Papers

This paper provides an explicit characterization of the (unique) equilibrium of the two-bidder all-pay auction with asymmetrically distributed, independent private values. The characterization is achieved through recasting the problem into its equivalence in the quantile space and thereby obtaining equilibrium bid functions that involve only integrals and inverses of the primitives. No regularity assumption is required: the value distributions can be continuous, discrete, singular continuous, or any mixture of these. The explicit formula makes comparative statics transparent. Raising one bidder's value distribution in first-order stochastic dominance raises that bidder's equilibrium bid distribution in the same order. Perturbing a symmetric-bidder model has different revenue effects depending on the direction of the perturbation: whereas slightly weakening one of the two bidders reduces expected revenue, slightly strengthening one of the two has an ambiguous effect. The explicit formula also turns some involved arguments in the literature into direct corollaries.

If a probability measure is a mean-preserving contraction of another, the two measures are said to be in convex order. This paper provides a complete characterization of mean-preserving contractions and their extreme points in the multidimensional setting, extending the results of Kleiner, Moldovanu, Strack, and Whitmeyer (2024) to incorporate fully revealing regions and lower-dimensional pooling regions. A central feature of our characterization is a "concentration " structure: each state can be mapped only to posterior means lying within its own irreducible component. We apply these results to the moment persuasion problem.

In this paper, we study criteria for social evaluation of resource distributions under risk when individuals have expected utility preferences but their utility functions are interpersonally non-comparable. In particular, we focus on cautious evaluation with respect to ex-post distributions. As a key rationality axiom, we adopt Negative Certainty Independence, introduced by Dillenberger (2010). Using this axiom together with Pareto conditions that are compatible with both the rationality axiom and ex-post equity, we characterize a class of social criteria called Cautious Equally Distributed Equivalent (CEDE) criteria. These criteria evaluate risky situations by the lowest certainty equivalent over a set of social utility functions constructed from individual utility functions.

Many digital platforms earn revenue by selling content access and displaying ads. We study monopoly screening by a platform allocating heterogeneous content and ads to heterogeneous consumers. Advertising generates revenue and affects information rents through nuisance, which alters the platform's incentives to allocate content. The optimal mechanism balances a trade-off between advertising and rent extraction: Expanding content access increases advertising revenue but reduces sales revenue by raising information rents. The mechanism features novel distortions in content access and ad exposure, rationalizes contracts across ad-supported platforms, and explains why greater ad profitability may weaken incentives to invest in content quality.

We study optimal growth in a Ramsey economy with irreversible pollution, where the natural absorption capacity is non-monotonic and non-concave a la Forster. In the absence of pollution control, the capital dynamics decouple from pollution, and we characterize a simple threshold on the maximal absorption capacity above which the optimal path is sustainable and below which an optimal regime of irreversible pollution sets in. We then introduce an optimal abatement pollution control to assess whether irreversible pollution ceases to be optimal. We derive a four-dimensional dynamical system for capital, consumption, pollution and the (shadow) cost of pollution, coupled with an algebraic rule for optimal abatement. First, we show that while optimal abatement does shift the irreversibility threshold, it may not rule out optimal irreversible pollution paths. Second, and more importantly, we show that embedding the Forster's pollution dynamics into a Ramsey growth model generates a novel and robust hybrid ecological-economic irreversibility condition that is invisible in pollution-only frameworks. Coupling ecosystem curvature with the social discount rate, it is structurally robust and preeminent over all feasibility conditions amenable to policy intervention, and defines the boundary between a world where sustainability is achievable and one where it is not.

This paper studies school choice when each school has an original priority order and an adjusted priority order reflecting policies such as affirmative action. We introduce a weak notion of stability that permits justified envy under one priority order only when the opposite priority relation is supported by the other. We characterize weakly stable matchings as stable matchings under the intersection of the two priority profiles. Using the efficiency-adjusted deferred acceptance algorithm, we obtain a weakly stable matching that cannot be Pareto improved upon, within the set of weakly stable matchings, for any group containing all improved students by the adjustment. We also show that any Pareto improvement over this outcome necessarily creates justified envy under both priority profiles. Finally, our mechanism is responsive to stronger priority adjustments: the outcome under a stronger affirmative action policy is not Pareto dominated by that under a weaker policy for any group containing all students improved by the stronger adjustment.

