arXiv subjects

Marc Lanctot

Publications and source records attributed to Marc Lanctot.

At least 19 recordsLinked to original sources

arXiv2026

Nash without Numbers: A Social Choice Approach to Mixed Equilibria in Context-Ordinal Games

Nash equilibrium serves as a fundamental mathematical tool in economics and game theory. However, it classically assumes knowledge of player utilities, whereas economics generally regards preferences as more fundamental. To leverage equilibrium analysis in strategic scenarios, one must first elicit numerical utilities consistent with player preferences, a delicate and time-consuming process. In this work, we forgo precise utilities and generalize the Nash equilibrium to a setting where we only assume a player is capable of providing an ordinal ranking of their actions within the context of other players' joint actions. The key technical challenge is to rethink the definition of a best-response. While the classical definition identifies actions maximizing expected payoff, we naturally look towards social choice theory for how to aggregate preferences to identify the most preferred actions. We define this generalized notion of a context-ordinal Nash equilibrium, establish its existence under mild conditions on aggregation methods, introduce notions of regularization, approximation, and regret, explore complexity for simple settings, and develop learning rules for computing such equilibria. In doing so, we provide a generalization of Nash equilibrium and demonstrate its direct applicability to elicited preferences in human experiments.

cs.GT↗

arXiv2026

Discovering Multiagent Learning Algorithms with Large Language Models

Much of the advancement in Multi-Agent Reinforcement Learning (MARL) for imperfect-information games has historically depended on the manual, iterative refinement of algorithmic baselines. Recently, evolutionary coding agents powered by Large Language Models (LLMs) have emerged as powerful tools to automate this discovery process. In this work, we deploy one of such agentic frameworks, AlphaEvolve, to navigate the design spaces of two distinct game-theoretic paradigms: counterfactual regret minimization (CFR) and policy-space response oracles (PSRO). This automated search yielded two algorithms: Volatility-Adaptive Discounted (VAD-) CFR and Smoothed Hybrid Optimistic Regret (SHOR-) PSRO, which are consistently competitive with state-of-the-art human-designed baselines across an 18-game evaluation suite spanning Poker, Goofspiel, Liar's Dice, Blotto, and Battleship variants. However, because the LLM optimizes for fitness on a specific training set, it often constructs highly synergistic, complex mechanisms tailored to those environments. Through systematic ablation studies, we demonstrate that while these mechanisms are tightly coupled, the true driver of generalization lies in a minimal algorithmic core. By distilling the LLM's discoveries down to their most fundamental principles, we produce two minimal solvers: Warm-started Optimistic Predictive (WOP-)CFR and Projection Matching (PM-)PSRO. These distilled versions achieve superior performance on generalization with greatly reduced structural complexity, providing a clear methodology for using LLMs in algorithmic discovery.

cs.GT↗

arXiv2026

Combining Tree-Search, Generative Models, and Nash Bargaining Concepts in Game-Theoretic Reinforcement Learning

Opponent modeling methods typically involve two crucial steps: building a belief distribution over opponents' strategies, and exploiting this opponent model by playing a best response. However, existing approaches typically require domain-specific heurstics to come up with such a model, and algorithms for approximating best responses are hard to scale in large, imperfect information domains. In this work, we introduce a scalable and generic multiagent training regime for opponent modeling using deep game-theoretic reinforcement learning. We first propose Generative Best Respoonse (GenBR), a best response algorithm based on Monte-Carlo Tree Search (MCTS) with a learned deep generative model that samples world states during planning. This new method scales to large imperfect information domains and can be plug and play in a variety of multiagent algorithms. We use this new method under the framework of Policy Space Response Oracles (PSRO), to automate the generation of an \emph{offline opponent model} via iterative game-theoretic reasoning and population-based training. We propose using solution concepts based on bargaining theory to build up an opponent mixture, which we find identifying profiles that are near the Pareto frontier. Then GenBR keeps updating an \emph{online opponent model} and reacts against it during gameplay. We conduct behavioral studies where human participants negotiate with our agents in Deal-or-No-Deal, a class of bilateral bargaining games. Search with generative modeling finds stronger policies during both training time and test time, enables online Bayesian co-player prediction, and can produce agents that achieve comparable social welfare and Nash bargaining score negotiating with humans as humans trading among themselves.

