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Journal articles on the topic 'Mean-field games'

Author: Grafiati

Published: 4 June 2021

Last updated: 14 December 2024

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1

Lasry, Jean-Michel, and Pierre-Louis Lions. "Mean field games." Japanese Journal of Mathematics 2, no. 1 (2007): 229–60. http://dx.doi.org/10.1007/s11537-007-0657-8.

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2

Tembine, Hamidou. "Mean-field-type games." AIMS Mathematics 2, no. 4 (2017): 706–35. http://dx.doi.org/10.3934/math.2017.4.706.

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3

Subramanian, Sriram Ganapathi, Matthew E. Taylor, Mark Crowley, and Pascal Poupart. "Decentralized Mean Field Games." Proceedings of the AAAI Conference on Artificial Intelligence 36, no. 9 (2022): 9439–47. http://dx.doi.org/10.1609/aaai.v36i9.21176.

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Multiagent reinforcement learning algorithms have not been widely adopted in large scale environments with many agents as they often scale poorly with the number of agents. Using mean field theory to aggregate agents has been proposed as a solution to this problem. However, almost all previous methods in this area make a strong assumption of a centralized system where all the agents in the environment learn the same policy and are effectively indistinguishable from each other. In this paper, we relax this assumption about indistinguishable agents and propose a new mean field system known as De

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4

Ullmo, Denis, Igor Swiecicki, and Thierry Gobron. "Quadratic mean field games." Physics Reports 799 (April 2019): 1–35. http://dx.doi.org/10.1016/j.physrep.2019.01.001.

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5

Tembine, Hamidou. "Nonasymptotic Mean-Field Games." IFAC Proceedings Volumes 47, no. 3 (2014): 8989–94. http://dx.doi.org/10.3182/20140824-6-za-1003.01869.

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6

Lions, Pierre-Louis, and Panagiotis Souganidis. "Extended mean-field games." Rendiconti Lincei - Matematica e Applicazioni 31, no. 3 (2020): 611–25. http://dx.doi.org/10.4171/rlm/907.

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7

Tembine, Hamidou. "Nonasymptotic Mean-Field Games." IEEE Transactions on Cybernetics 44, no. 12 (2014): 2744–56. http://dx.doi.org/10.1109/tcyb.2014.2315171.

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8

Bauso, Dario, Hamidou Tembine, and Tamer Başar. "Robust Mean Field Games." Dynamic Games and Applications 6, no. 3 (2015): 277–303. http://dx.doi.org/10.1007/s13235-015-0160-4.

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9

Cui, Kai, Wasiur R. KhudaBukhsh, and Heinz Koeppl. "Hypergraphon mean field games." Chaos: An Interdisciplinary Journal of Nonlinear Science 32, no. 11 (2022): 113129. http://dx.doi.org/10.1063/5.0093758.

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We propose an approach to modeling large-scale multi-agent dynamical systems allowing interactions among more than just pairs of agents using the theory of mean field games and the notion of hypergraphons, which are obtained as limits of large hypergraphs. To the best of our knowledge, ours is the first work on mean field games on hypergraphs. Together with an extension to a multi-layer setup, we obtain limiting descriptions for large systems of non-linear, weakly interacting dynamical agents. On the theoretical side, we prove the well-foundedness of the resulting hypergraphon mean field game,

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10

Yin, Huibing, Prashant G. Mehta, Sean P. Meyn, and Uday V. Shanbhag. "Learning in Mean-Field Games." IEEE Transactions on Automatic Control 59, no. 3 (2014): 629–44. http://dx.doi.org/10.1109/tac.2013.2287733.

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11

Tembine, Hamidou, Quanyan Zhu, and Tamer Basar. "Risk-Sensitive Mean-Field Games." IEEE Transactions on Automatic Control 59, no. 4 (2014): 835–50. http://dx.doi.org/10.1109/tac.2013.2289711.

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12

Cirant, Marco. "Stationary focusing mean-field games." Communications in Partial Differential Equations 41, no. 8 (2016): 1324–46. http://dx.doi.org/10.1080/03605302.2016.1192647.

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13

Gomes, Diogo A., and Vardan K. Voskanyan. "Extended Deterministic Mean-Field Games." SIAM Journal on Control and Optimization 54, no. 2 (2016): 1030–55. http://dx.doi.org/10.1137/130944503.

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14

Achdou, Yves, and Italo Capuzzo-Dolcetta. "Mean Field Games: Numerical Methods." SIAM Journal on Numerical Analysis 48, no. 3 (2010): 1136–62. http://dx.doi.org/10.1137/090758477.

