Related papers: Linear-Quadratic McKean-Vlasov Stochastic Differen…
Linear-quadratic Gaussian games provide a framework for modeling strategic interactions in multi-agent systems, where agents must estimate system states from noisy observations while also making decisions to optimize a quadratic cost.…
This paper studies a class of linear quadratic mean field games where the coefficients of quadratic cost functions depend on both the mean and the variance of the population's state distribution through its quantile function. Such a…
We consider Mean Field Games without idiosyncratic but with Brownian type common noise. We introduce a notion of solutions of the associated backward-forward system of stochastic partial differential equations. We show that the solution…
We study a general class of fully coupled backward-forward stochastic differential equations of mean-field type (MF-BFSDE). We derive existence and uniqueness results for such a system under weak monotonicity assumptions and without the…
Static potential games are non-cooperative games which admit a fictitious function, also referred to as a potential function, such that the minimizers of this function constitute a subset (or a refinement) of the Nash equilibrium strategies…
We formulate the MFG limit for $N$ interacting agents with a common noise as a single quasi-linear deterministic infinite-dimensional partial differential second order backward equation. We prove that any its (regular enough) solution…
We establish an existence of equilibrium result for a class of non-Markovian mean-field games with unbounded control space in weak formulation. Our result is based on new existence and stability results for quadratic-growth generalized…
In this paper we introduce the concept of split Nash equilibrium problems associated with two related noncooperative strategic games. Then we apply the Fan-KKM theorem to prove the existence of solutions to split Nash equilibrium problems…
For a non-cooperative differential game, the value functions of the various players satisfy a system of Hamilton-Jacobi equations. In the present paper, we consider a class of infinite-horizon games with nonlinear costs exponentially…
This paper addresses a class of two-person zero-sum stochastic differential equations, which encompass Markov chains and fractional Brownian motion, and satisfy some monotonicity conditions over an infinite time horizon. Within the…
We consider strongly monotone games with convex separable coupling constraints, played by dynamical agents, in a partial-decision information scenario. We start by designing continuous-time fully distributed feedback controllers, based on…
Many important real-world settings contain multiple players interacting over an unknown duration with probabilistic state transitions, and are naturally modeled as stochastic games. Prior research on algorithms for stochastic games has…
A Linear-quadratic optimal control problem is considered for mean-field stochastic differential equations with deterministic coefficients. By a variational method, the optimality system is derived, which turns out to be a linear mean-field…
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…
A fundamental problem in noncooperative dynamic game theory is the computation of Nash equilibria under different information structures, which specify the information available to each agent during decision-making. Prior work has…
We consider the stochastic optimal control problem of nonlinear mean-field systems in discrete time. We reformulate the problem into a deterministic control problem with marginal distribution as controlled state variable, and prove that…
We introduce a framework for stochastic games on large sparse graphs, covering continuous-time and discrete-time dynamic games as well as static games. Players are indexed by the vertices of simple, locally finite graphs, allowing both…
This paper aims to formulate and study the inverse problem of non-cooperative linear quadratic games: Given a profile of control strategies, find cost parameters for which this profile of control strategies is Nash. We formulate the problem…
Stochastic games are an important class of problems that generalize Markov decision processes to game theoretic scenarios. We consider finite state two-player zero-sum stochastic games over an infinite time horizon with discounted rewards.…
Mean field games (MFGs) offer a powerful framework for modeling large-scale multi-agent systems. This paper addresses MFGs formulated in continuous time with discrete state spaces, where agents' dynamics are governed by continuous-time…