Papers

We study a matching mechanism where agents and objects are described by features rather than complete rankings. A single spectral projection reduces the problem to a one-dimensional sort, computable in O(N log N) time. We prove that on descaled features and preferences, our algorithm obtains the exact Nash Social Welfare (NSW) optimum within the projected space, with an unconditional utilitarian-welfare guarantee and a conditional NSW guarantee. The proposed mechanism is stable against exogenous noise but not strategy-proof; we provide an explicit profitable misreport. On an agentic AI shopping application, the diagnostics correctly anticipate both a success and a failure case. A 100-instance robustness study confirms the findings.

We develop a dynamic three-sector model in which Marx's aggregate equalities (total price equals total value and total profit equals total surplus value) are treated as strict conservation constraints throughout capital reallocation and technical diffusion. Three price-value coefficients are determined by the two aggregate equalities and a closure that sets one sector's price-based profit rate equal to the contemporaneous value-based average (the anchor). Before innovation, capital inflow expands the receiving sector's output and, under both anchors, lowers its unit price and excess profitability. This endogenous fall in price as output rises supports a two-timescale reading: demand-related price movements may precede slower adjustment through capital mobility. A labour-saving, capital-intensifying innovation generates temporary extra surplus value, revalues committed capital, and changes the economy-wide profit rate. At constant real wages, the final uniform rate rises, consistent with Okishio's theorem. When real wages rise sufficiently to keep aggregate exploitation approximately constant, the organic composition increases and the final rate falls. Strict aggregate conservation is computationally coherent and yields distinct transitional predictions under explicit closure and wage assumptions.

A decision maker may have several information sources available and choose which one to consult only after learning the decision problem she faces. When is one such set of sources uniformly more valuable than another? For unrestricted Bayesian decision problems, we show that the answer can be stated entirely in terms of Blackwell comparisons. Form a tagged mixture by drawing a source independently of the state and revealing both its identity and its signal. One source set is more valuable in every decision problem if and only if each tagged mixture of the second source set is Blackwell dominated by some tagged mixture of the first. The result applies to compact, possibly infinite source sets and general signal spaces. It also has an exact quantitative counterpart: the largest normalized value shortfall is the directed Le Cam deficiency between the source sets' tagged hulls. The analogous program for monotone decision problems reveals a boundary. We call the passage from problem-by-problem source-set superiority to a problem-independent pairwise dominance a lifting. The Blackwell lifting does not extend directly to the Lehmann order: mixing sources that individually satisfy the monotone likelihood ratio property (MLRP) need not preserve MLRP, and even when it does, no fixed Lehmann-dominating mixture need exist. Requiring one source to serve a finite bundle of monotone decision problems restores the equivalence.

Access to past reports changes how consumers learn about competing information providers. A subscriber who has learned to interpret a familiar source may find an equally competent rival less useful. We study how opening the rival's archive changes renewal prices and the effect of outcome feedback. Better feedback strengthens the familiar source's advantage when rival reports are inaccessible, but can weaken it once some rival records are available. We derive the exact threshold in a Gaussian learning model with differentiated price competition. Opening further records narrows the renewal premium and raises consumer surplus. When the familiar source initially serves a sufficiently large share, however, partial opening can reduce aggregate forecasting quality and total surplus by drawing consumers toward a rival that remains less informative. Complete access improves both outcomes relative to every incomplete archive. These results concern a covered interior renewal market with inherited customer histories, before implementation costs. The results distinguish the quality of feedback from access to the records with which consumers combine it.

We study how learning about a forecasting method affects a seller's choice of evidence. More evidence improves the current forecast but makes the method's persistent component harder to identify. A monopolist may therefore collect less evidence initially to help customers interpret later forecasts. Because the seller captures only part of customers' gains from costly evidence, it switches to less initial evidence sooner than a welfare-maximizing regulator. A minimum evidence requirement improves welfare only for intermediate weights on future benefits. An independent assessment removes this learning trade-off but may be privately unprofitable despite being socially worthwhile.

