First-Price Auctions

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Latest papers 25

Sep 30, 2026cs.RO

Communication-Free Distributed Multi-Robot Task Allocation under Partial Observations Using Labeled Multi-Bernoulli Filtering

This paper proposes a communication-free multi-robot task allocation framework based solely on local observations. In this study, tasks are defined as reaching target locations. Each robot estimates the positions of neighboring robots using a Labeled Multi-Bernoulli (LMB) filter and independently assigns tasks through a greedy auction-based strategy. By continuously updating state estimates and reallocating tasks during execution, the proposed method enables decentralized coordination without explicit communication. Monte Carlo simulations demonstrate that the proposed method enables effective cooperative task allocation without inter-robot communication while remaining robust to measurement clutter and observation uncertainty.

Takumi Ito, Akiya Kamimura

National Institute of Advanced Industrial Science and Technology (AIST), Tsukuba, Ibaraki 305-8568, Japan

Multi-Robot Systems Decentralized Autonomous Organization First-Price Auctions

Aug 13, 2026cs.GT

Error-Aware Reverse Auction Mechanism for Large Language Model Routing

Routing each query to a cost-effective large language model (LLM) is critical for balancing quality and cost, yet most routers rely on a centralized task center to predict model performance, creating an information-risk mismatch and a scalability bottleneck as the model pool grows. We formulate LLM routing as a market-based allocation problem among strategic providers and propose a routing paradigm that shifts ex-ante prediction to LLM providers via a reverse auction, where providers submit self-predicted acceptance probabilities and execution costs. To account for noisy provider predictions and center evaluations, we introduce the \textit{\textbf{E}rror-\textbf{A}ware \textbf{R}everse \textbf{A}uction \textbf{M}echanism} (EA-RAM), which explicitly models this Dual Error. We prove that, under a private-evaluation-belief structure, truthful effective-surplus reporting is incentive compatible in the reduced-form score space and individually rational under sellers' subjective beliefs, establish sufficient conditions for center rationality, and derive an explicit social-welfare loss bound. We further identify robustness effects: opposite-signed errors can cancel, vanishing-tail link functions (e.g., logistic) stabilize clear-cut cases via saturation, and extra noise smooths belief maps and reduces their maximal local sensitivity. Simulations and real-world benchmarks show that EA-RAM is robust to Dual Error and achieves a better cost--performance Pareto frontier than centralized baselines, with additional gains from provider-side local information, validating its practical effectiveness.

Haolong Chen, Zhengyuan Xin, Liang Zhang +2

Shenzhen International Center for Industrial and Applied Mathematics · Shenzhen Research Institute of Big Data · The Chinese University of Hong Kong, Shenzhen +2

Large Language Model Routing First-Price Auctions Incentives Pareto Frontier

Aug 9, 2026cs.GT

Does a Toehold Make a Bidder Bolder? Preemption and Multiplicity in Multi-Round Takeover Auctions

A bidder can quietly buy a stake in a company before making an offer for it. That stake, a toehold, is supposed to pay for itself twice: it makes the bidder willing to bid harder, and it frightens rivals into staying out of the fight. The first effect is arithmetic. The second is what would justify the cost and exposure of taking one at all. Yet toeholds are rare in practice, a standing puzzle. We ask whether that second effect is there once the contest is modelled as several rounds of escalating offers rather than the single exchange classical models assume. We turn it into a game a computer can solve, and certify the answers to an accuracy a referee can check. Three findings. The auction fixes what the toehold-holder earns but not how it bids: the same contest supports a bidder who opens aggressively against a rival who folds, and one who opens cheaply against a rival who does not, with the same profit either way. Aggressive preemptive bidding still appears when the toehold is removed entirely, so it comes from bidding in public and in turns, not from owning the stake. And the tidy "bigger toehold, more deterrence" relationship holds only in a contest cut short after one round; give it a real second round and it stops responding. So the two reasons to buy a toehold do not fare alike. The profit reason holds up; the deterrence reason does not, which suggests why toeholds may be rarer than theory predicts, alongside the procedural costs of disclosure and price impact that this model omits. A warning follows for anyone computing economics from a game solver: solve this auction once and it returns a confident figure for what a preemptive bid is worth; solve it again from a different start and it returns a different one, equally converged. We also report which solvers cope with contests of this shape, including versions too large to enumerate. Code is released.

