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The policy iteration method is a classical algorithm for solving optimal control problems. In this paper, we introduce a policy iteration method for Mean Field Games systems, and we study the convergence of this procedure to a solution of…

Analysis of PDEs · Mathematics 2021-07-12 Simone Cacace , Fabio Camilli , Alessandro Goffi

Mean field games and controls involve guiding the behavior of large populations of interacting agents, where each individual's influence on the group is negligible but collectively impacts overall dynamics. Hybrid systems integrate…

Optimization and Control · Mathematics 2024-12-17 Tejaswi K. C. , Taeyoung Lee

We show that evolutionarily stable states in general (nonlinear) population games (which can be viewed as continuous vector fields constrained on a polytope) are asymptotically stable under a multiplicative weights dynamic (under…

Computer Science and Game Theory · Computer Science 2016-02-02 Ioannis Avramopoulos

The framework of Mean-field Games (MFGs) is used for modelling the collective dynamics of large populations of non-cooperative decision-making agents. We formulate and analyze a kinetic MFG model for an interacting system of non-cooperative…

Optimization and Control · Mathematics 2024-07-29 Piyush Grover , Mandy Huo

In this paper we model the role of a government of a large population as a mean field optimal control problem. Such control problems are constrainted by a PDE of continuity-type, governing the dynamics of the probability distribution of the…

Optimization and Control · Mathematics 2016-08-08 Giacomo Albi , Young-Pil Choi , Massimo Fornasier , Dante Kalise

We propose a new approach to mean field games with major and minor players. Our formulation involves a two player game where the optimization of the representative minor player is standard while the major player faces an optimization over…

Probability · Mathematics 2014-09-26 Rene Carmona , Xiuneng Zhu

We investigate mean-field games (MFG) in which agents can actively control their speed of access to information. Specifically, the agents can dynamically decide to obtain observations with reduced delay by accepting higher observation…

Optimization and Control · Mathematics 2025-06-03 Dirk Becherer , Christoph Reisinger , Jonathan Tam

This work considers stochastic differential games with a large number of players, whose costs and dynamics interact through the empirical distribution of both their states and their controls. We develop a new framework to prove convergence…

Probability · Mathematics 2022-03-24 Mathieu Laurière , Ludovic Tangpi

In this paper we extend the framework of evolutionary inspection game put forward recently by the author and coworkers to a large class of conflict interactions dealing with the pressure executed by the major player (or principal) on the…

Optimization and Control · Mathematics 2022-05-03 Vassili Kolokoltsov

The dynamics of minority games with agents trading on different time scales is studied via dynamical mean-field theory. We analyze the case where the agents' decision-making process is deterministic and its stochastic generalization with…

Disordered Systems and Neural Networks · Physics 2009-11-10 Andrea De Martino

To our knowledge, the populations are generally assumed to be homogeneous in the traditional approach to evolutionary game dynamics. Here, we focus on the inhomogeneous populations. A simple model which can describe the inhomogeneity of the…

Physics and Society · Physics 2007-05-23 Xiaojie Chen , Feng Fu , Long Wang , Tianguang Chu

Mean Field Game (MFG) models implicitly assume "rational expectations", meaning that the heterogeneous agents being modeled correctly know all relevant transition probabilities for the complex system they inhabit. When there is common…

Analysis of PDEs · Mathematics 2026-02-26 Benjamin Moll , Lenya Ryzhik

Traditional solvable game theory and mean-field-type game theory (risk-aware games) predominantly focus on quadratic costs due to their analytical tractability. Nevertheless, they often fail to capture critical non-linearities inherent in…

Optimization and Control · Mathematics 2025-05-09 Julian Barreiro-Gomez , Tyrone E. Duncan , Bozenna Pasik-Duncan , Hamidou Tembine

As Evolutionary Dynamics moves from the realm of theory into application, algorithms are needed to move beyond simple models. Yet few such methods exist in the literature. Ecological and physiological factors are known to be central to…

Populations and Evolution · Quantitative Biology 2025-05-20 Bryce Allen Bagley , Navin Khoshnan , Claudia K Petritsch

We study an atomic signaling game under stochastic evolutionary dynamics. There is a finite number of players who repeatedly update from a finite number of available languages/signaling strategies. Players imitate the most fit agents with…

Probability · Mathematics 2013-12-23 Michael J. Fox , Behrouz Touri , Jeff S. Shamma

We introduce a class of robust control problems formulated in min-max form, in which the principal agent is viewed as a central planner facing Nature. The agent's cost is a nonlinear function of all its possible realizations, encompassing…

Optimization and Control · Mathematics 2026-04-24 François Delarue , Pierre Lavigne

In a probabilistic mean field game driven by a L\'evy process an individual player aims to minimize a long run discounted/ergodic cost by controlling the process through a pair of increasing and decreasing c\`adl\`ag processes, while he is…

Optimization and Control · Mathematics 2025-05-30 Facundo Oliú

Controlling evolutionary game-theoretic dynamics is a problem of paramount importance for the systems and control community, with several applications spanning from social science to engineering. Here, we study a population of individuals…

Systems and Control · Electrical Eng. & Systems 2024-10-22 Lorenzo Zino , Mengbin Ye , Alessandro Rizzo , Giuseppe Carlo Calafiore

Mean field games (MFG) and mean field control (MFC) problems have been introduced to study large populations of strategic players. They correspond respectively to non-cooperative or cooperative scenarios, where the aim is to find the Nash…

Computer Science and Game Theory · Computer Science 2023-12-19 Rene Carmona , Gokce Dayanikli , Francois Delarue , Mathieu Lauriere

We consider a stationary Mean Field Games system defined on a network. In this framework, the transition conditions at the vertices play a crucial role: the ones here considered are based on the optimal control interpretation of the…

Analysis of PDEs · Mathematics 2015-05-20 Fabio Camilli , Claudio Marchi