matters because it means the mechanism produces a positive externality that career-concern models do not predict - improved judgment, not merely improved visibility of whatever judgment the agent already possessed.
There is an AI training implication worth flagging. Structured human judgments that are calibrated, attributed, and scored against outcomes constitute a qualitatively different training corpus from the compressed signals - prices, engagement metrics, unattributed text - on which current AI systems train. Because the competitive channel's incentive is secrecy while useful training data requires disclosure, the cooperative channel produces a class of training data that the competitive channel structurally cannot. A prediction developed in Beier (2026a) follows: disclosure that improves market coordination simultaneously improves AI training, since both systems draw on the same data stream and both benefit when that stream is enriched.
In game-theoretic terms, the Grossman-Stiglitz market is a pure competition game with an inefficient Nash equilibrium: information is underproduced relative to the social optimum because each informed trader's private return (trading profit) falls short of the social return (better price efficiency for all participants), producing a standard public goods problem (Samuelson, 1954; Arrow, 1962).
The Disclosure Incentive expands the strategy space by introducing a cooperative option. Agents can now compete (trade on private information), cooperate (disclose reasoning and accumulate track record capital), or do both. Because the cooperative strategy carries its own payoff function - one rooted in the judgment market rather than the asset market - the equilibrium shifts. The Nash outcome of the pure-competition game underproduces information; the augmented game sustains information production through the cooperative strategy even as the competitive return approaches zero, and the resulting equilibrium Pareto-dominates its predecessor in the sense that information production is higher, price efficiency is higher, and cooperative agents are compensated through a channel whose value does not erode with increasing efficiency. There is an affinity here with Aumann's (1974) correlated equilibria, which tend to be more efficient than Nash equilibria: the disclosure functions as a public signal coordinating traders' actions, effectively serving as an endogenous correlating device. The distinction is that Aumann's correlating device enters the game exogenously, whereas the Disclosure Incentive endogenizes signal production through the judgment market.
More broadly, what the augmented game illustrates is that introducing a cooperative strategy with an independent payoff into a competitive game can shift the equilibrium from an inefficient Nash outcome toward Pareto improvement. The mechanism design literature (Hurwicz, 1972; Myerson, 1981; Maskin, 1999) provides the natural frame: the track record verification system is a mechanism whose incentive compatibility rests on proper scoring rules making honest disclosure a dominant long-run strategy, and the formal proof of that incentive compatibility is the subject of companion work (Beier, 2026r).
Shannon's (1948) foundational result - that compressing a signal below its entropy rate necessarily destroys information - applies directly to what the price system does. Every transaction maps the high-dimensional judgment behind a decision into a scalar, and the information lost in that compression must be reconstructed, at cost, by every downstream user who needs it: analysts reverse-engineering corporate strategy from price movements, regulators inferring risk exposures from trading patterns, AI systems training on price data that has already been stripped of the reasoning it once carried. Reconstruction of this kind is a major economic activity in the financial services industry, consuming analyst hours, compliance budgets, and computational resources at enormous scale.
Under pure competition, the compression ratio stays high because the trading channel has no incentive to reduce it. The trader profits precisely from the gap between what the judgment contained and what the price reveals - preserving that gap is the source of trading profit, not a defect to be remedied. The price carries a compressed summary of private information, and the compression serves the trader's interest.
Adding the cooperative channel changes the information economics of compression. Disclosed reasoning enters the public domain in structured form, enriching the signal available to all participants before the price is observed. Shannon's framework provides the measure: the mutual information I(D;V|P), where D is the disclosure, V is the fundamental value, and P is the price, quantifies how much the disclosure tells participants about V beyond what the price already reveals. This quantity is positive whenever the disclosure carries structured reasoning about the constraint environment - a type of information the scalar price was never designed to hold and cannot reconstruct from its own signal.
