Papers

A honeytoken, a decoy credential or record whose use reveals an intruder, produces defence intelligence only if an adversary sometimes treats it as genuine. The adversary can instead pay to fingerprint it. I model this problem as information design followed by receiver information acquisition. Without fingerprinting, a defender whose installed trap prevalence exceeds the adversary's participation boundary places the attacked pool exactly at that boundary: calibrated bait. That posterior also maximises the gross value of any fixed informative diagnostic with finitely many signal outcomes. For a perfect covert test, the resulting appearance design has a closed-form, prior-dependent characterisation: expensive testing preserves calibrated bait, intermediate-cost testing produces under-calibrated bait, and cheap testing yields pooling, protected segmentation or abstention. Free and costless adjustment of trap prevalence makes non-degenerate segmentation unnecessary, but a sufficiently large adjustment cost around a sufficiently high inherited composition can sustain it. Finally, along an exogenously declining fingerprinting-cost path, lower cost reduces trap activation without reducing genuine compromise within the under-calibrated regime. Evaluation against fresh attackers can therefore overstate the durability of reusable bait.

We propose a measure of lottery complexity that combines probabilistic dispersion with dissimilarity between outcomes. Taking degenerate lotteries, which yield a single outcome with certainty, as the simplest alternatives, we measure complexity by proximity to this class. Specifically, for each degenerate lottery, we compute the expected distance between its certain outcome and the lottery's outcomes, and take the minimum across all degenerate lotteries. We provide an axiomatic characterization establishing uniqueness up to positive rescaling, study how complexity changes under outcome compression, and characterize maximally complex lotteries. Finally, we introduce Complexity-Adjusted Expected Utility preferences and characterize adherence to stochastic dominance and strong risk aversion.

AI is increasingly being used to help with AI R&D. Under certain conditions this feedback loop might be able to produce an intelligence explosion, with rapidly escalating AI capabilities. I explore the mathematics of the most explosive possibilities, with an eye to understanding what drives the dynamics. I show that singular growth (towards a vertical asymptote) is harder to achieve than would be expected from recent economics-inspired modelling, and that there is an important but neglected class of growth rates that are faster than exponential but don't lead to a vertical asymptote. I draw out the generation time (the time to go around the feedback loop) as a neglected parameter that plays a pivotal role in determining the behaviour of any intelligence explosion — one cannot have singular growth unless the generation time rapidly approaches zero.

This paper studies how information censoring enables a myopic cutoff rule in Bayesian sequential search. Under full information, Bayesian learning generally destroys the monotonicity of continuation values, preventing simple cutoff rules. We show that one-sided censoring restores monotonicity by limiting posterior fluctuations, thereby making a myopic cutoff rule optimal. By decomposing the intertemporal change in the marginal value of search into a fallback-value effect and a learning effect, we derive necessary and sufficient conditions for monotonicity under lower censoring and characterize the optimal cutoff rule. In contrast, under full revelation, monotonicity requires highly restrictive conditions. We further show that expected monotonicity (i.e., the supermartingale property) is characterized by the same conditions under both lower censoring and full revelation, owing to Bayes plausibility and the affine structure of the problem. Thus, censoring restores monotonicity not by altering expected learning, but by reducing posterior volatility. Finally, we apply our framework to job search, consumer price search, and product experimentation.

We formulate the voter's strategic information acquisition to control the future self's action as a Bayesian persuasion problem. Our main result shows that acquiring information that is irrelevant to the voter's objective can be a worst-case optimal solution: it can reduce the possibility that the future self is swayed by additional information whose content is ambiguous to the current voter.

We develop an axiomatic model of robust Bayesian persuasion where the sender cannot fully control the information available to the receiver. After selecting an information structure, the sender expects that more informative structures might be implemented. We model this by allowing the sender to assess each information structure under worst-case information leakage, represented by a set of more informative structures. The model encompasses a wide range of examples of information leakage, which we also explore.

We develop a model of interbank networks with random liquidity shocks. Networks of dilutable debt—e.g., long-term, unsecured—facilitate efficient liquidity transfers: Shocked banks pledge interbank claims as collateral for new senior debt, diluting existing debt. Unlike with non-dilutable debt, indebtedness and connectedness are sources of stability, not fragility. Dilution is thus a “backdoor bail-in” that reallocates losses absent a resolution authority, trigger security, or ex post renegotiation. We uncover a class of networks, “exponential networks,” that implement optimal contingent transfers via plain debt. Yet exponential networks are not pairwise stable, whereas some core–periphery networks are, rationalizing observed interbank structures and their under-insurance against crises.

