Large-Population Cost-Coupled LQG Problems With Nonuniform Agents: Individual-Mass Behavior and Decentralized $\varepsilon$-Nash Equilibria

Abstract

We consider linear quadratic Gaussian (LQG) games in large population systems where the agents evolve according to nonuniform dynamics and are coupled via their individual costs. A state aggregation technique is developed to obtain a set of decentralized control laws for the individuals which possesses an -Nash equilibrium property. A stability property of the mass behavior is established, and the effect of inaccurate population statistics on an isolated agent is also analyzed by variational techniques.

Decomposition and Mean-Field Approach to Mixed Integer Optimal Compensation Problems

“…The mean-field theory of dynamical games with large but finite populations of asymptotically negligible agents (as the population size grows to infinity) originated in the work of Huang et al [18][19][20] and independently in that of Lasry and Lions [21][22][23], where the now standard terminology of mean-field games (MFG) was introduced. In addition to this, the closely related notion of Oblivious Equilibria for large population dynamic games was introduced by Weintraub et al [24] in the framework of Markov decision processes.…”

“…This makes sense as the initial and final states of a regeneration interval are null by definition. The inequality constraints (18) and (20) impose that the accumulated demand in any subinterval may not exceed the ordered quantity over the same subinterval. Again, this is due to the condition that the states are nonnegative in any period of a regeneration interval.…”

“…In addition, the dependence on endogenous factors, represented by the averaging process, is the result of the interactions among the agents. In this case, our decomposition methodology becomes similar to mean-field methods in large population consensus [20,33,35]. We discuss below the mean-field approximations as well as the application of predictive control methods to approximate the computation.…”

Mean-Field Games and Dynamic Demand Management in Power Grids

“…The mean field theory of dynamical games with large but finite populations of asymptotically negligible agents (as the population size goes to infinity) originated in the work of M.Y. Huang, P. E. Caines and R. Malhamé [18][19][20] and independently in that of J. M. Lasry and P.L. Lions [23][24][25], where the now standard terminology of Mean Field Games (MFG) was introduced.…”

“…Mean field games arise in several applicative domains such as economics, physics, biology, and network engineering (see [1,17,20,22,37]). …”