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Theory · Game Theory

Abheek Ghosh, Tzeh Yuan Neoh, Nicholas Teh, Giannis Tyrovolas

We study a model of subscription-based platforms where users pay a fixed fee for unlimited access to content, and creators receive a share of the revenue. Existing approaches to detecting fraud predominantly rely on machine learning methods, engaging in an ongoing arms race with bad actors. We explore revenue division mechanisms that inherently disincentivize manipulation. We formalize three types of manipulation-resistance axioms and examine which existing rules satisfy these. We show that a mechanism widely used by streaming platforms, not only fails to prevent fraud, but also makes detecting manipulation computationally intractable. We also introduce a novel rule, ScaledUserProp, that satisfies all three manipulation-resistance axioms. Finally, experiments with both real-world and synthetic streaming data support ScaledUserProp as a fairer alternative compared to existing rules.

Theory · Game Theory

Zichen Wang, Chuanhao Li, Huazheng Wang

We investigate the problem of identifying the optimal scoring rule within the principal-agent framework for online information acquisition problem. We focus on the principal's perspective, seeking to determine the desired scoring rule through interactions with the agent. To address this challenge, we propose two algorithms: OIAFC and OIAFB, tailored for fixed confidence and fixed budget settings, respectively. Our theoretical analysis demonstrates that OIAFC can extract the desired $(\epsilon, \delta)$-scoring rule with a efficient instance-dependent sample complexity or an instance-independent sample complexity. Our analysis also shows that OIAFB matches the instance-independent performance bound of OIAFC, while both algorithms share the same complexity across fixed confidence and fixed budget settings.

Social Aspects · Alignment

Felix Hofstätter, Teun van der Weij, Jayden Teoh, Rada Djoneva, Henning Bartsch, Francis Rhys Ward

Capability evaluations are required to understand and regulate AI systems that maybe deployed or further developed. Therefore, it is important that evaluations providean accurate estimation of an AI system’s capabilities. However, in numerous cases,previously latent capabilities have been elicited from models, sometimes longafter initial release. Accordingly, substantial efforts have been made to developmethods for eliciting latent capabilities from models. In this paper, we evaluate theeffectiveness of capability elicitation techniques by intentionally training modelorganisms – language models with hidden capabilities that are revealed by apassword. We introduce a novel method for training model organisms, basedon circuit-breaking, which is more robust to elicitation techniques than standardpassword-locked models. We focus on elicitation techniques based on promptingand activation steering, and compare these to fine-tuning methods. Promptingtechniques can elicit the actual capability of both password-locked and circuit-broken model organisms in an MCQA setting, while steering fails to do so. Fora code-generation task, only fine-tuning can elicit the hidden capabilities of ournovel model organism. Additionally, our results suggest that combining techniquesimproves elicitation. Still, if possible, fine-tuning should be the method of choiceto improve the trustworthiness of capability evaluations.

Theory · Game Theory

Adrian Müller, Jon Schneider, EFSTRATIOS PANTELEIMON SKOULAKIS, Luca Viano, Volkan Cevher

In this paper, we investigate the existence of online learning algorithms with bandit feedback that simultaneously guarantee $O(1)$ regret compared to a given comparator strategy, and $\tilde{O}(\sqrt{T})$ regret compared to any fixed strategy, where $T$ is the number of rounds. We provide the first affirmative answer to this question whenever the comparator strategy supports every action. In the context of zero-sum games with min-max value zero, both in normal- and extensive form, we show that our results allow us to guarantee to risk at most $O(1)$ loss while being able to gain $\Omega(T)$ from exploitable opponents, thereby combining the benefits of both no-regret algorithms and minimax play.

Theory · Game Theory

Rui Ai, Boxiang Lyu, Zhaoran Wang, Zhuoran Yang, Haifeng Xu

We develop a framework for capturing the instrumentalvalue of data production processes, whichaccounts for two key factors: (a) the context ofthe agent’s decision-making; (b) how much dataor information the buyer already possesses. We"micro-found" our data valuation function by establishingits connection to classic notions of signalsand information design in economics. Wheninstantiated in Bayesian linear regression, ourvalue naturally corresponds to information gain.Applying our proposed data value in Bayesian linearregression for monopoly pricing, we show thatif the seller can fully customize data production,she can extract the first-best revenue (i.e., full surplus)from any population of buyers, i.e., achievingfirst-degree price discrimination. If data canonly be constructed from an existing data pool,this limits the seller’s ability to customize, andachieving first-best revenue becomes generallyimpossible. However, we design a mechanismthat achieves seller revenue at most $\log(\kappa)$ lessthan the first-best, where $\kappa$ is the condition numberassociated with the data matrix. As a corollary,the seller extracts the first-best revenue in themulti-armed bandits special case.

