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Theory · Game Theory

Ali Shirali

From media platforms to chatbots, algorithms shape how people interact, learn, and discover information. Such interactions between users and an algorithm often unfold over multiple steps, during which strategic users can guide the algorithm to better align with their true interests by selectively engaging with content. However, users frequently exhibit inconsistent preferences: they may spend considerable time on content that offers little long-term value, inadvertently signaling that such content is desirable. Focusing on the user side, this raises a key question: what does it take for such users to align the algorithm with their true interests? To investigate these dynamics, we model the user’s decision process as split between a rational "system 2" that decides whether to engage and an impulsive "system 1" that determines how long engagement lasts. We then study a multi-leader, single-follower extensive Stackelberg game, where users, specifically system 2, lead by committing to engagement strategies and the algorithm best-responds based on observed interactions. We define the burden of alignment as the minimum horizon over which users must optimize to effectively steer the algorithm. We show that a critical horizon exists: users who are sufficiently foresighted can achieve alignment, while those who are not are instead aligned to the algorithm’s objective. This critical horizon can be long, imposing a substantial burden. However, even a small, costly signal (e.g., an extra click) can significantly reduce it. Overall, our framework explains how users with inconsistent preferences can align an engagement-driven algorithm with their interests in a Stackelberg equilibrium, highlighting both the challenges and potential remedies for achieving alignment.

Theory · Game Theory

Piotr Faliszewski, Łukasz Janeczko, Andrzej Kaczmarczyk, Grzegorz Lisowski, Piotr Skowron, Stanisław Szufa, Mateusz Szwagierczak

We study strategic behavior of project proposers in the context of approval-based participatory budgeting (PB). In our model we assume that the votes are fixed and known and the proposers want to set as high project prices as possible, provided that their projects get selected and the prices are not below the minimum costs of their delivery. We study the existence of pure Nash equilibria (NE) in such games, focusing on the AV/Cost, Phragmen, and Method of Equal Shares rules. We also provide an experimental study of cost selection on real-life PB election data.

Reinforcement Learning · Deep RL

Oren Neumann, Claudius Gros

Neural scaling laws are observed in a range of domains, to date with no universal understanding of why they occur. Recent theories suggest that loss power laws arise from Zipf's law, a power law observed in domains like natural language. One theory suggests that language scaling laws emerge when Zipf-distributed task quanta are learned in descending order of frequency. In this paper we examine power-law scaling in AlphaZero, a reinforcement learning algorithm, using a model of language-model scaling. We find that game states in training and inference data scale with Zipf's law, which is known to arise from the tree structure of the environment, and examine the correlation between scaling-law and Zipf's-law exponents. In agreement with the quanta scaling model, we find that agents optimize state loss in descending order of frequency, even though this order scales inversely with modelling complexity. We also find that inverse scaling, the failure of models to improve with size, is correlated with unusual Zipf curves where end-game states are among the most frequent states. We show evidence that larger models shift their focus to these less-important states, sacrificing their understanding of important early-game states.

Theory · Game Theory

Rémi Castera, Felipe Garrido-Lucero, Patrick Loiseau, Simon Mauras, Mathieu Molina, Vianney Perchet

We consider matroid allocation problems under \textit{opportunity fairness} constraints: resources need to be allocated to a set of agents under matroid constraints (which includes classical problems such as bipartite matching). Agents are divided into $C$ groups according to a sensitive attribute, and an allocation is opportunity-fair if each group receives the same share proportional to the maximum feasible allocation it could achieve in isolation. We study the Price of Fairness (PoF), i.e., the ratio between maximum size allocations and maximum size opportunity-fair allocations. We first provide a characterization of the PoF leveraging the underlying polymatroid structure of the allocation problem. Based on this characterization, we prove bounds on the PoF in various settings from fully adversarial (worst-case) to fully random. Notably, one of our main results considers an arbitrary matroid structure with agents randomly divided into groups. In this setting, we prove a PoF bound as a function of the (relative) size of the largest group. Our result implies that, as long as there is no dominant group (i.e., the largest group is not too large), opportunity fairness constraints do not induce any loss of social welfare (defined as the allocation size). Overall, our results give insights into which aspects of the problem's structure affect the trade-off between opportunity fairness and social welfare.