This paper compares the stable improvement cycles (SIC) mechanism of Erdil and Ergin (2008) with the efficiency-adjusted deferred acceptance (EADA) mechanism of Kesten (2010) in school choice problems with incomplete priorities. When school priorities are strict partial orders, we show that the EADA mechanism produces a constrained efficient matching. Combined with earlier results for the SIC mechanism, this establishes the outcome equivalence of the two mechanisms: the sets of matchings attainable under them coincide. We then move beyond transitivity and consider acyclic priority relations. On this broader domain, neither mechanism is guaranteed to produce a constrained efficient matching, but their failures take opposite forms. The SIC mechanism may under-improve: its outcome is always stable but may be Pareto dominated by another stable matching. By contrast, the EADA mechanism may over-improve: its outcome is never Pareto dominated by any stable matching but may itself be unstable.

Past research highlights failures of "procedural invariance" when measuring economic preferences using choices versus valuations. We reassess these failures by examining theoretical connections between choices and valuations when preferences are stable but measurements are noisy and individuals are heterogeneous. Even under strong assumptions governing noise and heterogeneity, stability does not generally imply identical measurements. We develop new tests of stable preferences in conjunction with various ancillary assumptions about heterogeneity and noise. We implement these tests using existing data to understand if, in the domain of risk preferences, choices and valuations truly differ and to provide quantitative assessments of any deviations. Limiting to the types of data used in the prior literature, we rarely reject the null of stable preferences. With richer data linking individual choices and valuations and structural assumptions, we find evidence of instability which differs qualitatively from the received wisdom that choices implicate greater risk aversion than valuations.

We study a war of attrition in which each party chooses how far to escalate before conceding. If neither concedes before escalation reaches a random disaster threshold, both receive nothing; otherwise the confrontation ends peacefully. When the parties are ex-ante symmetric and their benefits are independent, improving both parties' private information about their own stakes raises both the probability of peace and each party's ex-ante equilibrium utility. The result holds for every nontrivial mean-preserving spread of posterior values—each party's expected benefit from prevailing given its private information. Higher stakes work in the opposite direction: a first-order stochastic increase in posterior values induces greater persistence, lowers the probability of peace, and can reduce both parties' ex-ante utilities. Starting from symmetry, a sufficiently small improvement in only one party's information also promotes peace; its first-order effect is exactly half that of improving both parties' information. At an asymmetric starting point, however, even a small one-sided improvement can instead lower the probability of peace.

This paper studies how willingness to pay for information depends on risk aversion. We model a decision maker who faces background risk and can acquire information before choosing from a menu of assets. We show that the comparative statics depend on two factors. The first is whether available assets constitute an investment menu, whose payoffs are procyclical with background wealth, or an insurance menu, whose payoffs are countercyclical. The second factor is the tail geometry of background risk. We show that willingness to pay for information decreases with risk aversion for investment menus when the density of background risk is log-concave, and that it increases with risk aversion for insurance menus when background risk is downward-log-convex. The proofs compare the distributions of terminal wealth with and without information. They develop new aggregation arguments for state-dependent single-crossing comparisons. We also construct reversals under strictly log-convex tails for investment menus and super-exponential left tails for insurance menus.

Experimental evidence suggests that ambiguity-sensitive choice can vary systematically with the circumstances of a decision. This paper isolates one channel within a stable preference relation: ambiguity weighting may depend on the act's certainty-equivalent level. After the standard Anscombe-Aumann calibration of consequence utility, a set of behavioral axioms yields a unique continuous family of normalized monotone capacities $\{\nu_v\}_{v\in(0,1)}$. Each nonendpoint act is evaluated by the Choquet integral associated with the capacity at its own interior certainty-equivalent level, while nonendpoint acts on the same indifference surface share the same capacity. Binary event comparisons identify local event weights at each elicited level and trace their cross-level variation, providing tests of the fixed-capacity restriction. Local uncertainty aversion is equivalent to convexity of $\nu_v$ and yields an implicit multiple-priors representation with certainty-equivalent-indexed local cores. Certainty translation invariance holds if and only if the capacity is fixed across levels, recovering the maintained nondegenerate fixed-capacity Choquet expected utility benchmark; global mixture-betweenness yields implicit additive utility, and imposing both restrictions recovers full-support subjective expected utility. The capacity schedule is a reduced-form ambiguity weighting whose variation may reflect changes in ambiguity perception, ambiguity attitude, or both.