cs.AI↗

arXiv2026

Code-Space Response Oracles: Generating Interpretable Multi-Agent Policies with Large Language Models

Recent advances in multi-agent reinforcement learning, particularly Policy-Space Response Oracles (PSRO), have enabled the computation of approximate game-theoretic equilibria in increasingly complex domains. However, these methods rely on deep reinforcement learning oracles that produce `black-box' neural network policies, making them difficult to interpret, trust or debug. We introduce Code-Space Response Oracles (CSRO), a novel framework that addresses this challenge by replacing RL oracles with Large Language Models (LLMs). CSRO reframes the best response computation as a code generation task, prompting an LLM to generate policies directly as human-readable code. This approach not only yields inherently interpretable policies but also leverages the LLM's pretrained knowledge to discover complex, human-like strategies. We explore multiple ways to construct and enhance an LLM-based oracle: zero-shot prompting, iterative refinement and \emph{AlphaEvolve}, a distributed LLM-based evolutionary system. We demonstrate that CSRO achieves performance competitive with baselines while producing a diverse set of explainable policies. Our work presents a new perspective on multi-agent learning, shifting the focus from optimizing opaque policy parameters to synthesizing interpretable algorithmic behavior.

cs.GT↗

arXiv2026

Active Evaluation of General Agents: Problem Definition and Comparison of Baseline Algorithms

As intelligent agents become more generally-capable, i.e. able to master a wide variety of tasks, the complexity and cost of properly evaluating them rises significantly. Tasks that assess specific capabilities of the agents can be correlated and stochastic, requiring many samples for accurate comparisons, leading to added costs. In this paper, we propose a formal definition and a conceptual framework for active evaluation of agents across multiple tasks, which assesses the performance of ranking algorithms as a function of number of evaluation data samples. Rather than curating, filtering, or compressing existing data sets as a preprocessing step, we propose an online framing: on every iteration, the ranking algorithm chooses the task and agents to sample scores from. Then, evaluation algorithms report a ranking of agents on each iteration and their performance is assessed with respect to the ground truth ranking over time. Several baselines are compared under different experimental contexts, with synthetic generated data and simulated online access to real evaluation data from Atari game-playing agents. We find that the classical Elo rating system -- while it suffers from well-known failure modes, in theory -- is a consistently reliable choice for efficient reduction of ranking error in practice. A recently-proposed method, Soft Condorcet Optimization, shows comparable performance to Elo on synthetic data and significantly outperforms Elo on real Atari agent evaluation. When task variation from the ground truth is high, selecting tasks based on proportional representation leads to higher rate of ranking error reduction.

cs.AI↗

arXiv2025

Code World Models for General Game Playing

Large Language Models (LLMs) reasoning abilities are increasingly being applied to classical board and card games, but the dominant approach -- involving prompting for direct move generation -- has significant drawbacks. It relies on the model's implicit fragile pattern-matching capabilities, leading to frequent illegal moves and strategically shallow play. Here we introduce an alternative approach: We use the LLM to translate natural language rules and game trajectories into a formal, executable world model represented as Python code. This generated model -- comprising functions for state transition, legal move enumeration, and termination checks -- serves as a verifiable simulation engine for high-performance planning algorithms like Monte Carlo tree search (MCTS). In addition, we prompt the LLM to generate heuristic value functions (to make MCTS more efficient), and inference functions (to estimate hidden states in imperfect information games). Our method offers three distinct advantages compared to directly using the LLM as a policy: (1) Verifiability: The generated CWM serves as a formal specification of the game's rules, allowing planners to algorithmically enumerate valid actions and avoid illegal moves, contingent on the correctness of the synthesized model; (2) Strategic Depth: We combine LLM semantic understanding with the deep search power of classical planners; and (3) Generalization: We direct the LLM to focus on the meta-task of data-to-code translation, enabling it to adapt to new games more easily. We evaluate our agent on 10 different games, of which 4 are novel and created for this paper. 5 of the games are fully observed (perfect information), and 5 are partially observed (imperfect information). We find that our method outperforms or matches Gemini 2.5 Pro in 9 out of the 10 considered games.