Theory · Game Theory

Yaolong Yu, Fan Yao, Sinno Jialin Pan

We employ a game-theoretic framework to study the impact of a specific strategic behavior among creators---group behavior---on recommendation platforms. In this setting, creators within a group collaborate to maximize their collective utility.We show that group behavior has a limited effect on the game's equilibrium when the group size is small. However, when the group size is large, group behavior can significantly alter content distribution and user welfare.Specifically, in a top-$K$ recommendation system with exposure-based rewards, we demonstrate that user welfare can suffer a significant loss due to group strategies, and user welfare does not necessarily increase with larger values of $K$ or more random matching, contrasting sharply with the individual creator case. Furthermore, we investigate user welfare guarantees through the lens of the Price of Anarchy (PoA). In the general case, we establish a negative result on the bound of PoA with exposure rewards, proving that it can be arbitrarily large. We then investigate a user engagement rewarding mechanism, which mitigates the issues caused by large group behavior, showing that $\text{PoA}\leq K+1$ in the general case and $\text{PoA}\leq 2$ in the binary case. Empirical results from simulations further support the effectiveness of the user engagement rewarding mechanism.

Theory · Game Theory

Quentin Bertrand, Juan Duque, Emilio Calvano, Gauthier Gidel

A growing body of computational studies shows that simple machine learning agents converge to cooperative behaviors in social dilemmas, such as collusive price-setting in oligopoly markets, raising questions about what drives this outcome. In this work, we provide theoretical foundations for this phenomenon in the context of self-play multi-agent Q-learners in the iterated prisoner’s dilemma. We characterize broad conditions under which such agents provably learn the cooperative Pavlov (win-stay, lose-shift) policy rather than the Pareto-dominated “always defect” policy. We validate our theoretical results through additional experiments, demonstrating their robustness across a broader class of deep learning algorithms.

Theory · Game Theory

Jiawei Ge, Yuanhao Wang, Wenzhe Li, Chi Jin

This paper examines multiplayer symmetric constant-sum games with more than two players in a competitive setting, such as Mahjong, Poker, and various board and video games. In contrast to two-player zero-sum games, equilibria in multiplayer games are neither unique nor non-exploitable, failing to provide meaningful guarantees when competing against opponents who play different equilibria or non-equilibrium strategies. This gives rise to a series of long-lasting fundamental questions in multiplayer games regarding suitable objectives, solution concepts, and principled algorithms. This paper takes an initial step towards addressing these challenges by focusing on the natural objective of *equal share*—securing an expected payoff of $C/n$ in an $n$-player symmetric game with a total payoff of $C$. We rigorously identify the theoretical conditions under which achieving an equal share is tractable and design a series of efficient algorithms, inspired by no-regret learning, that *provably* attain approximate equal share across various settings. Furthermore, we provide complementary lower bounds that justify the sharpness of our theoretical results. Our experimental results highlight worst-case scenarios where meta-algorithms from prior state-of-the-art systems for multiplayer games fail to secure an equal share, while our algorithm succeeds, demonstrating the effectiveness of our approach.