Public support for early adoption can affect what later users learn from observed choices. An adopter may have favourable private information, or may have received a rebate. We study a government that randomly assigns eligibility for a fixed rebate and chooses the program's coverage and reporting rule. We characterize when disclosing individual eligibility changes optimal coverage from zero to a positive rate under general convex program costs. This requires both a favourable marginal return to a disclosed program and a bound on the direct benefit available from a large opaque intervention. In the benchmark, disclosure allows the government to increase early adoption and welfare while leaving expected total adoption unchanged. We then allow imperfect compliance and private information for the late user. An eligibility label can be strictly informative without changing anyone's decision, in which case disclosure has no welfare value. The policy reversal survives when both extensions are present. The results identify when an eligibility record is a useful part of the design of an adoption program.

Cursed players understand the distribution of opponents' actions and the distribution of the payoff-relevant state, conditional on their own information, but respond as if the two were independent. Cursed equilibrium additionally requires statistically correct beliefs about the distribution of play. We propose a solution concept that separates the bias from equilibrium: cursed rationalizability iteratively deletes every action that is not a cursed response to a conjecture about opponents' surviving play. The cursed-rationalizable set is the interim correlated rationalizable set of a virtual game, in which payoffs are averaged over the state. Under strategic complements, cursed rationalizability yields the same bounds on behavior as cursed equilibrium. A cautious refinement, the analog of admissibility, delivers sharp predictions in the laboratory games that documented the winner's curse.

We study a continuous-time game in which two firms choose how quickly to advance their capabilities while an exogenous safety threshold advances at a fixed rate. When the capability frontier (max of firms' capabilities) exceeds the safety threshold, all firms are exposed to common disaster that arrives at a hazard rate increasing in the capability-safety difference. We characterize Markov perfect equilibria in terms of the disaster risk, how quickly safety advances, and flow payoffs: when they are low, only racing is an equilibrium; when they are intermediate, racing and pacing coexist; when they are high, only pacing survives. Across all subgame perfect equilibria, low risk induces perpetual racing while high risk rules it out and we bound the probability of disaster across all SPE. If internal capabilities are hidden with a fixed lag until deployment, it is harder to sustain pacing which highlights the importance of transparency about internal capabilities.

We formulate a complete-information two-player strategic timing game that we refer to as the reverse war of attrition (RWoA). Waiting yields a strictly positive current rent, and the player that outwaits its rival may earn an even higher flow. However, remaining in the waiting state when the rival has moved triggers a discrete late-mover penalty. The distinctive primitive is a player-owned productive buffer which enables the rent-generating activity while waiting, but is degraded by this activity. A rival's move can raise the waiting rent and accelerate depletion. We characterize a unique symmetric equilibrium. We apply RWoA to Bertrand competition in a homogeneous-good market, where vintage inventory serves as the buffer clock for timing repricing. We also discuss competitive maintenance. As an extension, we replicate the bilateral game across a continuum of disjoint heterogeneous local markets and, via the exact law of large numbers, derive deterministic aggregate state shares.

Matching theory has largely evolved around two canonical rules: deferred acceptance (DA) in the marriage problem and top trading cycles (TTC) in the object reallocation problem. Although the two rules operate through different procedures, we show that they rest on a common axiomatic foundation. In the marriage problem, stability decomposes into individual rationality and pair rationality, and a classic result characterizes DA by these two axioms together with strategy-proofness for the proposing side. We show that individual rationality, pair rationality, and strategy-proofness likewise characterize TTC. More strongly, three weak rationality axioms concerning individuals and pairs, together with strategy-proofness, uniquely determine TTC. Even weak rationality requirements therefore rule out strategy-proof implementation when there is a cap on the size of exchange cycles.

The design of credible auctions—mechanisms where a revenue-maximizing auctioneer has no incentive to deviate from the protocol—faces a fundamental cryptographic barrier when the auctioneer controls shill bidders. While a natural approach is to use Secure Multi-Party Computation (MPC) to remove the trusted auctioneer, the impossibility of fair coin flipping of Cleve (1986) implies that monolithic MPC protocols grant the auctioneer a "free option": they can learn the auction's outcome and unilaterally abort if the revenue is unsatisfactory. Cryptographic commitments with ex-ante penalties mitigate this abort asymmetry, but no finite penalty suffices for heavy-tailed distributions. We circumvent this barrier by introducing the MPC Decomposition Principle. Rather than encrypting the entire mechanism, we use MPC strictly as an information-restriction tool. We isolate the winner determination problem into a minimal MPC gadget that computes and reveals the winner's identity but no payment information. This qualitative restriction mathematically bounds the information leaked upon an abort. By combining this gadget with sequential revelation and finite economic penalties, we design the Sequential Revelation Auction (SRA). We prove that bounding the information leakage strictly bounds the value of the free option, showing that a penalty of $k \geq \sum_{i=1}^n Rev(F_i)$ is sufficient for credibility, and tight: for equal-revenue distributions, every smaller penalty admits a profitable deviation. Using constant-round MPC, the SRA resolves an open question of Akbarpour and Li (2020) and Ferreira and Weinberg (2020) by providing a constant-round, incentive-compatible, revenue-optimal credible auction for all product distributions with vanishing revenue tails

