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

From MaRDI portal
Publication:5282222

DOI10.1109/TAC.2007.904450zbMath1366.91016MaRDI QIDQ5282222

Peter E. Caines, M. Y. Huang, Roland P. Malhamé

Publication date: 27 July 2017

Published in: IEEE Transactions on Automatic Control (Search for Journal in Brave)




Related Items

A numerical algorithm for inverse problem from partial boundary measurement arising from mean field game problemMean Field Game Theory with a Partially Observed Major AgentOpinion Dynamics in Social Networks through Mean-Field GamesRobust mean field social control problems with applications in analysis of opinion dynamicsNonsmooth mean field games with state constraintsEquilibrium price formation with a major player and its mean field limitOn classical solutions to the mean field game system of controlsA mean–variance acreage modelExistence theory for non-separable mean field games in Sobolev spacesThe Master Equation in a bounded domain with Neumann conditionsStrong Convergence to the Mean Field Limit of a Finite Agent EquilibriumThe density evolution of the killed McKean–Vlasov processMultipopulation Minimal-Time Mean Field GamesDynamic optimization problems for mean-field stochastic large-population systemsRobust Mean Field Linear Quadratic Social Control: Open-Loop and Closed-Loop StrategiesLinear-quadratic mean field games of controls with non-monotone dataMaximum principle for mean-field SDEs under model uncertaintyErgodic mean-field games with aggregation of Choquard-typeA mean‐field game approach to equilibrium pricing in solar renewable energy certificate marketsMean field approximation of an optimal control problem for the continuity equation arising in smart chargingKullback–Leibler-Quadratic Optimal ControlA class of dimension-free metrics for the convergence of empirical measuresRandom lift of set valued maps and applications to multiagent dynamicsPartially observed discrete-time risk-sensitive mean field gamesDiscrete‐time mean field social control with a major agentControl theory approach to continuous-time finite state mean field gamesWeak KAM approach to first-order mean field games with state constraintsDiscrete approximation of stationary mean field gamesClosed-loop convergence for mean field games with common noiseOn non-uniqueness and uniqueness of solutions in finite-horizon Mean Field GamesThe mean field games system: Carleman estimates, Lipschitz stability and uniquenessDynamic Cournot-Nash equilibrium: the non-potential caseApproximate Nash Equilibria in Partially Observed Stochastic Games with Mean-Field InteractionsA Mean Field CompetitionOn Mean Field Games models for exhaustible commodities tradeTwo-scale homogenization of a stationary mean-field gameOn the mean field games system with lateral Cauchy data via Carleman estimatesViability analysis of the first-order mean field gamesConvergence analysis of splitting-up algorithm of the Zakai's equation with correlated noisesThe Convergence Problem in Mean Field Games with Neumann Boundary ConditionsPareto efficiency of finite-horizon mean-field cooperative stochastic differential games with Poisson jumpsEquilibrium pricing of securities in the co-presence of cooperative and non-cooperative populationsA fast proximal gradient method and convergence analysis for dynamic mean field planningLearning Optimal Policies in Potential Mean Field Games: Smoothed Policy Iteration AlgorithmsRobust Mean Field Linear-Quadratic-Gaussian Games with Unknown $L^2$-DisturbanceExistence and computation of stationary solutions for congestion-type mean field games via bifurcation theory and forward-forward problemsLinear-quadratic-Gaussian mean-field controls of social optimaBridging mean-field games and normalizing flows with trajectory regularizationQ-learning in regularized mean-field gamesReinforcement learning for non-stationary discrete-time linear-quadratic mean-field games in multiple populationsA unified approach to linear-quadratic-Gaussian mean-field team: homogeneity, heterogeneity and quasi-exchangeabilityModel-free policy iteration approach to NCE-based strategy design for linear quadratic Gaussian gamesInverse problems for mean field gamesPropagation of chaos of forward-backward stochastic differential equations with graphon interactionsTime-inconsistent LQ games for large-population systems and applicationsA coefficient inverse problem for the mean field games systemLinear-Quadratic Large-Population Problem with Partial Information: Hamiltonian Approach and Riccati ApproachA singular perturbation problem for mean field games of acceleration: application to mean field games of controlLinear quadratic leader-follower stochastic differential games for mean-field switching diffusionsLearning High-Dimensional McKean–Vlasov Forward-Backward Stochastic Differential Equations with General Distribution DependenceMean Field Equilibria for Resource Competition in Spatial SettingsA mean field game approach for a class of linear quadratic discrete choice problems with congestion avoidanceSelected topics in mean field gamesHölder stability and uniqueness for the mean field games system via Carleman estimatesAn Infinite-Horizon Mean Field Game of Growth and Capital Accumulation: A Markov Chain Approximation Numerical Scheme and Its ChallengesOn mean field games with common noise and McKean-Vlasov SPDEsStochastic recursive optimal control problem of reflected stochastic differential systemsMean-Field Game Strategies for Optimal ExecutionStackelberg