Related papers: Approximate Equilibrium Computation for Discrete-T…
In this letter, we study a class of linear-quadratic mean-field-type difference games with coupled affine inequality constraints. We show that the mean-field-type equilibrium can be characterized by the existence of a multiplier process…
There has been significant recent progress in algorithms for approximation of Nash equilibrium in large two-player zero-sum imperfect-information games and exact computation of Nash equilibrium in multiplayer strategic-form games. While…
This paper analyzes a class of infinite-time-horizon stochastic games with singular controls motivated from the partially reversible problem. It provides an explicit solution for the mean-field game (MFG) and presents sensitivity analysis…
In this book, we present a curated collection of existing results on inverse problems for Mean Field Games (MFGs), a cutting-edge and rapidly evolving field of research. Our aim is to provide fresh insights, novel perspectives, and a…
This paper proposes a new mathematical paradigm to analyze discrete-time mean-field games. It is shown that finding Nash equilibrium solutions for a general class of discrete-time mean-field games is equivalent to solving an optimization…
In this paper, linear quadratic mean field games (LQMFGs) under heterogeneous erroneous initial information are investigated, focusing on how to achieve error correction by calculation based on the agents' own actual state and interactions…
This paper is concerned with uniform stabilization and social optimality for general mean field linear quadratic control systems, where subsystems are coupled via individual dynamics and costs, and the state weight is not assumed with the…
This paper presents a general mean-field game (GMFG) framework for simultaneous learning and decision-making in stochastic games with a large population. It first establishes the existence of a unique Nash Equilibrium to this GMFG, and…
This paper investigates an indefinite linear-quadratic partially observed mean-field game with common noise, incorporating both state-average and control-average effects. In our model, each agent's state is observed through both individual…
Convergence of the policy iteration method for discrete and continuous optimal control problems holds under general assumptions. Moreover, in some circumstances, it is also possible to show a quadratic rate of convergence for the algorithm.…
Computing Nash equilibrium policies is a central problem in multi-agent reinforcement learning that has received extensive attention both in theory and in practice. However, provable guarantees have been thus far either limited to fully…
An iterative finite difference scheme for mean field games (MFGs) is proposed. The target MFGs are derived from control problems for multidimensional systems with advection terms. For such MFGs, linearization using the Cole-Hopf…
Many problems in robotics involve multiple decision making agents. To operate efficiently in such settings, a robot must reason about the impact of its decisions on the behavior of other agents. Differential games offer an expressive…
Considering linear-quadratic discrete-time games with unknown input/output/state (i/o/s) dynamics and state, we provide necessary and sufficient conditions for the existence and uniqueness of feedback Nash equilibria (FNE) in the…
Mean field games (MFGs) tractably model behavior in large agent populations. The literature on learning MFG equilibria typically focuses on finding Nash equilibria (NE), which assume perfectly rational agents and are hence implausible in…
Computational equilibrium finding in large zero-sum extensive-form imperfect-information games has led to significant recent AI breakthroughs. The fastest algorithms for the problem are new forms of counterfactual regret minimization [Brown…
The risk-neutral LQR controller is optimal for stochastic linear dynamical systems. However, the classical optimal controller performs inefficiently in the presence of low-probability yet statistically significant (risky) events. The…
This paper investigates the problem of computing the equilibrium of competitive games, which is often modeled as a constrained saddle-point optimization problem with probability simplex constraints. Despite recent efforts in understanding…
This paper explores the use of Maximum Causal Entropy Inverse Reinforcement Learning (IRL) within the context of discrete-time stationary Mean-Field Games (MFGs) characterized by finite state spaces and an infinite-horizon,…
Mean field games formalize dynamic games with a continuum of players and explicit interaction where the players can have heterogeneous states. As they additionally yield approximate equilibria of corresponding $N$-player games, they are of…