Matching mechanisms differ in how much of an agent's preference ranking must be determined and reported to obtain a particular object. A mechanism is singleton-attainable (SA) if every object that an agent can obtain through some report can also be obtained by reporting only that object as acceptable. With an SA mechanism, once an attainable object has been identified, the agent need not rank or report any other object. Singleton-attainability identifies a distinct dimension in matching theory and market design: transparent access to attainable outcomes, separate from incentives, stability, welfare or equity. We establish general conditions for SA and derive its strategic implications. Top-lift invariance and truncation invariance together imply SA, while strategyproofness and stability each imply SA. By contrast, no Pareto improvement over a strategyproof, individually rational, and non-wasteful mechanism is SA. In particular, every Pareto improvement over Deferred Acceptance violates SA. We introduce report width, which measures how many acceptable objects may have to be reported to obtain an object. SA mechanisms have report width one. Report width is unbounded for a large class of efficient mechanisms that Pareto-improve Deferred Acceptance. Stable selection with report-induced priorities has width one when priorities are monotone and maximal width under reverse priority dominance. Rank-welfare maximization has width one when the outside-option rank is fixed and maximal width when it is report-dependent. These results reveal a structural divide, which we call the width dichotomy: across all mechanisms and families in our classification and all structural classes we study, report width is either one or unbounded.

Macroeconomic crises are rare, yet they can have large effects on asset prices. Because the probability of entering a crisis from normal times is small relative to the probability of recovery, the dynamics are nearly reducible: setting the crisis-entry probability to zero makes crisis states unreachable from normal states. We develop a graph-theoretic and spectral analysis of long-run pricing under reducible and nearly reducible dynamics. We show that, at the reducible limit, physical and pricing dynamics induce the same classes of economic states and accessibility relations, but rank their long-run importance differently: by recurrence and by class-specific pricing rates. Moreover, a claim's price depends only on its pricing corridor—the classes of states lying on directed paths from the initial state to states where the payoff is positive—and the highest class-specific pricing rate within this corridor determines the claim's long-run pricing rate. When the reducible-limit corridor excludes the globally pricing-dominant class, we characterize how restoring rare transitions introduces a contribution from that class with a weight that vanishes as the transitions become rarer. This contribution becomes dominant only beyond a crossover maturity, which increases with the rarity of the connecting paths and decreases with the dominant class's pricing-rate advantage. Finally, a consumption-based disaster-recovery application shows how preferences, consumption risk, cash-flow exposure, and recovery timing jointly shape the long-run pricing dominance of disaster states and crossover maturities.

This paper develops a model of identifiable smooth ambiguity in a finite-state Anscombe-Aumann framework in which ambiguity perception and the ambiguity-attitude representation may depend on the act's endogenous certainty-equivalent utility level. The framework separates two sources of utility-level dependence that standard smooth-ambiguity models hold fixed. Neutral-transfer experiments within revealed cells recover conditional beliefs, while compensation experiments across cells recover cell weights and locally revealed ambiguity-attitude scales. These objects have distinct behavioral content. After the within-level structure is extended globally, ambiguity perception is identified at each certainty-equivalent level, whereas variation in admissible level-specific global attitude indices need not by itself reflect behaviorally identified variation in ambiguity attitude. Cross-level restrictions determine when the locally revealed attitude scales can instead be represented by one common global ambiguity-attitude index. The baseline characterization yields a doubly implicit smooth-ambiguity representation with level-specific perception and potentially level-specific global attitude indices. Requiring one common ambiguity-attitude index gives an intermediate stable-attitude model in which only perception may vary; imposing perception stability as well yields standard identifiable smooth ambiguity within the maintained full-support, neutrally separated, fixed-partition environment with at least three revealed cells. The contribution is therefore a behavioral decomposition of utility-level dependence in smooth ambiguity into separately revealed perception and attitude components.

