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106 recordsLinked to original sources

arXiv2026

On the Complexity of Bayesian Signal Processing

We develop a computational framework for Bayesian decision-making. We show that as long as no action is optimal in every state, Bayes-optimal choice is intractable. This hardness need not arise from large action, state, or signal spaces, nor from a complicated represented utility function: extracting enough information from a hard-to-interpret signal to act optimally can itself be computationally hard. We also characterize tractability across approximation notions and identify their sources of difficulty. Under the probably approximately correct criterion, sample-based Bayesian learning is tractable if and only if the signal support is bounded. Our results provide justifications for bounded rationality, costly Bayesian inference, and sample-based Bayesian learning.

econ.TH↗

arXiv2026

A 1.283 Price-of-Anarchy Bound for the Repeated Virtual First-Price Auction

We study the repeated allocation of a single indivisible resource among $n$ strategic players. Each player $i$ has a privately known value distribution $D_i$, and values are drawn independently across players and periods. The goal is to find fair and efficient mechanisms. We apply the repeated first-price auction with equal initial endowments of virtual money. We show that each player can asymptotically secure the same fair-floor guarantee $f(D_i)$ as in Csóka 2026; consequently, the mechanism is $1.283$-optimal. This provides a simpler and more robust alternative mechanism for this special case and may also help derive sharper upper bounds on the price of anarchy.

cs.GT↗

arXiv2026

Course design in the age of AI

I develop a model of learning-by-doing and course design, and use it to study the impacts of artificial intelligence (AI). A myopic student faces a sequence of tasks that he can work on or delegate to AI. Work requires costly effort but builds skill; delegation requires no effort but builds no skill. A teacher designs the task sequence ("course") to maximize the student's skill development, given his choices to work or delegate. Without AI, the teacher makes earlier tasks more effort-intensive and later tasks more skill-intensive. With AI, the teacher must redesign early tasks to induce effort, leading to less skill development. If AI complements effort, then improvements in AI quality make high-skill students learn faster but low-skill students learn slower.

econ.TH↗

arXiv2026

The Silent Distortion of Relative Prices

This paper presents a production network model of inflationary dynamics in which inflation can have near-zero correlation with the size of price change yet generate significant distortions in relative prices. New money enters unevenly across firms and percolates through buyer-seller links, thereby displacing relative prices even when every price is free to adjust and every market clears. The magnitude of price distortion depends critically on the spectral gap of the production network, which sets the rate at which the economy converges to equilibrium. We quantify the mechanism on a reconstructed production network with the universe of firms in the United States. At 1% inflation, the typical firm's relative-price distortion is of the same magnitude as the inflation rate. The size of price change remains essentially uncorrelated with the magnitude of relative price distortion.

econ.TH↗

arXiv2026

From the Social Choice Problem to a Collusion-Proof Tendering Mechanism for Dynamic Stochastic Projects

The VCG family and the AGV mechanism are two classical approaches to efficient implementation in the static social choice problem. In 2024, Csóka et al. showed that AGV has critical weaknesses. In contrast, the transferable-utility Guaranteed Utility Mechanism (TU-GUM) retains all the standard desirable properties of AGV while adding further ones, including collusion-proofness, because it implements efficiency in Guaranteed Utility Equilibrium. TU-GUM also applies to a more general dynamic setting with multiple extensions. Moreover, TU-GUM is a special case of an even more general and robust mechanism that combines contingent first-price tendering with the coordinated execution of dynamic stochastic multi-agent projects through a surprisingly simple rule. This paper summarizes and connects existing results from a different perspective, with some minor new observations.

