Related papers: A Maximum Principle approach to deterministic Mean…
We study necessary optimality conditions for the deterministic mean field type free-endpoint optimal control problem. Our study relies on the Lagrangian approach that treats the mean field type control system as a crowd of infinitely many…
In this paper, we consider the social optimal problem of discrete time finite state space mean field games (referred to as finite mean field games [1]). Unlike the individual optimization of their own cost function in competitive models, in…
In this paper, we study a class of discrete-time mean-field games under the infinite-horizon risk-sensitive discounted-cost optimality criterion. Risk-sensitivity is introduced for each agent (player) via an exponential utility function. In…
In a game theoretic framework, we study energy markets with a continuum of homogenous producers who produce energy from an exhaustible resource such as oil. Each producer simultaneously optimizes production rate that drives her revenues, as…
We study how risk-sensitive players act in situations where the outcome is influenced not only by the state-action profile but also by the distribution of it. In such interactive decision-making problems, the classical mean-field game…
The paper concerns the study of the Pontryagin Maximum Principle for an infinite dimensional and infinite horizon boundary control problem for linear partial differential equations. The optimal control model has already been studied both in…
We study the time-optimal robust control of a two-level quantum system subjected to field inhomogeneities. We apply the Pontryagin Maximum Principle and we introduce a reduced space onto which the optimal dynamics is projected down. This…
In the paper, we use the equivalent formulation of a finite state mean field game as a control problem with mixed constraints to study the dependence of solutions to finite state mean field game on an initial distribution of players. We…
In a mean field game of controls, a large population of identical players seek to minimize a cost that depends on the joint distribution of the states of the players and their controls. We first consider the classes of mean field games of…
The paper is concerned with the feedback approach to the deterministic mean field type differential games. Previously, it was shown that suboptimal strategies in the mean field type differential game can constructed based on functions of…
In this study, we consider an optimal control problem driven by a stochastic differential equation with state constraints. Here, the state constraints mean the constraints about the path of state. In order to show the maximum principe for…
In this article we derive a strong version of the Pontryagin Maximum Principle for general nonlinear optimal control problems on time scales in finite dimension. The final time can be fixed or not, and in the case of general boundary…
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…
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 studies an optimal investment-consumption problem for competitive agents with exponential or power utilities and a common finite time horizon. Each agent regards the average of habit formation and wealth from all peers as…
This paper is devoted to finite horizon deterministic mean field games in which the state space is a network. The agents control their velocity, and when they occupy a vertex, they can enter into any incident edge. The running and terminal…
We study a game of resource extraction of a common good under one-dimensional diffusive dynamics with player actions corresponding to singular stochastic control up to absorption at $0$, implying a trade-off between profitable resource…
This paper is concerned with the partial information optimal control problem of mean-field type under partial observation, where the system is given by a controlled mean-field forward-backward stochastic differential equation with…
The mean field limit of large-population symmetric stochastic differential games is derived in a general setting, with and without common noise, on a finite time horizon. Minimal assumptions are imposed on equilibrium strategies, which may…
We study deterministic optimal control problems for differential games with finite horizon. We propose new approximations of the strategies in feedback form, and show error estimates and a convergence result of the value in some weak sense…