Zain Naboulsi

Principal AI Competency Lead, Sparq

First-Price Auctions Bidding Preemption

Aug 3, 2026cs.AI

Evolving in the Agent Jungle via History-Informed Opponent Awareness

Learning to adapt strategies through interaction is a key step toward more general and autonomous LLM agents. Existing approaches typically achieve behavioral adaptation by revising skill libraries. However, in multi-agent environments, opponents may simultaneously update their strategies, causing the environment itself to evolve continuously. Applying skill-revision methods designed for static environments in such settings therefore amounts to updating against an obsolete reference. To address this challenge, we introduce OASE (Opponent-Aware Selective Evolution), which identifies and adopts genuinely beneficial skill revisions in dynamic multi-agent environments. Specifically, OASE conducts paired comparisons between a candidate skill and the incumbent under identical conditions anchored by historical snapshots of opponent strategies, and adopts the candidate only when its estimated payoff gain exceeds an acceptance threshold. We evaluate OASE in two decision-making scenarios: first-price auctions and private-cost Cournot competition. Experimental results show that, compared with a Reflexion-style baseline, OASE achieves a lower final equilibrium distance in both environments while accepting substantially fewer skill revisions, thereby suppressing strategy changes that lack sufficient payoff support. OASE therefore replaces blind updating with evidence-anchored selection, allowing agents to adapt stably and efficiently even as opponents continuously evolve.

Zhaofeng Zhang, Linhan Xia, Rui Liu +3

University of Edinburgh · University of Michigan · University of Oklahoma +5

First-Price Auctions

Jul 30, 2026cs.AI

Can LLM Agents Price Competitively? A Dynamic Multi-Attribute Auction Benchmark for Agentic Commerce

Agentic commerce is moving from concept to deployed infrastructure: payment networks, retailers, and AI platforms are setting the stage for agents to transact on behalf of merchants and consumers. Yet whether the LLMs behind these agents can price competently in real markets, where customer preferences are hidden, competitors adapt in real time, and demand can shift without warning, has not been systematically tested. We introduce Bazaar, a dynamic sealed-bid benchmark for multi-attribute auction under these conditions. Despite its dynamics, the benchmark is grounded in closed-form customer utilities, enabling exact evaluation. Across 11 frontier LLMs from four providers, the leading agents on customer acquisition (e.g. Gemini 3.1 Pro) are often not the leading agents on profit (e.g. Opus 4.6). The ranking shifts again under demand shocks: agents that learned fastest pre-shock are typically the slowest to revise their beliefs afterwards, while Gemini 3.1 Pro recovers fastest despite not leading on profit. However, even the strongest agent captures less than a third of hindsight-optimal profit, suggesting current LLMs are progressing in agentic commerce but leave substantial headroom.

Shimaa Ahmed, Yiwei Cai, Mohsen Minaei +1

Visa Research

Agentic Commerce Frontier Large Language Model Agents First-Price Auctions

Jul 25, 2026cs.GT

Online Fair Division with Budget Constraints

We study an online variant of discrete fair division under generalized assignment budget constraints. Goods arrive one at a time and must be assigned irrevocably to a feasible agent or to charity, which holds all unallocated goods, while fairness is evaluated only against budget-feasible subsets of every recipient's bundle. We first show that, without additional structure, no deterministic online algorithm can guarantee any fixed approximation to feasible envy-freeness, even in highly symmetric instances. We then identify bounded density spread as a structural condition that restores meaningful guarantees, obtaining approximation algorithms for arbitrary item sizes and showing that, under common valuations and sufficiently small goods, these guarantees can be strengthened to an optimal deterministic frontier. We further study resource augmentation, where the online algorithm is allowed slightly larger budgets than the fairness benchmark, and characterize the resulting improvement in the achievable guarantees. Finally, we develop a learning-augmented framework based on predicting joint value-size types, proving consistency under perfect predictions, robustness to prediction error, and showing that separate predictions of value and size marginals are insufficient to recover strong fairness guarantees.

