Papers

In this paper, we study models of restricted heterogeneity. While the random utility model allows for arbitrary heterogeneity among rational types, we consider the case when an analyst ex-ante restricts the set of rational types to some smaller set of allowable types. We study the behavioral content, the model fit, and the identification properties of restrictions of this form. We find that all three of these can be connected through a common value function that is constructed from observable data. Consistency with a model of restricted heterogeneity is characterized by this value function achieving a value of one, while model fit is given by a value that is potentially less than one. The partially identified set for a given model of restricted heterogeneity is characterized by way of the subdifferential of this value function.

We study the route-set allocation problem between end nodes in capacity-constrained flow networks with transfer costs. We introduce an origin–destination (OD) bidding language, in which a participant bids for bounded conic combinations of inlet–outlet–quantity licences and the mechanism performs the routing through a network-flow optimising winner-determination problem. We then study payment rules for the OD mechanism. Under a restricted model with openly and uniformly priced sources and bidders who are indifferent to the source of the gas, the Vickrey–Clarke–Groves (VCG) payment is core-stable; the key structural fact is that in this regime some optimal aggregate flows never use a physical pipe in both directions, so the winner-determination problem reduces to a single-commodity network flow whose value is submodular in the set of active bidders. If source access is allowed to depend on the individual consumer – a realistic feature, e.g. when gas deals are embedded in bilateral political bargaining – the reduction fails and VCG payments may lie strictly outside the core. For this general model we propose a dual (nodal) pricing rule derived from the shadow prices of the flow-conservation constraints, and prove it is always core-stable, at the cost of dominant-strategy incentive compatibility. Illustrative examples accompany each result.

Public debt supplies liquidity and collateral services only if institutions coordinate on using the same claim. We study this coordination when use carries a recurring cost and a benefit that rises with other users. Above a quality threshold, two positive-adoption equilibria exist, and under best responses the initial user base decides between collapse and high adoption. Under logit choice, as the population grows and noise vanishes, the long-run distribution selects high adoption only above a strictly higher threshold. Debt issuance improves market depth but eventually dilutes backing per claim. This trade-off creates a range of debt levels supporting the liquidity premium of public debt in macroeconomic models and a narrower range supporting its long-run selection. At the boundary of the wider range, the premium is discontinuous. A matching transfer that corrects the adoption externality makes stationary selection maximize network surplus. Transfers can also help launch a network without permanent support.

Many firms that run A/B tests struggle with low statistical power, increasing the risk that launch decisions are driven by noise rather than true impact. We argue that in decentralized organizations, low power can reflect misaligned incentives: product teams choose what and how to test on a customer-facing experience to maximize their private reward, while the experience owner sets evaluation rules and launch criteria to optimize the experience. We formalize this interaction via a principal-agent model and show that evaluating tests using raw impact estimates creates a reward to sampling noise. Correctly calibrated posterior-mean evaluation removes this reward and creates a local incentive to reallocate toward fewer, more precise tests of more ambitious ideas. Using data on A/B tests run at Amazon, we document patterns consistent with these model predictions. After an Amazon experience shifted to posterior-mean-based evaluation in 2024, test volume declined while both precision and the dispersion of true impacts increased, more than doubling signal-to-noise ratios. Our results highlight that A/B testing methodologies can shape not only measurement and launch decisions, but which tests are pursued in the first place.

We study how retained ownership supports the value of an asset that pays no dividends and is held only for resale. A sponsor chooses hidden maintenance that determines market survival, bears its full cost, and captures only the benefit accruing to its retained tokens. A positive stationary equilibrium exists if and only if retention meets an endogenous minimum. Under additional curvature restrictions, retention above this threshold supports two positive stationary equilibria. Conditional on survival, prices below the upper equilibrium converge to the lower one while the upper price is the largest feasible initial valuation. Greater retention expands the feasible price interval. Credible news that future retention will be below the minimum causes an immediate collapse through backward unraveling. The model identifies a governance channel through which insider unlocks can affect valuation without changing total token supply or fundamental cash flows.