We study a mechanism of cooperation in the Prisoner's Dilemma (PD). Incorporating social preferences as efficiency concerns into the PD game, we study how altruism translates into cooperation. Under complete information, cooperation requires the opponent's altruism to clear a threshold. We then introduce a subjective extension of Bayesian Nash equilibrium that relaxes the Common Prior Assumption, letting players hold heterogeneous, potentially misspecified beliefs about each other's altruistic type. Cooperation then depends on beliefs about altruism rather than altruism itself, and can be sustained even when opponents are, on average, only weakly altruistic. When fear of exploitation dominates the temptation to defect, beliefs about the opponent's cooperation become strategic complements, so a cooperative and an uncooperative equilibrium can coexist under identical payoffs and an identical, correctly specified prior. Using multiplier preferences, we then study how robust this belief-driven cooperation is to model misspecification. Cooperation is fragile: it survives only above a threshold level of confidence in one's own belief, and can unravel even when the belief itself correctly supports cooperation. As a formal extension, the same robust-control apparatus, applied to a player's action choice, nests Nash equilibrium, Bayesian Nash equilibrium, and logit Quantal Response Equilibrium as limiting cases. Cooperation depends less on how altruistic agents are than on what they believe about each other, and how confident they are that this belief is right.

Society constantly has to determine the boundaries of what it deems acceptable, from legislative decisions to the guardrails governing autonomous systems. We initiate the axiomatic study of collective consent: given individuals' attitudes toward options, which options should receive societal consent? We organize our analysis around three principles: sufficient support, minority protection, and dominance by decisively better options. Each captures a distinct reason for withholding societal consent from an option. For each principle, we develop a corresponding solution concept that transparently implements the principle and is canonical in a mathematically precise sense. For example, for minority protection, the resulting concept is a consent-adapted version of Moulin's Proportional Veto Core. Balancing multiple principles simultaneously is more challenging. To address this, we develop a game-theoretic characterization of our veto core that naturally gives rise to a family of related concepts. From this family, we identify the Approval-Weighted Veto Core as particularly desirable. By making minorities' blocking power depend on the approval support of the options being challenged, it smoothly interpolates between proportional minority protection and majority support. Experiments on five datasets spanning high-stakes decision-making (such as political elections, ethical AI evaluations, and moral decision-making) show that solution concepts violating a principle in theory also violate it empirically.

We study peer monitoring design in knowledge production. A principal leads agents who work on different but related tasks. By working on their own tasks, agents acquire information that is useful for evaluating their peers' performance. We consider robust contracts under which effort by all agents is the unique rationalizable outcome. The optimal contract induces a hierarchy of monitoring authority: agents easier for the principal to monitor directly are assigned greater authority to evaluate other agents. Task diversity improves information value but weakens peer monitoring. This tension distorts optimal public task assignment toward the principal's core expertise. Confidential random assignment relaxes this distortion by decoupling information production from the perceived monitoring structure.

We investigate the strategic communication of narratives under model uncertainty. The sender has private information about the true data-generating process of publicly observable data. The receiver is uncertain about how to interpret the data, but aware of the sender's incentives to strategically provide interpretations (“narratives”). We theoretically show that the size of the conflict of interest between the sender and the receiver is a crucial determinant of equilibrium communication. In particular, the stronger the sender's bias, (i) the more senders exaggerate their information and (ii) the more receivers correct the sender's action recommendations. In a laboratory experiment, we find evidence in line with both predictions, suggesting that people in complex and uncertain environments take a narrator's strategic incentives into account. Additional analyses reveal that narrative likelihood does not drive receiver behavior and that narratives are, on average, slightly persuasive only when bias is low.

In this paper we consider situations of (multidimensional) spatial majority voting. We analyze such situations having an even number (greater than or equal to 4) of voters and assume that each voter's preference over the set of policies is “Euclidean": i.e., each voter has a most preferred “ideal" policy and the voter's pay-offs from policies decrease as the (Euclidean) distance of the policies from the ideal policy goes up. We confine attention to voting situations for which the core has a single element belonging to the interior of the policy set. It is known that under conditions usual in this literature, this element of the core, generally, is not a Condorcet winner: i.e., there is at least one policy outside the core such that the core-policy cannot be reached from it by just one round of majority domination. We demonstrate that, however, under such conditions, starting from any policy in place, by a finite sequence of majority-dominations (we assume, implicitly, sincere voting) the policy in the core is reached eventually.

I derive an explicit mapping from initial assets, income and the real interest rate to consumption for an income fluctuation problem with a borrowing constraint and CARA utility. I show that there exists a threshold of initial wealth over which the partial equilibrium consumption response to a permanent increase in the real interest rate is positive, consistent with recent empirical evidence. I further show that precautionary savings reinforce the possibility of crowding in and that the possibility of a positive response extends to a more standard CRRA utility whenever the elasticity of intertemporal substitution is strictly less than 1.