Saar Cohen, Nicholas Teh, Paul W. Goldberg +1

Department of Computer Science, University of Oxford, UK

Algorithmic Fairness First-Price Auctions Learning-Augmented Algorithms Token Budget Allocation

Jul 10, 2026cs.AI

Agora: Enhancing LLM Agent Reasoning Via Auction-Based Task Allocation

Enhancing the reasoning capabilities of large language model (LLM) agents requires effective orchestration of diverse expert models and tools. However, existing frameworks typically call APIs, based on coarse-grained matching between tasks and the functions of expert models or tools, while overlooking critical factors such as performance variability and cost efficiency among functionally similar alternatives. To address this, we propose Agora, a framework that uses a confidence-calibrated auction to dynamically allocate tasks to expert models and tools. By treating reasoning steps as tradeable items, Agora bases allocation on calibrated competence rather than raw confidence. Across five main benchmarks, Agora improves or remains competitive with single-model, routing, and cascade baselines under matched candidate pools.

Kaiji Zhou, Aleš Leonardis, Yue Feng

University of Birmingham

Large Language Model Agents First-Price Auctions

Jul 7, 2026cs.GT

Contextual Procurement Auctions with Bandit Learning

We study repeated contextual procurement auctions in which producers have private costs and the platform must learn context-dependent product values from bandit feedback. The objective is welfare rather than revenue or a virtual-cost surrogate: regret is the total surplus loss relative to the full-information efficient procurement rule. We first show that the natural UCB allocation rule attains

\tilde O(\sqrt{ngT})

welfare regret under truthful bids, but its adaptive bid-dependent learning path does not by itself give a truthfulness guarantee. To obtain exact incentives, we design a bid-independent explore-then-commit mechanism with empirical critical payments; it is dominant-strategy truthful and has

\tilde O((ng)^{1/3}T^{2/3})

regret. We then introduce frozen-payment UCB, which estimates payments in an initial bid-independent exploration phase, freezes those payment estimates, and continues adaptive UCB allocation learning afterwards. Under a smoothed truthful-path margin condition, this mechanism gives a regret-incentive tradeoff: the near-UCB tuning attains

\tilde O(\sqrt{ngT})

welfare regret, while the average per-round gain from any fixed deviation is at most

\tilde O(T^{-1/4})

for fixed

n,g

. A matching lower bound shows that this frozen-payment frontier is unavoidable.

Yiling Chen, Shi Feng, Sadie Zhao

Harvard University

First-Price Auctions Contextual Bandit Framework Bandits Trade-Off

Jun 28, 2026cs.LG

Learning to Bid in Discriminatory Auctions with Budget Constraints

We study repeated bidding in multi-unit discriminatory (pay-as-bid) auctions for a single bidder with per-round utility equal to value minus

α

times payment, where

α\in[0,1]

is a cost-of-capital parameter. The bidder aims to maximize cumulative utility over

T

rounds subject to a total budget

B

. The problem is challenging even without budgets: the action space is exponential in

M

, the maximum demand of the bidder and the valuation vector (context) varies over time. Exploiting a decomposition of utility across units, we develop polynomial-time learning algorithms based on shortest paths in a directed acyclic graph, obtaining sublinear regret under both full-information and bandit feedback. In the bandit setting, the regret is independent of the number of contexts due to complete cross-learning: observing the utility of the chosen action under the realized context reveals the utility for the same action under all counterfactual contexts. With budget constraints, when the average normalized per-round budget

ρ=\frac{B}{MT}<1

, we design a coupled primal-dual algorithm in which the DAG-based procedure uses dual-adjusted edge weights for primal updates, while online gradient descent updates the dual variable, yielding

ρ

-approximate sublinear regret. Finally, we give implementations whose per-round time and space are independent of the number of contexts, enabling scalability to large or even infinite context spaces.

Negin Golrezaei, Sourav Sahoo

Sloan School of Management, Massachusetts Institute of Technology · Operations Research Center, Massachusetts Institute of Technology

First-Price Auctions Bidding Bandits Token Budget Allocation Vectors

Jun 27, 2026cs.CL

A3M: Adaptive, Adversarial and Multi-Objective Learning for Strategic Bidding in Repeated Auctions

Learning to bid in repeated multi-unit auctions with bandit feedback poses a fundamental challenge. Existing methods often rely on rigid explore-then-exploit schedules, assume stationary adversaries, and optimize solely for bidder utility, thereby limiting adaptability and strategic robustness. To address these limitations, we introduce the A3M framework, which integrates adaptive deep reinforcement learning (DRL), explicit adversarial reasoning, and principled multi-objective reward design for online auction strategy optimization. A3M employs an actor-critic DRL backbone to dynamically balance exploration and exploitation, an opponent model for fictitious play against non-stationary adversaries, and a composite reward function to jointly maximize utility, auctioneer revenue, and fairness. We provide the first comprehensive empirical evaluation of this integrated approach against established baselines in both discriminatory and uniform price auctions. Results show that A3M reduces final regret by 30--40% in standard settings, maintains robust performance against adversarial strategy shifts, scales favorably with the number of units

K

, and enables tunable multi-objective trade-offs. An extensive ablation study confirms the necessity of each core component. Our work establishes A3M as a powerful and flexible framework for learning in complex auction environments.