Exponential Second-Order Expected Utility (SOEU) underlies the entropic approach to model uncertainty. This paper explores in what sense that functional form is essential. In the misspecification-robust Smooth Ambiguity criterion, let a single parameter govern both the model-level robustness and the ambiguity-averse aggregation across models Cerreia-Vioglio, Hansen, Maccheroni, and Marinacci (2026). The two-layer criterion then equals Exponential SOEU for every compact set of models and every second-order prior, with the Bayesian predictive measure as the baseline. The main results are converses. On the aggregator side, matched curvature is necessary: at a fixed curvature no other continuous, strictly increasing aggregator delivers the reduction, and with mismatched curvature there are a model set and a prior for which no single-layer entropic value, at any curvature and any baseline, reproduces the criterion. On the cost side, within the power-divergence family, which contains chi-squared and reverse Kullback–Leibler (KL), only KL has a dual of the log-sum-exp form, and the other members first depart from it at the third cumulant. Finally, the value dual to Exponential SOEU is a robust-control value: it is motivated by Rational Inattention, but no Bayes-plausible information-acquisition problem about a fixed act generates it.

A collective rule must often choose a public outcome on a constrained boundary. We characterize truthful choice with diagonal unanimity on the entire boundary of any compact full-dimensional strictly convex body in finite dimension at least two. On the full domain of linear support preferences, ordinary individual strategy-proofness and diagonal unanimity force the rule to select one fixed participant's preferred point at every profile. The population is any fixed finite nonempty set. No Pareto condition, boundary smoothness, or continuity or measurability of the rule is assumed. If interior outcomes are allowed instead, two or more participants can use positive fixed weighted averages of preferred points for truthful non-dictatorial compromise on the same type domain. The proof derives regularity from the two agents' incentive inequalities, transports a common support-measure bound across reports, and makes every convexified attainable menu a Minkowski summand of the feasible body. Boundary generation then forces fixed control. The result extends the spherical public-good location question and identifies the role of boundary-valued choice in eliminating truthful compromise.

This paper studies agency problems when both parties worry that the model linking action to output is misspecified. With observable actions, an optimal contract is linear in output, so performance pay arises solely to share misspecification exposure, the slope reflects the parties' relative robustness concerns, and its allocation is Pareto efficient. With hidden actions, this sharing rule survives and incentives add a nonlinear correction. Misspecification concerns can polarize effort by making intermediate actions impossible to implement. Moreover, ambiguity across competing models has asymmetric effects: uncertainty about desired actions raises the principal's payoff, whereas uncertainty about deviations can lower it.

Consumers can invest resources to understand and avoid their behavioral mistakes, and their incentives to do so depend on the market consequences of remaining naive. We incorporate this feedback between consumers' cognitive states and market outcomes into a general contracting model. Firms face a trade-off between the depth and reach of exploitation: deeper exploitation raises profit from a naive consumer but induces greater cognitive investment, promoting sophistication and shrinking the exploitable consumer base. This trade-off disciplines exploitation and can cause policies that benefit consumers when cognition is fixed to backfire when cognition is endogenous.

We study how timestamps affect dynamic disclosure. At a random date, a sender privately obtains hard evidence about an evolving binary state and chooses when to disclose it. With timestamps, the unique equilibrium features immediate good-evidence disclosure and timestamp-dependent bad-evidence delay. Without timestamps, high priors relative to impatience generate a stock of undisclosed good evidence, which is stochastically purged before permanent transparency. High impatience yields immediate good-evidence disclosure, while bad evidence can be arbitrarily delayed and disclosed in bursts. Timestamps prevent pretending old good evidence is fresh and certify bad evidence is old, accelerating good-evidence disclosure and facilitating bad-evidence disclosure.

Institutions often face constraints richer than a single capacity. Protecting the priority of a student who cannot be accommodated may then block a lower-priority student who fits. We introduce COP-and-Choose, a cumulative offer process followed by a choice step, and show that its greedy version, which skips such blockers, leaves no student worse off than any fair matching or Knapsack Deferred Acceptance (KDA). Greedy is the unique consistent rule preserving this guarantee. With substitutability and size monotonicity at every school, greedy is strategy-proof and Pareto-undominated among strategy-proof mechanisms. If either fails at a school, one additional capacity-one school yields a market where, under every proposal order, greedy is manipulable and no strategy-proof mechanism weakly Pareto dominates it. In a three-resource refugee-resettlement calibration with simulated preferences, 19–33 percent of families gain relative to KDA and none lose, while 21–83 percent strongly envy another family.