In large markets, scarce attention limits partner evaluation and creates allocation loss, which stability magnifies. In an independent random market with average executable degree $d$, unmatched shares fall at rates $e^{-\sqrt d}$ under stability and $e^{-d}$ under maximum matching on the same graph. Changing consideration can make applications rejected in a provisional active-screen computation relevant again. Exact query-neutral implementation must retain allocation-relevant off-screen authorizations; otherwise, missing authorization must be reacquired. Limited-attention deferred acceptance (LA-DA) preserves valid authorizations and reengages eligible pairs. Conditional on exact next-best information and persistent execution rights, adaptive discovery saves a logarithmic factor in reached proposals relative to independent exposure. In an application to speed dating, bilateral reports let us compare stable and maximum matching on restricted graphs, separating missed opportunities from same-graph stability loss. In Chilean school choice, we document 9,502 applicants accepting higher-ranked or new placements through retained rankings.

An open problem in approval-based multiwinner voting concerns whether we can efficiently compute committees that satisfy both justified representation and Pareto optimality. We answer this question negatively by proving that, on the domain of all profiles, outputting a committee satisfying both axioms is NP-hard. An initial proof was found by ChatGPT Astra. This was then verified and rewritten by the author.

We study voluntary disclosure when investors observe firm reports through noisy information intermediaries such as auditors, analysts, rating agencies, or data providers. Any processing noise overturns the standard prediction of a unique partial-disclosure equilibrium. With low disclosure costs, the model unravels to full disclosure despite positive costs. With higher costs, the game admits two threshold equilibria featuring different disclosure probabilities. We characterize how the cost threshold for unraveling and the equilibrium set respond to changes in noise and fundamental uncertainty. In settings with high disclosure, both uncertainty and processing noise reduce disclosure, while higher certification costs can counterintuitively increase it. Endogenizing disclosure costs as optimal fees shows how profit-maximizing intermediaries select among equilibria, potentially generating a high-fee, high-disclosure regime. Extensions with bounded support, uncertain information endowment, endogenous noise, and competing information sources apply the insights to general information environments. The results caution against interpreting greater frictions as necessarily reducing disclosure.

We study why organizations conduct interim performance reviews when monetary rewards are limited. An interim review creates incentive capacity by allowing future work and career opportunities to serve as rewards for past performance. Optimal review policies map a continuum of performance outcomes into a simple incentive ladder: termination, tough or easy continuation, and, for exceptional performance, an early maximal reward with no further work. Review can even sustain high effort when terminal compensation alone cannot. Its timing balances two forces: waiting improves the information revealed by performance, but leaves less future work available to motivate the agent.

This paper studies the intensity of priority violations in matching markets. An agent is said to have very justified envy if she prefers another agent's match to her own and her priority advantage for the object exceeds $k$ ranks. I show that unless $k$ is prohibitively large, Pareto efficiency is incompatible with the elimination of very justified envy. A simple generalization of Deferred Acceptance and Immediate Acceptance is shown to eliminate very justified envy for any $k$. In simulations of random matching markets, I find that modest relaxations to justified envy can yield significant improvements in assignment ranks.

Generative AI has become an everyday advisor, and the systems people consult are live and interactive, not pre-scripted. We ask whether access to such a system changes behavior under risk. In an incentivized experiment (N = 158), participants made lottery choices with an optional decision aid presented as a conventional pre-written tool, a live one-shot AI, or a live interactive AI they could query, with information format held equivalent across conditions. Risk preferences are elicited via DOSE. We find no evidence that access to a live AI advisor changes risk aversion.

Roughly fifty thousand families in England appeal their school assignments each year through a centralized and understudied procedure that improves the placement of about one in five claimants. This paper shows that appeals are not an institutional afterthought: they change how parents report preferences to the education authority and the quality of placements it generates. Once the appeal stage is incorporated, Immediate Acceptance (IA) becomes less manipulable and can support equilibrium outcomes that Pareto dominate those of Deferred Acceptance (DA) under truth-telling, reversing the DA-IA welfare comparison. In a preregistered experiment, we find results consistent with the theoretical predictions: appeals increase truth-telling in IA, leaving DA essentially unchanged, and widen the IA-DA efficiency gap. Around 60% of the IA efficiency gain appears before any appeal is upheld, because subjects anticipating the possibility of a potential appeal rank schools differently.