The resilience and censorship resistance of a blockchain depend on where the validators and proposers of that blockchain physically operate. We study the economic incentives behind this location choice, both with a single proposer and with multiple concurrent proposers. Formally, we study a game where proposers first choose locations and then compete in a first-price auction for an opportunity whose common value is driven by information from geographically dispersed sources. A single proposer minimizes variance-weighted delay, locating at a weighted median of the sources and co-locating with any dominant one. By contrast, with two proposers, information both observe equally early earns no rent, and each proposer's expected profit is proportional to the standard deviation of the information it receives before its rival. We show that the location game admits the jointly unobserved variance as an ordinal potential, so global solutions of a weighted two-median problem are equilibria. With two sources, one proposer locates at each, however weak one is. With more proposers and at least as many sources, equilibrium locations are distinct under regular bidding. Multiple concurrent proposers thus do more than limit any single proposer's control over inclusion: by rewarding exclusive rather than shared information, they create an economic force toward geographic decentralization.

Relying on manipulable characteristics to target the allocation of resources is fraught with difficulties. Naively optimal rules lead to falsification and allocative inefficiency. Optimizing the rule for allocative efficiency while accounting for falsification typically induces falsification, at a heavy cost to the agents. Moreover, falsification generates negative externalities. We characterize optimal falsification-proof rules under a broad range of falsification technologies. We also provide an honesty condition under which they solve the unconstrained problem of a planner who maximizes a weighted sum of allocative surplus and agents' welfare.

A seller without commitment to future offers interacts with a buyer over time. There are many goods for sale, with the buyer's value for a bundle the sum of each bundled good's value. Each date, the seller jointly announces a menu of subsets of the remaining inventory and current prices, and the buyer may purchase one of the offered subsets or wait. In the next period, the seller may again offer any menu of the remaining goods. Neither buyer nor seller can commit to future behavior. I show that as players become maximally patient, if scope increases sufficiently fast compared to patience, revenue per good converges to expected value per good and buyer utility per good converges to zero, in any equilibrium. But if patience instead grows sufficiently fast compared to scope, seller revenue per good converges to the lowest possible value and the buyer captures all remaining surplus, in any equilibrium.

Artificial intelligence (AI) can synthesize dispersed information into balanced and informative content, raising the possibility that AI may help reduce polarization. We show that this promise can be undermined by the strategic response of content producers. We develop a game-theoretic model in which consumers acquire information to make downstream decisions, content producers allocate limited informational capacity between broadly valuable vertical information and horizontally differentiated information, and AI provides an alternative source of synthesized information. The effects of AI unfold in three phases as its reliability increases. When reliability is low, AI has no effect on the market. At intermediate levels, AI disciplines prices without attracting consumers or changing content. When AI becomes sufficiently reliable, consumers begin to substitute toward it, and content producers respond by shifting informational capacity away from the vertical dimension and toward horizontally differentiated content, thereby increasing content polarization. The mechanism operates through audience composition: AI attracts consumers who are less well matched to individual producers, leaving producers with stronger incentives to cater to their remaining audiences. The polarization effect intensifies with AI reliability but weakens with greater competition among content producers. Our findings highlight a potential wedge between AI's direct and equilibrium effects: a technology that provides consumers with more balanced information can indirectly make the broader content ecosystem more polarized.

We study a continuum version of the stable marriage problem, in which each agent has a variable mass to be paired to the opposite side. An agent's mass is interpretable as the divisible time of a single atomistic agent, or as a mass of infinitesimal agents of a particular type. Our object of interest is the mapping between the vector of masses to the set of stable matches. As in the canonical stable marriage model, the set of stable matches can be multi-valued, so this mapping is a correspondence. This correspondence is continuous if and only if the stable match is unique, implying that small changes in the masses may cause discontinuous jumps in the set of stable matches.

We study the unit-demand pricing problem under min-buying behavior, where customers purchase the lowest-priced item that yields non-negative utility. In contrast to the quasi-linear model, we show that uniform pricing becomes substantially more effective under min-buying. First, we study symmetric environments. We show that for min-buying customers with independent and identically distributed valuations, a uniform price across items is optimal. We then extend this optimality result to all valuations drawn from exchangeable and affiliated distributions. However, uniform pricing is not optimal in all symmetric environments: for min-buying customers we construct an exchangeable and non-affiliated valuation distribution for which the gap between uniform pricing and optimal item pricing is logarithmic in the number of items. This gap is tight and matches the worst-case gap in the quasi-linear setting. Next, we consider asymmetric environments in which valuations are independent but not identically distributed. When these valuations are regular and customers are min-buying, we show that a uniform price guarantees approximately 69.86% of the optimal item-pricing revenue and this is tight. Overall, our results highlight that the value of non-uniform pricing substantially diminishes, and often disappears entirely, under more conservative demand models in which customers engage in satisficing behaviors such as min-buying.