Junhan Li, Yuxin Zhang, Haoran Wang +1

Department of Computer Science Nanjing University

First-Price Auctions Bidding Stochastic Multi-Armed Bandits Offline Reinforcement Learning Adversarial Robustness

Jun 23, 2026cs.RO

Varying Bundle Size Reactive Multi-Task Assignment using Selective Cost Estimation for Multi-Agent Systems

This paper presents a scalable framework for multi-robot task allocation in complex environments where estimating task execution costs is computationally expensive. While combinatorial auction-based approaches offer reliable solutions, the exponential complexity of bundle generation typically renders them intractable for real-time reactive applications, particularly when accurate path planning is required for cost validation. We address this through a distributed, two-stage multi-fidelity bundle generation approach. Agents utilize a local search tree guided by a low-fidelity heuristic (such as euclidean distance) to rapidly explore the bundle space, applying high-fidelity path planning only to the most promising candidates in a best-first manner. These refined bids are then submitted to a central coordinator that solves a set packing problem to ensure global feasibility and maximize the overall utility. Simulation results in multiple environments demonstrate that the framework is able to improve the performance of reactive auction-based task allocation. Overall, the presented framework is shown to enable reactive task allocation with dynamic bundle sizes in multiple settings without exposing the agents' state and internal cost estimation models.

Niklas Dahlquist, Shridhar Velhal, George Nikolakopoulos

Luleå University of Technology, Luleå, SE-971 87 Sweden

Multi-Robot Systems First-Price Auctions Repair-Assignment Problem Path Planning Multi-Fidelity

Jun 8, 2026cs.GT

Duality for Optimal Multi-Item, Multi-Bidder Auction Design: Revenue Certificates through Deep Learning

Characterizing revenue-optimal auctions for multi-item, multi-bidder settings remains a fundamental open problem, with no known closed-form solution existing beyond restrictive binary-type instances. This has motivated interest in computational approaches to optimal auction design. In this paper, we introduce the first computational framework that directly tackles the dual problem for multi-item, multi-bidder auctions and dominant-strategy incentive compatibility (DSIC), generating certified revenue upper bounds. Our approach parametrizes Lagrange multipliers with a structurally guaranteed strict flow-conservation property using neural networks, enabling efficient optimization over feasible dual solutions via gradient descent. To bridge the gap between discrete computational methods and theoretical guarantees for continuous types, we develop a novel lifting technique that maps dual certificates from coarse discretizations to fine refinements. We prove that lifting gives valid revenue upper bounds for multi-item, multi-bidder auctions with continuous uniform valuations. Furthermore, we give a generalized lifting construction for arbitrary continuous distributions and demonstrate that these lifted duals converge to the revenue of the original continuous problem in the discrete limit. We validate this computational framework for the dual auction design problem by recovering known analytical mechanisms for canonical instances. For multi-item multi-bidder problems, our framework establishes a small gap between the optimal revenue and best-known DSIC mechanisms, providing computational certificates of near-optimality.

Yanchen Jiang, David C. Parkes, Tonghan Wang

Harvard University, USA · College of AI, Tsinghua University, China

First-Price Auctions Primal-Dual Methods Optimal Duality Certificates Deep Learning

May 29, 2026econ.TH

Comparing Market Mechanism Efficiencies

We develop a game-theoretic framework that compares welfare efficiency across three market mechanisms: continuous double auctions with transparent order books (lit exchanges), opaque order books (dark pools), and periodic batch auctions. Each mechanism is modeled as a queuing system where heterogeneous traders face trade-offs between the execution price, waiting costs, and transaction costs. Our main result establishes that under moderate arrival rates and bounded adverse selection, dark pools dominate both alternatives in aggregate ex-ante welfare. Observable order books create costly strategic timing games in which traders delay or rush submissions to optimize their position in the queue, generating wasteful social waiting costs. Opaque order books eliminate these timing games through information design. We formally characterize the equilibrium strategies in each mechanism and prove the welfare ranking

W^{DARK} > W^{LIT} > W^{BATCH}

. Extensions incorporate asymmetric information and endogenous venue choice. The results demonstrate how the information structure and the discipline of the service jointly determine efficiency in strategic matching environments.