The thermodynamic analogy is suggestive rather than exact. Landauer (1961) proved that erasing information in a physical computing device dissipates a minimum amount of energy at kT ln 2 per bit - a cost that cannot be recovered. Price compression is institutional signal compression rather than physical bit erasure in Landauer's strict sense, but the directional logic carries over: destroying information at one stage of a system forces expenditure downstream to reconstruct it. The cooperative channel reduces destruction at source, and the reconstruction cost falls accordingly. Whether the reduction carries a measurable thermodynamic signature or operates only through economic channels is an empirical question this paper leaves open. The economic direction, though, is unambiguous. A system that relies solely on competition forces expensive downstream reconstruction of compressed signals, while a system that pairs competition with cooperation preserves information at source that the competitive channel, left to itself, would have compressed away.
The competition-cooperation synthesis has implications for a problem far larger than financial markets: the price system's inability to mediate negative externalities at the point of consumption.
A flight from Boston to London costs four hundred dollars. Compressed into that scalar and invisible to every participant in the transaction are the atmospheric carbon accumulation from the fuel burn, the noise impact on communities near both airports, the interaction of this particular flight with every other flight happening simultaneously, the scaling trajectory of transatlantic air travel as demand grows, and the draw-down on the atmospheric carbon budget that the trip represents. None of this information enters the price because no mechanism exists for it to enter. Airlines compete on cost and consumers on convenience - a pure competition market - and no participant in the transaction has any institutional channel through which to disclose reasoning about the consequences of this specific consumption event at the moment it occurs.
The Pigouvian approach (Pigou, 1920) attempts to fix this from outside by computing a social cost and adding it to the ticket price. But the tax is itself a compressed signal, a single number asked to carry the full weight of atmospheric physics, intergenerational ethics, technological alternatives, and scaling consequences - a scalar compression layered on top of a scalar compression, with the reasoning behind both invisible to the participants who are supposed to respond to it. The difficulty is not merely philosophical. Nordhaus (2017) and Rennert et al. (2022) have proposed central estimates that diverge several-fold - roughly $31/ton in 2010 dollars and $185/ton in 2020 dollars respectively, with the gap driven primarily by differences in discount rates and updated damage functions rather than inflation. Pindyck (2019) has gone further, arguing that the integrated assessment models underlying all such estimates are so structurally flawed that any specific number is essentially arbitrary. Taken together, the divergence and the methodological critique confirm that the compression is too severe for a single scalar to carry.
The Disclosure mechanism operates on a different margin. Under the proposed framework, the airline discloses its fleet efficiency trajectory, its assessment of how its scaling interacts with atmospheric limits, the confidence level attached to that assessment, and the identity of the analyst who produced it. Other airlines can read and evaluate the reasoning. So can investors, regulators, and passengers - though the primary transmission runs through capital markets rather than consumer behavior. The track record accumulates across disclosures, and the information that was invisible in the four-hundred-dollar price becomes visible in the structured disclosure attached to the transaction.
Why would airlines voluntarily adopt this framework? The answer lies in financing costs. Diamond and Verrecchia (1991) established that when firms make more information public, the resulting reduction in adverse selection costs lowers the cost of capital - a result whose generality across institutional settings is confirmed by the voluntary disclosure literature that Verrecchia (2001) surveyed. The empirical case is strengthened by Friede, Busch, and Bassen's (2015) meta-analysis, the largest to date, covering over two thousand individual studies of the relationship between ESG management and financial performance across asset classes and regions. Their finding that firms managing sustainability constraints effectively tend to outperform financially is robust across methodologies and time periods. At the same time, Berg, Koelbel, and Rigobon (2022) documented a complementary problem that helps explain why existing ESG frameworks have not already solved the information problem: ESG ratings diverge dramatically across providers, with the divergence traceable to differences in what raters measure, how they measure it, and how they weight the components. The implication for the present argument is that existing disclosure mandates structure facts - emissions tonnage, board composition, waste metrics - rather than judgment about how the firm's operations interact with constraints at scale and how confident the analyst is in that assessment. If the divergence in ESG ratings reflects signal noise produced by compressing judgment into standardized fact sheets, then the Disclosure Incentive addresses the problem at its source: by structuring judgment with proper scoring and preserving the analytical reasoning behind the conclusion. The prediction is that firms adopting structured judgment disclosure will see a sharper and more consistent cost-of-capital benefit than firms relying on conventional ESG reporting, because calibrated constraint reasoning is distinguishable from compliance-driven fact assembly in a way that current ESG scores are not.
