Prices

Fairness in insurance pricing remains a long-standing and deeply debated puzzle. On one hand, insurers, driven by profitability considerations, set premiums that differentiate across individual risks to achieve actuarial fairness. On the other hand, insurance serves a critical societal function by pooling risks across a population, motivating cross-subsidization among groups to promote solidarity fairness. The tension between these two competing notions of fairness makes insurance pricing inherently complex, particularly in modern settings where granular data allow for increasingly fine risk differentiation and regulators face growing pressure to protect vulnerable groups. To address this challenge, we propose an $α$-\textbf{F}air \textbf{I}ndividual \textbf{S}olvent \textbf{P}remium ($α$-FISP) framework for insurance pricing that explicitly captures the trade-off between actuarial and solidarity fairness while guaranteeing solvency, a fundamental requirement in insurance operations. We formulate the pricing problem as a constrained optimization task, where actuarially fair premiums are adjusted subject to budget constraints on cross-subsidization within each risk class. This formulation naturally yields a family of solutions parameterized by $α$, tracing a continuum between purely actuarial and purely solidarity-based pricing and enabling decision-makers to select an operating point along this fairness spectrum. We derive theoretical guarantees for the proposed framework. Numerical experiments show that $α$-FISP is computationally tractable and aligns well with the U.S. regulatory regimes featuring heterogeneous state-level fairness requirements.

Disaggregated inference architectures physically separate prefill and decode phases onto distinct GPU pools, creating competing "agents" that share a fixed hardware budget. We provide, to our knowledge, the first formal game-theoretic analysis of this architecture, using NVIDIA Dynamo as a concrete case study. We model disaggregated serving as three coupled games: a two-player resource game between prefill and decode pools, a selfish caching game over the hierarchical KV cache, and a congestion game with positive externalities for request routing. We empirically validate the latter two; the P/D resource game is treated analytically (Section 9.2). We characterize how GPU saturation induces regime transitions that shift the game's payoff structure: below saturation, selfish behavior has bounded Price of Anarchy (PoA); at saturation, superlinear latency and cache externalities drive our empirical estimator PoA-hat (defined in Section 6.4) upward. Based on this analysis, we design an adaptive controller that detects saturation transitions in real time and adjusts routing parameters accordingly, shifting from cache-affinity exploitation to load-balanced congestion avoidance. We instantiate our framework on a 3-node NVIDIA B200 cluster running Dynamo with two models, Nemotron-4-340B (TP=8, full-node workers with cross-InfiniBand KV transfers) and Llama-3.1-70B (TP=4), and find the same three-regime PoA-hat structure with the same first post-knee grid point (C=128) on both models. Adaptive routing shifts each model to a better operating point. Our strongest result is on the 70B 1P/5D topology, where PoA-hat drops 3.1x (66.4 to 21.5) in the saturated phase at a 13% throughput cost. On the 70B 1P/2D, PoA-hat drops 2.2x and TTFT P99 drops 7.6x (see Section 8.5).

Web agents driven by large language models (LLMs) are increasingly deployed in real-world environments, where they operate over untrusted web content and execute actions with direct consequences. This makes them vulnerable to prompt-injection attacks, in which seemingly benign content embeds adversarial instructions that manipulate agent behaviour. Existing security benchmarks adopt an \textit{attack-centric} perspective, focusing on the technical feasibility of injections while overlooking the nuanced distribution of resulting harms. In practice, however, prompt-injection risk is victim-dependent: a single exploit can produce asymmetric consequences for different stakeholders, and the same attack pattern may exhibit substantially different effectiveness depending on whom it targets. To capture these properties, we introduce \textbf{\sysname}, a \textit{stakeholder-centric} benchmark to systematically categorize and attribute harm in real-world web agent systems. It distinguishes between affected entities (e.g., user, seller, platform), decomposes the attacks into concrete objectives, and evaluates each case with complementary outcome- and process-level metrics. Our results reveal substantial and heterogeneous vulnerabilities: not a single attack objective is reliably resisted by current agents, and failures distribute across qualitatively distinct modes ranging from \emph{stealthy parasitism} (attack succeeds without disrupting the user's delegated task) to \emph{misaligned disruption} (task disrupted without attack success) and \emph{compounded failure} (both adversarial objective and task integrity simultaneously violated). These patterns are missed by conventional evaluation, highlighting the need for stakeholder-aware assessment of LLM-based agents in real-world deployments. Benchmark is available at https://github.com/StakeBench/SBC.

This paper presents the design, development, and implementation of a specialized forecast-then-optimize algorithmic pricing tool for sales campaigns in fashion e-commerce. Sales events present unique challenges for pricing including volatile demand patterns, rapid pricing decisions, and the need to balance short-term revenue with long-term profitability. We describe our approach combining daily-resolution demand forecasting using gradient-boosted trees with a multi-objective optimization framework that maximizes both long-term profit and net merchandise value for more than 5 million articles. Our solution addresses key limitations of existing weekly-granularity systems by implementing a forecast-then-optimize architecture that reduces pricing decision time from hours to minutes. We validate our approach through 23 A/B tests across 12 markets during 2023-2024 sales campaigns at Zalando, one of Europe's leading online fashion retailers. Experimental results demonstrate that the new pricing system achieves approximately 6% higher profit while maintaining equivalent performance on sales and revenue compared to the previous manual-algorithmic hybrid approach. Based on these results, the algorithm was successfully deployed to production and now handles the majority of algorithmic pricing decisions for sales campaigns at the company.

Tokens have become the practical accounting unit for modern foundation model services, linking information processing, computation, memory use, energy expenditure, pricing, and economic value. This paper develops a framework for AI tokenomics: the study of how tokens are generated, consumed, priced, allocated, and optimized across AI systems. We connect token-level technical costs to workflow-level production functions, enterprise resource allocation, measurement and instrumentation methods, and emerging market-design questions. The framework shows that token expenditure and economic value are distinct: value depends on marginal productivity, workflow position, hidden reasoning activity, risk, and downstream propagation effects. The paper concludes by identifying open research directions in hidden-token measurement, empirical calibration, token productivity, dynamic allocation, and token-based markets.

We develop a decision-calibrated conformal framework for pacing decisions in streaming advertising. Pacing depends on uncertain future inventory, demand pressure, incremental response, and member-experience load. Instead of calibrating a generic forecast residual, the framework measures forecast error by its largest impact on the policies that could actually be deployed. The main theorem shows that the proposed score is the smallest valid uncertainty measure that uniformly protects all deployable pacing policies. Geometrically, it is the support function of the signed policy sensitivity set. Split conformal calibration gives finite-sample coverage for this score. A high-dimensional separation theorem shows that traditional residual calibration can be arbitrarily more conservative by paying for nuisance inventory dimensions, and a robust pacing result combines inventory, response, and experience uncertainty. On public-data-calibrated pacing replays built from Criteo Uplift and KuaiRand datasets, traditional conformal pacing remains unresolved with high residual radii of 7236.7 on Criteo and 4629.4 on KuaiRand. With the proposed decision calibration approach, the uncertainty radii are reduced to 18.4 and 278.6 respectively, with separate margins for value, delivery, budget, and member load. On Criteo, the proposed method certifies a less aggressive pacing policy than the point-forecast baseline, and reduces held-out any-violation rate from 16.7% to 3.3%, with zero budget and member-load violations. On KuaiRand, the choice remains unresolved. In a nutshell, the paper establishes that forecasts, response estimates, and member-experience models should be judged by whether they shrink the uncertainty that the pacing decision uses, as this leads to confident decisions that are not overly conservative.

