When one agent interacts with a multi-agent environment, it is challenging to deal with various opponents unseen before.

Despite the success of generative adversarial networks (GANs) in generating visually appealing images, they are notoriously challenging to train. In order to stabilize the learning dynamics in minimax games, we propose a novel recursive reasoning algorithm: Level $k$ Gradient Play (Lv.$k$

Hierarchical Reasoning Model (HRM) is a novel approach using two small neural networks recursing at different frequencies. This biologically inspired method beats Large Language models (LLMs) on hard puzzle tasks such as Sudoku, Maze, and ARC-AGI while trained with small models (27M parameters) on small data (around 1000 examples). HRM holds great promise for solving hard problems with small networks, but it is not yet well understood and may be suboptimal. We propose Tiny Recursive Model (TRM), a much simpler recursive reasoning approach that achieves significantly higher generalization than HRM, while using a single tiny network with only 2 layers. With only 7M parameters, TRM obtains 45% test-accuracy on ARC-AGI-1 and 8% on ARC-AGI-2, higher than most LLMs (e.g., Deepseek R1, o3-mini, Gemini 2.5 Pro) with less than 0.01% of the parameters.

Theory of Mind (ToM) -- the ability to understand that others can have differing knowledge and goals -- enables agents to reason about others' beliefs while planning their own actions. We present a novel approach to multi-agent cooperation by implementing ToM within active inference. Unlike previous active inference approaches to multi-agent cooperation, our method neither relies on task-specific shared generative models nor requires explicit communication. In our framework, ToM-equipped agents maintain distinct representations of their own and others' beliefs and goals. ToM agents then use an extended and adapted version of the sophisticated inference tree-based planning algorithm to systematically explore joint policy spaces through recursive reasoning. We evaluate our approach through collision avoidance and foraging simulations. Results suggest that ToM agents cooperate better compared to non-ToM counterparts by being able to avoid collisions and reduce redundant efforts. Crucially, ToM agents accomplish this by inferring others' beliefs solely from observable behaviour and considering them when planning their own actions. Our approach shows potential for generalisable and scalable multi-agent systems while providing computational insights into ToM mechanisms.

Theory of Mind (ToM) is a hallmark of human cognition, allowing individuals to reason about others' beliefs and intentions. Engineers behind recent advances in Artificial Intelligence (AI) have claimed to demonstrate comparable capabilities. This paper presents a model that surpasses traditional ToM tests designed for 3-year-old children, providing strong support for the presence of ToM in AI systems.

LLM-driven multi-agent-based simulations have been gaining traction with applications in game-theoretic and social simulations. While most implementations seek to exploit or evaluate LLM-agentic reasoning, they often do so with a weak notion of agency and simplified architectures. We implement a role-based multi-agent strategic interaction framework tailored to sophisticated recursive reasoners, providing the means for systematic in-depth development and evaluation of strategic reasoning. Our game environment is governed by the umpire responsible for facilitating games, from matchmaking through move validation to environment management. Players incorporate state-of-the-art LLMs in their decision mechanism, relying on a formal hypergame-based model of hierarchical beliefs. We use one-shot, 2-player beauty contests to evaluate the recursive reasoning capabilities of the latest LLMs, providing a comparison to an established baseline model from economics and data from human experiments. Furthermore, we introduce the foundations of an alternative semantic measure of reasoning to the k-level theory. Our experiments show that artificial reasoners can outperform the baseline model in terms of both approximating human behaviour and reaching the optimal solution.

Despite the success of generative adversarial networks (GANs) in generating visually appealing images, they are notoriously challenging to train. In order to stabilize the learning dynamics in minimax games, we propose a novel recursive reasoning algorithm: Level k Gradient Play (Lv. Our algorithm does not require sophisticated heuristics or second-order information, as do existing algorithms based on predictive updates. We show that as k increases, Lv. k GP converges asymptotically towards an accurate estimation of players' future strategy.Moreover, we justify that Lv. \infty GP naturally generalizes a line of provably convergent game dynamics which rely on predictive updates. Furthermore, we provide its local convergence property in nonconvex-nonconcave zero-sum games and global convergence in bilinear and quadratic games.

This paper explores the impact of variable pragmatic competence on communicative success through simulating language learning and conversing between speakers and listeners with different levels of reasoning abilities. Through studying this interaction, we hypothesize that matching levels of reasoning between communication partners would create a more beneficial environment for communicative success and language learning. Our research findings indicate that learning from more explicit, literal language is advantageous, irrespective of the learner's level of pragmatic competence. Furthermore, we find that integrating pragmatic reasoning during language learning, not just during evaluation, significantly enhances overall communication performance. This paper provides key insights into the importance of aligning reasoning levels and incorporating pragmatic reasoning in optimizing communicative interactions.

Following the remarkable success of the AlphaGO series, 2019 was a booming year that witnessed significant advances in multi-agent reinforcement learning (MARL) techniques. MARL corresponds to the learning problem in a multi-agent system in which multiple agents learn simultaneously. MARL is an interdisciplinary domain with a long history that includes game theory, machine learning, stochastic control, psychology, and optimisation. Although MARL has achieved considerable empirical success in solving real-world games, there is a lack of a self-contained overview in the literature that elaborates the game theoretical foundations of modern MARL methods and summarises the recent advances. In fact, the majority of existing surveys are outdated and do not fully cover the recent developments since 2010. In this work, we provide a monograph on MARL that covers both the fundamentals and the latest developments in the research frontier. The goal of our monograph is to provide a self-contained assessment of the current state-of-the-art MARL techniques from a game theoretical perspective. We expect this work to serve as a stepping stone for both new researchers who are about to enter this fast-growing domain and existing domain experts who want to obtain a panoramic view and identify new directions based on recent advances.