Irene Aldridge

First-Price Auctions Limit Order Book Welfare Imperfect-Information Games

May 29, 2026cs.LG

Learning to Bid in FCR Markets: A Best-of-Both-Worlds Approach

Bidding in the European Frequency Containment Reserve (FCR) market is challenging for flexibility providers because competing offers are hidden and bidders observe only partial feedback form the market, such as, clearing price and awarded quantity. For a participant active in a single country, we show that the multi-country FCR clearing problem can be recast as a repeated multi-unit uniform-price auction against an endogenous vector of opposing bids. This reformulation yields an online learning problem and allows us to adapt a Best-of-Both-Worlds combinatorial semi-bandit algorithm implementable from this standard market feedback. The resulting bidder achieves logarithmic pseudo-regret in stochastic environments and

\mathcal{O}(\sqrt{T})

regret in adversarial ones. Synthetic experiments confirm the expected scaling, and backtests on historical European FCR data show competitive performance in practice: the method performs especially well on stable products, while EXP3-type baselines can be safer under stronger non-stationarity. Overall, the results show that learning-based bidding in FCR markets is theoretically grounded and practically useful when the learning rule matches product-level market stability.

Marius Potfer, Cheng Wan, Pierre Gruet

ENSAE, CREST (Fairplay joint team), 5 Av. Le Chatelier, 91120, Palaiseau, France · EDF Lab Paris-Saclay, FiME (Laboratoire de Finance des Marchés de l’Énergie), 7 Bd Gaspard Monge, 91120, Palaiseau, France

First-Price Auctions Non-Stationarity World

May 29, 2026cs.GT

Model Monotonicity in Autobidding Auctions: When Do Better Predictions Lead to Better Outcomes?

Online advertising platforms rely on machine learning models to predict click-through rates (pCTR) and conversion rates (pCVR) for auction mechanisms. We introduce a novel framework to study the interaction between recommender system model quality, auction format, and autobidder behavior. We formalize when model improvements -- defined via a refinement relation inspired by filtrations in probability theory -- lead to improvements in platform-level Evaluation Criteria Metrics (ECM) such as revenue, welfare, or liquid welfare. Our main contributions are: (1) a formal definition of model improvement based on cluster refinement, and (2) a systematic characterization of ECM monotonicity across different combinations of bidder types (tCPA, max-CPA), auction formats (first-price, second-price, VCG), and budget constraints. We show that first-price auctions with uniform bidding guarantee revenue monotonicity for tCPA bidders without budgets (via Jensen's inequality), while second-price auctions and budget constraints can break this property. We provide full numerical constructions for the non-monotonicity results. Our findings have practical implications for advertising platforms seeking to align model improvements with business outcomes.

Ashwinkumar Badanidiyuru

Uber Technologies, Inc., San Francisco, CA, USA.

First-Price Auctions Bidding Click-Through Rate Prediction Ads Monotonicity Sequential Recommendation

May 27, 2026cs.LG

Learning to Bid in Repeated Second-Price Auctions with Dynamic Values and Aggregated Feedback

We study the problem of learning to bid when the bidder's value is dynamic, i.e., when the current value depends on past outcomes. Specifically, we consider a bidder participating in repeated second-price auctions whose value depends on the time elapsed since their last successful bid, with auctions arriving in continuous time and only aggregated feedback revealed at the end of the horizon. Such a bidder must (1) balance the immediate benefit of winning the current auction against its impact on future values and (2) learn unknown environmental parameters. We derive regret bounds for a class of learning methods that combine plug-in estimators with a differential-equation characterization of the optimal policy, and show that a specific confidence bound algorithm learns the optimal policy with a near optimal regret of

\widetilde{O}(\log N)

for piecewise linear primitives, and

\widetilde{O}(N^{1/3})

for general, smooth primitives, achieving these regrets without explicit randomization. These theoretical results are supported by numerical experiments.

