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This paper studies social optimal control of mean field LQG (linear-quadratic-Gaussian) models with uncertainty. Specially, the uncertainty is represented by a uncertain drift which is common for all agents. A robust optimization approach…
This work investigates a problem of simultaneous global cost minimization and Nash equilibrium seeking, which commonly exists in $N$-cluster non-cooperative games. Specifically, the agents in the same cluster collaborate to minimize a…
This paper investigates a linear-quadratic mean field games problem with common noise, where the drift term and diffusion term of individual state equations are coupled with both the state, control, and mean field terms of the state, and we…
An analysis of infinite horizon linear quadratic Gaussian (LQG) Mean Field Games is given within the general framework of Graphon Mean Field Games (GMFG) on dense infinite graphs (or networks) introduced in Caines and Huang (2018). For a…
In this paper, we consider a mean field game (MFG) model perturbed by small common noise. Our goal is to give an approximation of the Nash equilibrium strategy of this game using a solution from the original no common noise MFG whose…
We formulate a general framework for competitive gradient-based learning that encompasses a wide breadth of multi-agent learning algorithms, and analyze the limiting behavior of competitive gradient-based learning algorithms using dynamical…
This paper considers decentralized control and optimization methodologies for large populations of systems, consisting of several agents with different individual behaviors, constraints and interests, and affected by the aggregate behavior…
We study a model of strategic coordination based on a class of games with incomplete information known as Global Games. Under the assumption of Poisson-distributed signals and a Gamma prior distribution on state of the system, we…
In this paper, we investigate the robustness of stationary mean-field equilibria in the presence of model uncertainties, specifically focusing on infinite-horizon discounted cost functions. To achieve this, we initially establish…
Towards characterizing the optimization landscape of games, this paper analyzes the stability of gradient-based dynamics near fixed points of two-player continuous games. We introduce the quadratic numerical range as a method to…
This paper studies a class of partial information linear-quadratic mean-field game problems. A general stochastic large-population system is considered, where the diffusion term of the dynamic of each agent can depend on the state and…
We study a class of dynamic decision problems of mean field type with time inconsistent cost functionals, and derive a stochastic maximum principle to characterize subgame perfect Nash equilibrium points. Subsequently, this approach is…
This paper addresses a class of network games played by dynamic agents using their outputs. Unlike most existing related works, the Nash equilibrium in this work is defined by functions of agent outputs instead of full agent states, which…
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…
We consider a class of non-cooperative N-player non-zero-sum stochastic differential games with singular controls, in which each player can affect a linear stochastic differential equation in order to minimize a cost functional which is…
The theory of mean field games is a tool to understand noncooperative dynamic stochastic games with a large number of players. Much of the theory has evolved under conditions ensuring uniqueness of the mean field game Nash equilibrium.…
This paper explores aggregative games in a network of general linear systems subject to external disturbances. To deal with external disturbances, distributed strategy-updating rules based on internal model are proposed for the case with…
We analyze a simple variant of the Goldfarb-Idnani (GI) dual active-set method for computing variational generalized Nash equilibria of strongly monotone N-player games with convex quadratic costs and shared affine inequality and equality…
This paper studies the global Nash equilibrium problem of leader-follower multi-agent dynamics, which yields consensus with a privacy information encrypted learning algorithm. With the secure hierarchical structure, the relationship between…
We consider a market impact game for $n$ risk-averse agents that are competing in a market model with linear transient price impact and additional transaction costs. For both finite and infinite time horizons, the agents aim to minimize a…