cs.AI↗

arXiv2025

Evaluating Agents using Social Choice Theory

We argue that many general evaluation problems can be viewed through the lens of voting theory. Each task is interpreted as a separate voter, which requires only ordinal rankings or pairwise comparisons of agents to produce an overall evaluation. By viewing the aggregator as a social welfare function, we are able to leverage centuries of research in social choice theory to derive principled evaluation frameworks with axiomatic foundations. These evaluations are interpretable and flexible, while avoiding many of the problems currently facing cross-task evaluation. We apply this Voting-as-Evaluation (VasE) framework across multiple settings, including reinforcement learning, large language models, and humans. In practice, we observe that VasE can be more robust than popular evaluation frameworks (Elo and Nash averaging), discovers properties in the evaluation data not evident from scores alone, and can predict outcomes better than Elo in a complex seven-player game. We identify one particular approach, maximal lotteries, that satisfies important consistency properties relevant to evaluation, is computationally efficient (polynomial in the size of the evaluation data), and identifies game-theoretic cycles.

cs.AI↗

arXiv2025

Soft Condorcet Optimization for Ranking of General Agents

Driving progress of AI models and agents requires comparing their performance on standardized benchmarks; for general agents, individual performances must be aggregated across a potentially wide variety of different tasks. In this paper, we describe a novel ranking scheme inspired by social choice frameworks, called Soft Condorcet Optimization (SCO), to compute the optimal ranking of agents: the one that makes the fewest mistakes in predicting the agent comparisons in the evaluation data. This optimal ranking is the maximum likelihood estimate when evaluation data (which we view as votes) are interpreted as noisy samples from a ground truth ranking, a solution to Condorcet's original voting system criteria. SCO ratings are maximal for Condorcet winners when they exist, which we show is not necessarily true for the classical rating system Elo. We propose three optimization algorithms to compute SCO ratings and evaluate their empirical performance. When serving as an approximation to the Kemeny-Young voting method, SCO rankings are on average 0 to 0.043 away from the optimal ranking in normalized Kendall-tau distance across 865 preference profiles from the PrefLib open ranking archive. In a simulated noisy tournament setting, SCO achieves accurate approximations to the ground truth ranking and the best among several baselines when 59\% or more of the preference data is missing. Finally, SCO ranking provides the best approximation to the optimal ranking, measured on held-out test sets, in a problem containing 52,958 human players across 31,049 games of the classic seven-player game of Diplomacy.

cs.MA↗

arXiv2025

Learning in Games with Progressive Hiding

When learning to play an imperfect information game, it is often easier to first start with the basic mechanics of the game rules. For example, one can play several example rounds with private cards revealed to all players to better understand the basic actions and their effects. Building on this intuition, this paper introduces {\it progressive hiding}, an algorithm that balances learning the basic mechanics of an imperfect information game and satisfying the information constraints. Progressive hiding is inspired by methods from stochastic multistage optimization, such as scenario decomposition and progressive hedging. We prove that it enables the adaptation of counterfactual regret minimization to games where perfect recall is not satisfied. Numerical experiments illustrate that progressive hiding produces notable improvements in several settings.