Organizations pairing a human and a machine on a task decide, often by default, which executes each instance and what happens when both do. We account for what this attains under the squared rule, with performance distributed over instances to capture generalization difficulty. A gross stake lies between the skills' mean and best per instance. It splits at the best single skill into a systematic part, known from separate assessments and secured by commitment, and a residual, the expected value of perfect information on which skill each instance favors, known only from paired observation and split further by classes. Skills set the stake; workflows decide the take, via two channels. Routing directs work, weighting or selecting responses; with binary truth it is capped by the best skill per instance. Reading responses as joint evidence is not routing; what they jointly reveal caps it. Synergy lets skills interact before responding; bounded by no skill either way, its lift over independent responses must clear a break-even and can fall below one. As algorithms, arrangements form a ladder stating what each reads, holds and records, and a procedure whose checks keep earlier gains when class means are known and lose little on finite records given a margin. The theory extends to many skills, each worth what it adds where it beats all others held, and to competing skills, where at parity a single failure's allowed cost decides. In a public chest-radiograph study with 227 radiologists, they are near parity with the model and the stake is mostly residual; assisted reading, no better on average originally, returned less than averaging both responses; recalibrating the model alone beats any deployable arrangement of raw responses. Organizations can learn from their records what is at stake, which arrangement collects it and what evidence each step needs; pricing costs and errors is future work.

A principal funds an agent's project over two periods, with a midterm review providing a public signal about project quality. The agent privately knows the project's quality and always prefers more funding, while the principal wants to match funding to quality. A natural benchmark uses the review only after it arrives, to update beliefs and improve the second-period allocation. The optimal mechanism instead frontloads the review's information value: it also uses the review as an incentive device to elicit truthful reporting up front, thereby strictly improving the principal's first-period expected payoff. In the optimal mechanism, higher-quality projects receive more funding initially but face larger cuts after a bad review, leaving them with less funding than lower-quality projects. A good review increases funding, but the resulting allocation need not preserve the initial ranking of projects and eventually declines with quality.

We study generalized verifiable disclosure by a sender with type-independent preferences. We first characterize all perfect Bayesian equilibria as partitions of the sender's types into coalitions ordered by payoff. An equilibrium survives our coalition-proofness criterion if no group of types can profitably coordinate an announced deviation that only they are able and willing to join. Coalition-proof equilibria are greedy partitions: at each step, a coalition of the remaining types attains the highest payoff consistent with equilibrium. In our general setting, coalition-proof equilibria may fail to exist. We establish existence under restrictions on preferences and evidence: quasiconcavity with message completeness, betweenness, cheap talk with message completeness, and payoff degradation. For a disclosure game with maximally rich evidence, we show that the sender's ex-ante payoff in a coalition-proof equilibrium is a piecewise linear tent over the belief simplex, analogous to the concave closure in Bayesian persuasion and the quasiconcave closure in cheap talk.

When producers in a network compete in quantities, an innovator's profit contains none of the change in allocative efficiency that its innovation causes, whether a gain or a loss, because its own choices are optimal and other effects on its profit are transfers. A process innovator also forgoes its own and downstream markups on the output its innovation adds at a fixed allocation, worth 14 to 26 percent of its cost saving for U.S. public firms in 2015. For innovators accounting for 68 percent of sales, the change in allocative efficiency exceeds a tenth of the private return. In a Markov R&D game, reallocation of R&D across firms is likewise external to the innovator. Rivals' profits and market values can misstate the welfare cost of business stealing from them even in sign. With estimated spillovers, the social return to R&D is 5.39 times the private return, against 2.53 in output-based accounting with estimated business stealing, mainly because that accounting credits the innovator with its rivals' lost sales.

