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Learning a Game by Paying the Agents

ICLR 2026 Conference SubmissionAnonymous Authors
OpenReview Score: 6.0Download Report PDF
No-Regret LearningInverse Game TheoryRevealed PreferenceSteering
Abstract:

We study the problem of learning the utility functions of no-regret learning agents in a repeated normal-form game. Differing from most prior literature, we introduce a principal with the power to observe the agents playing the game, send agents signals, and give agents payments as a function of their actions. We show that the principal can, using a number of rounds polynomial in the size of the game, learn the utility functions of all agents to any desired precision ε>0\varepsilon > 0, for any no-regret learning algorithms of the agents. Our main technique is to formulate a zero-sum game between the principal and the agents, where the principal's strategy space is the set of all payment functions. Finally, we discuss implications for the problem of steering agents to a desired equilibrium: in particular, we introduce, using our utility-learning algorithm as a subroutine, the first algorithm for steering arbitrary no-regret learning agents without prior knowledge of their utilities.

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This report is AI-GENERATED using Large Language Models and WisPaper (A scholar search engine). It analyzes academic papers' tasks and contributions against retrieved prior work. While this system identifies POTENTIAL overlaps and novel directions, ITS COVERAGE IS NOT EXHAUSTIVE AND JUDGMENTS ARE APPROXIMATE. These results are intended to assist human reviewers and SHOULD NOT be relied upon as a definitive verdict on novelty.
NOTE that some papers exist in multiple, slightly different versions (e.g., with different titles or URLs). The system may retrieve several versions of the same underlying work. The current automated pipeline does not reliably align or distinguish these cases, so human reviewers will need to disambiguate them manually.
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Overview

Overall Novelty Assessment

The paper contributes a polynomial-time algorithm for learning utility functions of no-regret agents through strategic payments and signals, alongside a zero-sum game formulation for the principal-agent interaction. It resides in the 'Utility and Type Inference through Strategic Interaction' leaf, which contains only three papers total, indicating a relatively sparse research direction within the broader taxonomy. This leaf sits under 'Principal-Agent Incentive Design and Learning', distinguishing work where principals actively design incentives to infer agent characteristics from purely observational approaches.

The taxonomy reveals neighboring research directions that provide context. 'Incentive Contract Design under Information Asymmetry' (five papers) focuses on optimal contracts without learning objectives, while 'Dynamic and Adaptive Incentive Mechanisms' (three papers) examines time-varying incentive systems. The 'Agent Behavior Inference and Reward Learning' branch addresses preference learning without principal intervention, including reward function learning from observations. The paper's approach bridges these areas by combining strategic payment design with utility inference, positioning it at the intersection of mechanism design and learning theory in repeated games.

Among 26 candidates examined across three contributions, the analysis reveals varied novelty profiles. The polynomial-time utility learning algorithm (6 candidates examined, 0 refutable) and zero-sum game formulation (10 candidates examined, 0 refutable) show no clear prior work overlap within the limited search scope. The steering algorithm contribution (10 candidates examined, 1 refutable) appears to have more substantial prior work, with at least one candidate providing overlapping methods. This suggests the core utility learning mechanism may represent the more distinctive technical contribution, though the limited search scale means potentially relevant work outside the top-26 semantic matches remains unexamined.

Based on the top-26 semantic matches and taxonomy structure, the work appears to occupy a relatively underexplored niche combining no-regret learning dynamics with principal-designed payment mechanisms. The sparse population of its taxonomy leaf and limited refutable prior work suggest novelty, though the analysis cannot rule out relevant contributions beyond the examined candidate set. The steering algorithm's partial overlap with prior work indicates this application may be more incremental than the core learning framework.