We study strategic disclosure of the action space in principal-agent contracting, where an agent selects a disclosed action set to shape the principal's perception of her capabilities before contract design. Unaware of the strategic disclosure, the principal designs a revenue-optimal contract as if the disclosed action set were complete and accurate. We consider two variants distinguished by cost verifiability. When costs are unverifiable, the agent can extract the entire first-best surplus, leaving the principal with zero revenue. When costs are verifiable, we characterize the agent's optimal disclosure strategy in binary-outcome settings and, more generally, when the principal is restricted to linear contracts, reducing the agent's problem to a two-variable convex optimization problem. We prove that the agent can secure utility of at least a $1/e$ fraction of the first-best surplus, which also yields a $1/e$ welfare guarantee under optimal disclosure. While the principal's revenue can be arbitrarily small compared to the first-best surplus, when the ratio of maximum to minimum expected reward among non-null base actions is at most $L$, we establish a revenue guarantee of $\Theta(1/\log L)$ relative to the first-best surplus. We also compare utilities and welfare under strategic disclosure with their counterparts in the canonical model. Finally, we extend the agent's $1/e$ utility guarantee to general outcome spaces without restricting the principal to linear contracts. Our results show how strategic action-space disclosure changes the distribution of surplus while preserving a constant-factor welfare guarantee under the agent's optimal disclosure.

This paper provides a theoretical framework to evaluate the trade-off between the self-regulated peer review system and independent government inspection (PCAOB) in the auditing profession. We model the peer review system as a Judgment Regime, where a stakeholder utilizes professional expertise, captured as a private signal, to make ex-post decisions on verifying audit failures. In contrast, PCAOB inspection is modeled as a Commitment Regime, where the stakeholder lacks private information but can commit ex-ante to a predetermined level of verification. We find that the Judgment Regime benefits from a resource-allocation effect and a deterrence effect driven by informed verification, whereas the Commitment Regime deters audit failures through the first-mover advantage of ex-ante commitment. Our analysis demonstrates that the stakeholder prefers the peer review system if and only if the private signal is sufficiently informative. Furthermore, comparative statics reveal that higher verification costs or stronger audit incentives shift the stakeholder's preference toward PCAOB inspection.

An expert may misreport her forecast to influence a decision she cares about. We study contracts that elicit both her belief about a verifiable state and her stake in a binary action. If every belief is possible at two distinct stakes, exact incentive compatibility prevents a belief-only mechanism from letting the action depend on the report. Asking about both belief and stake allows the action to respond, but may require implementation rent. For threshold rules, we show that minimum rent equals the cutoff's positive curvature weighted by the belief distribution. The principal therefore chooses a cutoff by balancing virtual surplus against the implementation rent of truthful reporting. We characterize the best cutoff rule and give sufficient conditions under which it is optimal even among randomized mechanisms.

A government may ask for a high tax because it faces a genuine expense. The same demand can also be made by a government that intends to keep the proceeds. We study this ambiguity in a two-period reputation model with privately observed spending needs and an endogenous tax base. The opportunist chooses between outright confiscation and levies that an honest government might impose. We characterize the three possible regimes through a single equilibrium equation. A mean-preserving spread of legitimate needs weakly raises the opportunist's lifetime value, with a strict increase precisely when the spread changes the upper tail relevant for mimicry. We then give a necessary and sufficient curvature condition for this ordering to extend to a general reputational continuation prize. Verification reduces the value of concealment, but also changes how the opportunist extracts. In the benchmark economy, greater auditing weakly lowers current citizen welfare, even before audit costs, while improving the future allocation through better information. The welfare case for verification consequently depends on the balance between these two effects. Examples yield no auditing, an optimum within a regime, and an optimum at the boundary between regimes.

This paper studies social learning when buying access to previous decisions also determines whose decision enters the record. Individuals first receive private information and then decide whether to pay for access. A positive price selects relatively weak private beliefs. With one founding observation, every buyer copies it, and the record acquires no further information. With a richer initial history, buyers can disagree and the record can improve; nevertheless, a price bounded away from zero prevents complete learning, even with unbounded private beliefs. We then consider a rule under which a buyer makes a preliminary choice before access and a revised choice afterward. A positive probability of implementing the preliminary choice makes it follow the private signal. Retaining both choices restores complete learning under a fixed effective fee or pooled myopic pricing, including with bounded beliefs. The rule reduces willingness to pay and sacrifices some current decision accuracy. A worked example shows how the subsequent improvement in information can outweigh both initial losses. The results show why preserving a judgment made before exposure can change what later users learn from the same selected population.