solution of first-order mean field game with a major playerA stochastic Evans-Aronsson problemϵ-Nash mean-field games for linear-quadratic systems with random jumps and applicationsComputational Methods for First-Order Nonlocal Mean Field Games with ApplicationsConvergence of a Finite Difference Scheme to Weak Solutions of the System of Partial Differential Equations Arising in Mean Field GamesMild and weak solutions of Mean Field Games problem for linear control systemsMean‐field games for multiagent systems with multiplicative noisesMinimal-time mean field gamesUnnamed ItemMean Field Games with Partial ObservationExistence of weak solutions to first-order stationary mean-field games with Dirichlet conditionsCournot--Nash Equilibrium and Optimal Transport in a Dynamic SettingThe Supermarket GameControlled Markov chains with non-exponential discounting and distribution-dependent costsDiscrete-time mean field games with risk-averse agentsTime-Dependent Mean-Field Games in the Subquadratic CaseContact rate epidemic control of COVID-19: an equilibrium viewSocial Optima in Mean Field Linear-Quadratic-Gaussian Control with Volatility UncertaintyRelationship between backward and forward linear-quadratic mean-field-game with terminal constraint and optimal asset allocation for insurers and pension fundsClosed-Loop Equilibrium for Time-Inconsistent McKean--Vlasov Controlled ProblemGraphon Mean Field Games and Their EquationsMean-field stochastic H2/H control with delayMean field games systems of first orderOn the Graphon Mean Field Game equations: Individual agent affine dynamics and mean field dependent performance functionsMean-Field Controls with Q-Learning for Cooperative MARL: Convergence and Complexity AnalysisAlgorithms for solving high dimensional PDEs: from nonlinear Monte Carlo to machine learningMcKean–Vlasov Optimal Control: Limit Theory and Equivalence Between Different FormulationsEntropy Regularization for Mean Field Games with LearningTerminal Ranking GamesA mean-field optimal control for fully coupled forward-backward stochastic control systems with Lévy processesApproachability in population gamesLinear-quadratic-Gaussian mean-field-game with partial observation and common noiseHerd behaviors in epidemics: a dynamics-coupled evolutionary games approachA class of interference induced games: asymptotic Nash equilibria and parameterized cooperative solutionsRates of convergence for the policy iteration method for mean field games systemsMean-field stochastic linear-quadratic optimal control with Markov jump parametersLinear-quadratic mean field gamesDecomposition and mean-field approach to mixed integer optimal compensation problemsLinear quadratic mean field social optimization: Asymptotic solvability and decentralized controlSystemic risk and interbank lendingA characterization of sub-game perfect equilibria for SDEs of mean-field typeEfficiency of the price formation process in presence of high frequency participants: a mean field game analysisRandom features for high-dimensional nonlocal mean-field gamesNumerical methods for mean field games based on Gaussian processes and Fourier featuresA class of hybrid LQG mean field games with state-invariant switching and stopping strategiesOpinion dynamics and stubbornness via multi-population mean-field gamesMultivariable feedback particle filterSecond order local minimal-time mean field gamesParticle approximation of one-dimensional mean-field games with local interactionsMalliavin method for optimal investment in financial markets with memoryPareto-based guaranteed cost control of the uncertain mean-field stochastic systems in infinite horizonSmoothing properties of McKean-Vlasov SDEsOne-dimensional stationary mean-field games with local couplingRobust mean field gamesLeader-following discrete consensus control of multi-agent systems with fixed and switching topologiesFinite horizon mean-field stochastic \(H_2/H_\infty\) control for continuous-time systems with \((x,v)\)-dependent noiseMean field stochastic linear quadratic games for continuum-parameterized multi-agent systemsMean field linear quadratic games with set up costsContinuous time finite state mean field gamesThe convergence problem in mean field games with local couplingAn optimal control problem for mean-field forward-backward stochastic differential equation with noisy observationConsensus via multi-population robust mean-field gamesSobolev regularity for the first order Hamilton-Jacobi equationExistence for stationary mean-field games with congestion and quadratic HamiltoniansDiscrete-time mean-field stochastic linear-quadratic optimal control problems. II: Infinite horizon caseDistributed control of multi-agent systems with random parameters and a major agentTwo numerical approaches to stationary mean-field gamesDiscrete-time mean-field stochastic \(H_2/H_\infty\) controlControl and Nash games with mean field effectTotal reward semi-Markov mean-field games with complementarity propertiesOne-dimensional, non-local, first-order stationary mean-field games with congestion: a Fourier approachPrice of anarchy in electric vehicle charging control games: when Nash equilibria achieve social welfareLinear quadratic mean field Stackelberg differential gamesProbabilistic interpretation for Sobolev solutions of McKean-Vlasov partial differential equationsSteering the distribution of agents in mean-field games systemOn the convergence of finite state mean-field games through \(\Gamma\)-convergenceDistributed output