Theory · Game Theory

Scott Emmons, Caspar Oesterheld, Vincent Conitzer, Stuart Russell

We study partially observable assistance games (POAGs), a model of the human-AI value alignment problem which allows the human and the AI assistant to have partial observations. Motivated by concerns of AI deception, we study a qualitatively new phenomenon made possible by partial observability: would an AI assistant ever have an incentive to interfere with the human's observations? First, we prove that sometimes an optimal assistant must take observation-interfering _actions_, even when the human is playing optimally, and even when there are otherwise-equivalent actions available that do not interfere with observations. Though this result seems to contradict the classic theorem from single-agent decision making that the value of perfect information is nonnegative, we resolve this seeming contradiction by developing a notion of interference defined on entire _policies_. This can be viewed as an extension of the classic result that the value of perfect information is nonnegative into the cooperative multiagent setting. Second, we prove that if the human is simply making decisions based on their immediate outcomes, the assistant might need to interfere with observations as a way to query the human's preferences. We show that this incentive for interference goes away if the human is playing optimally, or if we introduce a communication channel for the human to communicate their preferences to the assistant. Third, we show that if the human acts according to the Boltzmann model of irrationality, this can create an incentive for the assistant to interfere with observations. Finally, we use an experimental model to analyze tradeoffs faced by the AI assistant in practice when considering whether or not to take observation-interfering actions.

Theory · Game Theory

Yudong Hu, Haoran Li, Congying Han, Tiande Guo, Bonan Li, Mingqiang Li

Solving the Nash equilibrium in normal-form games with large-scale strategy spaces presents significant challenges. Open-ended learning frameworks, such as PSRO and its variants, have emerged as effective solutions. However, these methods often lack an efficient metric for evaluating strategy improvement, which limits their effectiveness in approximating equilibria.In this paper, we introduce a novel evaluative metric called Advantage, which possesses desirable properties inherently connected to the Nash equilibrium, ensuring that each strategy update approaches equilibrium. Building upon this, we propose the Advantage Policy Space Response Oracle (A-PSRO), an innovative unified open-ended learning framework applicable to both zero-sum and general-sum games. A-PSRO leverages the Advantage as a refined evaluation metric, leading to a consistent learning objective for agents in normal-form games. Experiments showcase that A-PSRO significantly reduces exploitability in zero-sum games and improves rewards in general-sum games, outperforming existing algorithms and validating its practical effectiveness.

Theory · Game Theory

Ermis Soumalias, Jakob Heiss, Jakob Weissteiner, Sven Seuken

We study the design of *iterative combinatorial auctions (ICAs)*.The main challenge in this domain is that the bundle space grows exponentially in the number of items. To address this, recent work has proposed machine learning (ML)-based preference elicitation algorithms that aim to elicit only the most critical information from bidders to maximize efficiency.However, while the SOTA ML-based algorithms elicit bidders' preferences via *value queries*, ICAs that are used in practice elicit information via *demand queries*. In this paper, we introduce a novel ML algorithm that provably makes use of the full information from both value and demand queries, and we show via experiments that combining both query types results in significantly better learning performance in practice. Building on these insights, we present MLHCA, a new ML-powered auction that uses value and demand queries. MLHCA significantly outperforms the previous SOTA, reducing efficiency loss by up to a factor 10, with up to 58% fewer queries. Thus, MLHCA achieves large efficiency improvements while also reducing bidders' cognitive load, establishing a new benchmark for both practicability and efficiency. Our code is available at https://github.com/marketdesignresearch/MLHCA.

Theory · Game Theory

Jeremy McMahan

We extend anytime constraints to the Markov game setting and the corresponding solution concept of anytime-constrained equilibrium (ACE). Then, we present a comprehensive theory of anytime-constrained equilibria that includes (1) a computational characterization of feasible policies, (2) a fixed-parameter tractable algorithm for computing ACE, and (3) a polynomial-time algorithm for approximately computing ACE. Since computing a feasible policy is NP-hard even for two-player zero-sum games, our approximation guarantees are the best possible so long as $P \neq NP$. We also develop the first theory of efficient computation for action-constrained Markov games, which may be of independent interest.

Theory · Game Theory

Renzhe Xu, Kang Wang, Bo Li

Data heterogeneity across multiple sources is common in real-world machine learning (ML) settings. Although many methods focus on enabling a single model to handle diverse data, real-world markets often comprise multiple competing ML providers. In this paper, we propose a game-theoretic framework—the Heterogeneous Data Game—to analyze how such providers compete across heterogeneous data sources. We investigate the resulting pure Nash equilibria (PNE), showing that they can be non-existent, homogeneous (all providers converge on the same model), or heterogeneous (providers specialize in distinct data sources). Our analysis spans monopolistic, duopolistic, and more general markets, illustrating how factors such as the ``temperature'' of data-source choice models and the dominance of certain data sources shape equilibrium outcomes. We offer theoretical insights into both homogeneous and heterogeneous PNEs, guiding regulatory policies and practical strategies for competitive ML marketplaces.

