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This paper introduces the backward mean-field (MF) linear-quadratic-Gaussian (LQG) games (for short, BMFLQG) of weakly coupled stochastic large-population system. In contrast to the well-studied forward mean-field LQG games, the individual state in our large-population system follows the backward stochastic differential equation (BSDE) whose terminal instead initial condition should be prescribed. Two classes of BMFLQG games are discussed here and their decentralized strategies are derived through the consistency condition. In the first class, the individual agents of large-population system are weakly coupled in their state dynamics and the full information can be accessible to all agents. In the second class, the coupling structure lies in the cost functional with only partial information structure. In both classes, the asymptotic near-optimality property (namely, $\epsilon$- Nash equilibrium) of decentralized strategies are verified. To this end, some estimates to BSDE, are presented in the large-population setting. [ABSTRACT FROM AUTHOR]

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 influenced by the aggregate behavior of the overall population. For such large-scale systems, the theory of aggregative and mean field games has been established and successfully applied in various scientific disciplines. While the existing literature addresses the case of unconstrained agents, we formulate deterministic mean field control problems in the presence of heterogeneous convex constraints for the individual agents, for instance arising from agents with linear dynamics subject to convex state and control constraints. We propose several model-free feedback iterations to compute in a decentralized fashion a mean field Nash equilibrium in the limit of infinite population size. We apply our methods to the constrained linear quadratic deterministic mean field control problem. [ABSTRACT FROM PUBLISHER]

We consider a dynamic collective choice problem where a large number of agents are cooperatively choosing between multiple destinations while being influenced by the behavior of the group. For example, in a robotic swarm exploring a new environment, a robot might have to choose between multiple sites to visit, but at the same time it should remain close to some group to achieve coordinated tasks. Finding a social optimum for our problem reduces to solving a set of linear quadratic regulator problems, whose number, however, increases exponentially with the size of the population. Alternatively, we develop via the mean field games methodology a set of decentralized strategies characterized via the fixed points of a suitable operator. In the homogeneous parameter agents case, the procedure reduces to solving a vector fixed point equation of size $l$ equal to the number of destinations, followed by each agent comparing only $l$ regulator costs, independently of the number of agents. When the latter is sufficiently large, the strategies qualify as approximately socially optimal. To compute the approximate social optimum, each agent only needs to know its own state and the statistical distributions of the agents’ initial states and problem parameters. A numerical example illustrates the benefits of cooperative strategies compared to noncooperative ones in achieving an adequate splitting of agents among multiple destinations that each require collective attention. [ABSTRACT FROM AUTHOR]