相关论文: Value Iteration Algorithm for Mean-field Games

We study auction-theoretic scheduling in cellular networks using the idea of mean field equilibrium (MFE). Here, agents model their opponents through a distribution over their action spaces and play the best response. The system is at an…

We consider a mean field game describing the limit of a stochastic differential game of $N$-players whose state dynamics are subject to idiosyncratic and common noise and that can be absorbed when they hit a prescribed region of the state…

We extend the classic regret minimization framework for approximating equilibria in normal-form games by greedily weighing iterates based on regrets observed at runtime. Theoretically, our method retains all previous convergence rate…

We introduce and analyze a new finite-difference scheme, relying on the theta-method, for solving monotone second-order mean field games. These games consist of a coupled system of the Fokker-Planck and the Hamilton-Jacobi-Bellman equation.…

This paper presents a technique for approximating, up to any precision, the set of subgame-perfect equilibria (SPE) in discounted repeated games. The process starts with a single hypercube approximation of the set of SPE. Then the initial…

We formulate a stochastic game of mean field type where the agents solve optimal stopping problems and interact through the proportion of players that have already stopped. Working with a continuum of agents, typical equilibria become…

Recent techniques based on Mean Field Games (MFGs) allow the scalable analysis of multi-player games with many similar, rational agents. However, standard MFGs remain limited to homogeneous players that weakly influence each other, and…

In a mean field game of controls, a large population of identical players seek to minimize a cost that depends on the joint distribution of the states of the players and their controls. We first consider the classes of mean field games of…

Mean field games is a recent area of study introduced by Lions and Lasry in a series of seminal papers in 2006. Mean field games model situations of competition between large number of rational agents that play non-cooperative dynamic games…

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 formulate the fixed budget resource allocation game to understand the performance of a distributed market-based resource allocation system. Multiple users decide how to distribute their budget (bids) among multiple machines…

In this paper, we study the infinite-time mean field games with discounting, establishing an equilibrium where individual optimal strategies collectively regenerate the mean-field distribution. To solve this problem, we partition all agents…

We study a simple first-order mean field game in which the coupling with the mean field is only in the final time and gives an incentive for players to congregate. For a short enough time horizon, the equilibrium is unique. We consider the…

We present an algorithm for computing pure-strategy epsilon-perfect Bayesian equilibria in sequential auctions with continuous action and value spaces. Importantly, our algorithm includes a verification phase that computes an upper bound on…

In this paper we propose a high-order numerical scheme for time-dependent mean field games systems. The scheme, which is built by combining Lagrange-Galerkin and semi-Lagrangian techniques, is consistent and stable for large time steps…

We explore a mechanism of decision-making in Mean Field Games with myopic players. At each instant, agents set a strategy which optimizes their expected future cost by assuming their environment as immutable. As the system evolves, the…

We present a new combined \textit{mean field control game} (MFCG) problem which can be interpreted as a competitive game between collaborating groups and its solution as a Nash equilibrium between groups. Players coordinate their strategies…

Value Iteration is a widely used algorithm for solving Markov Decision Processes (MDPs). While previous studies have extensively analyzed its convergence properties, they primarily focus on convergence with respect to the infinity norm. In…

In this paper, we present a new development of inspection games in a mean field setting. In our dynamic version of an inspection game, there is one inspector and a large number N interacting inspectees with a finite state space. By applying…

This work presents a novel policy iteration algorithm to tackle nonzero-sum stochastic impulse games arising naturally in many applications. Despite the obvious impact of solving such problems, there are no suitable numerical methods…