Invasive alien species (IAS) generate substantial ecological and economic damages that often transcend political boundaries, creating strong incentives for coordinated management. We develop a two-region ecological-economic model of IAS control that integrates prevention and eradication measures with population dynamics characterized by logistic growth and an Allee effect. We derive analytical results on the interaction between ecological thresholds and strategic behaviour and compare outcomes under cooperation (central planner) and non-cooperation (open loop Nash equilibrium and Markovian Nash equilibrium). We show that, under realistic control costs, neither prevention nor eradication can eliminate invasive populations in finite time, and complete prevention of cross-border spread is generally not optimal. In the absence of an Allee effect, the zero-population equilibrium is unstable, implying long-run persistence of the invasive species. By contrast, the presence of an Allee effect fundamentally alters system dynamics by making extinction locally stable and creating a basin of attraction within which eradication becomes feasible. This finding highlights the economic significance of ecological thresholds and demonstrates how delays in management can shift populations beyond critical levels, after which eradication is unlikely regardless of subsequent control efforts. Numerical simulations further show that cooperative management expands the set of initial conditions leading to eradication and consistently reduces aggregate social costs relative to decentralized management. The results provide a formal rationale for rapid intervention, precautionary regulation, and stronger multilateral cooperation in IAS management, particularly in jurisdictions such as the European Union where listing and control actions may be delayed pending evidence of harm.

We study capital budgeting when a manager privately knows project productivity and her empire-building benefits, while headquarters lacks credible priors. Headquarters minimizes maximum regret relative to informed investment. Without compensation, the optimal policy is a spending cap balancing empire-building overinvestment against profitable investment forgone. Compensation helps when empire-building incentives are weak. The optimal payment incentivizes restraint, declines with investment, and reaches zero at the spending cap, supporting greater managerial discretion. When empire-building incentives are strong, compensation cannot distinguish productive investment from biased expansion; therefore, a spending cap alone is optimal.

We study the optimal sequential aggregation of randomly arriving votes from a finite population to identify an unknown majority preference before a fixed deadline, trading off decision accuracy against the cost of delay. The optimal policy is a dynamic majority-quorum rule: a joint, time-varying threshold on vote lead and count, in which quorum and supermajority requirements emerge as the solution to an inference problem about non-participants' preferences. At each date, the continuation region is lens-shaped: the lead required to stop grows with turnout until too few voters remain to overturn it, and it vanishes at the deadline. We characterize conditions under which the boundary is monotone in the stakes, the arrival process, and time. Because the exact boundary admits no closed form, we derive a large-population approximation that reduces the two-dimensional rule onto a single sufficient statistic, and express the rule as a sequential significance test set by a single error tolerance. Calibrated on Polkadot governance data, an out-of-sample evaluation finds that our rule with a 2% error tolerance halves decision times relative to the incumbent mechanism.

How should consumers learn when a seller chooses a menu of product qualities and prices? We study information design when the seller observes the learning policy, but not consumers' private signals, before choosing its menu. Under cost-curvature conditions, we characterize optimal learning when consumer surplus receives greater weight than profit. Even with two valuations, every optimal posterior distribution combines an interval of posterior types with an efficiently served atom at the highest valuation. The induced menu features a continuum of differentiated products. Strikingly, optimal learning can also induce a lower posterior atom, separated from this interval by a support gap. Buyers in this atom either purchase an isolated low-quality product or are excluded, even when trade with every buyer creates gains. Both configurations can be optimal for the same prior and welfare weight. Served buyers with distinct posterior types are never bunched at the same quality. General finite priors can yield several separating regions and trading atoms. We also characterize the optimal joint design of learning and valuation-dependent segmentation, showing, among other results, that every posterior type with positive gains from trade must be served. Joint design can raise both consumer surplus and profit relative to buyer-optimal private learning alone. Even random assignment to segments with different learning policies and separate menus can give consumers more surplus than any single market yielding the same profit. Additional price discrimination can therefore benefit consumers, even when privacy restrictions require segmentation to reveal nothing about valuations to the seller.

A sender with commitment provides additional information to an already informed receiver. Final posterior means must be more dispersed than initial means and less dispersed than the state, in convex order. We characterize when these two plausibility constraints are also sufficient, so that every distribution satisfying them can be induced. If the state has a positive density, they are sufficient exactly under interval-partition information: the receiver learns which interval of a partition contains the state and nothing more, where an interval may be a single point. Otherwise, a nonempty open set of distributions satisfying both constraints cannot be induced, even when the sender observes the receiver's information. We use the sufficient case to derive an optimal symmetric disclosure rule in a second-price auction where bidders initially know valuation intervals.