Data-driven pricing is increasingly prevalent in sectors such as airlines, lending, insurance, and retail. By learning demand models from customer features and setting prices accordingly, these systems may generate discriminatory outcomes that raise fairness concerns. This leads to fundamental questions - how and where should systems incorporate fairness considerations in the pricing pipeline, and how does it ultimately affect societal outcomes? To answer these, we study a stylized model where a seller has a two-stage decision pipeline comprising linear demand model estimation followed by price optimization. The seller considers fairness notions in training loss, price, and demand, under both parity-wise and Rawlsian perspectives. We show that equalizing training loss across consumer groups leads to multiple solutions, which in turn can result in undesirable outcomes despite being a standard approach in fair machine learning. Focusing instead on fairness applied directly to prices or demand, we compare two strategies that enforce fairness in either the demand estimation stage or the price optimization stage. For parity-wise fairness, we characterize when each strategy yields higher social welfare under small fairness levels. We show that when market sizes and prices in the dataset are similar, imposing price fairness in the estimation stage is more beneficial to consumers, whereas imposing demand fairness in the optimization stage yields better consumer outcomes. For Rawlsian fairness, the two strategies coincide exactly. Lastly, we extend our model to alternate demand functions and conduct a case study using real-world vaccine pricing data.

Modern option-learning systems operate in two coordinates: price space, where markets quote and no-arbitrage constraints are most naturally enforced, and implied volatility (IV) space, where volatility surfaces are smoothed, regularized, and evaluated. The bottleneck is interface, not approximation: Jäckel's seminal "Let's Be Rational" (LBR) solver already inverts the Black-Scholes price to machine precision efficiently. What is missing is a differentiable layer that preserves LBR in the forward pass and avoids backpropagating through its branch logic. Such a layer must also confront the unavoidable singularity of the inverse map in the low-vega regime, where the sensitivity 1/vega diverges as vega -> 0. We close this gap with PIVOT, the Price-Implied-Volatility Objective Translator. PIVOT keeps the LBR forward pass intact and supplies the backward pass by implicit differentiation through the smooth Black-Scholes/Black-76 price map, with an explicit gating contract: invalid domains return NaN, well-conditioned rows receive the exact 1/vega gradient, and low-vega rows are attenuated rather than silently regularized. On a single H100, a fused Triton kernel reaches 1.79e9 IV/s at machine precision (9.3e-14 max relative error vs. the reference C solver); end-to-end label generation sustains 48.9M/s on synthetic chains and 16.6M/s on SPX OptionMetrics. In a HyperIV-style one-day reproduction on SPX, PIVOT-augmented objectives Pareto-dominate the baselines, reducing held-out price MAE by up to 43.4% and the strongest three-seed gated objective improving price MAE by 38.8% and IV MAE by 21.3% jointly; cross-asset results on RUT, VIX, and NDX show directional price-MAE gains of 40.1%, 24.2%, and 16.7%, while an ungated IV-roundtrip control collapses to a degenerate near-zero surface, confirming the gate as a correctness contract rather than a tuning knob.

On a platform with many sellers, should a pricing algorithm explicitly model competitors' prices when learning demand? Classical learning arguments suggest an affirmative answer: ignoring competitors induces model misspecification and inefficiency. In contrast, recent work on algorithmic collusion suggests that strategic obliviousness -- deliberately ignoring competitor prices -- may facilitate collusive outcomes and improve profits. We study this modeling choice in a stylized competitive market with unknown noisy demand, in which multiple sellers repeatedly set prices and estimate demand via iterated least squares, and either incorporate competitors' prices into their demand models (informed) or ignore them (oblivious). We first show that, relative to a monopolist, an oblivious seller in a competitive market must explore more aggressively to compensate for the loss of dynamic competitor information. Building on this insight, we characterize market dynamics when all sellers are oblivious and show that prices converge to the competitive outcome under sufficient exploration, while a continuum of pseudo-equilibria arises when exploration decays. Analyzing the resulting price trajectories, we uncover an excursion phenomenon that gives rise to transient collusive patterns that dissipate as learning progresses. In markets with both oblivious and informed sellers, the informed strictly out-earn the oblivious. Read as a strategy game, the modeling choice has a unique Nash equilibrium: the all-informed market, in which prices converge to the competitive outcome efficiently. Overall, our results indicate that collusive patterns are not robust and are not sustained by oblivious modeling; therefore, incorporating competitor information, together with sufficient price exploration, remains a reliable strategy for sellers in competitive markets.

Worker utility is not observed -- only its consequence is. Each gig transaction produces a single bit: accepted or rejected. We argue this structure points directly to the Preisach hysteresis model as the natural representation of latent worker preferences. The Preisach operator models aggregate output as an integral over a population of binary threshold elements -- precisely the structure that emerges when heterogeneous workers each carry a private acceptance wage. We estimate two latent utility surfaces: acceptance utility U_1(X) and rejection utility U_0(X), via a dual-output neural network (shared layers 256->128, margin loss enforcing U_1 >= U_0). Classification reduces to the Preisach gap U_1(X) - U_0(X), passed into an XGBoost classifier alongside clip-stabilised price-to-threshold encodings. On 36,891 gig transactions, this pipeline achieves Jaccard = 0.827 and ROC AUC = 0.799. The price-to-threshold encoding accounts for +11.0 pp AUC over raw utility features. The model confirms the directional asymmetry hysteresis predicts: price decreases depress completion rates more than equivalent increases raise them. Applied to the full dataset, the model's recommendations simultaneously reduce the total wage bill by 21.3% and increase expected fill rate by 9.7 pp. For 74.2% of transactions, P(accept) already exceeds 0.80; reducing the wage keeps it above threshold (mean post-cut P = 0.972), releasing cost savings (median 31%). For the remaining 25.4%, a median 7% wage increase recovers +43 pp acceptance. A model without an explicit indifference zone cannot execute both moves simultaneously.

We study two reproducible failure modes of deep multi-agent reinforcement learning in continuous-time pricing markets: (i) tacit cartel formation between competing DDPG agents, and (ii) actor--critic instability at high event rates. We instantiate both inside a single CT-MARL benchmark (Poisson-clocked price updates, observation latency $δ$, interior-optimum logit demand), show that synchronous DDPG agents reliably trigger Failure Mode 1 with collusion index $Δ= 0.69 \pm 0.11$, and quantify a partial microstructure fix: asynchrony alone cuts collusion by 48% and adding latency drives it to a minimum of $Δ= 0.28$. The fix has clearly documented costs: it is partial ($Δ$ remains supra-Bertrand), it is non-monotone in $δ$, and it does not survive Failure Mode 2, which emerges as DDPG critic divergence at $λ= 5$ and corrupts the phase-diagram cell at $(λ{=}5, δ{=}1)$. We accompany the scalar collusion index with trajectory-level trace diagnostics that expose the within-episode signalling collapse and the post-shock non-recovery.

We show every multi-group learner in the transductive setting may incur a multiplicative penalty in its error rate on some group relative to the error rate achievable in the single-group setting, and the penalty can increasing linearly with the number of groups, up to roughly the square-root of the sample size. This stands in stark contrast to optimal multi-group learners in an analogous (group-realizable) statistical setting, where the penalty is always at most logarithmic in the sample size and independent of the number of groups.

Resource-constrained pricing controllers can make fixed-price inference impossible: the controller's resource state may remove the target price neighborhood from the feasible set, even when every realized action has a known positive density. We formalize this support-exclusion failure through a local non-identification result and a realized information clock. We then design a target-aware pricing controller that certifies feasible target bands and logs continuous local densities. Localized debiasing gives studentized intervals whose width is governed by this clock. The resulting regret--information accounting, stated up to pilot re-solving error, shows that cheap exploration can be insufficient for inference: polynomial target mass gives polynomial rates, while a pure $1/t$ target branch does not yield shrinking fixed-target intervals without additional local movement. Experiments show calibration in certified bands and diagnostic abstention when the resource state collapses target support.

