Article
Physics, Multidisciplinary
Yunong Chen, Andrew Belmonte, Christopher Griffin
Summary: This paper analyzes a social imitation model incorporating internal energy caches, cost of living, death, and reproduction into the Ultimatum Game. The study shows that in societies that do not collapse, imitation leads to a natural correlation between selfishness and cost of living, resulting in non-Nash sharing strategies as the de facto outcome. The results are explained through a mean-field approximation of the internal energy cache informed by time-varying distributions extracted from experimental data.
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS
(2021)
Article
Physics, Fluids & Plasmas
Ryosuke Yano, Hisayasu Kuroda
Summary: In this paper, the crowd evacuation from a room is investigated using mean field game theory. The effects of pedestrian predictability on the evacuation process are examined by applying the Cristiani-Santo-Mensi method to solve the Hamilton-Jacobi-Bellman equation coupled with the Fokker-Planck equation. Numerical tests are conducted to analyze the impacts of predictability, mass diffusion, interactive force and domain, and the form of the running cost function on the evacuation process. Furthermore, the effects of predictability on the evacuation process are studied when two exits are alternately opened and closed.
Article
Automation & Control Systems
Alexander Aurell, Rene Carmona, Gokce Dayanikli, Mathieu Lauriere
Summary: Motivated by epidemic control models, this paper studies a Stackelberg mean field game model between a principal and a mean field of agents. The game is analyzed using a probabilistic approach and applied to an SIR-type epidemic model. An innovative numerical method is proposed to compute the solutions.
SIAM JOURNAL ON CONTROL AND OPTIMIZATION
(2022)
Article
Physics, Multidisciplinary
Thibaut Arnoulx de Pirey, Guy Bunin
Summary: Models of many-species ecosystems suggest that these systems often experience near-extinction processes, where population sizes approach zero for a period of time before rebounding, accompanied by a slowdown in dynamics (aging). In this study, a solvable many-variable model is introduced to investigate the connection between near-extinction and aging. It is found that aging is a generic phenomenon when random interactions occur between populations. Population sizes remain exponentially close to the absorbing values for extended periods, with rapid transitions between the two values. The mechanism for aging is different from that in typical glassy systems, with the system evolving near unstable fixed points rather than marginal ones.
PHYSICAL REVIEW LETTERS
(2023)
Article
Mathematics, Applied
Wei Zhang, Ulrik Brandes
Summary: This article introduces an evolutionary game model that combines local neighborhood and global group interactions in a finite networked population through long-range links. Theoretical analysis and simulations reveal that the density of mixing links plays a crucial role in the emergence and sustainability of cooperation in the game.
APPLIED MATHEMATICS AND COMPUTATION
(2023)
Article
Multidisciplinary Sciences
Ivan Specht, Kian Sani, Yolanda Botti-Lodovico, Michael Hughes, Kristin Heumann, Amy Bronson, John Marshall, Emily Baron, Eric Parrie, Olivia Glennon, Ben Fry, Andres Colubri, Pardis C. Sabeti
Summary: During COVID-19, allocating testing resources to close contacts of institution members can effectively control case counts.
SCIENTIFIC REPORTS
(2022)
Article
Physics, Multidisciplinary
Reja H. Wilke, Thomas Koehler, Felix A. Palm, Sebastian Paeckel
Summary: We introduce a mechanism that stabilizes a one-dimensional quantum many-body phase by exploiting an emergent Z(2) symmetry based on a simple geometric modification. By constructing the solution of the full quantum many-body problem of hardcore bosons on a wheel geometry, we demonstrate the effectiveness of this mechanism, which is known to form Bose-Einstein condensates. The robustness of the condensate against interactions is numerically shown by adding nearest-neighbor interactions, which typically destroy Bose-Einstein condensates. Further applications, such as geometrically inducing finite-momentum condensates, are discussed. Since our solution strategy is based on a generic mapping, our findings are applicable in a broader context where a particular state needs to be protected by introducing an additional center site.
COMMUNICATIONS PHYSICS
(2023)
Article
Physics, Multidisciplinary
David Krueger, Michael Potthoff
Summary: In this study, a generic model of a Chem insulator with a Hubbard interaction in arbitrary even dimension D was explored. The model remains nontrivial in the D -> infinity limit, with dynamical mean-field theory predicting a phase diagram featuring a continuum of topologically different phases. The unconventional features, such as the elusive distinction between insulating and semimetal states, are discussed, with topological phases characterized by a nonquantized Chern density as D -> infinity.
PHYSICAL REVIEW LETTERS
(2021)
Article
Physics, Multidisciplinary
Jacky J. Chong, Zehua Zhao
Summary: This paper extends the local-in-time Fock space approximation of the exact dynamics of squeezed states to a global-in-time approximation for a wider range of initial data. Key ingredients include previous work on local well-posedness theory, recent global estimates, and quantitative results on the uniform global well-posedness of the time-dependent Hartree-Fock-Bogoliubov system.
ANNALES HENRI POINCARE
(2022)
Article
Computer Science, Artificial Intelligence
Zejian Zhou, Hao Xu
Summary: This article discusses the decentralized optimal tracking control problem for a large-scale autonomous vehicle system with heterogeneous system dynamics. The study introduces the mean-field game theory and proposes a novel mean-field Stackelberg game method to address the challenges faced by traditional algorithms. A specialized A(2)C(2) M algorithm is designed to learn optimal policies, with numerical simulations conducted to demonstrate the method's effectiveness.
IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS
(2021)
Article
Operations Research & Management Science
Guanxing Fu, Paulwin Graewe, Ulrich Horst, Alexandre Popier
Summary: The study explores an optimal portfolio liquidation mean field game (MFG) under asymmetric information, showing that the solution can be characterized by a forward-backward stochastic differential equation. By extending continuation methods to linear-quadratic FBSDEs with a singular driver, it is proven that the MFG has a unique solution. The existence and uniqueness result allows for the approximation of the MFG with a possibly singular terminal condition by a sequence of MFGs with finite terminal values.
MATHEMATICS OF OPERATIONS RESEARCH
(2021)
Article
Computer Science, Artificial Intelligence
Zejian Zhou, Hao Xu
Summary: This paper investigates the intelligent design for the pursuit-evasion game with large scale multi-pursuer and multi-evader. The Mean Field Games (MFG) theory is utilized to solve the optimal pursuit-evasion strategies by using a probability density function (PDF) instead of detailed information from all players/agents. The proposed scheme reduces information exchange and computation dimension, and the effectiveness is demonstrated through numerical simulations.
Article
Multidisciplinary Sciences
Hao Guo, Chen Shen, Shuyue Hu, Junliang Xing, Pin Tao, Yuanchun Shi, Zhen Wang
Summary: Cooperative AI has played a crucial role in solving the problem of cooperation, and researchers have conducted a thorough analysis on the influence of cooperative and defective Autonomous Agents (AAs) on human cooperation. The study reveals that the impact of cooperative and defective AAs on human cooperation varies in different social dilemma games, and population structure and imitation strength are critical factors determining cooperation.
Article
Mathematics, Interdisciplinary Applications
Eduardo Velasco Stock, Roberto da Silva
Summary: In this study, a simple stochastic agent-based model is proposed to explain the revenue dynamics of a nightclub venue based on the relationship between profit and spatial occupation. The model consists of a square lattice representing the nightclub's dance floor, where attendees can move to neighboring cells. Each attendee has a specific time interval between drinks, denoted as τ, and will move towards the bar when feeling thirsty. After leaving the bar area, τ time steps should pass before feeling thirsty again. The model highlights the importance of optimization rather than simply filling the bar to maximize profit, taking into account the income and ticket cost ratio.
CHAOS SOLITONS & FRACTALS
(2023)
Article
Mathematics, Applied
Zhenfu Wang, Xianliang Zhao, Rongchan Zhu
Summary: In this paper, we consider the asymptotic behavior of the fluctuations for the empirical measures of interacting particle systems with singular kernels. We prove the convergence of the sequence of fluctuation processes to a generalized Ornstein-Uhlenbeck process. Our result extends classical results to singular kernels, including the Biot-Savart law, and applies to the point vortex model approximating the 2D incompressible Navier-Stokes equation and the 2D Euler equation. We also show that the limiting Ornstein-Uhlenbeck process is Gaussian and has optimal regularity. The method relies on the martingale approach and the Donsker-Varadhan variational formula, and involves estimating exponential integrals using cancellations and combinatorics techniques, which is of the type of the large deviation principle.
ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS
(2023)
Article
Economics
Alexander Aurell, Boualem Djehiche
TRANSPORTATION RESEARCH PART B-METHODOLOGICAL
(2019)
Article
Mathematics, Interdisciplinary Applications
Alexander Aurell, Rene Carmona, Gokce Dayanikli, Mathieu Lauriere
Summary: This article examines a continuous game involving a continuum of non-identical players on a finite state space. The players' interactions, represented by a graphon, are characterized as the limit of a dense random graph. The article develops a mathematical framework for the game, analyzes Nash equilibria, and proposes a numerical approach using machine learning methods. Experimental results on different applications to compartmental models in epidemiology are also presented.
DYNAMIC GAMES AND APPLICATIONS
(2022)
Article
Mathematics, Applied
Alexander Aurell, Rene Carmona, Mathieu Lauriere
Summary: In this paper, we analyze linear-quadratic stochastic differential games with a continuum of players interacting through graphon aggregates. We provide conditions for the determinism of graphon aggregates and the uniqueness of the linear state equation. The Pontryagin maximum principle is used to derive equilibrium conditions for the graphon game, and we study how graphon games approximate games with finitely many players over graphs with random weights.
APPLIED MATHEMATICS AND OPTIMIZATION
(2022)
Article
Automation & Control Systems
Alexander Aurell, Rene Carmona, Gokce Dayanikli, Mathieu Lauriere
Summary: Motivated by epidemic control models, this paper studies a Stackelberg mean field game model between a principal and a mean field of agents. The game is analyzed using a probabilistic approach and applied to an SIR-type epidemic model. An innovative numerical method is proposed to compute the solutions.
SIAM JOURNAL ON CONTROL AND OPTIMIZATION
(2022)
Article
Mathematics, Applied
Alexander Aurell, Boualem Djehiche
SIAM JOURNAL ON APPLIED MATHEMATICS
(2020)