Benjamin Heymann, Otmane Sakhi

Criteo AI Lab

First-Price Auctions Bidding Optimal Policies Feedback

May 21, 2026stat.ML

Do Not Trust The Auctioneer: Learning to Bid in Feedback-Manipulated Auctions

Shilling is the use of artificial bids to make competition appear stronger and push prices upward. We study repeated first-price auctions in which shilling affects feedback but not allocation: the learner wins or loses against the real competing bid, but after a loss observes the maximum of the real bid and an independent shill bid. Thus the manipulation changes what the learner observes and hence how it learns to bid, without changing the outcome of the current auction. We analyze regret with respect to the best bid benchmark, assuming that the shill-bid distribution is known. Even then, shilling can mask the real bid, while useful side information appears only through intermittent low-shill events. Our algorithm combines a robust interval-elimination branch, which ignores the shilled report and achieves the dynamic-pricing rate

\tilde{\mathcal{O}}(T^{2/3})

, with an optimistic branch that debiases losing-side reports and exploits the resulting suffix information when it is reliable and achieves the first-price auctions rate

\tilde{\mathcal{O}}(\sqrt{T})

. A validation and racing procedure lets the algorithm use these optimistic updates without knowing the right scale or feedback geometry in advance. We complement the upper bounds with a matching lower bound, up to logarithmic factors, in the single-active-region case. Overall, the results show that even feedback-only shilling can sharply alter the statistical difficulty of repeated bidding.

Luigi Foscari, Matilde Tullii, Vianney Perchet

LAILA, Università degli Studi di Milano · Fairplay Team, Crest-Ensae, IP Paris · Fairplay Team, Crest-Ensae, IP Paris, CRITEO AI Team, Paris

First-Price Auctions Bidding Incentives Feedback

May 10, 2026cs.LG

Learning to Bid with Unknown Private Values in Budget-Constrained First-Price Auctions

The transition to First-Price Auctions (FPA) in digital advertising has spurred significant research, yet existing work typically assumes access to a valuation oracle, ignoring the reality that values must be inferred from censored data. While Linear Treatment Effect (LTE) models address this by learning value uplift, they have not been adapted to realistic settings with hard Budget constraints or Return-on-Spend (RoS) targets requiring regret and violation control. In this work, we propose a unified primal-dual framework for constrained FPAs that jointly learns the latent LTE valuation parameters and the competitor's bid distribution. This simultaneous learning introduces a critical technical challenge: the estimation error is dynamically scaled by the Lagrangian multiplier, potentially leading to unbounded regret. We resolve this by leveraging a strong Slater condition and a novel adaptive burn-in procedure to stabilize the dual variables. Our approach achieves near-optimal regret guarantees, providing the first theoretically grounded solution for constrained bidding with latent valuations.

Zihao Hu, Yuxiao Wen, Yuan Yao +2

Department of Mathematics, The Hong Kong University of Science and Technology · Department of IEDA, The Hong Kong University of Science and Technology · Stern School of Business, New York University

First-Price Auctions Learning-Augmented Algorithms Primal-Dual Methods Value Heterogeneous Treatment Effects Rise

May 3, 2026cs.GT

The (Marginal) Value of a Search Ad: An Online Causal Framework for Repeated Second-price Auctions

Existing auto-bidding algorithms in digital advertising often treat the value of an ad opportunity as the revenue obtained when an ad is shown and/or clicked, and bid accordingly. This can lead to wasteful spending because the true value is the marginal gain from paid exposure: even without winning a sponsored slot, an advertiser may still earn revenue via an organic search result (e.g., on Google or Amazon). Motivated by recent work, we model ad value as a treatment effect--the outcome difference between winning and losing the auction--and study online learning for bidding in second-price (Vickrey) auctions under this causal perspective. We develop algorithms that attain rate-optimal regret under several feedback models. A key ingredient exploits the information revealed by the second-price payment rule, which strictly improves regret relative to analogous learning problems in first-price auctions.