The mechanism's operation, once the framework is adopted, runs through capital allocators. Pension funds, sovereign wealth funds, and insurance companies observe disclosed constraint reasoning from airlines and other consumption-facing firms, evaluate it against their own analysis (drawing on their own track records where available), and allocate capital accordingly. Firms whose constraint reasoning is well-calibrated attract cheaper financing; firms whose reasoning is absent, poor, or fabricated face rising financing costs as their track records diverge from outcomes. Cost of capital becomes the transmission channel through which the cooperative function (honest disclosure) and the competitive function (capital allocation disciplined by demonstrated judgment quality) together make the externality visible - without requiring any regulator to compute the unknowable scalar.
What distinguishes this mechanism from prior models of voluntary disclosure or commons governance is how quickly it can operate when embedded in regulated financial markets. The participants are already identified by name and subject to fiduciary obligations; the transactions are iterative, with the same fund manager allocating capital daily, the same bank extending credit weekly, the same insurer pricing risk quarterly; and the capital at stake is measured in trillions. The regulatory infrastructure enforcing identity, reporting, and accountability already exists. What is missing is only the cooperative channel - the institutional structure through which constraint reasoning enters the information environment in structured, scored, attributed form.
Once that channel exists, each disclosure enriches the information available to every other participant, creating a combinatorial dynamic. Admati and Pfleiderer (2000) formalized why voluntary disclosure is typically undersupplied: each firm's disclosure benefits competitors and counterparties, but the disclosing firm bears the full cost while capturing only a fraction of the benefit. The Disclosure Incentive addresses this under-provision by providing an individual return - track record capital - that compensates the discloser for the public good they produce. Coase (1960) showed that externalities can be internalized through private bargaining when transaction costs are sufficiently low; the Disclosure Incentive reduces the information transaction cost - the cost of knowing what the other party knows about the constraint environment - to near zero in regulated markets where the infrastructure already exists.
The resulting system produces real-time pricing of sustainability through the continuous aggregation of structured, scored, attributed judgments by the agents closest to the constraints, rather than through a regulator's computation or a tax proxy. It scales because it requires almost nothing new: every regulated financial market already has identity verification, reporting cycles, fiduciary obligations, and capital at stake. The disclosure architecture adds one structured file to transactions that already occur millions of times daily, on an open-source schema, with voluntary adoption - any firm can begin disclosing, any firm can decline, and the market evaluates both choices. The only regulatory intervention required is a safe harbor protecting good-faith analytical disclosure made on a best-efforts basis, analogous to the protections for forward-looking statements under the Private Securities Litigation Reform Act of 1995. With that single provision, any jurisdiction can adopt the framework.
The analysis here is confined to regulated financial markets, where the institutional infrastructure already exists. But the combinatorial logic of the Disclosure Incentive applies wherever structured, scored, attributed disclosure can be attached to decisions that affect shared constraints - which is to say, wherever the Grossman-Stiglitz resolution has purchase on coordination problems that the price system, operating through competition alone, has failed to solve.
The framework generates the following predictions, each testable with existing or near-term data. Magnitude estimates are prior expectations calibrated to the empirical literature cited; they serve as benchmarks for future testing, not as point estimates.