Theory · Game Theory

Vikram Kher, Manolis Zampetakis

When can the distributional assumptions of theorems and learning algorithms be trusted? Inspired by this question, Rubinfeld and Vasilyan (2023) initiated the study of testable learning. In this schema, we always learn one of the following two things: either we have achieved the desired accuracy regardless of whether the distributional assumptions are satisfied, or the input distribution does not satisfy the original distributional assumptions. Motivated by the challenge of relying on strong distributional assumptions in many theorems in mechanism design, we develop a testable learning framework for mechanism design. Traditional models in mechanism design assume that value distributions satisfy some notion of regularity. Unfortunately, testing regularity is not possible in the original testable learning framework as we show. To bypass this impossibility, we propose a regularized version of the testable learning framework. Under this framework, we always learn one of the following two things: either we achieve high revenue compared to the best possible revenue of any regular distribution close to the input distribution, or the input distribution does not satisfy regularity. We then use this framework to provide: 1) a tester-learner pair for revenue optimal mechanisms, 2) a tester for whether the fundamental Bulow-Klemperer Theorem (Bulow and Klemperer 1996) is applicable to a given dataset, and 3) a tester to confirm the existence of an anonymous reserve price that results in the anonymous price auction securing a constant fraction of the optimal revenue.

Theory · Game Theory

Niclas Boehmer, Sara Fish, Ariel Procaccia

A key task in certain democratic processes is to produce a concise slate of statements that proportionally represents the full spectrum of user opinions. This task is similar to committee elections, but unlike traditional settings, the candidate set comprises all possible statements of varying lengths, and so it can only be accessed through specific queries. Combining social choice and large language models, prior work has approached this challenge through a framework of generative social choice. We extend the framework in two fundamental ways, providing theoretical guarantees even in the face of approximately optimal queries and a budget limit on the overall length of the slate. Using GPT-4o to implement queries, we showcase our approach on datasets related to city improvement measures and drug reviews, demonstrating its effectiveness in generating representative slates from unstructured user opinions.

Theory · Game Theory

Fivos Kalogiannis, Emmanouil-Vasileios Vlatakis-Gkaragkounis, Ian Gemp, Georgios Piliouras

We contribute the first provable guarantees of global convergence to Nash equilibria (NE) in two-player zero-sum convex Markov games (cMGs) by using independent policy gradient methods. Convex Markov games, recently defined by Gemp et al.(2024), extend Markov decision processes to multi-agent settings with preferences that are convex over occupancy measures, offering a broad framework for modeling generic strategic interactions. However, even the fundamental min-max case of cMGs presents significant challenges, including inherent nonconvexity, the absence of Bellman consistency, and the complexity of the infinite horizon.Our results follow a two-step approach. First, leveraging properties of hidden-convex–hidden-concave functions, we show that a simple nonconvex regularization transforms the min-max optimization problem into a nonconvex–proximal Polyak-Łojasiewicz (NC-pPL) objective. Crucially, this regularization can stabilize the iterates of independent policy gradient methods and ultimately lead them to converge to equilibria. Second, building on this reduction, we address the general constrained min-max problems under NC-pPL and two-sided pPL conditions, providing the first global convergence guarantees for stochastic nested and alternating gradient descent-ascent methods, which we believe may be of independent interest.