econ.TH↗

arXiv2026

Mechanism Design for Alignment and Control

We develop a framework for mechanism design with AI agents whose alignment (preferences) and capabilities (feasible actions and information) are unknown. We want such agents to act on our behalf so mechanisms must incentivize both honesty and obedience. A one-sided imitation structure---capabilities can be concealed but not counterfeited---yields a revelation principle, a characterization of implementable policies via nested cyclical monotonicity, and conditions under which eliciting higher-order beliefs can discipline multiple agents. We apply our framework to stylized examples of (i) sandbagging in which a more capable agent pretends to be less capable; (ii) an alignment--interpretability trade-off, where the two are substitutes in the instrument but complements in value; (iii) discipline via peer scoring; (iv) coupling rewards to induce competition among multiple agents; and (v) scalable oversight and reward shaping.

econ.TH↗

arXiv2026

Scale-robust Auctions

We study auctions that are robust at any scale, i.e., they can be applied to sell both expensive and cheap items and achieve the best multiplicative approximation of the optimal revenue in the worst case. We first show that it is without loss of optimality to restrict attention to scale-invariant mechanisms whenever the family of possible distributions is closed under every positive rescaling. This conclusion uses no regularity or other distributional shape restriction. We then solve the two-agent, single-item problem with values drawn i.i.d. from an unknown regular distribution when only a high value bidder can receive a positive allocation. The robustly optimal mechanism in this class randomizes between the second-price auction, with probability approximately 0.806, and a markup auction that offers the item to the highest-valued bidder at a price equal to 2.447 times the second-highest value. Its worst-case approximation ratio is approximately 1.907.

cs.GT↗

arXiv2026

The Non-Orientable Topology of Condorcet's Paradox

Preference cycles are prevalent in problems of decision-making, and are contradictory when preferences are assumed to be transitive. This contradiction underlies Condorcet's Paradox, a pioneering result of social choice theory, wherein intuitive and seemingly desirable constraints on decision-making necessarily lead to contradictory preference cycles. Topological methods have since broadened social choice theory and elucidated existing results. However, characterisations of preference cycles in topological social choice theory are lacking. In this paper, we address this gap by introducing a framework for topologically modelling preference cycles that generalises Baryshnikov's existing topological model of strict, ordinal preferences on 3 alternatives. In our framework, the contradiction underlying Condorcet's Paradox topologically corresponds to the non-orientability of a surface homeomorphic to either the Klein bottle or real projective plane, depending on how preference cycles are represented. These findings allow us to reformulate Arrow's Impossibility Theorem in terms of the orientability of a surface as well.

math.AT↗

arXiv2026

Refundable Deposits: How to Restore Cooperation in Finitely Repeated Games

While infinitely repeated games admit a rich set of Nash equilibria, finitely repeated games typically have a much smaller and often inefficient one. We show how to enlarge this set using deposits: in each period a player may place a refundable sum with a neutral intermediary, returned when the game ends and forfeited following a deviation. Paying these deposits is voluntary and incentive compatible at every stage, so no commitment by the players is assumed, the only commitment required being that of the intermediary to a refund rule fixed before play begins. The mechanism sustains payoff profiles more efficient than those of the standard equilibria, without altering the underlying game and without transfers between players. We demonstrate it on the prisoner's dilemma, a congestion game, and a public goods game, all settings where cooperation cannot emerge in the standard finitely repeated version. We also apply it to a dynamic common-pool resource, suggesting that the construction extends beyond repeated stage-games.

cs.GT↗

arXiv2026

Near-Optimal Mechanisms for Resource Allocation Without Monetary Transfers

We study the problem in which a central planner sequentially allocates a single resource to multiple strategic agents using their utility reports at each round, but without using any monetary transfers. We consider general agent utility distributions and two standard settings: a finite horizon $T$ and an infinite horizon with $γ$ discounts. We provide general tools to characterize the convergence rate between the optimal mechanism for the central planner and the first-best allocation if true agent utilities were available. This heavily depends on the utility distributions, yielding rates anywhere between $1/\sqrt T$ and $1/T$ for the finite-horizon setting, and rates faster than $\sqrt{1-γ}$, including exponential rates for the infinite-horizon setting as agents are more patient $γ\to 1$. On the algorithmic side, we design mechanisms based on the promised-utility framework to achieve these rates and leverage structure on the utility distributions. Intuitively, the more flexibility the central planner has to reward or penalize any agent while incurring little social welfare cost, the faster the convergence rate. In particular, discrete utility distributions typically yield the slower rates $1/\sqrt T$ and $\sqrt{1-γ}$, while smooth distributions with density typically yield faster rates $1/T$ (up to logarithmic factors) and $1-γ$.