Yuxiao Wen, Zihao Hu, Yanjun Han +2

Courant Institute of Mathematical Sciences, New York University · Department of Mathematics, Hong Kong University of Science and Technology · Courant Institute of Mathematical Sciences and the Center for Data Science, New York University +2

First-Price Auctions Bidding

Apr 27, 2026cs.GT

Strategic Bidding in 6G Spectrum Auctions with Large Language Models

Efficient and fair spectrum allocation is a central challenge in 6G networks, where massive connectivity and heterogeneous services continuously compete for limited radio resources. We investigate the use of Large Language Models (LLMs) as bidding agents in repeated 6G spectrum auctions with budget constraints in vehicular networks. Each user equipment (UE) acts as a rational player optimizing its long-term utility through repeated interactions. Using the Vickrey-Clarke-Groves (VCG) mechanism as a benchmark for incentive-compatible, dominant-strategy truthfulness, we compare LLM-guided bidding against truthful and heuristic strategies. Unlike heuristics, LLMs leverage historical outcomes and prompt-based reasoning to adapt their bidding behavior dynamically. Results show that when the theoretical assumptions guaranteeing truthfulness hold, LLM bidders recover near-equilibrium outcomes consistent with VCG predictions. However, when these assumptions break -- such as under static budget constraints -- LLMs sustain longer participation and achieve higher utilities, revealing their ability to approximate adaptive equilibria beyond static mechanism design. This work provides the first systematic evaluation of LLM bidders in repeated spectrum auctions, offering new insights into how AI-driven agents can interact strategically and reshape market dynamics in future 6G networks.

Ismail Lotfi, Ali Ghrayeb

College of Science and Engineering, Hamad Bin Khalifa University, Doha, Qatar

Bidding First-Price Auctions

Apr 20, 2026cs.LG

An `Inverse' Experimental Framework to Estimate Market Efficiency

Digital marketplaces processing billions of dollars annually represent critical infrastructure in sociotechnical ecosystems, yet their performance optimization lacks principled measurement frameworks that can inform algorithmic governance decisions regarding market efficiency and fairness from complex market data. By looking at orderbook data from double auction markets alone, because bids and asks do not represent true maximum willingnesses to buy and true minimum willingnesses to sell, there is little an economist can say about the market's actual performance in terms of allocative efficiency. We turn to experimental data to address this issue, `inverting' the standard induced value approach of double auction experiments. Our aim is to predict key market features relevant to market efficiency, particularly allocative efficiency, using orderbook data only -- specifically bids, asks and price realizations, but not the induced reservation values -- as early as possible. Since there is no established model of strategically optimal behavior in these markets, and because orderbook data is highly unstructured, non-stationary and non-linear, we propose quantile-based normalization techniques that help us build general predictive models. We develop and train several models, including linear regressions and gradient boosting trees, leveraging quantile-based input from the underlying supply-demand model. Our models can predict allocative efficiency with reasonable accuracy from the earliest bids and asks, and these predictions improve with additional realized price data. The performance of the prediction techniques varies by target and market type. Our framework holds significant potential for application to real-world market data, offering valuable insights into market efficiency and performance, even prior to any trade realizations.

Thomas Asikis, Heinrich H. Nax

1*Behavioral Game Theory, University of Zurich, Andreasstrasse, Zurich, 8050, Switzerland.

Matching Markets First-Price Auctions Welfare Inverse Design

Oct 17, 2025cs.GT

HOB: A Holistically Optimized Bidding Strategy under Heterogeneous Bidding Environments

Optimizing a single advertising campaign across heterogeneous channels is a central challenge in industrial autobidding. Auction mechanisms vary across channels in ranking rules (pure eCPM vs. UE-augmented scoring), pricing formats (first- vs. second-price), and bidding conventions (uniform vs. non-uniform), while advertisers impose shared campaign-level constraints. We propose HOB, which makes marginal cost (MC) computable and alignable across heterogeneous channels, especially for first-price auctions (FPA) with organic-paid coexistence, where existing bidding formulations do not yield a practical aligned MC form. At the global level, HOB derives channel-specific MC forms and coordinates disparate channels through a shared MC target. At the local level, HOB models free-win probability and winning-price uncertainty with a zero-inflated exponential distribution, yielding an efficient surplus-optimal bidding strategy for non-uniform first-price auctions. We show that any interior optimum satisfies MC equalization across channels. Experiments on a controlled offline benchmark, industrial log replay, and large-scale online A/B tests demonstrate that HOB consistently delivers significant performance gains. Deployed on a large-scale commercial DSP, HOB delivers a 3.0% lift in GMV while maintaining return on advertising spend (ROAS) constraints.