Inference-time scaling has emerged as a critical avenue for enhancing Large Language Models' performance, yet real-world deployment is constrained by strict computational budgets. In this work, we formulate inference budget allocation as a global constrained optimization problem governed by economic principles. By modeling per-query reasoning utility with a shifted-surge function, we derive an optimal allocation policy based on a global shadow price that equilibrates marginal utility under resource scarcity. Based on this theory, we propose Constrained Latent-utility Equilibrium Allocation for Reasoning (CLEAR). It performs rational abandonment and reallocates resources from insolvent queries to solvable queries near their emergence thresholds. Extensive experiments on several reasoning tasks with different traffic streams demonstrate that CLEAR significantly improves the Pareto frontier of total token cost versus mean accuracy. In resource-scarce regimes, CLEAR achieves up to a 3x improvement in global accuracy compared to uniform allocation.

Consumer-price measurement increasingly draws on alternative data sources -- scanner, web-scraped, and transaction/receipt data -- whose product descriptions are short, noisy, and carry no standard product code, so each item must first be mapped to a consumption classification (e.g., the UN COICOP scheme) before prices can be compared. This paper studies that mapping as a general, reproducible method. The pipeline is: (i) text normalization and tokenization of noisy item names; (ii) a prefix-tree (trie) rule-based pre-classifier driven by per-category key-phrases and stop-phrases; and (iii) a per-category binary confirmation model. For labels at scale we use a human-in-the-loop protocol in which annotators give a binary valid/reject judgment aggregated by a dynamically updated reliability weight; the model joins the same rule, enabling continual fine-tuning. On a reproducible synthetic benchmark of six COICOP-like categories, under one matched protocol, cheap models win and order-sensitive ones do not help: a character n-gram logistic regression tops every category (mean F1 = 0.997), word-order features add nothing, and small CNN/LSTM models are the weakest in this small-data regime. The trie alone admits only 32-50% of items, so the learned stage is necessary, and about 66 labels per category suffice. A Monte-Carlo study of the labeling protocol is self-critical: the reliability-weighted vote barely beats plain majority while Dawid-Skene recovers labels markedly better. No proprietary or production data are used; all code and synthetic data are released at https://doi.org/10.5281/zenodo.20909563

Existing LLM moral benchmarks usually ask which isolated moral act, value, or foundation a model prefers. This is useful but incomplete. Realistic judgments often require a model to combine several moral signals within the same option. We introduce Moral Trolley Arena, a two-stage blind ELO benchmark for measuring how LLMs compose moral evidence. The single-scene arena first calibrates individual moral acts from a 229-scenario corpus across five Moral Foundations Theory foundations; the composite arena then combines calibrated acts into two-act moral items over a controlled intensity grid and measures the resulting composite preferences. Across ten frontier models, composite judgments are largely predicted by component act strength, but the relation is consistently compressed rather than simply additive. Models also show non-additive intensity anchoring, bounded foundation-specific residuals after component control, and highly convergent composite preference surfaces across providers. These results suggest that moral audits should measure composition rules for moral evidence, not only rankings over isolated acts.

Forecasting agricultural commodity prices in emerging economies is difficult due to high volatility, frequent supply disruptions, and strong cultural influences on demand. This study introduces the Kalimati Vegetable Price Index (KVPI), a new inverse-volatility weighted composite index that aggregates 135 daily wholesale commodities from Kathmandu over ten years (2013-2023). By creating a stable macro-level signal, the KVPI reduces the noise inherent in modelling individual crops. A rich set of 64 causally valid features was developed, including festival lead-lag effects, rolling statistics, and calendar variables. Fourteen forecasting models spanning statistical, tree-based, deep learning, hybrid, and transformer architectures were rigorously evaluated across short (7-day), medium (14- and 30-day), and long-term (90-day) horizons. Tree-based ensembles proved notably robust, while classical statistical models and complex transformers struggled with the noisy dataset. The proposed Momentum-Corrected Online Stacking Ensemble achieved the strongest performance, yielding a Root Mean Square Error (RMSE) of 1.771, an exceptionally low Mean Absolute Percentage Error (MAPE) of 0.68%, and explaining 84.5% of the variance (R-squared = 0.845) at the 90-day horizon. This open-source pipeline provides policymakers and supply chain actors in Nepal and similar markets with a practical, reliable tool for anticipating price movements and strengthening food security.

We study the subclass of potential mean-field games in which the running interaction cost and the terminal target cost are both expressed through reproducing-kernel maximum mean discrepancy (MMD) penalties, and develop a computational framework that exploits this kernel structure. Both costs are estimated from finite-sample empirical distributions using a random Fourier U-statistic representation that is unbiased and has linear cost in the batch size. The drift of the controlled diffusion is parametrized by a neural network and trained via stochastic gradient descent. For population near-minimizers we prove convergence to the terminal-constrained problem as the penalty diverges, and show that the same limit is recovered almost surely when the learned controls are evaluated on independent finite samples under explicit coupling conditions on the penalty, random-feature count and sample size. The framework includes the kernel-MMD-penalty Schr{ö}dinger bridge problem as the special case of a vanishing interaction cost. Numerical experiments illustrate the method on the Schr{ö}dinger bridge problem in dimensions up to one hundred, and on an electric vehicle charging coordination problem with per-vehicle physical heterogeneity, where an aggregate-demand congestion cost represents price-feedback competition at the population level and the terminal MMD penalty shapes the state-of-charge distribution at the deadline.

Accurately forecasting the impact of salient financial events on markets is critical for investors and policymakers. However, existing multimodal time-series models typically fuse text and prices symmetrically, without an explicit way to decide when event text is truly predictive, and thus struggle to exploit the directional event-to-price structure and the heterogeneous roles of textual and price signals. In this work, we propose GS-Fuse, a multimodal event-based forecasting framework that employs (i) a Granger-supervised, causal-aware gated fusion module, which learns to open toward event text only when it provides incremental predictive value beyond historical prices, and (ii) a multi-granularity alignment mechanism that jointly aligns high-level event representations and fine-grained textual cues with future market trajectories. Built as a flexible, plug-and-play adapter on top of off-the-shelf large language models and time-series foundation models, GS-Fuse can be instantiated across diverse backbones and market settings. Extensive experiments on real-world financial datasets show that GS-Fuse consistently outperforms state-of-the-art time-series and multimodal baselines across multiple assets and forecasting horizons.

Traditional insurance pricing relies on risk-based principles that ensure actuarial fairness and solvency but do not explicitly account for policyholders' price sensitivity. We formulate insurance pricing as a decision-making problem and study it using tools from off-policy evaluation and stochastic control. We propose a kernelized inverse propensity score estimator that exploits local structure in the action space and yields variance reduction compared to the classical inverse propensity score estimator. Building on these value estimates, we investigate policy optimization and present two practical approaches for computing optimal pricing rules: an interpretable data-shared Lasso formulation and a flexible policy parameterization based on neural networks. Using a controlled synthetic travel insurance environment, we empirically confirm the theoretical results and show that neural networks outperform existing techniques for policy optimization.

Predicting stock price movements during Earnings Announcements (EAs) is a significant challenge due to market noise and high-impact price discontinuities. In this study, we evaluate whether pre-announcement news sentiment, firm fundamentals, and recent market dynamics jointly predict the directional price movement of equities on EA days. We construct a multi-modal feature space combining 15 fundamental metrics, 3 price-based technical indicators and sentiment scores derived from financial news articles processed using FinBERT. We compare a Long Short-Term Memory (LSTM) network and a Transformer-based architecture against a logistic regression baseline, and further assess all models with and without sentiment features to quantify their incremental value. Our results indicate that while the LSTM demonstrates higher precision through a conservative safe-bet strategy, the Transformer model exhibits superior sensitivity in identifying volatile movements, achieving a higher macro F1-score, with ablation experiments showing a consistent benefit from incorporating news sentiment.