Prediction 1 (Volume of disclosed judgment). Within five years of a track record verification platform launching in a financial sector, the volume of publicly attributed, structured analytical judgments should increase by at least an order of magnitude relative to the pre-platform baseline of attributed sell-side research in the same sector. The increase should concentrate in long-horizon, constraint-based analysis (climate risk, resource depletion, infrastructure resilience) rather than short-horizon earnings estimates, because the marginal Disclosure Incentive return is highest where the trading profit mechanism is weakest.
Identification strategy: Difference-in-differences comparing sectors with and without platform adoption. The counterfactual is the volume of attributed research in comparable sectors where the platform has not launched.
Prediction 2 (Track record premium). Agents with verified track records of above-median calibration quality should command a wage premium of 15-40% in advisory and capital allocation roles, controlling for education, experience, institutional affiliation, and assets under management. The premium should increase with record length at a diminishing rate, consistent with Bayesian updating on calibration precision.
Identification strategy: Cross-sectional wage regression using track record scores as the independent variable, with institutional fixed effects and experience controls. The 15-40% range is calibrated to the premium that Tetlock and Gardner (2015) documented for superforecaster-level calibration in analogous advisory settings.
Prediction 3 (Price adjustment speed). In sectors where disclosure ecosystems develop, the half-life of price adjustment to constraint events (regulatory changes, resource discoveries, infrastructure failures) should decrease by 30-60% relative to sectors without such ecosystems, measured through standard event-study methodology.
Identification strategy: Event studies comparing cumulative abnormal returns around constraint-relevant announcements in treatment sectors (active disclosure) versus control sectors (no disclosure ecosystem). The comparison should control for sector-level differences in analyst coverage and trading volume.
Prediction 4 (Institutional affiliation premium erosion). The wage premium for employment at top-tier financial institutions relative to independent analysts should decrease by 10-25% within five years of track record verification adoption, as demonstrated calibration partially substitutes for institutional reputation as a quality signal.
Identification strategy: Difference-in-differences comparing the institutional premium before and after platform adoption, using sectors without adoption as control.
Prediction 5 (AI training corpus quality). Machine learning models trained on structured, attributed, scored human judgments should achieve calibration improvements of 20-50% on tail-event prediction relative to models trained on equivalent token volumes of unattributed compressed data (prices, unattributed news, social media text). The improvement should be largest for events with base rates below 5%, where the calibration training signal is most valuable.
Identification strategy: Controlled training experiments holding model architecture, compute budget, and data volume constant while varying training data composition. The 20-50% range is a prior estimate based on the calibration improvements Lichtenstein and Fischhoff (1980) observed in human subjects receiving structured feedback.
Prediction 6 (Reconstruction expenditure decline). Sectors adopting structured disclosure should show a 10-30% reduction in analyst coverage per unit of capital deployed (number of sell-side analysts covering the sector, normalized by market capitalization) within five years, because the information that analysts reconstruct from compressed signals is partially provided directly through disclosure. Compliance expenditure as a share of transaction volume should decline by a comparable margin.
Identification strategy: Panel regression of analyst-to-market-cap ratios and compliance-to-transaction ratios on disclosure adoption indicators, with sector and year fixed effects.
The formal model in Section 4 provides a general equilibrium framework with existence and uniqueness results and four proved propositions, but several extensions remain for future work. The model assumes homogeneous information cost c and homogeneous risk aversion gamma; relaxing these to allow heterogeneous costs and preferences would produce richer equilibrium predictions about the composition of the discloser and trader populations. The judgment market is modeled through the reduced-form return function r-bar_D(lambda_D) with four assumptions (J1-J4); a complete micro-foundation specifying how principals evaluate and compensate calibration quality would strengthen the formal apparatus. The incentive compatibility of honest disclosure under track record verification is argued from the properties of proper scoring rules but not formally proved here; that proof is the subject of companion work.