feedback control of Markov jump multi-agent systemsMean field production output control with sticky prices: Nash and social solutionsAn integral control formulation of mean field game based large scale coordination of loads in smart gridsExistence of weak solutions to time-dependent mean-field gamesExistence of a solution to an equation arising from the theory of mean field gamesDecentralized control of discrete-time system with delay in mean field LQR problemA dynamic collective choice model with an advertiserNonlinear elliptic systems and mean-field gamesSharp semi-concavity in a non-autonomous control problem and \(L^p\) estimates in an optimal-exit MFGStrategic thinking under social influence: scalability, stability and robustness of allocationsMean field games: the master equation and the mean field limitFirst-order, stationary mean-field games with congestionErgodic theory for controlled Markov chains with stationary inputsOn the existence of solutions for stationary mean-field games with congestionLinear quadratic mean field type control and mean field games with common noise, with application to production of an exhaustible resourceMean field games for stochastic growth with relative utilityMean-field-game model for botnet defense in cyber-securityErgodic behavior of control and mean field games problems depending on accelerationMean-field-game model of corruptionLinear quadratic mean-field-game of backward stochastic differential systemsMean field linear-quadratic control: uniform stabilization and social optimalitySome recent aspects of differential game theoryMean-field game modeling the bandwagon effect with activation costsNumerical methods for finite-state mean-field games satisfying a monotonicity conditionStationary mean-field games with logistic effectsHigh order variational numerical schemes with application to Nash-MFG vaccination gamesMean field games with state constraints: from mild to pointwise solutions of the PDE systemHomogenization of the backward-forward mean-field games systems in periodic environmentsExistence theory for a time-dependent mean field games model of household wealthErgodic mean field games with Hörmander diffusionsWeakly coupled mean-field game systemsImage-dependent conditional McKean-Vlasov SDEs for measure-valued diffusion processesLinear-quadratic non-zero sum differential game for mean-field stochastic systems with asymmetric informationLinear-quadratic \(N\)-person and mean-field games: infinite horizon games with discounted cost and singular limitsSecure discrete-time linear-quadratic mean-field gamesDynamic pricing of new products in competitive markets: a mean-field game approachSplitting methods for a class of non-potential mean field gamesRobust designs through risk sensitivity: an overviewLinear quadratic mean field games: decentralized \(O(1/N)\)-Nash equilibriaA maximum principle for mean-field stochastic control system with noisy observationReinforcement learning and stochastic optimisationMean field games with heterogeneous groups: application to banking systemsPartially-observed decentralized optimal control for large population two-wheeled vehicles: a differential game approachLong-time behavior of first-order mean field games on Euclidean spaceVariational time-fractional mean field gamesMean field games with common noises and conditional distribution dependent FBSDEsApproximating Nash equilibrium for optimal consumption in stochastic growth model with jumpsMean field games of controls: propagation of monotonicitiesSolvability of infinite horizon McKean-Vlasov FBSDEs in mean field control problems and gamesLinear quadratic mean field social control with common noise: a directly decoupling methodPMP-based numerical solution for mean field game problem of general nonlinear systemDynamic optimization of large-population systems with partial informationExploratory LQG mean field games with entropy regularizationGame theoretic decentralized feedback controls in Markov jump processesBackward propagation of chaosShort-time existence of solutions for mean-field games with congestionMean field games with monotonous interactions through the law of states and controls of the agentsMaximum principle for general partial information nonzero sum stochastic differential games and applicationsWellposedness of Mean Field Games with Common Noise under a Weak Monotonicity ConditionLinear quadratic mean field game with control input constraintUnified reinforcement Q-learning for mean field game and control problemsMarkov--Nash Equilibria in Mean-Field Games with Discounted CostExistence of solutions to contact mean-field games of first orderExistence of Weak Solutions to Stationary Mean-Field Games through Variational InequalitiesTime-Dependent Mean-Field Games with Logarithmic NonlinearitiesMean field games of controls: finite difference approximationsOn the convergence of closed-loop Nash equilibria to the mean field game limitGeometry of information structures, strategic measures and associated stochastic control topologiesExistence, uniqueness and exponential ergodicity under Lyapunov conditions for McKean-Vlasov SDEs with Markovian switchingLinear quadratic mean field games with a major player: the multi-scale approach\(\epsilon\)-Nash mean-field games for general linear-quadratic systems with applicationsLinear-Quadratic-Gaussian Mixed Mean-Field Games with Heterogeneous Input ConstraintsOpen-loop Nash equilibrium in polynomial differential games via state-dependent Riccati equationAlgorithmic