We study stochastic dynamic matching with abandonment, a fundamental model in which agents of different types arrive over time, may abandon the market while waiting, and can be matched in pairs for rewards that depend on their types. No online policy can guarantee more than $0.5$ of the omniscient benchmark, which knows all arrival and departure times. Whether this guarantee is achievable has been a central open problem, even in special cases. We resolve this problem by showing that, on every instance, a simple static priority policy, which is computable in polynomial time, earns at least $0.5$ of the omniscient benchmark. This establishes that the optimal competitive ratio is exactly $0.5$, improving the previous best guarantee of 0.192 for the general model [Li et al. 2026; Collina et al. 2020] Our analysis rests on a key stochastic result, which is a new lower bound on the probability that some agent from a given set of types is available. Building on this bound, we develop two approaches: a primal approach that reads the priorities from an optimal solution of a novel linear program, and a dual approach that assigns a “value” to each type, and prioritizes matches with high “surplus” (reward minus value of involved agents). These values are the unique solution of a fixed-point equation derived from linear programming duality. We also show that the two approaches are closely connected.

"Security by obscurity," or the idea that hiding how a system works helps protect it from adversaries, has long been poorly regarded in the security community. Yet its intuitive appeal persists, and it has resurfaced repeatedly in industry practices and public debates over the years. The logic, on the one hand, is that open scrutiny of systems is the best way to find and respond to problems; and on the other hand, that too much openness can increase risk by giving adversaries a roadmap for attack. This isn't purely a technical question, but a human one: it's about how attackers and good-faith security researchers respond to openness in the real world. As such, security experts base their stance on decades of community experience; however, the field lacks empirical or theoretical foundations to back up these long-standing beliefs. We provide the first rigorous modeling of "security by obscurity," aiming to capture how rational actors will respond to openness or obscurity in fallible systems. We prove that in equilibrium under realistic model conditions, "obscured" systems are more likely to suffer successful attacks than "open" systems — establishing theoretical support for the longstanding received wisdom.

Parents seeking childcare often face long waitlists. At the same time, vacancies at childcare centers can remain unfilled for extended periods. We trace this paradox to two persistent features of childcare services. First, families consider multiple child care options due to enrollment uncertainties, resulting in phantom listings that remain on waitlists even after families have found care elsewhere or no longer need a slot. Second, filling a slot is time-consuming: centers learn whether a family is actively seeking enrollment only after making an offer and waiting for a response. As families pursue alternatives while they wait and their children age, these delays and feedback effects amplify the mismatch between demand and available capacity. We study two operational remedies. First, we examine regular verification that removes phantom listings before offers are made, improving the efficiency of enrollment and reducing vacancies. Second, we study mixed-age classrooms, in which some slots designated for older children can be flexibly used by younger children. This flexibility increases utilization, shortens waits, and reduces wasted offers. Its benefits extend beyond conventional pooling: as children move between age groups, classrooms can be filled through internal flows rather than costly external search, further reducing enrollment delays. Together, verification and mixed use offer a way to expand effective capacity in early childhood classrooms, where regulatory and operational constraints make adding physical capacity particularly costly.

A second-price auction must determine its price but need not learn how far losing values lie below it. We show that protecting this information from the seller conflicts with auction credibility. In deterministic protocols with private communication, lower-tail privacy forces the first informative question to reveal whether a bidder has the highest possible value. The seller can then manipulate the winner's payment without any bidder detecting the deviation, increasing revenue at some valuation profiles and never reducing it. A descending protocol conceals losing values below the price but permits manipulation; with mandatory sale, a credible ascending protocol reveals them.

We study social welfare rules with strict individual and social preferences. A preference profile is dictatorial for a rule if the social preference coincides with some agent's preference and no agent with a different preference can change the social preference unilaterally. We establish that (i) a rule is dictatorial if and only if all of its profiles are dictatorial; and (ii) if a rule satisfies unanimity and independence (of irrelevant alternatives), then all its profiles must be dictatorial. These results constitute a proof of Arrow's Impossibility Theorem.