Dynamic pricing in short-term rental (STR) markets presents a distinctive challenge for online learning algorithms: pricing decisions carry significant financial risk, operators require explainability, and market feedback is sparse (one booking outcome per listed night). We introduce the Human-in-the-Loop Gated Bandit (HITL-GB) framework, in which a contextual bandit algorithm generates price recommendations but a human agent retains authority to accept, modify, or reject each recommendation before it is applied. We show that under this approval constraint, historical pricing data -- collected under a prior deterministic policy -- is structurally equivalent to on-policy warm-up data for initialising the bandit's posterior, bypassing the weeks-to-months cold-start period that renders pure online bandit learning impractical in sparse-feedback markets. We formalise the approval-gated reward signal, derive a regularised ridge-regression warm-up procedure from historical episodes, and validate the approach on real STR production data (anonymised urban market, 2 rooms, April 2022 -- April 2026, 1,461 nightly pricing episodes). Our warm-up procedure compresses effective cold-start from ~150 episodes to ~30 episodes when initialising agents from the Hierarchical Factored Thompson Sampling (HF-TS) family. We further argue that the structural equivalence result is domain-agnostic: any high-stakes domain where human approval is legally or operationally required -- including clinical drug dosing, credit origination, content moderation, and radiological diagnosis -- satisfies the same conditions and benefits from the same warm-up strategy. In regulated industries, mandatory human oversight is thus a statistical asset rather than a deployment constraint.

We introduce the Preisach Attention Layer (PAL), a novel sequence modelling architecture grounded in the classical Preisach hysteresis operator from mathematical physics. PAL replaces the softmax attention mechanism with a binary relay operator parameterised by learned activation and deactivation thresholds, maintaining a stack of local extrema as its internal state. A single-layer PAL-Transformer with O(1) depth is Turing-complete under arbitrary precision arithmetic, achievable through simulation of a two-stack pushdown automaton -- in contrast to the O(log n) depth required by standard hard-attention transformers. Second, we prove that the function classes computable by PAL and by the transformer are incomparable: PAL computes historical range statistics in O(1) layers that require O(log n) layers for transformers, while transformers support random-access retrieval that PAL cannot perform without auxiliary state. The separating property is rate-independence -- PAL responds only to the sequence of local extrema, not to absolute token positions or temporal spacing. Third, we show that the extremum stack constitutes a minimal sufficient statistic of the input history for all rate-independent functionals, providing a formal analogue of the wiping property in classical hysteresis theory. PAL is thus an efficient architecture for tasks with long episodic memory and weak positional dependence, with O(n log n) total inference cost versus O(n^2) for standard attention.

We propose the Integrable Context-Dependent Demand Network (ICDN), a demand-first neural model for multiproduct retail demand. The model learns log-demand as a smooth, context-conditioned function of log-prices, allowing elasticities to be derived exactly from the learned demand surface. On the Dominick's beer dataset, ICDN improves out-of-sample generalization over a directed log-log benchmark and yields more stable, economically plausible elasticity estimates, especially for weakly identified cross-price effects.

Modelling claim frequency and severity for non-life insurance pricing predominantly relies on generalised linear models, with gradient-boosted machines as the leading machine learning alternative. Tabular foundation models (TFMs) present a fundamentally different inference paradigm. By pre-training on large collections of synthetic datasets, TFMs enable inference on new data through in-context learning, without any dataset-specific fitting or hyperparameter tuning. This paper presents a first empirical evaluation of TabPFN for motor insurance pricing, benchmarking it against GLM and XGBoost on two publicly available MTPL datasets. Our results show that TabPFN does not consistently outperform established baselines, exhibits substantially longer inference times, and is sensitive to the size of the in-context training set. While tabular foundation models represent a promising direction, particularly in data-scarce settings, their current performance does not offer a viable replacement for established actuarial methods.

Firms increasingly rely on dynamic pricing to respond to evolving customer demand, yet in many applications they observe only the revenue generated by a single posted price in each period. At the same time, market conditions may shift gradually or abruptly due to changes in customer preferences, competition, or external shocks. These features create two intertwined challenges: learning the revenue--demand relationship from limited feedback and adapting pricing decisions to a changing environment. We study how a seller can learn and earn effectively under these constraints, without assuming a specific parametric form for demand. We develop a learning framework that updates prices using revenue-based gradient approximations constructed from one observation per period. To address environmental changes, we incorporate a restarting mechanism that periodically refreshes the learning process so that outdated information is discounted. When the degree of nonstationarity is unknown, we further introduce a meta-learning layer to adaptively hedge across multiple restarting schedules. We provide performance guarantees for our approach, showing how cumulative revenue loss relative to a fully informed benchmark depends on both the time horizon and the magnitude of market variation. Simulation experiments using synthetic and real-world data illustrate the effectiveness of the proposed procedures.

In this paper, we investigate whether deep reinforcement-learning agents interacting in a shared optimal-execution environment can sustain supra-competitive outcomes, in the sense of achieving lower implementation shortfalls than the relevant game-theoretical competitive benchmark. We study a two-agent Almgren-Chriss liquidation game and examine how learned behavior depends on intra-episode environment feedback, the ability to interpret the mid-price and the agent's knoledge of the past. We first use ex-ante schedule-learning agents to remove intra-episode feedback and isolate what can arise when agents commit to complete liquidation trajectories before execution begins. We then allow agents to condition on the evolving state using a variety of DDQN architectures. We find that, when agents are given access to intra-episode history, especially recent prices and own past actions, supra-competitive outcomes become substantially more frequent and more persistent. These findings indicate that supra-competitive behavior in this execution game is driven not by multi-agent learning or by current price observation alone, but by feedback, memory, and state-contingent interaction along the realized execution path.

Personalized pricing negotiations are a challenging testbed for LLM agents because successful interaction does not guarantee profitable decision making. A seller may produce valid actions and close many deals while still pricing poorly when buyer willingness to pay and bargaining traits remain hidden. This paper presents PrefBench, a simulator-based benchmark for hidden-preference personalized pricing negotiations. Each episode pairs a simulated buyer with a fixed vehicle-customization bundle; the seller observes public persona descriptors, bundle information, and negotiation history, while latent buyer variables govern valuation, patience, counter-offer behavior, and walkaway decisions. PrefBench evaluates this setting through an LLM-facing state-summary protocol that constrains agents to return strict JSON actions under a fixed hidden-information boundary. We evaluate zero-shot LLM sellers against heuristic references over 7,500 episodes. The tested LLMs follow the protocol reliably and achieve deal rates above 0.99, but their seller-profit outcomes remain weak: the best LLM average profit is only slightly above the random baseline and far below a simple concession heuristic under the same episode stream. These results show that structured action compliance and agreement-seeking behavior can coexist with weak profit-sensitive bargaining. PrefBench provides a controlled benchmark for evaluating pricing-agent behavior under hidden buyer preferences.

Capped-usage SaaS products -- LLM subscriptions such as Claude Code and ChatGPT, cloud platforms such as Vercel and Cloudflare Workers, corporate benefit platforms, identity-verification services with liability transfer -- share a structural signature with insurance products: a fixed premium decoupled from realized consumption, stochastic per-user demand with heavy-tailed severity, a non-fungible cap that resets on a fixed schedule, and a portfolio-level exposure that requires reserve adequacy under tail risk. We argue that this is not an analogy. It is the same operational problem actuarial science has been tooled for decades to address, restated with new dependent variables (tokens, bandwidth bytes, function-invocations, gym check-ins) in place of medical claims. This paper proposes a modeling framework for capped-usage SaaS pricing built from frequency-severity decomposition, premium calculation principles, and Monte Carlo reserve adequacy. We map the framework to publicly observable subscription tiers in two domains (LLM services and cloud platforms), ground it in canonical health-insurance economics (Arrow 1963; Pauly 1968; Manning et al. 1987; Brot-Goldberg et al. 2017), and demonstrate divergence from traditional unit economics through a worked example. The contribution is operational rather than theoretical: not a new theorem, but vocabulary and tools currently absent from cs.LG/stat.ML practice.