We study the design of priority pricing systems with heterogeneous agents in environments in which improving quality for some agents reduces the average quality that can be provided. Contrary to the equity-efficiency tradeoff emphasized in public debates, we show that under economically natural conditions priority pricing can Pareto-improve on an equal-allocation benchmark. Three priority tiers suffice for such an improvement, combining higher quality for a fee, lower quality with compensation, and an intermediate tier at the benchmark quality; two tiers are never enough. Our results provide a framework for overcoming equity-efficiency tensions in applications such as lane pricing, waiting-line design, public provision, and insurance.

We study a representative-agent Epstein-Zin economy with geometric dividends and a hidden finite-state Markov drift. We allow the price-dividend ratio to contain an additional positive, absolutely continuous valuation factor and, within the class $\mathfrak C$ defined below and under the regularity, admissibility, and positivity conditions of our main theorem, equilibrium forces this factor to be constant, yielding belief-Markovian prices. In the two-state case, under the stated positivity condition and strictly positive transition intensities, we prove existence, uniqueness, endpoint smoothness, interior analyticity, and uniform bounds for the positive solution of the pricing equation. For $0<\theta\leq1$, this solution supports an equilibrium under any continuous short rate satisfying the model's one-sided portfolio condition. Finally, in the two-state subregion $\eta>0$, we derive belief-dependent stock volatility, a European option-pricing PDE, and a leading short-maturity conditional risk-neutral log-return skewness expansion.

Suppose an economy moves continuously along a closed path of fundamentals and returns exactly to its initial state. A regular Walrasian equilibrium price followed continuously along that path need not return to itself. For every number of commodities $L\ge3$, we construct a closed one-parameter family of pure-exchange economies in which all preferences are fixed, only three individual endowments vary, and aggregate resources remain constant. Along the loop, two regular equilibrium-price branches are exchanged while a third returns to itself; at the end, every economic primitive is exactly as it was initially. The construction uses at most $2L+2$ consumers. We also provide an exact realization with at most $2L$ consumers in which all endowments are fixed and only one preference varies; the two families generate identical aggregate excess demand. The key realization problem is parametric: classical aggregate-realization results guarantee an economy at each fixed parameter value, but not a continuous loop of realizing primitives. We construct such a loop explicitly. The resulting monodromy is structurally stable under sufficiently small $C^1$ perturbations. It is impossible with one or two commodities, making three commodities the sharp threshold. Thus local regularity guarantees local continuation but not a globally path-independent identity of an equilibrium branch, with implications for global comparative statics under multiplicity and for equilibrium selection based on continuation.

Many allocation rules give priority to applicants satisfying favored conditions, including disability, homelessness, and veteran status. Because these conditions are not directly observed, a rule ranking applicants by characteristics must first determine what submitted certificates prove. This paper studies allocation with hard but partial evidence: a disability document may prove disability without proving the absence of a disqualifying tenancy record. A claim is certifiable exactly when every intended claimant has a feasible certificate excluding all outsiders. Chain rules—scores, lexicographic orders, and scalar rankings—require certification of every priority cutoff, whereas reserve rules require certification of each eligibility class. Allocation rules thus select the claim family to be certified. When certification fails, canonical repairs demote unsupported chain priorities and delete unsupported reserve labels. Nonempty reserve eligibility classes can be represented as upper contours of a single chain if and only if they are nested. A housing application illustrates the consequences.

Consider an auction with buyers whose values depend on an underlying state (e.g., market fundamentals). How does the auction format shape the information that buyers' bids reveal about the state? We recast auctions as statistical experiments and compare different auction formats in terms of the (Lehmann) informativeness of the induced experiments. Our main finding is that among a large class of auctions (e.g., $k$th-price, all-pay), the first-price auction is the most informative. As a result, this auction guarantees the highest payoffs to a decision-maker who uses the information revealed by buyers' bids in a monotone decision problem (e.g., a prediction problem or the choice of a reserve price in a future auction).