Trading, Stochastic Control, and Mutually Exciting ProcessesFrom mean field games to the best reply strategy in a stochastic frameworkMean-field games and swarms dynamics in Gaussian and non-Gaussian environmentsMaximum principle for mean-field zero-sum stochastic differential game with partial information and its application to financeConvergence to the mean field game limit: a case studyDynamic marketing policies with rating-sensitive consumers: a mean-field games approachA mean-field game model for homogeneous flockingOn quasi-stationary mean field games modelsDeterministic limit of mean field games associated with nonlinear Markov processesMean field games on prosumersRobust mean field games for coupled Markov jump linear systemsSocio-economic applications of finite state mean field gamesFrom the master equation to mean field game limit theory: a central limit theoremDecentralized strategies for finite population linear-quadratic-Gaussian games and teamsPolicy iteration method for time-dependent mean field games systems with non-separable HamiltoniansA primal-dual partial inverse algorithm for constrained monotone inclusions: applications to stochastic programming and mean field gamesMean field games models of segregationOn a mean field optimal control problemLinear-quadratic mean field stochastic zero-sum differential gamesConvex analysis for LQG systems with applications to major-minor LQG mean-field game systemsValue iteration algorithm for mean-field gamesMean field games: A toy model on an Erdös-Renyi graph.Proximal Methods for Stationary Mean Field Games with Local CouplingsSustainable management of tourist flow networks: a mean field modelDynamic games with strategic complements and large number of playersNecessary/sufficient conditions for Pareto optimality in finite horizon mean-field type stochastic differential gameA Mean Field Game of Optimal StoppingComputational mean-field games on manifoldsOn the existence of classical solutions for stationary extended mean field gamesDecentralized tracking-type games for multi-agent systems with coupled ARX models: asymptotic Nash equilibriaStochastic Games for Fuel Follower Problem: $N$ versus Mean Field GameAn introduction to mean field game theoryOptimal partial transport problem with Lagrangian costsOn non-uniqueness in mean field gamesViscosity Solutions for Controlled McKean--Vlasov Jump-DiffusionsAn invariance principle in large population stochastic dynamic gamesSocial optima of backward linear-quadratic-Gaussian mean-field teamsStrong averaging principle for two-time-scale stochastic McKean-Vlasov equationsA mean-field game approach to price formationEquilibria of dynamic games with many players: existence, approximation, and market structureDesign and Analysis of Distributed Optimal Controller for Identical Multiagent SystemsMean field game for linear-quadratic stochastic recursive systemsLinear-quadratic mean field control: the invariant subspace methodConnections between mean-field game and social welfare optimizationOn an optimal control problem of time-fractional advection-diffusion equationPreface: DGAA special issue on mean field gamesA mean field capital accumulation game with HARA utilityAdaptive mean field games for large population coupled ARX systems with unknown coupling strengthThe derivation of ergodic mean field game equations for several populations of playersLinear-quadratic time-inconsistent mean field gamesPreface: DGAA 2nd special issue on mean field gamesMean field games models -- a brief surveyMean-field games and dynamic demand management in power gridsOn the efficiency of equilibria in mean-field oscillator gamesOn the rate of convergence for the mean-field approximation of controlled diffusions with large number of playersRisk-sensitive mean field games via the stochastic maximum principleExtended Deterministic Mean-Field GamesTime-dependent mean-field games in the superquadratic caseBackward-forward linear-quadratic mean-field games with major and minor agentsLinear-quadratic Stackelberg game for mean-field backward stochastic differential system and applicationLarge tournament gamesShort time solution to the master equation of a first order mean field gameA policy iteration method for mean field gamesDiscrete-time average-cost mean-field games on Polish spacesAn extended mean field game for storage in smart gridsRestoring uniqueness to mean-field games by randomizing the equilibriaC\(^{1,1}\)-smoothness of constrained solutions in the calculus of variations with application to mean field gamesApproximate Markov-Nash Equilibria for Discrete-Time Risk-Sensitive Mean-Field GamesFourier approximation methods for first-order nonlocal mean-field gamesThe finite difference approximation preserving conjugate properties of the mean-field game equationsDistributed Algorithms for Aggregative Games on GraphsLeader-follower decentralized optimal control for large population hexarotors with tilted propellers: a Stackelberg game approachStationary focusing mean-field gamesLinear quadratic optimal control problems for mean-field backward stochastic differential equationsMean Field Stochastic Games with Discrete States and Mixed PlayersA Note on Nonconvex Mean Field GamesThe variational structure and time-periodic solutions for mean-field games systemsDisplacement convexity for first-order mean-field gamesMean Field Control and Mean Field Game Models with Several PopulationsApproximations of two-dimensional mean field games with nonsymmetric controls