Theory · Game Theory

Tom Yan, Chicheng Zhang

With businesses starting to deploy agents to act on their behalf, an emerging challenge that businesses have to contend with is how to incentivize other agents with differing interests to work alongside its own agent. In present day commerce, payment is a common way that different parties use to \emph{economically} align their interests. In this paper, we study how one could analogously learn such payment schemes for aligning agents in the decentralized multi-agent setting. We model this problem as a Stackelberg Markov game, in which the leader can commit to a policy and also designate a set of outcome-based payments. We are interested in answering the question: when do efficient learning algorithms exist? To this end, we characterize the computational and statistical complexity of planning and learning in general-sum and cooperative games. In general-sum games, we find that planning is computationally intractable. In cooperative games, we show that learning can be statistically hard without payment and efficient with payment, showing that payment is necessary for learning even with aligned rewards. Altogether, our work aims to consolidate our theoretical understanding of outcome-based payment algorithms that can economically align decentralized agents.

Theory · Game Theory

Gergely Csáji, Alexander Gundert, Jörg Rothe, Ildikó Schlotter

We study fundamental connections between coalition formation games and clustering, illustrating the cross-disciplinary relevance of these concepts. We focus on graphical hedonic games where agents' preferences are compactly represented by a friendship graph and an enemy graph. In the context of clustering, friendship relations naturally align with data point similarities, whereas enmity corresponds to dissimilarities. We consider two stability notions based on single-agent deviations: local popularity and local stability. Exploring these concepts from an algorithmic viewpoint, we design efficient mechanisms for finding locally stable or locally popular partitions. Besides gaining theoretical insight into the computational complexity of these problems, we perform simulations that demonstrate how our algorithms can be successfully applied in clustering and community detection. Our findings highlight the interplay between coalition formation games and data-driven clustering techniques, offering fresh perspectives and applications in both areas.

Theory · Game Theory

Nan An, Weian Li, Qi Qi, Changyuan Yu, Liang Zhang

Accurate attribution for multiple platforms is critical for evaluating performance-based advertising. However, existing attribution methods rely heavily on the heuristic methods, e.g., Last-Click Mechanism (LCM) which always allocates the attribution to the platform with the latest report, lacking theoretical guarantees for attribution accuracy. In this work, we propose a novel theoretical model for the advertising attribution problem, in which we aim to design the optimal dominant strategy incentive compatible (DSIC) mechanisms and evaluate their performance. We first show that LCM is not DSIC and performs poorly in terms of accuracy and fairness. To address this limitation, we introduce the Peer-Validated Mechanism (PVM), a DSIC mechanism in which a platform's attribution depends solely on the reports of other platforms. We then examine the accuracy of PVM across both homogeneous and heterogeneous settings, and provide provable accuracy bounds for each case. Notably, we show that PVM is the optimal DSIC mechanism in the homogeneous setting. Finally, numerical experiments are conducted to show that PVM consistently outperforms LCM in terms of attribution accuracy and fairness.

Theory · Game Theory

Tianrun Zhao, Xiaojie Mao, Yong Liang

In this paper, we study an online strategic classification problem, where a principal aims to learn an accurate binary linear classifier from sequentially arriving agents. For each agent, the principal announces a classifier. The agent can strategically exercise costly manipulations on his features to be classified as the favorable positive class. The principal is unaware of the true feature-label distribution, but observes all reported features and only labels of positively classified agents. We assume that the true feature-label distribution is given by a halfspace model subject to arbitrary feature-dependent bounded noise (i.e., Massart Noise). This problem faces the combined challenges of agents' strategic feature manipulations, partial label observations, and label noises. We tackle these challenges by a novel learning algorithm. We show that the proposed algorithm yields classifiers that converge to the clairvoyant optimal one and attains a regret rate of $ O(\sqrt{T})$ up to poly-logarithmic and constant factors over $T$ cycles.