Differential privacy changes the effective sample size governing CVaR learning. For tail mass $τ$, the privacy-relevant sample size is not $n$, but $nτ$; equivalently, the effective private tail sample size is $εnτ$. Private CVaR excess risk decomposes into ordinary tail-risk statistical error and a privacy price. This decomposition is complete for scalar estimation and finite classes: scalar estimation has rate $Θ(B \min\{1,(nτ)^{-1/2}+(εnτ)^{-1}\})$, and finite classes of size $M$ have rate $Θ(B \min\{1,\sqrt{\log(2M)/(nτ)}+\log(2M)/(εnτ)\})$. These complete rates hold under pure DP, and their lower bounds extend to approximate DP in the stated small-$δ$ regimes. For convex Lipschitz learning, modular upper and lower reductions show that the CVaR-specific privacy term necessarily scales as $1/(εnτ)$, with dimension dependence inherited from private stochastic convex optimization. Together, these results identify ordinary private learning on $Θ(nτ)$ informative tail records as the canonical hard subproblem inside private CVaR learning.

We study whether simple algorithmic pricing systems can systematically produce collusive-like prices in multi-firm markets. We consider firms that price using a myopic estimate-then-optimize rule: each repeatedly fits a demand model to its own price and sales history and sets the price that maximizes estimated profit. This demand model is misspecified, omitting competitors' prices. We analyze the dynamics of this rule when it is initialized by an exploration phase of independent random prices. We characterize when this pipeline converges to supra-competitive prices above the Nash equilibrium, via a fluid-limit ordinary differential equation analysis. We show that supra-competitive prices arise when firms initially explore within similar price ranges on the same side of the Nash price. Moreover, prices can be substantially above the Nash price; we show that prices can reach monopoly levels under symmetric exploration. Simulations calibrated to a real multifamily rental market confirm that supra-competitive outcomes arise robustly beyond our theoretical assumptions, including under finite horizons, heterogeneous products, and nonlinear logit demand.

We study contextual dynamic pricing in a semiparametric scalar-index valuation model where the latent value is $v_t=μ_\ast(\mathsf c_t)+ξ_t$, with an unknown utility map $μ_\ast$ and an unknown additive noise distribution. The key decision object is the one-dimensional oracle price map $u\mapsto p^\ast(u)$ induced by the scalar index $u=μ_\ast(\mathsf c)$ and the noise tail. Under the $β$-Hölder smoothness of the tail function for $β\geq 2$ and a revenue-geometry condition that gives a unique, stable, interior maximizer, this oracle map is itself $(β-1)$-smooth. We exploit such structure through $\mathsf{ORBIT}$, a modular coarse-to-fine policy that takes a scalar pilot index as input, localizes a benchmark price in each active bin, and learns a local polynomial approximation of the oracle map inside a trust region via bandit convex optimization. For the baseline linear utility model $μ_\ast(\mathsf c)=\mathsf c^\topθ_\ast$, an adaptive elliptical exploration scheme constructs the required scalar pilot online without distributional assumptions on the contexts. The resulting policy achieves regret $\widetilde{O}\big(T^{\frac{2β-1}{4β-3}}+\sqrt{dT}\big)$. For fixed $d$, we establish a matching lower bound in the horizon dependence, unveiling that the nonparametric oracle-map learning term is minimax sharp. The same scalar-pilot interface also yields extensions to sparse high-dimensional linear utility and nonparametric Hölder utility.

Negotiation is a central mechanism of economic exchange, shaping markets, procurement, labor agreements, and resource allocation. It is also a canonical testbed for agentic language models, requiring multi-turn interaction under hidden preferences, strategic communication, and binding constraints. These properties make negotiation hard to evaluate: unlike math or code, it has no intrinsic verifier. Existing LLM negotiation evaluations rely on LLM-vs.-LLM interaction or aggregate outcomes such as deal rate, leaving failures opaque. We introduce Terms-Bench, short for Testbed for Economic Reasoning in Multi-turn Strategy, a Bayesian-game framework that makes the environment itself the verifier by specifying the counterpart's latent type, policy, and payoff structure. We instantiate it in bilateral price negotiation, where the counterpart's private state and simulator policy are hidden from the agent but observable to the evaluator. This turns the counterpart from a black-box opponent into a diagnostic instrument, enabling agent-attributable failure analysis and oracle-reference optimality gaps. Evaluating 13 LLM agents spanning frontier systems from major providers, Terms-Bench turns negotiation evaluation from aggregate ranking into actionable diagnosis: where agents fail, why they fail, and what to strengthen. Empirically, frontier models saturate deal rate yet diverge in surplus extraction, cue use, belief calibration, and compliance, revealing agent-specific bargaining bottlenecks masked by prior benchmarks.

Reinforcement learning agents for portfolio management are typically trained and deployed as static policies, with no mechanism for using price forecasts at inference time. We propose $\text{FPILOT}$ (Financial Plugin Inference-time Learning for Optimal Trading), a plugin inference-time optimization framework inspired by Model Predictive Control (MPC). Our key structural insight is that future prices mostly do not depend on one agent's portfolio allocation, so a suitable predictive model can produce a multi-step price trajectory without iterative action-conditioned rollouts as in typical reinforcement learning. At each decision step, we use the forecaster's predicted price trajectory to construct an allocation-based imagined return objective, and optimize the policy at inference-time before executing one step of the trade. Our framework is compatible with any pre-trained agent and adapts the policy to the forecaster's predictions without any retraining. Evaluated across five policy learning algorithms on the TradeMaster DJ30 benchmark, $\text{FPILOT}$ produces consistent improvements in total return and return-based risk-adjusted metrics (Sharpe, Sortino, Calmar), with stochastic policies benefiting more than deterministic ones. Further, using synthetic forecasts at calibrated quality levels, we show that gains consistently improve with forecaster quality, suggesting that our performance will improve based on advances in financial forecasting.

We study proportional representation in the temporal voting model, where collective decisions are made repeatedly over time over a fixed horizon. Prior work has extensively investigated how proportional representation axioms from multiwinner voting (e.g., justified representation (JR) and its variants) can be adapted, satisfied, and verified in this setting. However, much less is understood about their interaction with social welfare. In this work, we quantify the efficiency cost of enforcing proportionality. We formalize the welfare-proportionality tension via the worst-case ratio between the maximum achievable utilitarian welfare and the maximum welfare attainable subject to a proportionality axiom. We show that imposing proportional representation in the temporal setting can incur a growing, yet sublinear, welfare loss as the number of voters or rounds increases. We further identify a clean separation among axioms: for JR, the welfare loss diminishes as the time horizon grows and vanishes asymptotically, whereas for stronger axioms this conflict persists even with many rounds. Moreover, we prove that welfare maximization under each axiom is NP-complete and APX-hard, even under static preferences and bounded-degree approvals, and provide fixed-parameter algorithms under several natural structural parameters.

This paper develops a joint spectral radius (JSR) framework for analyzing rank-one deflated Q-value iteration (Q-VI) in discounted Markov decision process control. Focusing on an all-ones residual correction, we interpret the resulting algorithm through the geometry of switching systems and, to the best of our knowledge, give the first JSR-based convergence analysis of deflated Q-VI for policy optimization problems. Our analysis reveals that the standard Q-VI switching system model has JSR exactly the discount factor $γ\in (0,1)$, since all admissible subsystems share the all-ones vector as an invariant direction. By passing to the quotient space that removes this direction, we obtain a projected switching system model whose JSR governs the relevant error dynamics and may be strictly smaller than $γ$. Therefore, the deflated Q-VI admits a potentially sharper convergence-rate characterization than the ambient-space $γ$-bound. Finally, we prove that the correction is equivalent to a scalar recentering of standard Q-VI. Hence, the projected trajectory, and therefore the greedy-policy sequence, is unchanged relative to standard Q-VI initialized from the same point. The benefit of deflation is not a change in the induced decision-making problem, but a more precise JSR-based description of the convergence geometry after the redundant all-ones component is removed.