The empirical conditions under which the track record return exceeds information acquisition cost are not yet established at scale because the market infrastructure does not yet exist. The gaming and manipulation challenges - Sybil attacks, coordinated poisoning, generative AI producing hollow disclosures - require careful analysis and are addressed in companion work on adversarial disclosure economics (Beier, 2026an). The conditions under which proper scoring rules make honesty dominant (single agent, no selection over which forecasts to publicize, no information about others' reports) are acknowledged as idealized. Strategic selection over which forecasts to publish and coordinated manipulation of track records represent potential structural failures that cannot be dismissed as edge cases. If track record capital is valuable, it will attract adversarial behavior. The companion work must establish the conditions under which the mechanism remains robust to these attacks.
The relationship between the Disclosure Incentive and existing disclosure mandates (XBRL, CSRD, TCFD) is noted but not developed; these mandates structure facts, not judgment, and the distinction matters but is beyond this paper's scope.
The relationship to prediction markets deserves fuller treatment than prior versions of this paper provided. Prediction markets (Hanson, 2003; Wolfers and Zitzewitz, 2004; Arrow et al., 2008) aggregate point estimates by paying participants based on accuracy, but the payoff is a per-round market return - structurally, trading profit on a prediction contract. This means prediction markets inherit the Grossman-Stiglitz structure for the production of the underlying reasoning: if the market price of the prediction contract fully reflects available analysis, no participant has incentive to produce the analysis that would make it reflect that analysis. The Disclosure Incentive addresses the layer beneath: not "what probability should the market assign?" but "what reasoning supports that probability, and who produced it?" Where prediction markets compress judgment into a scalar contract price, the Disclosure Incentive preserves reasoning in structured form - and the two are complements rather than substitutes. Prediction markets excel at transmitting probability assessments into prices; the Disclosure Incentive generates the analytical substrate on which those assessments depend.
The safe harbor proposed in Section 8, modeled on the Private Securities Litigation Reform Act of 1995, is offered as a precedent demonstrating legislative willingness to protect good-faith prospective analytical disclosure; the specific statutory form of an appropriate safe harbor for Disclosure Incentive participants requires legal expertise beyond this paper's scope and likely differs across jurisdictions.
For forty-six years, the Grossman-Stiglitz paradox has constrained our understanding of how information enters prices. The paradox is genuine within its assumptions, and this paper does not challenge the logic. What it shows is that one of those assumptions - that information production is incentivized exclusively through trading profit - is a modeling choice rather than a necessity, and that relaxing it resolves the contradiction. The CARA-normal general equilibrium model in Section 4 establishes the resolution formally: the disclosure channel sustains information production even in the limiting case where noise vanishes and the trading channel collapses entirely.
Beyond the paradox itself, the resolution makes visible a relationship between competition and cooperation that the original framing concealed by excluding the cooperative channel from the model. Disclosers produce information and are compensated through track record capital; traders carry that information into prices and are compensated through trading profit. The coordination mechanism requires both functions operating simultaneously, and what forty-six years of literature treated as an impossibility turns out to have been a consequence of modeling the system with only one of its two channels active.
This structural pattern recurs across disciplines - in the open-source development model in computer science, as a game-theoretic equilibrium shift in mathematics, and as a suggestive thermodynamic analogy linking information preservation to reduced reconstruction cost in physics. Four disciplines, approaching the same mechanism from different directions, encounter the same structural relationship at different levels of formality.
The implication for externalities follows directly. Prices fail to mediate negative externalities at the moment of consumption because the cooperative channel through which constraint information would enter the price has never been built. Structured disclosure with track record incentives supplies that channel, and the information that was invisible in the price becomes visible - through the continuous aggregation of scored, attributed judgments by the agents closest to the constraints, rather than through a regulator's attempt to compute the unknowable scalar.
This paper presents results from the Prolegomena to the Unification of Economics, Computer Science, Mathematics, and Physics (Beier, forthcoming 2026). The four-entrance structure - showing a single mechanism simultaneously visible from economics, computer science, mathematics, and physics - is not a rhetorical device but a concrete instance of the unification the Prolegomena proposes. Each entrance admits its own research program. The author invites the relevant communities to develop them.