Self-evolution offers a scalable path to stronger reasoning: a pretrained language model improves itself with only minimal external supervision. Yet existing methods either depend on extensively curated or teacher-generated training data, or, when the generator runs unsupervised, reward it by a difficulty heuristic that need not improve the solver. We introduce INFUSER, an iterative co-training framework with two co-evolving roles: a Generator that drafts questions and reference golden answers from a pool of unstructured, automatically collected documents, and a Solver that improves by training on them. The solver is trained with standard correctness rewards against the generator-provided answers, while the generator is rewarded by an optimizer-aware influence score that measures whether each proposed question would actually improve the solver on the target distribution. Because this continuous, noisy influence score is poorly served by standard GRPO, we propose DuGRPO, a dual-normalized variant of GRPO, for generator training. Together, these turn the document pool into an adaptive curriculum that favors questions useful to the current solver, not just hard ones. On Qwen3-8B-Base, INFUSER outperforms strong self-evolution baselines with over 20% relative improvement on Olympiad and SuperGPQA benchmarks, and an 8B INFUSER co-evolving generator outperforms a frozen 32B thinking generator on math and coding. Ablations confirm each design choice is necessary, and two extensions, applying INFUSER to an instruction-finetuned anchor and augmenting it with rule-verifiable RLVR data, further demonstrate the flexibility and generalizability of the framework. Code is available at https://github.com/FFishy-git/INFUSER.

Game Theory: Why did Africa boycott the 1966 World Cup? Game Theory Why did Africa boycott the 1966 World Cup? A record 10 African teams are competing at the 2026 World Cup. But 60 years ago, not one African nation played in the 1966 World Cup. Al Jazeera's Samantha Johnson looks at the 1966 boycott that helped reshape the tournament for generations to come. Why are World Cup tickets so expensive?

Firms' algorithm development practices are often homogeneous. Whether firms train algorithms on similar data or rely on similar pre-trained models, the result is correlated predictions. In the context of personalized pricing, correlated algorithms can be viewed as a means to collude among competing firms, but whether or not this conduct is legal depends on the mechanisms of achieving collusion. We investigate the precise mechanisms through a formal game-theoretic model. Indeed, we find that (1) higher correlation diminishes consumer welfare and (2) as consumers become more price sensitive, firms are increasingly incentivized to compromise on the accuracy of their predictions in exchange for coordination. We demonstrate our theoretical results in a stylized empirical study where two firms compete using personalized pricing algorithms. Our results demonstrate a new mechanism for achieving collusion through correlation, which allows us to analyze its legal implications. Correlation through algorithms is a new frontier of anti-competitive behavior that is largely unconsidered by US antitrust law.

Accurate attribution for multiple platforms is critical for evaluating performancebased 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.

Shapley values have emerged as a critical tool for explaining which features impact the decisions made by machine learning models. However, computing exact Shapley values is difficult, generally requiring an exponential (in the feature dimension) number of model evaluations. To address this, many model-agnostic randomized estimators have been developed, the most influential and widely used being the KernelSHAP method (Lundberg & Lee, 2017). While related estimators such as unbiased KernelSHAP (Covert & Lee, 2021) and LeverageSHAP (Musco & Witter, 2025) are known to satisfy theoretical guarantees, bounds for KernelSHAP have remained elusive. We describe a broad and unified framework that encompasses KernelSHAP and related estimators constructed using both with and without replacement sampling strategies.

We consider the problem of computing stationary points in min-max optimization, with a focus on the special case of Nash equilibria in (two-)team zero-sum games. We first show that computing ϵ-Nash equilibria in 3-player adversarial team games--wherein a team of 2players competes against a single adversary-- is CLS-complete, resolving the complexity of Nash equilibria in such settings. Our proof proceeds by reducing from symmetric ϵ-Nash equilibria in symmetric, identical-payoff, two-player games, by suitably leveraging the adversarial player so as to enforce symmetry--without disturbing the structure of the game. In particular, the class of instances we construct comprises solely polymatrix games, thereby also settling a question left open by Hollender, Maystre, and Nagarajan (2024). Moreover, we establish that computing symmetric (first-order) equilibria in symmetric min-max optimization is PPAD-complete, even for quadratic functions. Building on this reduction, we show that computing symmetric ϵ-Nash equilibria in symmetric, 6-player (3 vs. 3) team zero-sum games is also PPAD-complete, even for ϵ = poly(1/n). As a corollary, this precludes the existence of symmetric dynamics--which includes many of the algorithms considered in the literature-- converging to stationary points. Finally, we prove that computing a non-symmetric poly(1/n)-equilibrium in symmetric min-max optimization is FNP-hard.

Data Shapley is an important tool for data valuation, which quantifies the contribution of individual data points to machine learning models. In practice, group-level data valuation is desirable when data providers contribute data in batch. However, we identify that existing group-level extensions of Data Shapley are vulnerable to shell company attacks, where strategic group splitting can unfairly inflate valuations. We propose Faithful Group Shapley Value (FGSV) that uniquely defends against such attacks. Building on original mathematical insights, we develop a provably fast and accurate approximation algorithm for computing FGSV. Empirical experiments demonstrate that our algorithm significantly outperforms state-of-the-art methods in computational efficiency and approximation accuracy, while ensuring faithful group-level valuation.

This position paper argues for two claims regarding AI testing and evaluation. First, to remain informative about deployment behaviour, evaluations need account for the possibility that AI systems understand their circumstances and reason strategically. Second, game-theoretic analysis can inform evaluation design by formalising and scrutinising the reasoning in evaluation-based safety cases. Drawing on examples from existing AI systems, a review of relevant research, and formal strategic analysis of a stylised evaluation scenario, we present evidence for these claims and motivate several research directions.

We examine the problem of efficiently learning coarse correlated equilibria (CCE) in polyhedral games, that is, normal-form games with an exponentially large number of actions per player and an underlying combinatorial structure--such as the classic Colonel Blotto game or congestion games. Achieving computational efficiency in this setting requires learning algorithms whose regret and per-iteration complexity scale at most polylogarithmically with the size of the players' action sets. This challenge has recently been addressed in the full-information setting, primarily through the use of kernelization; however, in the more realistic partial information setting, the situation is much more challenging, and existing approaches result in suboptimal and impractical runtime complexity to learn CCE. We address this gap via a novel kernelization-based framework for payoff-based learning in polyhedral games, which we then apply to certain key classes of polyhedral games--namely Colonel Blotto, graphic matroid and network congestion games. In so doing, we obtain a range of computationally efficient payoff-based learning algorithms which significantly improve upon prior work in terms of the runtime for learning CCE.

We propose GAM-Agent, a game-theoretic multi-agent framework for enhancing vision-language reasoning. Unlike prior single-agent or monolithic models, GAM-Agent formulates the reasoning process as a non-zero-sum game between base agents--each specializing in visual perception subtasks--and a critical agent that verifies logic consistency and factual correctness. Agents communicate via structured claims, evidence, and uncertainty estimates. The framework introduces an uncertainty-aware controller to dynamically adjust agent collaboration, triggering multi-round debates when disagreement or ambiguity is detected.