Related papers: Linear Programming Fictitious Play algorithm for M…

We study Stackelberg equilibria in finitely repeated games, where the leader commits to a strategy that picks actions in each round and can be adaptive to the history of play (i.e. they commit to an algorithm). In particular, we study…

We investigate reinforcement learning in the setting of Markov decision processes for a large number of exchangeable agents interacting in a mean field manner. Applications include, for example, the control of a large number of robots…

Fictitious Play (FP) is a simple and natural dynamic for repeated play with many applications in game theory and multi-agent reinforcement learning. It was introduced by Brown (1949,1951) and its convergence properties for two-player…

Self-play post-training methods has emerged as an effective approach for finetuning large language models and turn the weak language model into strong language model without preference data. However, the theoretical foundations for…

We tackle the problem of learning equilibria in simulation-based games. In such games, the players' utility functions cannot be described analytically, as they are given through a black-box simulator that can be queried to obtain noisy…

We investigate how well continuous-time fictitious play in two-player games performs in terms of average payoff, particularly compared to Nash equilibrium payoff. We show that in many games, fictitious play outperforms Nash equilibrium on…

This paper investigates a class of multi-player discrete games where each player aims to maximize its own utility function. Each player does not know the other players' action sets, their deployed actions or the structures of its own or the…

Reinforcement learning is a powerful tool to learn the optimal policy of possibly multiple agents by interacting with the environment. As the number of agents grow to be very large, the system can be approximated by a mean-field problem.…

Independent learners are agents that employ single-agent algorithms in multi-agent systems, intentionally ignoring the effect of other strategic agents. This paper studies mean-field games from a decentralized learning perspective, with two…

We propose a numerical method for stationary Mean Field Games defined on a network. In this framework a correct approximation of the transition conditions at the vertices plays a crucial role. We prove existence, uniqueness and convergence…

In adversarial settings, a mobile agent may strategically plan its motion to influence an opponent's inference about its intended goal. We study deceptive path planning in a scenario where a mobile agent aims to reach a privately selected…

We study first order evolutive Mean Field Games whose operators are non-coercive. This situation occurs, for instance, when some directions are `forbidden' to the generic player at some points. Under some regularity assumptions, we…

Mean field approximation is a popular method to study the behaviour of stochastic models composed of a large number of interacting objects. When the objects are asynchronous, the mean field approximation of a population model can be…

This paper considers linear quadratic (LQ) mean field games with a major player and analyzes an asymptotic solvability problem. It starts with a large-scale system of coupled dynamic programming equations and applies a re-scaling technique…

We discuss consistency of Vanishing Smooth Fictitious Play, a strategy in the context of game theory, which can be regarded as a smooth fictitious play procedure, where the smoothing parameter is time-dependent and asymptotically vanishes.…

This paper represents the first attempt to develop a theory for linear-quadratic mean field games in possibly infinite dimensional Hilbert spaces. As a starting point, we study the case, considered in most finite dimensional contributions…

We study the mean field game problem for a nervous system consisting of a large number of neurons with mean-field interaction. In this system, each neuron can modulate its spiking activity by controlling its membrane potential to…

In this paper, we study a class of linear-quadratic (LQ) mean field games of controls with common noises and their corresponding $N$-player games. The theory of mean field game of controls considers a class of mean field games where the…

Recently, the paper [12] introduces a derivative-free consensus-based particle method that finds the Nash equilibrium of non-convex multiplayer games, where it proves the global exponential convergence in the sense of mean-field law. This…

We propose an algorithm to actively estimate the parameters of a linear dynamical system. Given complete control over the system's input, our algorithm adaptively chooses the inputs to accelerate estimation. We show a finite time bound…