Theory · Game Theory

Alex Clinton, Thomas Zeng, Yiding Chen, Jerry Zhu, Kirthevasan Kandasamy

Modern data marketplaces and data sharing consortia increasingly rely on incentive mechanisms to encourage agents to contribute data. However, schemes that reward agents based on the quantity of submitted data are vulnerable to manipulation, as agents may submit fabricated or low-quality data to inflate their rewards. Prior work has proposed comparing each agent’s data against others’ to promote honesty: when others contribute genuine data, the best way to minimize discrepancy is to do the same. Yet prior implementations of this idea rely on very strong assumptions about the data distribution (e.g. Gaussian), limiting their applicability. In this work, we develop reward mechanisms based on a novel, two-sample test statistic inspired by the Cramér-von Mises statistic. Our methods strictly incentivize agents to submit more genuine data, while disincentivizing data fabrication and other types of untruthful reporting. We establish that truthful reporting constitutes a (possibly approximate) Nash equilibrium in both Bayesian and prior-agnostic settings. We theoretically instantiate our method in two canonical data sharing problems and show that it relaxes key assumptions made by prior work. Empirically, we demonstrate that our mechanism incentivizes truthful data sharing via simulations and on real-world language and image data.

Theory · Game Theory

Jiaxin Song, Pooja Kulkarni, Parnian Shahkar, Bhaskar Ray Chaudhury

The rapid growth of data-driven technologies and the emergence of various data-sharing paradigms have underscored the need for efficient and stable data exchange protocols. In any such exchange, agents must carefully balance the benefit of acquiring valuable data against the cost of sharing their own. Ensuring stability in these exchanges is essential to prevent agents—or groups of agents—from departing and conducting local (and potentially more favorable) exchanges among themselves. To address this, we study a model where $n$ agents participate in a data exchange. Each agent has an associated payoff for the data acquired from other agents and a cost incurred during sharing its own data. The net utility of an agent is payoff minus the cost. We adapt the classical notion of *core-stability* from cooperative game theory to data exchange. A data exchange is core-stable if no subset of agents has any incentive to deviate to a different exchange. We show that a core-stable data exchange is guaranteed to exist when agents have concave payoff functions and convex cost functions-- a setting typical in domains like PAC learning and random discovery models. We show that relaxing either of the foregoing conditions may result in the nonexistence of core-stable data exchanges. Then, we prove that finding a core-stable exchange is *PPAD-hard*, even when the potential blocking coalitions are restricted to constant size. To the best of our knowledge, this provides the first known PPAD-hardness result for core-like guarantees in data economics. Finally, we show that data exchange can be modelled as a *balanced* $n$-person game. This immediately gives a pivoting algorithm via Scarf's theorem [Scarf1967core]. We show that the pivoting algorithm works well in practice through our empirical results.

Theory · Game Theory

Eric Balkanski, Nicholas DeFilippis, Vasilis Gkatzelis, Xizhi Tan

We study the problem of designing procurement auctions for the strategic uncapacitated facility location problem: a company needs to procure a set of facility locations in order to serve its customers and each facility location is owned by a strategic agent. Each owner has a private cost for providing access to their facility (e.g., renting it or selling it to the company) and needs to be compensated accordingly. The goal is to design truthful auctions that decide which facilities the company should procure and how much to pay the corresponding owners, aiming to minimize the total cost, i.e., the monetary cost paid to the owners and the connection cost suffered by the customers (their distance to the nearest facility). We evaluate the performance of these auctions using the \emph{frugality ratio}. We first analyze the performance of the classic VCG auction in this context and prove that its frugality ratio is exactly $3$. We then leverage the learning-augmented framework and design auctions that are augmented with predictions regarding the owners' private costs. Specifically, we propose a family of learning-augmented auctions that achieve significant payment reductions when the predictions are accurate, leading to much better frugality ratios. At the same time, we demonstrate that these auctions remain robust even if the predictions are arbitrarily inaccurate, and maintain reasonable frugality ratios even under adversarially chosen predictions. We finally provide a family of ``error-tolerant'' auctions that maintain improved frugality ratios even if the predictions are only approximately accurate, and we provide upper bounds on their frugality ratio as a function of the prediction error.