Article 14 of the EU AI Act requires that a high-risk system be overseen by natural persons who understand its limits, remain alert to automation bias, and can disregard or override its output. That capability is invisible in the output and decays precisely when the system is good. A provider can certify it only by an outcome-contingent liability commitment, and how large a commitment courts will enforce is itself open. After Cavendish the enforceable multiple of actual loss is measured against the legitimate interest the clause protects; where that interest is preserved oversight capability, it exists only if the market separates, which requires a sufficiently permissive doctrine. We model the enforceable ceiling as a fixed point of an expectations map on a complete lattice. Existence follows from Knaster-Tarski. Because no case separates at compensation, compensation is always an equilibrium; once the doctrinal uplift clears a threshold set by the case population, a permissive equilibrium and a watershed appear, and the map inherits the provider's solvency cap, so an insurance withdrawal deep enough and long enough can destroy the permissive equilibrium, which returning cover does not restore. Perturbing the adjustment yields a closed-form long-run tipping point, exact recovery times, and the noise levels at which irreversibility fails. The welfare cost of the resulting trap is capped at the drafting cost of primary-obligation substitutes. The order-theoretic core is machine-checked in Lean 4 with an axiom-free report. Both AI-side parameters, shared-base-model intensity and provability, are matched to instruments available in 2026.

In organized crime, membership can adjust around enforcement while division norms remain in place. We model this in three stages: division norms fix how every possible coalition divides its proceeds; the authority then attaches deterrence capacity to named members before knowing which coalition will form; membership adjusts last, among those who remain undeterred. Under population-monotone division, where no incumbent loses rent as a coalition expands, the minimum budget needed to block every coalition is the cost of a shortest dismantling path, removing one member at a time. A high-rent hub can be the best first target because her removal lowers the rents of those who remain. Holding coalition proceeds fixed, the Shapley value applied to every coalition uniquely maximizes this budget among population-monotone norms whenever it is itself population monotone. It does so by making every removal order equally costly. Allowing part of the proceeds to be reallocated after capacities are observed weakly raises the budget for any fixed population-monotone norm, although exact Shapley optimality can fail even when the reallocated share is arbitrarily small.

We solve a natural bimatrix game related to graphs. We consider a finite directed graph $G=(V,E),$ where the strategy set of Player I is the set of vertices $V$ and that of Player II is the set of edges $E.$ There are two sets of positive weights ${\{\alpha_e\}}_{e\in E}$ and ${\{\beta_e\}}_{e\in E}.$ If Player I chooses a vertex $v$ and Player II chooses an edge $e,$ then the payoff to both players is zero if $v$ and $e$ are not incident. If $e$ originates from $v,$ then Player I obtains $\alpha_e$ and Player II obtains $-\beta_e.$ If $e$ terminates at $v,$ then Player I obtains $-\alpha_e$ and Player II obtains $\beta_e.$ For this game the payoff matrices are weighted incidence matrices of the graph $G.$ We show that when the graph is acyclic, Player I has a unique strategy in any equilibrium. At this strategy, every vertex is chosen with a probability that is proportional to the maximum length over all directed paths originating from that vertex. Defining the path matrix of the graph, it is shown that the set of all equilibrium strategies of Player II is the convex hull of the column vectors of the path matrix. This work extends earlier results of Bapat and Tijs (1997) for zero-sum games.

This paper studies general equilibrium when households and firms choose price-contingent schedules and market clearing determines prices. A unilateral schedule change therefore changes both an agent's realized allocation and the price at which it is evaluated. We call the resulting outcome a schedule equilibrium. The central object is the response of the clearing price to an agent's own schedule. This residual price response enters the household and firm first-order conditions, provides the strategic component of markups, and links conduct to observable equilibrium variation. We give conditions for existence, derive a trembling-hand refinement, and show how competitive, Cournot, and supply-function models arise as special cases. Applications to monopoly and vertical market power show how general-equilibrium feedback can alter familiar partial-equilibrium conclusions. We then allow firm mass, ownership, and technology to be endogenous. Free entry need not be efficient because entrants do not internalize their effect on the rest of the economy. Households choose capitalization and thereby ownership and firm creation, while investment moves active firms through production-function space. The same price-response mechanism therefore links market power, entry, ownership, and technological change within a common general-equilibrium framework.