Qi Li, Wendong Huang, Qichen Ye +9

Alibaba Group Beijing, China · Tsinghua University Beijing, China

First-Price Auctions Structural Constraints Device Environment

May 5, 2025cs.GT

Plan-Driven Adaptive Bidding for First-Price Auctions with Budget Constraints under Nonstationarity

We study budget pacing in repeated first-price auctions when an advertiser's private-value distributions change over time and the stationary competing-bid distribution is unknown. We ask how a feasible expenditure plan should enter online bid shading, learning, and hard budget control. We establish a plan-to-performance decomposition for a plan-driven projected-dual policy. The policy uses any feasible expenditure plan as a soft target, learns an unknown stationary competing-bid CDF from thresholds revealed after each auction, and enforces the campaign budget on every sample path. Against a distribution-informed expected-budget fluid benchmark, the uniform-plan reward gap is

O(\sqrt T)+O(\mathcal W_T)

, where

\mathcal W_T

measures heterogeneity in private-value distributions. With a supplied feasible plan, the global gap decomposes into a one-sided

O(\sqrt{T})

fixed-plan execution term and a plan-mismatch term bounded by

(b/2a)PlanError

. The same analysis provides guarantees for strict and relaxed period-cap comparators, exact recovery of the global benchmark under a specific allowance vector, and separate lower bounds establishing the necessity of the temporal-heterogeneity and Plan Error terms. An upstream planner can translate forecasts or managerial priorities into a feasible spending trajectory, while the online controller adapts bids using realized thresholds and expenditures. The guarantee is modular: it evaluates the final normalized or projected plan through

PlanError

. A specific forecasting model can be linked to the guarantee by establishing how its primitive estimation errors propagate to this plan-quality metric.

Yige Wang, Jiashuo Jiang

Department of Industrial Engineering & Decision Analytics, Hong Kong University of Science and Technology

First-Price Auctions Token Budget Allocation Non-Stationarity

Oct 31, 2023cs.GT

Data Market Design through Deep Learning

The data market design problem is a problem in economic theory to find a set of signaling schemes (statistical experiments) to maximize expected revenue to the information seller, where each experiment reveals some of the information known to a seller and has a corresponding price [Bergemann et al., 2018]. Each buyer has their own decision to make in a world environment, and their subjective expected value for the information associated with a particular experiment comes from the improvement in this decision and depends on their prior and value for different outcomes. In a setting with multiple buyers, a buyer's expected value for an experiment may also depend on the information sold to others [Bonatti et al., 2022]. We introduce the application of deep learning for the design of revenue-optimal data markets, looking to expand the frontiers of what can be understood and achieved. Relative to earlier work on deep learning for auction design [Dütting et al., 2023], we must learn signaling schemes rather than allocation rules and handle obedience constraints

-

these arising from modeling the downstream actions of buyers

-

in addition to incentive constraints on bids. Our experiments demonstrate that this new deep learning framework can almost precisely replicate all known solutions from theory, expand to more complex settings, and be used to establish the optimality of new designs for data markets and make conjectures in regard to the structure of optimal designs.

Sai Srivatsa Ravindranath, Yanchen Jiang, David C. Parkes

Harvard John A. Paulson School of Engineering and Applied Sciences

Bayesian Experimental Design First-Price Auctions Bidding Deep Learning Economies

Feb 3, 2023cs.LG

Robust Budget Pacing with a Single Sample

Major Internet advertising platforms offer budget pacing tools as a standard service for advertisers to manage their ad campaigns. Given the inherent non-stationarity in an advertiser's value and also competing advertisers' values over time, a commonly used approach is to learn a target expenditure plan that specifies a target spend as a function of time, and then run a controller that tracks this plan. This raises the question: how many historical samples are required to learn a good expenditure plan? We study this question by considering an advertiser repeatedly participating in

T

second-price auctions, where the tuple of her value and the highest competing bid is drawn from an unknown time-varying distribution. The advertiser seeks to maximize her total utility subject to her budget constraint. Prior work has shown the sufficiency of

T\log T

samples per distribution to achieve the optimal

O(\sqrt{T})

-regret. We dramatically improve this state-of-the-art and show that just one sample per distribution is enough to achieve the near-optimal

\tilde O(\sqrt{T})

-regret, while still being robust to noise in the sampling distributions.

Santiago Balseiro, Rachitesh Kumar, Vahab Mirrokni +2

DRO, Columbia Business School, New York, NY, USA · Google Research, New York, NY, USA · IEOR, Columbia University, New York, NY, USA

First-Price Auctions \Widetilde{\Mathcal{O}}(\Sqrt{T})$ Regret Token Budget Allocation Adaptive Sampling