State Of Major Agent Research Articles

$\epsilon$-Nash Equilibria for Major–Minor LQG Mean Field Games With Partial Observations of All Agents

The partially observed major minor LQG and nonlinear mean field game (PO MM LQG MFG) systems where it is assumed the major agent's state is partially observed by each minor agent, and the major agent completely observes its own state have been analysed in the literature. In this paper, PO MM LQG MFG problems with general information patterns are studied where (i) the major agent has partial observations of its own state, and (ii) each minor agent has partial observations of its own state and the major agent's state. The assumption of partial observations by all agents leads to a new situation involving the recursive estimation by each minor agent of the major agent's estimate of its own state. For a general case of indefinite LQG MFG systems, the existence of $\epsilon$-Nash equilibria together with the individual agents' control laws yielding the equilibria are established via the Separation Principle.

$\epsilon$-Nash Equilibria for Partially Observed LQG Mean Field Games With a Major Player

Huang (2010) and Nguyen and Huang (2012) solved the linear quadratic mean field systems and control problem in the case where there is a major agent (i.e. non-asymptotically vanishing as the population size goes to infinity) together with a population of minor agents (i.e. individually asymptotically negligible). The new feature in this case is that the mean field becomes stochastic and then, by minor agent state extension, the existence of $\epsilon$ -Nash equilibria together with the individual agents' control laws that yield the equilibria may be established. This paper presents results initially announced by Caines and Kizilkale (2013, 2014) where it is shown that if the major agent's state is partially observed by the minor agents, and if the major agent completely observes its own state, all agents can recursively generate estimates (in general individually distinct) of the major agent's state and the mean field, and thence generate feedback controls yielding $\epsilon$ -Nash equilibria.

Backward-forward linear-quadratic mean-field games with major and minor agents

This paper studies the backward-forward linear-quadratic-Gaussian (LQG) games with major and minor agents (players). The state of major agent follows a linear backward stochastic differential equation (BSDE) and the states of minor agents are governed by linear forward stochastic differential equations (SDEs). The major agent is dominating as its state enters those of minor agents. On the other hand, all minor agents are individually negligible but their state-average affects the cost functional of major agent. The mean-field game in such backward-major and forward-minor setup is formulated to analyze the decentralized strategies. We first derive the consistency condition via an auxiliary mean-field SDEs and a 3×2 mixed backward-forward stochastic differential equation (BFSDE) system. Next, we discuss the wellposedness of such BFSDE system by virtue of the monotonicity method. Consequently, we obtain the decentralized strategies for major and minor agents which are proved to satisfy the e-Nash equilibrium property.

Mean Field Game Theory with a Partially Observed Major Agent

Mean field game (MFG) theory where there is a major agent and many minor agents (MM-MFG) has been formulated for both the linear quadratic Gaussian (LQG) case and for the case of nonlinear state dynamics and nonlinear cost functions. In this framework, even asymptotically (as the population size $N$ approaches infinity), and in contrast to the situation without major agents, the mean field term becomes stochastic due to the stochastic evolution of the state of the major agent; furthermore, the best response control actions of the minor agents depend on the state of the major agent as well as the stochastic mean field. In a decentralized environment, one is led to consider the situation where the agents are provided only with partial information on the major agent's state; in this work such a scenario is considered for systems with nonlinear dynamics and cost functions, and an $\epsilon$-Nash MFG theory is developed for this MM-MFG setup. The approach to the problem of partially observed MM-MFG systems adopted in this work is to follow the procedure of constructing the associated completely observed system via the application of nonlinear filtering theory; consequently, as a first step, nonlinear filtering equations are obtained for partially observed stochastic dynamical systems whose state equations contain a measure term corresponding to the distribution of the solution of a state process. Stochastic control theory for systems with random parameters is next generalized to the partially observed case by lifting the analysis to the infinite-dimensional domain. To achieve this, the Itô--Kunita lemma is first generalized to processes taking values in a subset of $L^1$ consisting of the space of solutions of the conditional density process generated by the filtering equations. The existence and uniqueness of solutions to the MFG system of equations is next established by a fixed point argument in the Wasserstein space of random probability measures in which the robustness property of nonlinear filtering theory is used. Finally, the $\epsilon$-Nash property of such a solution is analyzed in this setting where the state consists of finite- and infinite-dimensional (density) valued stochastic processes.

Mean Field Estimation for Partially Observed LQG Systems with Major and Minor Agents

In the work of Huang (2010) and Nguyen and Huang (2012) the linear quadratic mean field systems and control problem is solved in the case where there is a major agent (i.e. non-asymptotically vanishing as the population size goes to infinity) together with a population of minor agents (i.e. individually asymptotically negligible). The new feature in this case is that the mean field becomes stochastic and by minor agent state extension Nguyen and Huang (2012) establish the existence of e-Nash equilibria together with the individual agents' control laws that yield the equilibria. This paper presents results initially announced in Caines and Kizilkale (2013); Caines (2013) where it is shown that if the major agent's state is partially observed by the minor agents, and if the major agent completely observes its own state, all agents can recursively generate estimates (in general individually distinct) of the major agent's state and the mean field, and thence generate feedback controls yielding ∈-Nash equilibria.