Clinical algorithms can perform differently across patient groups, a concern that grows as these algorithms increasingly take the form of artificial intelligence (AI) models. In the United States, a 2024 federal rule bars healthcare providers that receive federal funds from discriminating through their use of clinical algorithms, which exposes them to liability when such use disadvantages a protected patient group. We examine how such liability considerations reshape (i) an AI firm's model design decisions that drive group-specific accuracy and (ii) a physician's decisions to use AI in healthcare delivery. The firm designs an AI model for two patient groups, and improving accuracy for the disadvantaged group is more costly. The physician (who remains the accountable decision maker) then decides whether to consult AI, weighing the reduction in clinical uncertainty against expected liability exposure when AI errors disproportionately affect the disadvantaged group. We find that this liability can induce disparate use of AI: the physician may reduce AI use overall and, over an intermediate range of liability, rely on AI less for disadvantaged patients. The effect is non-monotone. As liability increases, the physician's use of AI for disadvantaged patients first declines, then rises as the firm reallocates investment toward reducing disparity or switches to an equal-accuracy design. Mandating equal algorithmic accuracy across patient groups can then inadvertently harm both groups, because a uniform accuracy requirement distorts the firm's investment incentives and the physician's equilibrium AI-use decisions.

We study a platform that prefers to sell the more profitable of two products. It designs an algorithm that determines the product the consumer encounters first, conditional on her best match. The algorithm simultaneously manipulates consumer attention (steers) and communicates information about match quality (informs). When the algorithm is opaque, it is difficult for a consumer to understand how product order is generated and what it reveals. In the platform's preferred equilibrium, it places the profitable product first. When the algorithm is transparent, the consumer understands the algorithm and what it conveys. Thus, the algorithm can persuade as well as steer. In some cases, the equilibrium algorithm deters search, in others, encourages it. In the former case, transparency helps consumers; in the latter, it harms some or all of them. Extending or shifting transparency requirements uncouples steering from information provision, reverting the consumer's welfare to opacity.

AI predicts; humans use its predictions to make decisions. These predictions are combined with human verification and analysis, queries to other statistical models, and so on. The economic value of an AI, therefore, depends on how it interacts with the surrounding decision environment. We describe the value of AI as part of this “composite experiment” where AI makes a coarse prediction of the state of the world, show what this means for optimal model training via a geometric argument, explain why optimal training can be discontinuous in economic variables, and study how heterogeneous users or monopoly model trainers affect these results. In particular, maximizing the unconditional accuracy of AI predictions is generally suboptimal.

We study two observable queues with identical service rates, serving agents who arrive stochastically over time. Agents join the queue that minimizes their expected waiting time. Assuming one queue uses the ubiquitous First-Come-First-Served (FCFS) service rule, we show that by simply modifying its service order, the other queue can capture a strict majority of the demand. We establish an upper bound on the arrival share any rule can capture against FCFS. When both queues can design their service order, we show a novel variant of Last-Come-First-Served (LCFS) is an equilibrium in a low congestion regime. Without commitment, the picture changes, and there is an equilibrium where both queues use FCFS, and agents route to the queue with the shorter waitlist.

We extend the concept of priority-neutral matching, introduced by Reny (2022) in the school choice context, to the roommate problem. We prove three main results. First, a blocking-neutral matching always exists in constrained roommate problems under arbitrary feasibility constraints (Theorem 1). Second, the set of stable matchings is contained in the set of blocking-neutral matchings, which in turn is contained in the set of Pareto-optimal matchings (Theorem 2). Third, whenever stable matchings exist, the set of blocking-neutral matchings coincides with the set of stable matchings (Theorem 3). We also show that existence fails under weak preferences and extend the concept to two-sided school choice.