Although social mobility is widely viewed as desirable, we document an 'inverse-U' shaped relationship with well-being: mobility is positively associated with well-being when low, but the association diminishes as mobility increases and eventually becomes negative. To explain this, we build a model in which agents are embedded in a social comparison network and suffer from falling behind their peers. The model highlights two channels that can cause welfare to be decreasing in mobility at high levels. First, when mobility is high, further increases widen already significant gaps between agents from similar parental backgrounds but of different abilities. Second, when mobility is high, high-ability agents are already relatively well off. So further increases in social mobility increase inequality. We find evidence supportive of both channels in US data. The model also predicts, and data supports, that social integration – where relationships form more along ability than background lines – allows societies to benefit from mobility for longer. We interpret this as social mobility being multidimensional with both economic and social dimensions that are complementary.

I propose a novel, tractable model of pro-social norms in large communities with slightly altruistic agents. Agents participate in the norm to influence others to participate in the norm, influencing further agents. A continuum of equilibria sustain the pro-social norm, varying in the distribution of how much agents are influenced by their observations. If agents' effective altruism $\alpha$ is larger than their impatience $1-\delta$, equilibria exist that are robust to a population of bad actors. Greater strategic homogeneity increases the robustness of the norm. Robustness is not improved by increasing the number of observers of each action beyond 1.

Building on the pioneering paper of Kearns, Roth, and Ryu (SODA'26), we study information aggregation in a networked learning model. The model captures a central pattern in agentic AI: each agent sees only part of the data and passes on only its own conclusion. Their model considers a linear regression problem with the mean squared error (MSE) loss. Agents sit in a DAG and each sees only a subset of the features and its parents' predictions, fits a linear predictor, and passes only its prediction forward. The benchmark is the full-feature learner that sees all raw features. A path of depth $D$ is $M$-covered if every block of $M$ consecutive agents collectively sees all raw features. Kearns, Roth, and Ryu proved that the excess mean squared error of the last agent on such a path is $O(M/\sqrt D)$, and gave a cyclic instance with excess error $\Omega(M/D)$ for $D<M^2$. We close this gap: the correct rate is constant up to depth $M^2$, and $\Theta(M^2/D)$ beyond it. We first give a sharper analysis of the cyclic instance and improve its lower bound to $\Omega(\sqrt{M/D})$ for $D<M^2$. We then construct, for every depth $D\ge M^2$, an $M$-covered path of depth $D$ with excess error $\Omega(M^2/D)$. The same instance gives the constant lower bound for all $D < M^2$. We also show that for any fixed distribution the excess error contracts geometrically along the path, ruling out any single instance that witnesses any polynomial lower bound at every depth. Finally, we prove the same optimal rate for logistic classification in the logit-passing model of Bateni et al., which considers the binary cross-entropy (BCE) loss. The same improved upper bound of $O(M^2/D)$ holds, and we transfer all the regression lower bounds by showing that on those examples the logistic path follows the least-squares path up to rescaling.

We represent a non-Bayesian agent as one who does not completely trust the information they receive. The behavioral expression of complete trust lies in a homogeneity property of Bayesian updating: posterior beliefs do not change if a signal is made arbitrarily rare by scaling down its likelihood vector. We show that simply dropping this property and retaining all other Bayesian behavioral properties yields a unique representation where the agent is still Bayesian but has subjective uncertainty over the information structure generating the signal. The representation result is proved using the Fundamental Theorem of Projective Geometry. We analyze how various updating biases may be rationalized by a lack of trust.

We study tournaments with managerial discretion in hiring. A manager selects a coworker from a pool of candidates and then competes against him in a Lazear–Rosen–style tournament with a prize equal to a share of total output. A profit-maximizing principal sets the prize share together with a head start (or handicap)—an advantage (or disadvantage) in the output comparison—granted to the manager. The head start affects output through three channels: (i) encouraging the manager, (ii) discouraging the new hire, and (iii) inducing the manager to hire a stronger candidate. The hiring effect dominates the discouragement effect until the strongest candidate is hired; beyond that point, any further head start discourages the new hire more than it encourages the manager. The optimal contract therefore grants a head start just large enough to induce the manager to hire the strongest candidate.

I provide the first analytic construction of a canonical Aiyagari economy exhibiting at least three steady states. Along the way, I provide new upper and lower bounds on the stationary capital supply for the case where the net return on saving is negative. I also give parameter restrictions that guarantee the existence of a steady state with a rental rate in the neighborhood of a remarkably simple number: the capital share times the depreciation rate.