Theory · Game Theory

Shiyun Lin, Simon Mauras, Nadav Merlis, Vianney Perchet

We study matching markets with ties, where workers on one side of the market may have tied preferences over jobs, determined by their matching utilities. Unlike classical two-sided markets with strict preferences, no single stable matching exists that is utility-maximizing for all workers. To address this challenge, we introduce the \emph{Optimal Stable Share} (OSS)-ratio, which measures the ratio of a worker's maximum achievable utility in any stable matching to their utility in a given matching. We prove that distributions over only stable matchings can incur linear utility losses, i.e., an $\Omega (N)$ OSS-ratio, where $N$ is the number of workers. To overcome this, we design an algorithm that efficiently computes a distribution over (possibly non-stable) matchings, achieving an asymptotically tight $O (\log N)$ OSS-ratio. When exact utilities are unknown, our second algorithm guarantees workers a logarithmic approximation of their optimal utility under bounded instability. Finally, we extend our offline approximation results to a bandit learning setting where utilities are only observed for matched pairs. In this setting, we consider worker-optimal stable regret, design an adaptive algorithm that smoothly interpolates between markets with strict preferences and those with statistical ties, and establish a lower bound revealing the fundamental trade-off between strict and tied preference regimes.

Theory · Game Theory

Sihan Zeng, Benjamin Patrick Evans, Sujay Bhatt, Leo Ardon, Sumitra Ganesh, Alec Koppel

We study policy optimization in Stackelberg mean field games (MFGs), a hierarchical framework for modeling the strategic interaction between a single leader and an infinitely large population of homogeneous followers. The objective can be formulated as a structured bi-level optimization problem, in which the leader needs to learn a policy maximizing its reward, anticipating the response of the followers. Existing methods for solving these (and related) problems often rely on restrictive independence assumptions between the leader’s and followers’ objectives, use samples inefficiently due to nested-loop algorithm structure, and lack finite-time convergence guarantees. To address these limitations, we propose AC-SMFG, a single-loop actor-critic algorithm that operates on continuously generated Markovian samples. The algorithm alternates between (semi-)gradient updates for the leader, a representative follower, and the mean field, and is simple to implement in practice. We establish the finite-time and finite-sample convergence of the algorithm to a stationary point of the Stackelberg objective. To our knowledge, this is the first Stackelberg MFG algorithm with non-asymptotic convergence guarantees. Our key assumption is a "gradient alignment" condition, which requires that the full policy gradient of the leader can be approximated by a partial component of it, relaxing the existing leader-follower independence assumption. Simulation results in a range of well-established economics environments demonstrate that AC-SMFG outperforms existing multi-agent and MFG learning baselines in policy quality and convergence speed.