Theory · Game Theory

Alex Clinton, Yiding Chen, Jerry Zhu, Kirthevasan Kandasamy

We study a collaborative learning problem where $m$ agents aim to estimate a vector $\mu =(\mu_1,\ldots,\mu_d)\in \mathbb{R}^d$ by sampling from associated univariate normal distributions $(\mathcal{N}(\mu_k, \sigma^2))\_{k\in[d]}$. Agent $i$ incurs a cost $c_{i,k}$ to sample from $\mathcal{N}(\mu_k, \sigma^2)$. Instead of working independently, agents can exchange data, collecting cheaper samples and sharing them in return for costly data, thereby reducing both costs and estimation error. We design a mechanism to facilitate such collaboration, while addressing two key challenges: ensuring *individually rational (IR) and fair outcomes* so all agents benefit, and *preventing strategic behavior* (e.g. non-collection, data fabrication) to avoid socially undesirable outcomes.We design a mechanism and an associated Nash equilibrium (NE) which minimizes the social penalty-sum of agents' estimation errors and collection costs-while being IR for all agents. We achieve a $\mathcal{O}(\sqrt{m})$-approximation to the minimum social penalty in the worst case and an $\mathcal{O}(1)$-approximation under favorable conditions. Additionally, we establish three hardness results: no nontrivial mechanism guarantees *(i)* a dominant strategy equilibrium where agents report truthfully, *(ii)* is IR for every strategy profile of other agents, *(iii)* or avoids a worst-case $\Omega(\sqrt{m})$ price of stability in any NE. Finally, by integrating concepts from axiomatic bargaining, we demonstrate that our mechanism supports fairer outcomes than one which minimizes social penalty.

Theory · Game Theory

Evi Micha, Vasilis Varsamis

Aggregating preferences under incomplete or constrained feedback is a fundamental problem in social choice and related domains. While prior work has established strong impossibility results for pairwise comparisons, this paper extends the inquiry to improvement feedback, where voters express incremental adjustments rather than complete preferences. We provide a complete characterization of the positional scoring rules that can be computed given improvement feedback. Interestingly, while plurality is learnable under improvement feedback—unlike with pairwise feedback—strong impossibility results persist for many other positional scoring rules. Furthermore, we show that improvement feedback, unlike pairwise feedback, does not suffice for the computation of any Condorcet-consistent rule. We complement our theoretical findings with experimental results, providing further insights into the practical implications of improvement feedback for preference aggregation.

Chanwoo Park, Xiangyu Liu, Asuman Ozdaglar, Kaiqing Zhang

Large language models (LLMs) have been increasingly employed for (interactive) decision-making, via the development of LLM-based autonomous agents. Despite their emerging successes, the performance of LLM agents in decision-making has not been fully investigated through quantitative metrics, especially in the multi-agent setting when they interact with each other, a typical scenario in real-world LLM-agent applications. To better understand the limits of LLM agents in these interactive environments, we propose to study their interactions in benchmark decision-making settings in online learning and game theory, through the performance metric of regret. We first empirically study the no-regret behaviors of LLMs in canonical non-stochastic online learning problems, as well as the emergence of equilibria when LLM agents interact through playing repeated games. We then provide some theoretical insights into the no-regret behaviors of LLM agents, under certain assumptions on the supervised pre-training and the rationality model of human decision-makers who generate the data. Notably, we also identify (simple) cases where advanced LLMs such as GPT-4 fail to be no-regret. To further promote the no-regret behaviors, we propose a novel unsupervised training loss of regret-loss, which, in contrast to the supervised pre-training loss, does not require the labels of (optimal) actions. Finally, we establish the statistical guarantee of generalization bound for regret-loss minimization, and more importantly, the optimization guarantee that minimizing such a loss may automatically lead to known no-regret learning algorithms, when single-layer self-attention models are used. Our further experiments demonstrate the effectiveness of our regret-loss, especially in addressing the above “regrettable” cases.

Theory · Game Theory

Safwan Hossain, Evi Micha, Yiling Chen, Ariel Procaccia

We propose a new variant of the strategic classification problem: a principal reveals a classifier, and $n$ agents report their (possibly manipulated) features to be classified. Motivated by real-world applications, our model crucially allows the manipulation of one agent to affect another; that is, it explicitly captures inter-agent externalities. The principal-agent interactions are formally modeled as a Stackelberg game, with the resulting agent manipulation dynamics captured as a simultaneous game. We show that under certain assumptions, the pure Nash Equilibrium of this agent manipulation game is unique and can be efficiently computed. Leveraging this result, PAC learning guarantees are established for the learner: informally, we show that it is possible to learn classifiers that minimize loss on the distribution, even when a random number of agents are manipulating their way to a pure Nash Equilibrium. We also comment on the optimization of such classifiers through gradient-based approaches. This work sets the theoretical foundations for a more realistic analysis of classifiers that are robust against multiple strategic actors interacting in a common environment.