We study the strategic design of learning algorithms in a canonical continuous-time pricing game. We introduce a meta-game in which firms select learning rates for a gradient dynamic, evaluating payoffs as the discounted sum of profits accrued along the entire learning path. We uncover a fundamental dichotomy driven by stage-game incentives: if the stage game exhibits strategic substitutability, firms unambiguously prefer the fastest possible algorithms to rapidly exploit a gradually adjusting opponent. Under strategic complementarity, however, an excessively fast algorithm accelerates the rival's competitive response, destroying transitional profit margins. Even though the competitive price is a strictly dominant action in the underlying stage game, we prove that firms optimally design sluggish algorithms, extracting surplus during a prolonged convergence to the competitive equilibrium.

An agent learns from data that many parameters of her model explain equally well. Berk's theorem states that her belief concentrates on the parameters that best fit the data, but does not select between them. We show that, with a continuum of parameters, the posterior concentrates on the best-fitting parameters with the smallest local learning coefficient. We propose a definition of narratives, subsets of the best-fitting parameters on which the learning coefficient is constant. Narratives are characterized by the number of coincidences they require (complexity) and how exactly each must hold (robustness). When the agent's actions affect her data, every long-run action is a singular equilibrium, a best reply to a belief supported on the least complex and most robust narratives. Singular equilibrium refines Berk-Nash and self-confirming equilibrium by restricting overly complex or knife-edge off-path beliefs, and its strict uniform version characterizes uniformly stable actions.

Standard theories trace information asymmetry to privately held information, heterogeneous signals, or costly information acquisition. We identify a distinct mechanism: otherwise identical rational agents observing a common Markov state at asynchronous times can hold different predictive distributions because their information differs in age. When the transition kernel separates information ages, independent Bernoulli observation arrivals make such divergence recur infinitely often almost surely, even with identical arrival probabilities. When agents instead choose costly updating intensities, independent update realizations can regenerate heterogeneous information ages among ex ante identical agents. In a stationary Gaussian AR(1) environment, the consequences depend on common staleness as well as the age gap: holding the gap fixed, older information raises individual uncertainty while reducing expected squared forecast disagreement and the value of certifying relative freshness. This generates stale consensus: low disagreement despite high uncertainty. With multiple ordered ages, costly certification supports partial-unraveling equilibria in which fresher types certify and sufficiently stale types pool. Under geometric information ages, more frequent updating weakly lowers the smallest and largest equilibrium disclosure cutoffs wherever positive-certification equilibria exist. The framework has implications for credit, insurance, financial markets, and multi-agent AI.

This paper develops a general framework for dynamic mechanism and information design with AI agents, encompassing optimal contracting and integrating evolving hidden information and hidden action with partial verification, technological authorization, and multi-agent interaction. It nests conventional dynamic screening, hidden-action contracting, and conditional dynamic information design, while allowing reporting, action, and information-use decisions to interact through a common continuation mechanism. We establish a dynamic revelation principle and a recursive characterization of implementability in which truthful reporting and post-report obedience are jointly determined through continuation incentives. In quasilinear optimal-contracting environments, dynamic envelope and integral-monotonicity methods yield a verification-adjusted dynamic virtual-surplus representation and identify three distinct margins: dynamic information rents, verification rents, and the implementation cost of hidden action. These margins generate a branched hierarchy separating conventional dynamic screening, hidden-action contracting, and their joint problem. We also study the joint design of monitoring, information use, and incentives: more informative monitoring capacity expands the designer's opportunity set, but full disclosure need not be optimal, and information use can itself alter hidden-action incentives. With multiple agents, correlated information, peer discipline, coupled incentives, joint feasibility, and continuation opportunities create additional strategic interactions. Although motivated by AI-agent environments, the framework applies more broadly to dynamic agency settings with similar economic features.

Can noisier threshold selection produce a group with higher mean true value? We answer this question by varying the scale of a fixed assessment error. Holding the selection rate fixed, less noise yields a first-order stochastically dominant distribution of selected values. At a fixed threshold, however, more noise can raise the selected mean even as selection loss, which weights selection mistakes by the distance of true value from the threshold, increases. Under joint Gaussianity, we characterize when the selected mean rises or falls with noise. In treatment selection, noise alone can generate subgroup differences in participants' average gains despite identical population gain distributions.