When generative AI drives the marginal cost of a persuasive expert artefact toward zero, production-cost signals of competence collapse and outcome-contingent liability commitments take their place. Such commitments look robust to better AI: a positive failure rate always leaves a residual to price. We show that this robustness rests on an unstated homogeneity assumption, and that a liability commitment faces three ceilings, not one. AI error decomposes into idiosyncratic and common components; capability growth eliminates the idiosyncratic part faster (Kim et al., 2025), so the residual becomes progressively common - and common error is precisely what a verifier drawn from the same foundation model cannot observe: judge scores correlate with judge-generator model similarity at an average r=0.84 (Goel et al., 2025). Provability is therefore state-dependent, theta_eff = theta_0(1 - xi*kappa). Separation requires the commitment that must be posted to fall below what can be posted, v/theta_eff <= min{Lbar, mv}, yielding the survival condition xi*kappabar <= 1 - 1/(M*theta_0) with M = min{Lbar/v, m} and a regime switch at the ticket size v* = Lbar/m: small engagements are constrained by the penalty doctrine, large ones by capital. Calibrated to six engagement types across four jurisdictions, the generative-AI insurance exclusions effective January 2026 shift eight of twenty-four cells from doctrine-bound to solvency-bound and cut the cells surviving xi=0.4 from twelve to four. The insurance withdrawal is a civil-law event; the common-law cells were already at the boundary.

A number of recent empirical papers rely on a collective model to analyze the portfolio choice of spouses, their heterogeneous risk preferences, and intra-household bargaining. I study applications of this model and highlight some important shortcomings. In its classic form, the model generates a counterintuitive result: an increase in the risk aversion of a household member can lead to an increase in household risk-taking. I offer a formal characterization of this pattern and link it to previous theoretical findings. I highlight further issues with applications of the collective approach to the portfolio choice problem in the contexts of bargaining and wealth inequality. I reconcile recent household finance papers with these findings and point to potential confusion in the literature. I emphasize existing alternatives that do not exhibit most of these issues, yet argue that there is a lack of a consistent and rigorous modeling approach.

Full justified representation (FJR) is among the strongest known satisfiable proportionality axioms for approval-based committee elections. Recent work has shown that an FJR committee can be found in polynomial time, but verifying whether a given committee satisfies FJR remains coNP-complete. We introduce FJR+, a strict strengthening of FJR and EJR+ that can be verified and satisfied in polynomial time. We then analyze the Residual-Budget Greedy (RBG) algorithm and prove that it selects a partial committee such that every size-$k$ completion satisfies FJR+. This freedom allows us to use sequential Phragmén to obtain a priceable completion. The resulting rule always satisfies FJR+ and the sub-core, and it is priceable whenever at least $k$ candidates receive an approval. We also obtain a Droop-quota version of FJR+. Finally, we extend FJR+ to approval-based participatory budgeting with arbitrary project costs. A project-specific version of RBG computes this property in polynomial time and can be continued to a priceable outcome satisfying a cost-based version of the sub-core.

How should institutions compare group diversity, and which group should they select when they value diversity and merit? We take a target-based approach that evaluates the entire group composition without treating any type as intrinsically diversity-enhancing. Because different diversity indices may rank groups differently, we instead adapt majorization to construct an ordinal diversity preorder. We show that its maximally diverse selections are exactly those maximizing every index in a broad class. This characterization yields a reserve-and-quota policy that selects a maximally diverse group and, among such groups, the highest-merit agents. Any alternative is less diverse, less meritorious, or both.

What determines the speed of AI-driven labor displacement? I study this question in a microeconomic model in which users choose between labor and AI to complete tasks of different complexity. Profit-maximizing AI providers set the price of AI, and AI systems improve through task-specific learning from deployment. In an initial technological state where labor has the comparative advantage at complex tasks, the providers' profit maximization incentives suppress AI deployment on complex tasks, even though these are most valuable for frontier learning. I characterize when this tension gives rise to an accelerating path of AI adoption or a learning trap. Competition can accelerate AI adoption relative to monopoly by shifting AI deployment toward more complex tasks, which boosts frontier learning. Asymmetric competition can further accelerate AI adoption by inducing providers to specialize, which concentrates complex-task data.

Every statistic on laws with finite pth moment that is additive across independent risks and monotone in mean-preserving spreads depends only on an additive function of the mean when p is strictly less than 2, and only on such a function and a nonnegative multiple of the variance when p is no less than 2.

A principal seeks to allocate $k$ identical objects among n sequentially arriving, impatient agents. Each agent privately observes her valuation, and the principal's payoff from allocating an object depends on the recipient's valuation. The principal can perfectly verify the valuation of at most $m$ agents, where $m < k$, and commits to a mechanism before any agent arrives. We characterize the class of optimal mechanisms. Our main result establishes that, in states where the number of remaining objects exceeds the number of available verification checks, the optimal mechanism may involve probabilistic verification.

