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We develop the linear programming approach to mean-field games in a general setting. This relaxed control approach allows to prove existence results under weak assumptions, and lends itself well to numerical implementation. We consider…

Games have long been used as benchmarks and testing environments for research in artificial intelligence. A key step in supporting this research was the development of game description languages: frameworks that compile domain-specific code…

Optimal policies in standard MDPs can be obtained using either value iteration or policy iteration. However, in the case of zero-sum Markov games, there is no efficient policy iteration algorithm; e.g., it has been shown that one has to…

This paper examines the reasoning capabilities of Large Language Models (LLMs) from a novel perspective, focusing on their ability to operate within formally specified, rule-governed environments. We evaluate four LLMs (Gemini 2.5 Pro and…

While discounted payoff games and classic games that reduce to them, like parity and mean-payoff games, are symmetric, their solutions are not. We have taken a fresh view on the constraints that optimal solutions need to satisfy, and…

We investigate the resolution of second-order, potential, and monotone mean field games with the generalized conditional gradient algorithm, an extension of the Frank-Wolfe algorithm. We show that the method is equivalent to the fictitious…

In many games, moves consist of several decisions made by the player. These decisions can be viewed as separate moves, which is already a common practice in multi-action games for efficiency reasons. Such division of a player move into a…

We consider surveillance-evasion differential games, where a pursuer must try to constantly maintain visibility of a moving evader. The pursuer loses as soon as the evader becomes occluded. Optimal controls for game can be formulated as a…

This paper investigates repeated win-lose coordination games (WLC-games). We analyse which protocols are optimal for these games, covering both the worst case and average case scenarios, i,e., optimizing the guaranteed and expected…

With the vast amount of data collected on football and the growth of computing abilities, many games involving decision choices can be optimized. The underlying rule is the maximization of an expected utility of outcomes and the law of…

Games have a long history as benchmarks for progress in artificial intelligence. Approaches using search and learning produced strong performance across many perfect information games, and approaches using game-theoretic reasoning and…

We introduce the notion of universal graphs as a tool for constructing algorithms solving games of infinite duration such as parity games and mean payoff games. In the first part we develop the theory of universal graphs, with two goals:…

In this paper, we propose an explicit, non-strict representation of search trees in constraint-logic object-oriented programming. Our search tree representation includes both the non-deterministic and deterministic behaviour during…

General game playing (GGP) is a framework for evaluating an agent's general intelligence across a wide range of tasks. In the GGP competition, an agent is given the rules of a game (described as a logic program) that it has never seen…

We introduce the study of search games between a mobile Searcher and an immobile Hider in a new setting in which the Searcher has some potentially erroneous information, i.e., a prediction on the Hider's position. The objective is to…

Reasoning is not just about solving problems -- it is also about evaluating which problems are worth solving at all. Evaluations of artificial intelligence (AI) systems primarily focused on problem solving, historically by studying how…

We show that natural classes of regularized learning algorithms with a form of recency bias achieve faster convergence rates to approximate efficiency and to coarse correlated equilibria in multiplayer normal form games. When each player in…

Playing video games requires perception, memory, and planning, exactly the faculties modern large language model (LLM) agents are expected to master. We study the major challenges in using popular video games to evaluate modern LLMs and…

Iterative methods for computing matrix functions have been extensively studied and their convergence speed can be significantly improved with the right tuning of parameters and by mixing different iteration types. Handtuning the design…

Gradient-based methods are often used for policy optimization in deep reinforcement learning, despite being vulnerable to local optima and saddle points. Although gradient-free methods (e.g., genetic algorithms or evolution strategies) help…