cs.GT↗

arXiv2025

Mastering Board Games by External and Internal Planning with Language Models

Advancing planning and reasoning capabilities of Large Language Models (LLMs) is one of the key prerequisites towards unlocking their potential for performing reliably in complex and impactful domains. In this paper, we aim to demonstrate this across board games (Chess, Fischer Random / Chess960, Connect Four, and Hex), and we show that search-based planning can yield significant improvements in LLM game-playing strength. We introduce, compare and contrast two major approaches: In external search, the model guides Monte Carlo Tree Search (MCTS) rollouts and evaluations without calls to an external game engine, and in internal search, the model is trained to generate in-context a linearized tree of search and a resulting final choice. Both build on a language model pre-trained on relevant domain knowledge, reliably capturing the transition and value functions in the respective environments, with minimal hallucinations. We evaluate our LLM search implementations against game-specific state-of-the-art engines, showcasing substantial improvements in strength over the base model, and reaching Grandmaster-level performance in chess while operating closer to the human search budget. Our proposed approach, combining search with domain knowledge, is not specific to board games, hinting at more general future applications.

cs.AI↗

arXiv2025

Re-evaluating Open-ended Evaluation of Large Language Models

Evaluation has traditionally focused on ranking candidates for a specific skill. Modern generalist models, such as Large Language Models (LLMs), decidedly outpace this paradigm. Open-ended evaluation systems, where candidate models are compared on user-submitted prompts, have emerged as a popular solution. Despite their many advantages, we show that the current Elo-based rating systems can be susceptible to and even reinforce biases in data, intentional or accidental, due to their sensitivity to redundancies. To address this issue, we propose evaluation as a 3-player game, and introduce novel game-theoretic solution concepts to ensure robustness to redundancy. We show that our method leads to intuitive ratings and provide insights into the competitive landscape of LLM development.

cs.GT↗

arXiv2025

Deviation Ratings: A General, Clone-Invariant Rating Method

Many real-world multi-agent or multi-task evaluation scenarios can be naturally modelled as normal-form games due to inherent strategic (adversarial, cooperative, and mixed motive) interactions. These strategic interactions may be agentic (e.g. players trying to win), fundamental (e.g. cost vs quality), or complementary (e.g. niche finding and specialization). In such a formulation, it is the strategies (actions, policies, agents, models, tasks, prompts, etc.) that are rated. However, the rating problem is complicated by redundancy and complexity of N-player strategic interactions. Repeated or similar strategies can distort ratings for those that counter or complement them. Previous work proposed ``clone invariant'' ratings to handle such redundancies, but this was limited to two-player zero-sum (i.e. strictly competitive) interactions. This work introduces the first N-player general-sum clone invariant rating, called deviation ratings, based on coarse correlated equilibria. The rating is explored on several domains including LLMs evaluation.

cs.GT↗

arXiv2025

Jackpot! Alignment as a Maximal Lottery

Reinforcement Learning from Human Feedback (RLHF), the standard for aligning Large Language Models (LLMs) with human values, is known to fail to satisfy properties that are intuitively desirable, such as respecting the preferences of the majority \cite{ge2024axioms}. To overcome these issues, we propose the use of a probabilistic Social Choice rule called \emph{maximal lotteries} as a replacement for RLHF. We show that a family of alignment techniques, namely Nash Learning from Human Feedback (NLHF) \cite{munos2023nash} and variants, approximate maximal lottery outcomes and thus inherit its beneficial properties. We confirm experimentally that our proposed methodology handles situations that arise when working with preferences more robustly than standard RLHF, including supporting the preferences of the majority, providing principled ways of handling non-transitivities in the preference data, and robustness to irrelevant alternatives. This results in systems that better incorporate human values and respect human intentions.

cs.AI↗

arXiv2024

Steering Language Models with Game-Theoretic Solvers

Mathematical models of interactions among rational agents have long been studied in game theory. However these interactions are often over a small set of discrete game actions which is very different from how humans communicate in natural language. To bridge this gap, we introduce a framework that allows equilibrium solvers to work over the space of natural language dialogue generated by large language models (LLMs). Specifically, by modelling the players, strategies and payoffs in a "game" of dialogue, we create a binding from natural language interactions to the conventional symbolic logic of game theory. Given this binding, we can ask existing game-theoretic algorithms to provide us with strategic solutions (e.g., what string an LLM should generate to maximize payoff in the face of strategic partners or opponents), giving us predictors of stable, rational conversational strategies. We focus on three domains that require different negotiation strategies: scheduling meetings, trading fruit and debate, and evaluate an LLM's generated language when guided by solvers. We see that LLMs that follow game-theory solvers result in dialogue generations that are less exploitable than the control (no guidance from solvers), and the language generated results in higher rewards, in all negotiation domains. We discuss future implications of this work, and how game-theoretic solvers that can leverage the expressivity of natural language can open up a new avenue of guiding language research.