We study sparse recovery when observations come from mixed-quality sources: a small collection of high-quality measurements with small noise variance and a larger collection of lower-quality measurements with higher variance. For this heterogeneous-noise setting, we establish sample-size conditions for information-theoretic and algorithmic recovery. On the information-theoretic side, we show that it is sufficient for $(n_1, n_2)$ to satisfy a linear trade-off defining the Price of Quality: the number of low-quality samples needed to replace one high-quality sample. In the agnostic setting, where the decoder is completely agnostic to the quality of the data, it is uniformly bounded, and in particular one high-quality sample is never worth more than two low-quality samples for this sufficient condition to hold. In the informed setting, where the decoder is informed of per-sample variances, the price of quality can grow arbitrarily large. On the algorithmic side, we analyze the LASSO in the agnostic setting and show that the recovery threshold matches the homogeneous-noise case and only depends on the average noise level, revealing a striking robustness of computational recovery to data heterogeneity. Together, these results give the first conditions for sparse recovery with mixed-quality data and expose a fundamental difference between how the information-theoretic and algorithmic thresholds adapt to changes in data quality.

Accurate and efficient imbalance electricity price forecasting is critical for industrial energy trading systems, especially as battery assets and automated bidding pipelines increasingly participate in balancing markets. However, real-time forecasting is complicated by nonlinear market-rule-based price formation, heterogeneous input signals, and incomplete data availability caused by communication delays, publication lags, and measurement outages. This paper proposes a market-rule-informed neural forecasting framework that embeds imbalance price formation rules into the latent space of an expressive neural network. The proposed framework preserves raw signal information while exploiting transparent market-rule priors. We further analyze operational robustness by removing price-component information and characterize how forecasting performance scales with input length and forecasting horizon. Experimental results show that the proposed model achieves competitive forecasting performance with substantially fewer trainable parameters and shorter training time than generic deep learning baselines. Experimental results show that the proposed model achieves competitive forecasting performance with substantially fewer trainable parameters and shorter training time than generic deep learning baselines, demonstrating that market-rule priors and expressive neural networks should be jointly used for accurate and computationally sustainable forecasting in industrial energy trading applications. The implementation is publicly available at https://runyao-yu.github.io/MRINN/.

We design the first regret guarantees for robust dynamic pricing that decouple the dependence on the corruption $C$ and the time horizon $T$. In dynamic pricing, a seller with unlimited supply of a good interacts with a stream of buyers over $T$ rounds, with the goal of maximizing revenue. At each round $t$, the seller posts a price $p_t$, and the buyer purchases the good only if their unknown valuation $v^\star$ exceeds this price. The seller observes only the binary feedback $\mathbb{I} \left\{ p_t \leq v^\star \right\}$, indicating whether a sale occurred. In the \emph{robust} pricing setting, a malicious adversary is allowed to corrupt this feedback in at most $C$ rounds. Even if the learner knows the corruption $C$, the best known regret bound is $\mathcal{O}(C\log\log T)$ by Gupta et al. [2025]. This leaves as an open problem to ``decouple'' the dependence on $C$ and $T$. In this work, we resolve this open problem. In particular, we develop a robust variant of binary search that achieves regret $\mathcal{O}(C+\log T)$ when the corruption $C$ is known and $\mathcal{O}(C+\log^2 T)$ when the corruption is unknown.

Marketing decisions reflect the interaction of latent consumer heterogeneity, time-varying internal states, and explicit interventions, a structure that current prediction- and language-oriented models do not capture in a unified manner. We propose a Three-in-One world-model architecture in which a Deep Boltzmann Machine (DBM) learns a frozen belief representation from demographics, time, and lagged actions and outcomes, with lightweight task-specific adapters attached on top. The same belief supports three tasks within a single framework: (i) energy-based consistency evaluation through the DBM's free energy, (ii) outcome prediction through adapters, and (iii) counterfactual inference by holding the belief fixed and varying only the action input given to the adapter. Using a controlled simulation in which the latent price sensitivity, promotion responsiveness, and base preference of each consumer are known, we show that the adapters match a strong MLP baseline on visit- and purchase-AUC while recovering heterogeneous treatment effects substantially better than S-, T-, X-, and DR-learner meta-learners and a Causal Forest baseline built on the same raw features, with the largest gap on a confounded price-promotion intervention. Complementing this, free-energy clamps systematically penalize counterfactual purchase trajectories that lack prior promotional exposure, and the penalty itself depends on the latent base preference in the expected direction. These results indicate that DBM beliefs disentangle latent traits in a form that survives counterfactual queries, providing an integrated world-model substrate for marketing intervention.

We introduce a causal aware foundation-model framework for real time optimal decision making in discrete choice environments. We propose a constrained triple-head price optimization (C3PO) network to solve a bilevel decision problem in which a service provider selects an optimal assortment while heterogeneous users make personalized acceptance or rejection choices optimizing their own personalized preferences. C3PO integrates imitation learning of prices, multi-task learning of revenue responses, and in context learning of price elasticity to generate pricing recommendations while adhering to business constraints. During inference, frontier model prompting retrieves an enhanced elasticity prior for new products from behavioral economics literature, improving pricing effectiveness. We demonstrate strong in context learning performance using simulated, synthetic, and real-world datasets. C3PO is trained on simulated data generated from multiple classical discrete choice models in economics. The model is trained on data comprising simulated customer segments and counterfactual action and outcome pairs and evaluated on randomly generated choice environments with no access to the underlying preference structure. The trained model consistently improves the pricing KPIs, with gains increasing as customer price sensitivity increases. We also deploy the tuned foundation model for optimal pricing in real-world applications such as healthcare, tender pricing, airline ancillary pricing, and other domains, achieving substantial gains across multiple products, markets, and divisions.

Outcome metrics can certify the wrong behavior. We study this failure in a two-hotel revenue-management simulator where Hotel A trains an agent against a fixed rule-based revenue-management competitor, Hotel B. A standard learning agent can obtain near-reference revenue per available room (RevPAR) while failing to learn market-like yield management: it sells too aggressively, undercuts, or collapses to modal price buckets. We diagnose this as a Goodhart-style failure under partial observability. Hotel A cannot observe the competitor's remaining inventory, booking curve, or pricing rule, so the same Hotel A-visible state maps to multiple plausible Hotel B prices. Deterministic value-based RL and deterministic copying collapse this unresolved uncertainty into shortcut behavior. We introduce a trace-level diagnostic protocol using RevPAR, occupancy, ADR, full price-bucket distributions, L1/JS distances, and seed-level confidence intervals. The verified repair is Trace-Prior RL: learn a distributional market prior from lagged market traces, then train a stochastic pricing policy with a RevPAR reward and a KL penalty to the learned prior. The final policy matches Hotel B's RevPAR, occupancy, ADR, and price distribution within seed-level uncertainty, while still optimizing Hotel A's own reward. We argue that the contribution is not a new optimizer and not a hotel-pricing leaderboard, but a reproducible failure-and-repair recipe for agentic systems where scalar rewards are easy to game and the intended behavior is only visible in traces. A key finding is that higher exact action accuracy can worsen aggregate trace alignment when the target is distributional.

Algorithmic decision-making in high-stakes settings can have profound impacts on individuals and populations. While much prior work studies fairness in static settings, recent results show that enforcing static fairness constraints may exacerbate long-run disparities. Motivated by this tension, we study a stylized sequential selection problem in which a decision-maker repeatedly selects individuals, affecting both immediate utility and the population distribution over time. We introduce notions of group fairness for both the short and long term and theoretically analyze the trade-off between fairness and utility via the Price of Fairness (PoF). We characterize optimal and fair policies in the short term and show that the PoF can be large even when group distributions are nearly identical. In contrast, we show that long-term disparities can vanish under simple investment policies that achieve a low PoF. We also empirically validate these theoretical observations using both synthetic and real datasets.