We develop a behavioural model of bank run exposure in a paycheck-to-paycheck economy with loss averse depositors. Income is received through demand deposits, and consumption ratcheting embeds reference dependence in a parsimonious asset-pricing framework. We show that sufficiently high subjective bad-state probabilities endogenously increase liquidity demand and generate equilibrium stress states supporting bank runs. These states define a Bank Run Exposure State Space and yield a martingale representation for exposure dynamics. A proof-of-concept empirical implementation using Call Report data constructs bank-level exposure proxies from funding and lending composition. A regression-weighted composite measure modestly improves fit relative to a retail-share benchmark, with stronger amplification among small banks and during the post-Silicon Valley Bank (SVB) collapse period. The framework highlights how behavioural liquidity demand alters equilibrium reserve holdings and can crowd out productive lending.

We study a decision-maker who explores — dynamically choosing what to learn — before stopping to act. We first reduce this dynamic control problem to a static one: any exploration-and-stopping strategy is equivalent to a choice of the joint distribution of the stopped state and the stopping time, subject to one information-budget constraint at each date, and we characterize exactly which distributions are attainable. The reduced problem is a convex program with a linear objective; its dual prices information over time, and the optimal policy concavifies the stopping payoff net of these shadow prices. The curvature of the decision-maker's time preference then governs the shape of optimal exploration: convex time preference induces Poisson exploration, concave time preference confines stopping to a window whose length is controlled by the dispersion of the marginal cost of delay — forcing an initial phase of pure exploration when the window is short — and the linear case lies at the boundary between them. We apply the framework to real options, to the speed–accuracy tradeoff in information acquisition, and to a continuous-time exploration contest.

Inspired by possible future markets of autonomous routing and driving (ARAD), we introduce competitive mediator games and their equilibria which generalize the (coarse) correlated equilibria, which have become a popular research area recently as they not only can be more socially efficient than Nash equilibria but also are limits of algorithmic no-regret multi-agent learning dynamics. We discuss the basic properties of competitive mediator games and prove that in the generic setting of anonymous congestion(routing) games with market-share maximizing mediators all competitive mediator equilibria are monopolies whenever one of the mediators is weakly preferred to other mediators by all users. We apply and interpret these results in the context of new markets of competing ARAD service providers. We also provide a comprehensive overview of these markets and discuss the future mechanism design thereof.

We present a model of associative networks that captures how decision makers expand their consideration set through mental associations between alternatives. Our model provides a tractable approach to study how associations shape choice when some alternatives are available and others are merely observable but unavailable. We characterize the model within a random attention framework and demonstrate unique identification of all parameters. This framework delivers a unified account of several prominent choice anomalies, including classic menu effects and their “phantom” counterparts. We illustrate how associative links serve as a strategic variable in applications such as branding, imitation, and platform design.

A principal must decide whether to implement a project. She privately knows the cost, an agent privately knows the benefit. Monetary transfers are not available, and compared to the principal, the agent does not fully internalize the cost. We show that the principal-optimal mechanism does not require the agent to report. Instead, it either ignores the agent or endows the agent with free information and full decision authority.

We consider the problem of bargaining when transfers between agents are possible. Such situations are typically modelled as coalitional games with transferable utilities. However this model makes a strong implicit assumption: the outcome can only depend on the total surplus that each coalition of agents can achieve, not on which agents within the coalition generate the surplus. Is this assumption justified? We define a richer model in which solutions may depend on who generates the surplus. In this model, the classical axiomatisation of the Shapley value fails: a broad family of solutions satisfy efficiency, anonymity, the dummy property, and additivity. Nevertheless, we obtain an axiomatisation of the Shapley value in the richer model by adding continuity and individual rationality to the original axioms.

When generative AI makes the deliverable uninformative, a professional-services provider can still certify the preserved human capability to catch the machine's errors, through a liability pledge whose expected cost falls in that capability. The pledge is credible only up to what can be collected, and that ceiling is set by an underwriter, which bears part of the pledge and audits the insured. The range of client stakes over which one certificate separates has a width bounded by the provider's own capital plus the audited share of the underwriter's capacity, so unmonitored capacity adds nothing to it. Blind capital instead relocates that range upward, through a cross-subsidy that exists only under class rating. Monitoring converts capital into width, removes the cross-subsidy, raises the return to preserving skill, and, because audit information leaks, makes the certificate redundant beyond an interior precision.