cs.CL↗

arXiv2024

Multi-Agent Training beyond Zero-Sum with Correlated Equilibrium Meta-Solvers

Two-player, constant-sum games are well studied in the literature, but there has been limited progress outside of this setting. We propose Joint Policy-Space Response Oracles (JPSRO), an algorithm for training agents in n-player, general-sum extensive form games, which provably converges to an equilibrium. We further suggest correlated equilibria (CE) as promising meta-solvers, and propose a novel solution concept Maximum Gini Correlated Equilibrium (MGCE), a principled and computationally efficient family of solutions for solving the correlated equilibrium selection problem. We conduct several experiments using CE meta-solvers for JPSRO and demonstrate convergence on n-player, general-sum games.

cs.MA↗

arXiv2024

Learning not to Regret

The literature on game-theoretic equilibrium finding predominantly focuses on single games or their repeated play. Nevertheless, numerous real-world scenarios feature playing a game sampled from a distribution of similar, but not identical games, such as playing poker with different public cards or trading correlated assets on the stock market. As these similar games feature similar equilibra, we investigate a way to accelerate equilibrium finding on such a distribution. We present a novel "learning not to regret" framework, enabling us to meta-learn a regret minimizer tailored to a specific distribution. Our key contribution, Neural Predictive Regret Matching, is uniquely meta-learned to converge rapidly for the chosen distribution of games, while having regret minimization guarantees on any game. We validated our algorithms' faster convergence on a distribution of river poker games. Our experiments show that the meta-learned algorithms outpace their non-meta-learned counterparts, achieving more than tenfold improvements.

cs.GT↗

arXiv2024

Easy as ABCs: Unifying Boltzmann Q-Learning and Counterfactual Regret Minimization

We propose ABCs (Adaptive Branching through Child stationarity), a best-of-both-worlds algorithm combining Boltzmann Q-learning (BQL), a classic reinforcement learning algorithm for single-agent domains, and counterfactual regret minimization (CFR), a central algorithm for learning in multi-agent domains. ABCs adaptively chooses what fraction of the environment to explore each iteration by measuring the stationarity of the environment's reward and transition dynamics. In Markov decision processes, ABCs converges to the optimal policy with at most an O(A) factor slowdown compared to BQL, where A is the number of actions in the environment. In two-player zero-sum games, ABCs is guaranteed to converge to a Nash equilibrium (assuming access to a perfect oracle for detecting stationarity), while BQL has no such guarantees. Empirically, ABCs demonstrates strong performance when benchmarked across environments drawn from the OpenSpiel game library and OpenAI Gym and exceeds all prior methods in environments which are neither fully stationary nor fully nonstationary.

cs.LG↗

arXiv2024

Approximating the Core via Iterative Coalition Sampling

The core is a central solution concept in cooperative game theory, defined as the set of feasible allocations or payments such that no subset of agents has incentive to break away and form their own subgroup or coalition. However, it has long been known that the core (and approximations, such as the least-core) are hard to compute. This limits our ability to analyze cooperative games in general, and to fully embrace cooperative game theory contributions in domains such as explainable AI (XAI), where the core can complement the Shapley values to identify influential features or instances supporting predictions by black-box models. We propose novel iterative algorithms for computing variants of the core, which avoid the computational bottleneck of many other approaches; namely solving large linear programs. As such, they scale better to very large problems as we demonstrate across different classes of cooperative games, including weighted voting games, induced subgraph games, and marginal contribution networks. We also explore our algorithms in the context of XAI, providing further evidence of the power of the core for such applications.

cs.GT↗