Related papers: Linearly-Solvable Mean-Field Approximation for Mul…
We develop a game-theoretic framework for predicting and steering the behavior of populations of large language models (LLMs) through Nash equilibrium (NE) analysis. To avoid the intractability of equilibrium computation in open-ended text…
Autonomous racing has gained significant attention as a platform for high-speed decision-making and motion control. While existing methods primarily focus on trajectory planning and overtaking strategies, the role of sportsmanship in…
For prediction of interacting agents' trajectories, we propose an end-to-end trainable architecture that hybridizes neural nets with game-theoretic reasoning, has interpretable intermediate representations, and transfers to downstream…
We propose a tactical homotopy-aware decision-making framework for game-theoretic motion planning in urban environments. We model urban driving as a generalized Nash equilibrium problem and employ a mixed-integer approach to tame the…
This paper studies the limits of empirical means of open-loop Nash equilibria of linear-quadratic stochastic differential games as the number of players goes to infinity, when the corresponding mean field game is of potential type and may…
Robots navigating in crowded areas should negotiate free space with humans rather than fully controlling collision avoidance, as this can lead to freezing behavior. Game theory provides a framework for the robot to reason about potential…
Mean field games (MFG) and mean field control (MFC) problems have been introduced to study large populations of strategic players. They correspond respectively to non-cooperative or cooperative scenarios, where the aim is to find the Nash…
Historically, traffic modelling approaches have taken either a particle-like (microscopic) approach, or a gas-like (meso- or macroscopic) approach. Until recently with the introduction of mean-field games to the controls community, there…
We consider stochastic differential games with $N$ players, linear-Gaussian dynamics in arbitrary state-space dimension, and long-time-average cost with quadratic running cost. Admissible controls are feedbacks for which the system is…
In this paper, we consider the problem of finding a Nash equilibrium in a multi-player game over generally connected networks. This model differs from a conventional setting in that players have partial information on the actions of their…
Mean field game theory studies the behavior of a large number of interacting individuals in a game theoretic setting and has received a lot of attention in the past decade (Lasry and Lions, Japanese journal of mathematics, 2007). In this…
In this paper, the problem of finding a generalized Nash equilibrium (GNE) of a networked game is studied. Players are only able to choose their decisions from a feasible action set. The feasible set is considered to be a private linear…
We study a class of nonzero-sum stochastic differential games between two teams with agents in each team interacting through graphon aggregates. On the one hand, in each large population group, agents act together to optimize a common…
We present a framework for computing approximate mixed-strategy Nash equilibria of continuous-action games. It is a modification of the traditional double oracle algorithm, extended to multiple players and continuous action spaces. Unlike…
We consider a typical problem in Mean Field Games: the congestion case, where in the cost that agents optimize there is a penalization for passing through zones with high density of agents, in a deterministic framework. This equilibrium…
We develop a probabilistic framework to approximate Nash equilibria in symmetric $N$-player games in the large population regime, via the analysis of associated mean field games (MFGs). The approximation is achieved through the analysis of…
In this paper we present a novel generic mapping between Graphical Games and Markov Random Fields so that pure Nash equilibria in the former can be found by statistical inference on the latter. Thus, the problem of deciding whether a…
We introduce a general representation of large-population games in which each player s influence ON the others IS centralized AND limited, but may otherwise be arbitrary.This representation significantly generalizes the class known AS…
We consider a class of mean field games in which the agents interact through both their states and controls, and we focus on situations in which a generic agent tries to adjust her speed (control) to an average speed (the average is made in…
Empirically derived continuum models of collective behavior among large populations of dynamic agents are a subject of intense study in several fields, including biology, engineering and finance. We formulate and study a mean-field game…