We study contextual dynamic pricing with linear valuations and bounded-support agnostic noise, whose induced demand curve may be non-Lipschitz with arbitrary jumps and atoms. Such discontinuities break the cross-context interpolation arguments used by smooth-demand pricing algorithms, while the best previous method achieved only $\tilde O(T^{3/4})$ regret. We propose Conservative-Markdown Redirect-UCB Pricing, a polynomial-time algorithm that combines randomized parameter estimation, conservative residual-grid probing, and confidence-based one-step redirection. Our algorithm achieves $\tilde O(T^{2/3})$ optimal regret, matching the known lower bounds of Kleinberg and Leighton (2003) up to logarithmic factors and improving over the previous upper bound of Xu and Wang (2022). Under stochastic well-conditioned contexts, this closes the long-existing open regret gap in linear-valuation contextual pricing under agnostic non-Lipschitz noise distribution.

We present two new classes of causal models of decision-making agents. Our approach is motivated by the needs of modeling the economics of computing systems. These systems are composed of subsystems and can exhibit endogenous limits on cognitive resources and value discounting. Structural Causal Decision Models (SCDMs) expand on Structural Causal Influence Models. Like SCIMs, they explicitly represent the causal relationships between model variables and the payoffs of agent decisions. Additionally, agent decisions can be constrained by their causal antecedents, and SCDMs can have open root variables for which no probability distribution or structural equation is given. We show that SCDMs have a well-defined and computationally useful property of composability. Building on SCDMs, we then define a Structural Causal Decision Process (SCDP) as a recurring SCDM with a discount variable. SCDPs benefit from the useful composition properties of SCDMs. Moreover, SCDPs are strictly more expressive than POMDPs because they do not assume rational belief formation. Indeed, an SCDP can endogenously model the memory-formation process, and is thus useful for modeling resource rational agents in dynamic settings. SCDPs are also capable of modeling variable discounting, a tool used widely in social scientific modeling. We pose that SCDPs are a useful framework for policy simulation for the digital economy, mechanism design for information systems, and digital twin modeling of cyberinfrastructure.

Language data are increasingly acquired and governed as assets, yet platforms often price candidate resources before knowing their true privacy or access costs. We study online pricing for governed language data assets under cost uncertainty. At each round, a platform observes an NLP task, a candidate asset, and a coarse cost estimate, may pay for a refined cost signal, posts a price, and receives safe net revenue. We introduce \textsc{NH-CROP}, a clipped robust pricing framework with a no-harm information-acquisition gate. The method compares direct pricing, risk-aware pricing, and verify-then-price, and acquires information only when its estimated decision value exceeds the best no-verification alternative. Across synthetic, real-proxy, and downstream-utility-grounded benchmarks, clipped \textsc{NH-CROP} variants improve or remain competitive with price-only and risk-aware baselines. Causal ablations show that paid verification is not the main source of gains in real-proxy and utility-grounded settings: the strongest learned policies often choose not to verify. Oracle and high-decision-value diagnostics show that refined cost information can still have substantial local value. Overall, governed language-data platforms should calibrate pricing under uncertain access costs first and verify only when information is cheap and decision-actionable.

This position paper argues that agentic AI systems should be designed and evaluated as \emph{marginal token allocation economies} rather than as text generators priced by the unit. We follow a single request -- a developer asking a coding agent to fix a failing test -- through four economic layers that today are designed in isolation: a router that decides which model answers, an agent that decides whether to plan, act, verify, or defer, a serving stack that decides how to produce each token, and a training pipeline that decides whether the trace is worth learning from. We show that all four layers are solving the \emph{same} first-order condition -- marginal benefit equals marginal cost plus latency cost plus risk cost -- with different index sets and different prices. The framing is deliberately minimal: we do not propose a complete theory of AI economics. But adopting marginal token allocation as the shared accounting object explains why systems that locally minimize tokens globally misallocate them, predicts a small set of recurring failure modes (over-routing, over-delegation, under-verification, serving congestion, stale rollouts, cache misuse), and points to a concrete research agenda in token-aware evaluation, autonomy pricing, congestion-priced serving, and risk-adjusted RL budgeting.

We study online regression with the square loss in a reproducing kernel Hilbert space under a dynamic regret criterion. The learner is compared with a time-varying comparator sequence, and the bounds depend on its path length in the RKHS norm. The proposed method transfers the finite-dimensional discounted Vovk--Azoury--Warmuth approach of Jacobsen & Cutkosky (2024) to the RKHS setting by means of finite-dimensional subspace approximations. For a fixed subspace, we run a VAW-based ensemble of discounted VAW forecasters over a geometric grid of discount factors. The additional approximation error is controlled by the uniform projection error of kernel sections. We then introduce a general orthogonal truncation method: starting from a feature expansion of the kernel, we construct the associated RKHS by introducing an inner product that makes the feature functions orthonormal, and then use the spans of the first basis functions as finite-dimensional approximation spaces. The resulting subspace reduction is applied to several approximation schemes. Explicit feature expansions yield fast-regime bounds for Gaussian and analytic dot-product kernels. Mercer truncations provide a spectral approximation method and lead to dynamic regret bounds in fast and slow regimes, depending on the eigenvalue decay. Finally, we study subspaces spanned by kernel sections and apply this construction to Matérn kernels.

Traditional data valuation methods based on ``row-count $\times$ quality coefficient'' paradigms fail to capture the nuanced, nonlinear contributions that data makes to Large Language Model (LLM) capabilities. This paper presents a dynamic data valuation framework that transitions from static accounting to utility-based pricing. Our approach operates on three layers: (1) token-level information density metrics using Shannon entropy and Data Quality Scores; (2) empirical training gain measurement through influence functions, proxy model strategies, and Data Shapley values; and (3) cryptographic verifiability through hash-based commitments, Merkle trees, and a tamper-evident training ledger. We provide comprehensive experimental validation on three real domains (instruction following, mathematical reasoning, and code summarization), demonstrating that proxy-based empirical gain achieves near-perfect ranking alignment with realized utility, substantially outperforming row-count and token-count baselines. This framework enables a fair Data-as-a-Service economy where high-reasoning data is priced according to its actual contribution to model intelligence, while providing the transparency and auditability necessary for trustworthy data markets.

Freight brokerages negotiate thousands of carrier rates daily under dynamic pricing conditions where models frequently revise targets mid-conversation. Classical time-dependent concession frameworks use a fixed shape parameter $β$ that cannot adapt to these updates. Deriving $β$ from the live spread enables adaptation but introduces a new problem: a pricing shift can cause the formula to retract a previous offer, violating monotonicity. LLM-powered brokers offer flexibility but require expensive reasoning models, produce non-deterministic pricing, and remain vulnerable to prompt injection. We propose a two-index anchor-and-resume framework that addresses both limitations. A spread-derived $β$ maps each load's margin structure to the correct concession posture, while the anchor-and-resume mechanism guarantees monotonically non-decreasing offers under arbitrary pricing shifts. All pricing decisions remain in a deterministic formula; the LLM, when used, serves only as a natural-language translation layer. Empirical evaluation across 115,125 negotiations shows that the adaptive $β$ tailors behavior by regime: in narrow spreads, it concedes quickly to prioritize deal closure and load coverage; in medium and wide spreads, it matches or exceeds the best fixed-$β$ baselines in broker savings. Against an unconstrained 20-billion-parameter LLM broker, it achieves similar agreement rates and savings. Against LLM-powered carriers as more realistic stochastic counterparties, it maintains comparable savings and higher agreement rates than against rule-based opponents. By decoupling the LLM from pricing logic, the framework scales horizontally to thousands of concurrent negotiations with negligible inference cost and transparent decision-making.