cs.GT↗

arXiv2026

The Endogeneity of Miscalibration: Impossibility and Escape in Scored Reporting

An agent's probability report is paid for twice: by a strictly proper scoring rule, and by an approval rule for the decision it triggers. In this classical decision-coupled setting, non-affine approval is known to defeat truthful reporting. We show the conflict is endogenous: when feasible, the welfare-maximizing approval rule is never affine. The distortion, however, is predictable and can be designed around. There is a reserve report at which pretending to be the marginal type costs exactly the approval prize. Approving at or above the reserve screens types perfectly under every strictly proper score, and the reserve does not depend on the type distribution. A Lipschitz rule with a single kink attains first-best exactly; under strict feasibility no continuously differentiable rule does. The binding constraint is steepness, not smoothness. First-best is attainable within a slope budget if and only if the budget is at least the critical slope: the steepest chord of the pretending cost up to the reserve. Below it the welfare loss is cubic in the shortfall. Where the pretending cost is convex up to the reserve, as for Brier, log and power scores, the critical slope is closed-form. The instances are AI-agent oversight and marketplace operation.

cs.GT↗

arXiv2026

Modeling the Structure of Human Behavior with AI Prompt Vectors

We introduce a general, easy-to-implement AI-based method for modeling and analyzing the structure and complexity of human behavior. We assign a large language model a "type vector" and then prompt it to choose actions across settings in which we observe human choices. For instance, the type vector (2, 4) becomes "You are a player characterized by the following profile: Altruism: 2 out of 5, Risk Aversion: 4 out of 5," after which it is prompted to make choices. We vary the dimensions (e.g., Altruism, Fairness, Trust,...) and values (e.g., 1-5) to minimize distance to human choices. Applying the method to 119,147 decisions made by 78,657 subjects from more than 35 countries across 10 classic economic game roles, we find that human behavior can be closely matched using three dimensions: Risk Aversion, Strategic Sophistication, and Trust. Moreover, the types needed to fit individuals across games cluster into fewer than a dozen groups, and can predict behavior in held-out games with different rules and available actions. The results suggest that behavior across diverse settings can be approximated by a low-dimensional, portable representation, supporting the possibility of general yet parsimonious theories across the behavioral sciences. More broadly, this new modeling method can provide insights into the structure of many human behaviors.

econ.TH↗

arXiv2026

Diversity-Fair Online Selection

Online selection problems arise in applications such as crowdsourcing and recruitment, where decision makers may seek representation across multiple, potentially overlapping demographic or skill dimensions. We study diversity-fair online selection under adversarial arrivals. A recruiter must immediately and irrevocably decide whether to accept each candidate while selecting at most $K$ candidates. Before arrivals begin, the recruiter observes aggregate marginal information: the total number of candidates contributing to each of the $d$ diversity dimensions. When the candidate pool is large, this information may be estimated from demographic statistics of the applicant population. We evaluate the expected utilities across dimensions using the generalized mean $M_p=(d^{-1}\sum_{k=1}^d U_k^p)^{1/p}, -\infty\le p\le 1,$ where $U_k$ denotes the expected utility of dimension $k$. We first study max-min fairness, corresponding to $p=-\infty$. We prove that no online policy can achieve a competitive ratio better than $O(1/\sqrt d)$ and develop a policy with a competitive ratio $1/[4(2+\sqrt2)\sqrt d]$, establishing the optimal dependence on $d$ up to a constant factor. Without exact marginal information, the optimal worst-case rate falls to $Θ(1/d)$, demonstrating the value of this information. We also extend the max-min analysis to nonbinary attributes and characterize the optimal dependence on their value range. Finally, we study generalized-mean objectives. For $0\le p\le1$, we establish an optimal competitive ratio of $Θ(1/\log d)$. For each fixed finite negative mean $p=-q$, where $q>0$, our policy achieves $d^{-q/(2q+1)}$ up to polylogarithmic factors, matching the exponent of the corresponding impossibility bound.