Theory · Game Theory

Yichi Zhang, Shengwei Xu, Grant Schoenebeck, David Pennock

Eliciting reliable human feedback is essential for many machine learning tasks, such as learning from noisy labels and aligning AI systems with human preferences. Peer prediction mechanisms incentivize truthful reporting without ground truth verification by scoring agents based on correlations with peers. Traditional mechanisms, which ensure that truth-telling maximizes the \textbf{expected scores} in equilibrium, can elicit honest information while assuming agents' utilities are \textbf{linear functions} of their scores. However, in practice, non-linear payment rules are usually preferred, or agents' utilities are inherently non-linear. We propose \emph{stochastically dominant truthfulness (SD-truthfulness)} as a stronger guarantee: the score distribution of truth-telling stochastically dominates all other strategies, incentivizing truthful reporting for a wide range of monotone utility functions. Our first observation is that no existing peer prediction mechanism naturally satisfies this criterion without strong assumptions. A simple solution - rounding scores into binary lotteries — can enforce SD-truthfulness, but often degrades \emph{sensitivity}, a key property related to fairness and statistical efficiency. We demonstrate how a more careful application of rounding can better preserve sensitivity. Furthermore, we introduce a new enforced agreement (EA) mechanism that is theoretically guaranteed to be SD-truthful in binary-signal settings and, under mild assumptions, empirically achieves the highest sensitivity among all known SD-truthful mechanisms.

Theory · Game Theory

Javier Cembrano, Felix Fischer, Max Klimm

We study the selection of agents based on mutual nominations, a theoretical problem with many applications from committee selection to AI alignment. As agents both select and are selected, they may be incentivized to misrepresent their true opinion about the eligibility of others to influence their own chances of selection. Impartial mechanisms circumvent this issue by guaranteeing that the selection of an agent is independent of the nominations cast by that agent. Previous research has established strong bounds on the performance of impartial mechanisms, measured by their ability to approximate the number of nominations for the most highly nominated agents. We study to what extent the performance of impartial mechanisms can be improved if they are given a prediction of a set of agents receiving a maximum number of nominations. Specifically, we provide bounds on the consistency and robustness of such mechanisms, where consistency measures the performance of the mechanisms when the prediction is correct and robustness its performance when the prediction is incorrect. For the general setting where up to $k$ agents are to be selected and agents nominate any number of other agents, we give a mechanism with consistency $1-O\big(\frac{1}{k}\big)$ and robustness $1-\frac{1}{e}-O\big(\frac{1}{k}\big)$. For the special case of selecting a single agent based on a single nomination per agent, we prove that $1$-consistency can be achieved while guaranteeing $\frac{1}{2}$-robustness. A close comparison with previous results shows that (asymptotically) optimal consistency can be achieved with little to no sacrifice in terms of robustness.

Theory · Game Theory

Baiting Chen, Tong Zhu, Jiale Han, Lexin Li, Gang Li, Xiaowu Dai

Large Language Models (LLMs) have demonstrated strong generative capabilities but remain prone to inconsistencies and hallucinations. We introduce Peer Elicitation Games (PEG), a training-free, game-theoretic framework for aligning LLMs through a peer elicitation mechanism involving a generator and multiple discriminators instantiated from distinct base models. Discriminators interact in a peer evaluation setting, where utilities are computed using a determinant-based mutual information score that provably incentivizes truthful reporting without requiring ground-truth labels. We establish theoretical guarantees showing that each agent, via online learning, achieves sublinear regret in the sense their cumulative performance approaches that of the best fixed truthful strategy in hindsight. Moreover, we prove last-iterate convergence to a truthful Nash equilibrium, ensuring that the actual policies used by agents converge to stable and truthful behavior over time. Empirical evaluations across multiple benchmarks demonstrate significant improvements in factual accuracy. These results position PEG as a practical approach for eliciting truthful behavior from LLMs without supervision or fine-tuning.

Theory · Reinforcement Learning and Planning

Sungee Hong, Jiayi Wang, Zhengling Qi, Raymond K. W. Wong

In reinforcement learning, distributional off-policy evaluation (OPE) focuses on estimating the return distribution of a target policy using offline data collected under a different policy. This work focuses on extending the widely used fitted Q-evaluation---developed for expectation-based reinforcement learning---to the distributional OPE setting. We refer to this extension as fitted distributional evaluation (FDE). While only a few related approaches exist, there remains no unified framework for designing FDE methods. To fill this gap, we present a set of guiding principles for constructing theoretically grounded FDE methods. Building on these principles, we develop several new FDE methods with convergence analysis and provide theoretical justification for existing methods, even in non-tabular environments. Extensive experiments, including simulations on linear quadratic regulators and Atari games, demonstrate the superior performance of the FDE methods.