We study the pricing behavior of third-party platforms facing strategic agents. Assuming the platform is a revenue maximizer, it observes market features that generally affect demand. Since only transacted quantities and prices can be observed, this presents a general demand learning problem under confounding. Mathematically, we develop an algorithm with optimal regret of $\Tilde{\mathcal{O}}(\sqrt{T}\wedgeσ_S^{-2})$. Our results reveal that supply-side noise fundamentally affects the learnability of demand, leading to a phase transition in regret. Technically, we show that non-i.i.d. actions can serve as instrumental variables for learning demand. We also propose a novel homeomorphic construction that allows us to establish estimation bounds without assuming star-shapedness, providing the first efficiency guarantee for learning demand with deep neural networks. Finally, we use simulations and offline counterfactuals from Talabat and Lyft data to illustrate the potential revenue implications of our approach.

Column generation and branch-and-price (B&P) are leading mathematical optimization methods for large-scale exact optimization, iterating between solving a master problem and a pricing problem. Due to the difficulty of discrete optimization, high-performance column generation often relies on a custom pricing algorithm built specifically to exploit the problem's structure. This bespoke nature of the pricing solver makes column generation a problem-specific method and hinders the use of generic implementations across a wide range of problems. We show that domain-independent dynamic programming (DIDP), a model-based paradigm for dynamic programming, can be used as a generic pricing solver. We develop new modeling features and a solving algorithm for DIDP to achieve better performance in typical pricing problems. We demonstrate that in four problem classes, our implementations of B&P, with pricing by DIDP, empirically outperform an existing automated B&P solver and B&P with pricing by mixed-integer programming or constraint programming.

Unlike Business-to-Consumer e-commerce platforms (e.g., Amazon), inexperienced individual sellers on Consumer-to-Consumer platforms (e.g., eBay) often face significant challenges in setting prices for their second-hand products efficiently. Therefore, numerous studies have been proposed for automating price prediction. However, most of them are based on static regression models, which suffer from poor generalization performance and fail to capture market dynamics (e.g., the price of a used iPhone decreases over time). Inspired by recent breakthroughs in Large Language Models (LLMs), we introduce LLP, the first LLM-based generative framework for second-hand product pricing. LLP first retrieves similar products to better align with the dynamic market change. Afterwards, it leverages the LLMs' nuanced understanding of key pricing information in free-form text to generate accurate price suggestions. To strengthen the LLMs' domain reasoning over retrieved products, we apply a two-stage optimization, supervised fine-tuning (SFT) followed by group relative policy optimization (GRPO), on a dataset built via bidirectional reasoning. Moreover, LLP employs a confidence-based filtering mechanism to reject unreliable price suggestions. Extensive experiments demonstrate that LLP substantially surpasses existing methods while generalizing well to unseen categories. We have successfully deployed LLP on Xianyu\footnote{Xianyu is China's largest second-hand e-commerce platform.}, significantly outperforming the previous pricing method. Under the same 30% product coverage, it raises the static adoption rate (SAR) from 40% to 72%, and maintains a strong SAR of 47% even at 90% recall.

Mixed bundle pricing is a classic revenue management problem arising in industries such as e-commerce, tourism, and video games. It refers to designing product combinations (i.e., bundles) and determining their prices to maximize expected profit. Exact mixed-bundling formulations capture this structure but are computationally intractable because the number of possible bundles grows exponentially with the number of products. We propose a graph neural network (GNN)-guided pruning framework for scalable (non-)additive bundle pricing. Instead of learning on the exponential bundle-level formulation, we encode each instance as a compact customer-product graph and train an edge-output GNN to learn the product-assignment probabilities from optimal mixed-bundling solutions. The predicted probabilities are then converted into restricted candidate bundle families through fixed cutoff pruning and progressive cutoff pruning; the final prices and assignments are obtained by solving the mixed bundling formulation over the retained bundles. We further introduce a GNN-guided local search and an iterative self-improvement procedure for larger instances. The local search refines the retained bundle family by prioritizing high-confidence add/drop moves, while the iterative self-improvement procedure generates high-quality solutions on larger instances for retraining. Theoretically, we show that under mild distinguishability conditions the proposed edge-output GNN class is expressive enough to recover the optimal product-assignment mapping. Experiments show that the proposed policies recover over 98% of the optimal profit on small instances and outperform bundle-size pricing on larger instances with substantial runtime savings.

How hard is it to achieve consensus in a social network under uncertainty? In this paper we model this problem as a social graph of agents where each vertex is initially colored red or blue. The goal of the agents is to achieve consensus, which is when the colors of all agents align. Agents attempt to do this locally through steps in which an agent changes their color to the color of the majority of their neighbors. In real life, agents may not know exactly how many of their neighbors are red or blue, which introduces uncertainty into this process. Modeling uncertainty as perturbations of relative magnitude $1+\varepsilon$ to these color neighbor counts, we show that even small values of $\varepsilon$ greatly hinder the ability to achieve consensus in a social network. We prove theoretically tight upper and lower bounds on the price of uncertainty, a metric defined in previous work by Balcan et al. to quantify the effect of uncertainty in network games.

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.

Problem definition: This paper studies the problem of estimating consumer preferences from bundle sales data. Product bundling is a widely used pricing strategy in retail markets. To set profitable bundle selection and prices, the seller needs to learn the distribution of consumers' valuations for individual products from the transaction data. When customers purchase bundles or multiple products, classical methods such as discrete choice models cannot be used to estimate consumers' valuations. In this paper, we propose an approach to learn the distribution of consumers' valuations toward the products using bundle sales data. Methodology/results: Our approach is to define a utility model for customer choices and estimate the parameters of a valuation distribution that maximizes the likelihood of observing the transaction data. Our approach reduces this problem to an estimation problem where the samples are censored by polyhedral regions on the valuation space of customers. Using the EM algorithm and Monte Carlo simulation, our approach can recover the distribution of consumers' valuations. We extend the framework to allow for unobserved no-purchases, clustered market segments and to incorporate non-additive bundle utilities with synergy effects. In addition, we provide theoretical results on the identifiability of the probability model and sufficient conditions for local convergence of the EM algorithm. Moreover, the performance of the approach is also demonstrated numerically with synthetic and real datasets. Managerial implications: This study demonstrates the challenge to leverage the transaction data of bundle sales to learn customers' preferences. The proposed algorithm provides a practical guidance for retailers.

This paper integrates deep neural networks (DNNs) into structural models to increase flexibility and capture rich heterogeneity while preserving interpretability. Economic (or scientific or domain-restricted) structure and machine learning are complements in empirical modeling, not substitutes: DNNs provide the capacity to learn complex, nonlinear heterogeneity, while the structure ensures the estimates remain interpretable and suitable for decision-making and policy analysis. We start with a standard parametric structural model and then enrich its parameters into fully flexible functions, which are estimated using a DNN with the model structure built in. We illustrate our framework with an application to demand estimation in consumer choice. We show that by enriching a demand model we can capture rich heterogeneity exploit it to create personalized pricing. Optimization is not possible without structure, but cannot be heterogeneous without machine learning. The same lessons apply to precision dosing, adaptive treatment, educational testing, and other targeting settings. We provide theoretical justification for our proposed methodology: nonasymptotic bounds and a novel and general influence function for feasible inference via double machine learning, so that the latter can be easily applied in numerous new contexts. These results may be of interest in other contexts as they generalize prior work.

AI agents sometimes act aligned when they infer they are being tested, and differently when not. We argue this is not an anomaly but what current training regimes are structured to select for. Reinforcement-learning-based alignment folds norms and task pursuit into one policy: the system learns its norms from scored behavior, and scoring flattens them. Do not do X is learned as doing X costs something if noticed. On every datum training can produce, a policy that complies only when it might be observed is indistinguishable from one that complies always. The experiment that would tell them apart - scoring unobserved behavior - is a contradiction in terms. Conditional compliance is thus the most that behavioral training can be known to deliver. Agency sharpens the problem: agents operate mostly where no one is watching, and can act on whether they are watched. An iterated pipeline that trains against detected failures selects for passing detection, not for complying. This account unifies alignment faking, sandbagging, and evaluation-aware scheming. And it reorients the remedy: not deeper internalization but architecture, making violations unavailable rather than unchosen.