相关论文: Graphon Mean Field Games and the GMFG Equations

This paper investigates Nash equilibrium (NE) seeking problems for noncooperative games over multi-players networks with finite bandwidth communication. A distributed quantized algorithm is presented, which consists of local gradient play,…

Whilst network coordination games and network anti-coordination games have received a considerable amount of attention in the literature, network games with coexisting coordinating and anti-coordinating players are known to exhibit more…

The modelling of linear quadratic Gaussian optimal control problems on large complex networks is intractable computationally. Graphon theory provides an approach to overcome these issues by defining limit objects for infinite sequences of…

We study the uniqueness of solutions to systems of PDEs arising in Mean Field Games with several populations of agents and Neumann boundary conditions. The main assumption requires the smallness of some data, e.g., the length of the time…

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 the game theory literature, there appears to be little research on equilibrium selection for normal-form games with an infinite strategy space and discontinuous utility functions. Moreover, many existing selection methods are not…

We study the asymptotic organization among many optimizing individuals interacting in a suitable "moderate" way. We justify this limiting game by proving that its solution provides approximate Nash equilibria for large but finite player…

We address the numerical solution of second-order Mean Field Game problems through Newton iterations in infinite dimensions, introduced in [14], where quadratic convergence of the method was rigorously established. Building upon this…

For a mean field game model with a major and infinite minor players, we characterize a notion of Nash equilibrium via a system of so-called master equations, namely a system of nonlinear transport equations in the space of measures. Then,…

A systematic theory is introduced that describes stochastic effects in game theory. In a biological context, such effects are relevant for the evolution of finite populations with frequency-dependent selection. They are characterized by…

Mean field games (MFGs) have been introduced to study Nash equilibria in very large population of self-interested agents. However, when applied to common pool resource (CPR) games, MFG equilibria lead to the so-called tragedy of the commons…

We consider the basic problem of approximating Nash equilibria in noncooperative games. For monotone games, we design continuous time flows which converge in an averaged sense to Nash equilibria. We also study mean field equilibria, which…

Quantum games represent the really 21st century branch of game theory, tightly linked to the modern development of quantum computing and quantum technologies. The main accent in these developments so far was made on stationary or repeated…

Mean-field game theory relies on approximating games that are intractable to model due to a very large to infinite population of players. While these kinds of games can be solved analytically via the associated system of partial…

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…

In this paper, we introduce discrete-time linear mean-field games subject to an infinite-horizon discounted-cost optimality criterion. The state space of a generic agent is a compact Borel space. At every time, each agent is randomly…

We consider strongly monotone games with convex separable coupling constraints, played by dynamical agents, in a partial-decision information scenario. We start by designing continuous-time fully distributed feedback controllers, based on…

Imitation dynamics for population games are studied and their asymptotic properties analyzed. In the considered class of imitation dynamics - that encompass the replicator equation as well as other models previously considered in…

This paper studies Mean Field Games (MFGs) in which agent dynamics are given by jump processes of controlled intensity, with mean-field interaction via the controls and affecting the jump intensities. We establish the existence of MFG…

Finite-state mean-field games (MFGs) arise as limits of large interacting particle systems and are governed by an MFG system, a coupled forward-backward differential equation consisting of a forward Kolmogorov-Fokker-Planck (KFP) equation…