Taxonomy

Core-task Taxonomy Papers
44
3
Claimed Contributions
26
Contribution Candidate Papers Compared
1
Refutable Paper

Research Landscape Overview

Core task: learning utility functions of no-regret agents through payments and signals. The field structure reflects a broad landscape spanning theoretical foundations and practical applications of incentive design. Principal-Agent Incentive Design and Learning encompasses classical contract theory and modern adaptive mechanisms that infer agent preferences through strategic interaction, often drawing on foundational work such as Optimal Incentive Contracts[13] and Theory of Incentives[29]. Agent Behavior Inference and Reward Learning focuses on extracting hidden preferences from observed actions, addressing challenges like imperfect knowledge and human feedback noise, as seen in Imperfect Knowledge Hidden Rewards[14] and Human Feedback Challenges[15]. Multi-Agent Coordination and Reward Design examines how incentives shape collective behavior in settings ranging from congestion games to cooperative dilemmas, while Applied Incentive Systems and Behavioral Studies explore real-world domains such as transactive energy markets, spatial crowdsourcing, and gig economy taxation. Rational Choice Theory and Behavioral Foundations provides the underlying decision-theoretic models, including critiques and extensions of classical rationality assumptions. A particularly active line of work investigates how principals can learn agent types or utilities by strategically offering payments or information signals, balancing exploration of unknown preferences with exploitation of learned models. Learning Game Paying Agents[0] sits squarely within this vein, focusing on utility inference for no-regret learners through carefully designed payment schemes. It shares thematic ground with Active Inference Incentive[34], which also considers how agents update beliefs and respond to incentives, and with Strategic Incentives Information Sale[3], which examines information provision as a lever for influencing strategic behavior. Compared to Imperfect Knowledge Hidden Rewards[14], which addresses hidden reward structures in single-agent settings, Learning Game Paying Agents[0] emphasizes the interactive, game-theoretic dimension where the principal must adapt to agent learning dynamics. This positioning highlights ongoing questions about how to efficiently elicit preferences when agents themselves are adapting, and how payment mechanisms can serve dual roles as both incentives and informative signals.

Claimed Contributions

Polynomial-time algorithm for learning utility functions of no-regret agents via payments

The authors introduce an algorithm that enables a principal to learn the utility functions of agents playing a repeated normal-form game by providing payments and signals. The algorithm works for arbitrary no-regret learning agents and achieves learning in polynomially many rounds with respect to game size.

6 retrieved papers
Zero-sum game formulation between principal and agents for utility learning

The core technical contribution is a novel formulation where the principal and agents play a zero-sum game. The principal chooses payment functions while agents choose actions to maximize rewards. This formulation enables the principal to learn utility functions through convergence to equilibrium.

10 retrieved papers
First steering algorithm for no-regret agents without prior utility knowledge

The authors present the first algorithm that can steer no-regret learning agents toward desired equilibria without requiring prior knowledge of the agents' utility functions. This is achieved by combining their utility-learning algorithm with a steering procedure, and they characterize the optimal achievable value through correlated equilibrium with payments.

10 retrieved papers
Can Refute

Core Task Comparisons

Comparisons with papers in the same taxonomy category

Contribution Analysis

Detailed comparisons for each claimed contribution

Contribution

Polynomial-time algorithm for learning utility functions of no-regret agents via payments

The authors introduce an algorithm that enables a principal to learn the utility functions of agents playing a repeated normal-form game by providing payments and signals. The algorithm works for arbitrary no-regret learning agents and achieves learning in polynomially many rounds with respect to game size.

Contribution

Zero-sum game formulation between principal and agents for utility learning

The core technical contribution is a novel formulation where the principal and agents play a zero-sum game. The principal chooses payment functions while agents choose actions to maximize rewards. This formulation enables the principal to learn utility functions through convergence to equilibrium.

Contribution

First steering algorithm for no-regret agents without prior utility knowledge

The authors present the first algorithm that can steer no-regret learning agents toward desired equilibria without requiring prior knowledge of the agents' utility functions. This is achieved by combining their utility-learning algorithm with a steering procedure, and they characterize the optimal achievable value through correlated equilibrium with payments.

Table of Contents