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.

Multi-agent Inverse Reinforcement Learning (MAIRL) aims to recover agent reward functions from expert demonstrations. We characterize the feasible reward set in Markov games, identifying all reward functions that rationalize a given equilibrium. However, equilibrium-based observations are often ambiguous: a single Nash equilibrium can correspond to many reward structures, potentially changing the game's nature in multi-agent systems. We address this by introducing entropyregularized Markov games, which yield a unique equilibrium while preserving strategic incentives. For this setting, we provide a sample complexity analysis detailing how errors affect learned policy performance. Our work establishes theoretical foundations and practical insights for MAIRL.

Federated continual learning (FCL) has garnered increasing attention for its ability to support distributed computation in environments with evolving data distributions. However, the emergence of new tasks introduces both temporal and cross-client shifts, making catastrophic forgetting a critical challenge. Most existing works aggregate knowledge from clients into a global model, which may not enhance client performance since irrelevant knowledge could introduce interference, especially in heterogeneous scenarios. Additionally, directly applying decentralized approaches to FCL suffers from ineffective group formation caused by task changes. To address these challenges, we propose a decentralized dynamic cooperation framework for FCL, where clients establish dynamic cooperative learning coalitions to balance the acquisition of new knowledge and the retention of prior learning, thereby obtaining personalized models. To maximize model performance, each client engages in selective cooperation, dynamically allying with others who offer meaningful performance gains.

This paper provides the first expert sample complexity characterization for learning a Nash equilibrium from expert data in Markov Games. We show that a new quantity named the all policy deviation concentrability coefficient is unavoidable in the non-interactive imitation learning setting, and we provide an upper bound for behavioral cloning (BC) featuring such coefficient. BC exhibits substantial regret in games with high concentrability coefficient, leading us to utilize expert queries to develop and introduce two novel solution algorithms: MAIL-BRO and MURMAIL. The former employs a best response oracle and learns an ε-Nash equilibrium with O(ε 4)expert and oracle queries.

We introduce TRiCo, a novel triadic game-theoretic co-training framework that rethinks the structure of semi-supervised learning by incorporating a teacher, two students, and an adversarial generator into a unified training paradigm. Unlike existing co-training or teacher-student approaches, TRiCo formulates SSL as a structured interaction among three roles: (i) two student classifiers trained on frozen, complementary representations, (ii) a meta-learned teacher that adaptively regulates pseudo-label selection and loss balancing via validation-based feedback, and (iii) a non-parametric generator that perturbs embeddings to uncover decision boundary weaknesses. Pseudo-labels are selected based on mutual information rather than confidence, providing a more robust measure of epistemic uncertainty. This triadic interaction is formalized as a Stackelberg game, where the teacher leads strategy optimization and students follow under adversarial perturbations. By addressing key limitations in existing SSL frameworks--such as static view interactions, unreliable pseudo-labels, and lack of hard sample modeling--TRiCo provides a principled and generalizable solution. Extensive experiments on CIFAR10, SVHN, STL-10, and ImageNet demonstrate that TRiCo consistently achieves state-of-the-art performance in low-label regimes, while remaining architectureagnostic and compatible with frozen vision backbones.

On many learning platforms, the optimization criteria guiding model training reflect the priorities of the designer rather than those of the individuals they affect. Consequently, users may act strategically to obtain more favorable outcomes. While past work has studied strategic user behavior on learning platforms, the focus has largely been on individual strategic responses to a deployed model, without considering the behavior of other users. In contrast, look-ahead reasoning takes into account that user actions are coupled, and--at scale--impact future predictions. Within this framework, we first formalize level-k thinking, a concept from behavioral economics, where users aim to outsmart their peers by looking one step ahead. We show that, while convergence to an equilibrium is accelerated, the equilibrium remains the same, providing no benefit of higher-level reasoning for individuals in the long run. Then, we focus on collective reasoning, where users take coordinated actions by optimizing through their joint impact on the model. By contrasting collective with selfish behavior, we characterize the benefits and limits of coordination; a new notion of alignment between the learner's and the users' utilities emerges as a key concept. Look-ahead reasoning can be seen as a generalization of algorithmic collective action; we thus offer the first results characterizing the utility trade-offs of coordination when contesting algorithmic systems.

In this paper, we examine the convergence landscape of multi-agent learning under uncertainty. Specifically, we analyze two stochastic models of regularized learning in continuous games--one in continuous and one in discrete time--with the aim of characterizing the long-run behavior of the induced sequence of play. In stark contrast to deterministic, full-information models of learning (or models with a vanishing learning rate), we show that the resulting dynamics do not converge in general. In lieu of this, we ask instead which actions are played more often in the long run, and by how much. We show that, in strongly monotone games, the dynamics of regularized learning may wander away from equilibrium infinitely often, but they always return to its vicinity in finite time (which we estimate), and their long-run distribution is sharply concentrated around a neighborhood thereof. We quantify the degree of this concentration, and we show that these favorable properties may all break down if the underlying game is not strongly monotone--underscoring in this way the limits of regularized learning in the presence of persistent randomness and uncertainty.

When a prediction algorithm serves a collection of users, disparities in prediction quality are likely to emerge. If users respond to accurate predictions by increasing engagement, inviting friends, or adopting trends, repeated learning creates a feedback loop that shapes both the model and the population of its users. In this work, we introduce evolutionary prediction games, a framework grounded in evolutionary game theory which models such feedback loops as natural-selection processes among groups of users. Our theoretical analysis reveals a gap between idealized and real-world learning settings: In idealized settings with unlimited data and computational power, repeated learning creates competition and promotes competitive exclusion across a broad class of behavioral dynamics. However, under realistic constraints such as finite data, limited compute, or risk of overfitting, we show that stable coexistence and mutualistic symbiosis between groups becomes possible. We analyze these possibilities in terms of their stability and feasibility, present mechanisms that can sustain their existence, and empirically demonstrate our findings.

Many emerging applications--such as adversarial training, AI alignment, and robust optimization--can be framed as zero-sum games between neural nets, with von Neumann-Nash equilibria (NE) capturing the desirable system behavior. While such games often involve non-convex non-concave objectives, empirical evidence shows that simple gradient methods frequently converge, suggesting a hidden geometric structure. In this paper, we provide a theoretical framework that explains this phenomenon through the lens of hidden convexity and overparameterization. We identify sufficient conditions--spanning initialization, training dynamics, and network width--that guarantee global convergence to a NE in a broad class of non-convex min-max games. To our knowledge, this is the first such result for games that involve two-layer neural networks. Technically, our approach is twofold: (a) we derive a novel path-length bound for the alternating gradient descent-ascent scheme in min-max games; and (b) we show that the reduction from a hidden convex-concave geometry to two-sided Polyak-Łojasiewicz (PL) min-max condition hold with high probability under overparameterization, using tools from random matrix theory.

Correlated equilibria--and their generalizations known as Φ-equilibria--are a fundamental object of study in game theory, offering a more tractable alternative to Nash equilibria in multi-player settings. While computational aspects of equilibrium computation are well-understood in some settings, fundamental questions are still open in generalized games, that is, games in which the set of strategies allowed to each player depends on the other players' strategies. These classes of games model fundamental settings in economics, and have been a cornerstone of economics research since the seminal paper of Arrow and Debreu [1954]. Recently, there has been growing interest, both in economics and in computer science, in studying correlated equilibria in generalized games. It is known that finding a social welfare maximizing correlated equilibrium in generalized games is NP-hard. However, the existence of efficient algorithms to find any equilibrium remains an important open question.