econ.TH↗

arXiv2026

Optimal Rates for Agentic Networked Information Aggregation

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 $Ω(M/D)$ for $D<M^2$. We close this gap: the correct rate is constant up to depth $M^2$, and $Θ(M^2/D)$ beyond it. We first give a sharper analysis of the cyclic instance and improve its lower bound to $Ω(\sqrt{M/D})$ for $D<M^2$. We then construct, for every depth $D\ge M^2$, an $M$-covered path of depth $D$ with excess error $Ω(M^2/D)$. 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.

cs.LG↗

arXiv2026

Algorithmic Collusion by Large Language Models

We conduct experiments with algorithmic pricing agents based on Large Language Models (LLMs). In oligopoly settings, LLM-based pricing agents quickly and autonomously reach supracompetitive prices and profits. Variation in seemingly innocuous phrases in LLM instructions ("prompts") substantially influence the degree of supracompetitive pricing. We develop novel techniques for behavioral analysis of LLMs and use them to uncover price-war concerns as a contributing factor. Our results extend to auction settings. Our findings uncover unique challenges to any future regulation of LLM-based pricing agents, and AI-based pricing agents more broadly.

econ.GN↗

arXiv2026

How Wasteful is Signaling?

Signaling is wasteful. But how wasteful? We study the fraction of surplus dissipated in a separating equilibrium. For isoelastic environments, this waste ratio has a simple formula: $β/(β+σ)$, where $β$ is the benefit elasticity (reward to higher perception) and $σ$ is the elasticity of higher types' relative cost advantage. The ratio is constant across types and is independent of other parameters, including convexity of cost in the signal. We show that the directional effects of $β$ and $σ$ on waste extend to non-isoelastic environments. In an application to signaling tournaments, more competitors or fewer prizes increase waste, with full dissipation in large tournaments.

econ.GN↗

arXiv2026

Machine Learning Classification and Portfolio Construction: Does the Loss Function Matter?

Classification outperforms regression across matched machine learning models in portfolio construction. A stacking ensemble of gradient boosted tree, random forest, and neural network yields a value-weighted annualized Sharpe ratio of 2.08 for classification and 1.39 for regression. This outperformance strengthens with class granularity and persists across subsamples and after transaction costs. Spanning tests show that classification retains economically large alphas after we control for regression, whereas regression alphas shrink substantially once we control for classification. These results indicate that classification extracts more return information than matched regression. Our diagnostics trace classification's advantage to more precise separation of return deciles.

q-fin.GN↗

arXiv2026

Redefining Stablecoins from Nominal to Real Value: A Maximum Likelihood Approach

Stablecoins, typically pegged to fiat currencies, cannot achieve true stability because they inherit fluctuations in the underlying unit of account. To overcome this limitation, we introduce a stablecoin pegged to the Maximum Likelihood Value (MLV), a newly defined unit of account derived as the most probable configuration of latent real-value movements that explains observed nominal-value (price) changes. Grounded in inferential statistics and modern portfolio theory, MLV represents the most stable unit of account, as it enforces a zero real return on the minimum-variance portfolio. Empirical results confirm the operational viability of an MLV-pegged stablecoin: MLV can be computed in real time from 500 asset price series and improves annualized returns and Sharpe ratios while substantially reducing turnover in portfolio optimization.

cs.CE↗