Theory · Everything Else

Miranda Christ, Daniel Reichman, Jonathan Shafer

We study protocols for verifying approximate optimality of strategies in multi-armed bandits and normal-form games. As the number of actions available to each player is often large, we seek protocols where the number of queries to the utility oracle is sublinear in the number of actions. We prove that such verification is possible for sufficiently smooth strategies that do not put too much probability mass on any specific action and provide protocols for verifying that a smooth policy for a multi-armed bandit is close to optimal. Our verification protocols require provably fewer arm queries than learning. Furthermore, we show how to use cryptographic tools to reduce the communication cost of our protocols. We complement our protocol by proving a nearly tight lower bound on the query complexity of verification in our settings. As an application, we use our bandit verification protocol to build a protocol for verifying approximate optimality of a strong smooth Nash equilibrium, with sublinear query complexity.

Social Aspects · Fairness, Equity, Justice and Safety

Joshua Engels, David Baek, Subhash Kantamneni, Max Tegmark

Scalable oversight, the process by which weaker AI systems supervise stronger ones, has been proposed as a key strategy to control future superintelligent systems. However, it is still unclear how scalable oversight itself scales. To address this gap, we propose a framework that quantifies the probability of successful oversight as a function of the capabilities of the overseer and the system being overseen. Specifically, our framework models oversight as a game between capability-mismatched players; the players have oversight-specific Elo scores that are a piecewise-linear function of their general intelligence, with two plateaus corresponding to task incompetence and task saturation. We validate our framework with a modified version of the game Nim and then apply it to four oversight games: Mafia, Debate, Backdoor Code and Wargames. For each game, we find scaling laws that approximate how domain performance depends on general AI system capability. We then build on our findings in a theoretical study of Nested Scalable Oversight (NSO), a process in which trusted models oversee untrusted stronger models, which then become the trusted models in the next step. We identify conditions under which NSO succeeds and derive numerically (and in some cases analytically) the optimal number of oversight levels to maximize the probability of oversight success. We also apply our theory to our four oversight games, where we find that NSO success rates at a general Elo gap of 400 are 13.5\% for Mafia, 51.7\% for Debate, 10.0\% for Backdoor Code, and 9.4\% for Wargames; these rates decline further when overseeing stronger systems.

General Machine Learning · Representation Learning

Rafael Elberg, Felipe del Río, Mircea Petrache, Denis Parra

Compositionality in knowledge and language—the ability to represent complex concepts as a combination of simpler ones—is a hallmark of human cognition and communication. Despite recent advances, deep neural networks still struggle to acquire this property reliably. Neural models for emergent communication look to endow artificial agents with compositional language by simulating the pressures that form human language. In this work, we introduce CELEBI (Compressive-Expressive Language Emergence through a discrete Bottleneck and Iterated learning), a novel self-supervised framework for inducing compositional representations through a reconstruction-based communication game between a sender and a receiver. Building on theories of language emergence and the iterated learning framework, we integrate three mechanisms that jointly promote compressibility, expressivity, and efficiency in the emergent language. First, Progressive Decoding incentivizes intermediate reasoning by requiring the receiver to produce partial reconstructions after each symbol. Second, Final-State Imitation trains successive generations of agents to imitate reconstructions rather than messages, enforcing a tighter communication bottleneck. Third, Pairwise Distance Maximization regularizes message diversity by encouraging high distances between messages, with formal links to entropy maximization. Our method significantly improves both the efficiency and compositionality of the learned messages on the Shapes3D and MPI3D datasets, surpassing prior discrete communication frameworks in both reconstruction accuracy and topographic similarity. This work provides new theoretical and empirical evidence for the emergence of structured, generalizable communication protocols from simplicity-based inductive biases.