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15

Hu, Yaozhong, Bernt Øksendal, and Agnès Sulem. "Singular mean-field control games." Stochastic Analysis and Applications 35, no. 5 (2017): 823–51. http://dx.doi.org/10.1080/07362994.2017.1325745.

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16

Achdou, Yves, and Alessio Porretta. "Mean field games with congestion." Annales de l'Institut Henri Poincaré C, Analyse non linéaire 35, no. 2 (2018): 443–80. http://dx.doi.org/10.1016/j.anihpc.2017.06.001.

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17

Bauso, Dario, Ben Mansour Dia, Boualem Djehiche, Hamidou Tembine, and Raul Tempone. "Mean-Field Games for Marriage." PLoS ONE 9, no. 5 (2014): e94933. http://dx.doi.org/10.1371/journal.pone.0094933.

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18

Cissé, Abdoul Karim, and Hamidou Tembine. "Cooperative Mean-Field Type Games." IFAC Proceedings Volumes 47, no. 3 (2014): 8995–9000. http://dx.doi.org/10.3182/20140824-6-za-1003.01870.

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19

Mazanti, Guilherme, and Filippo Santambrogio. "Minimal-time mean field games." Mathematical Models and Methods in Applied Sciences 29, no. 08 (2019): 1413–64. http://dx.doi.org/10.1142/s0218202519500258.

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This paper considers a mean field game model inspired by crowd motion where agents want to leave a given bounded domain through a part of its boundary in minimal time. Each agent is free to move in any direction, but their maximal speed is bounded in terms of the average density of agents around their position in order to take into account congestion phenomena. After a preliminary study of the corresponding minimal-time optimal control problem, we formulate the mean field game in a Lagrangian setting and prove existence of Lagrangian equilibria using a fixed point strategy. We provide a furthe

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20

Bensoussan, A., K. C. J. Sung, S. C. P. Yam, and S. P. Yung. "Linear-Quadratic Mean Field Games." Journal of Optimization Theory and Applications 169, no. 2 (2015): 496–529. http://dx.doi.org/10.1007/s10957-015-0819-4.

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21

Huang, Minyi, Huanshui Zhang, Roland P. Malhamé, and Tielong Shen. "Special issue on “Mean Field Games and Mean Field Control”." Asian Journal of Control 26, no. 2 (2024): 563–64. http://dx.doi.org/10.1002/asjc.3365.

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22

Campi, Luciano, and Markus Fischer. "$N$-player games and mean-field games with absorption." Annals of Applied Probability 28, no. 4 (2018): 2188–242. http://dx.doi.org/10.1214/17-aap1354.

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23

Arjmand, Saeed Sadeghi, and Guilherme Mazanti. "Multipopulation Minimal-Time Mean Field Games." SIAM Journal on Control and Optimization 60, no. 4 (2022): 1942–69. http://dx.doi.org/10.1137/21m1407306.

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24

Andrade, Pêdra D. S., and Edgard A. Pimentel. "Stationary fully nonlinear mean-field games." Journal d'Analyse Mathématique 145, no. 1 (2021): 335–56. http://dx.doi.org/10.1007/s11854-021-0193-0.

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25

Djehiche, Boualem, Alain Tcheukam, and Hamidou Tembine. "Mean-Field-Type Games in Engineering." AIMS Electronics and Electrical Engineering 1, no. 1 (2017): 18–73. http://dx.doi.org/10.3934/electreng.2017.1.18.

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26

Chan, Patrick, and Ronnie Sircar. "Fracking, Renewables, and Mean Field Games." SIAM Review 59, no. 3 (2017): 588–615. http://dx.doi.org/10.1137/15m1031424.

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27

Bertucci, Charles, Jean-Michel Lasry, and Pierre-Louis Lions. "Some remarks on mean field games." Communications in Partial Differential Equations 44, no. 3 (2019): 205–27. http://dx.doi.org/10.1080/03605302.2018.1542438.

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28

Bauso, Dario. "Dynamic Demand and Mean-Field Games." IEEE Transactions on Automatic Control 62, no. 12 (2017): 6310–23. http://dx.doi.org/10.1109/tac.2017.2705911.

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29

Bensoussan, Alain, Thomas Cass, Man Ho Michael Chau, and Sheung Chi Phillip Yam. "Mean Field Games With Parametrized Followers." IEEE Transactions on Automatic Control 65, no. 1 (2020): 12–27. http://dx.doi.org/10.1109/tac.2019.2910945.

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30

Carmona, René, and François Delarue. "Probabilistic Analysis of Mean-Field Games." SIAM Journal on Control and Optimization 51, no. 4 (2013): 2705–34. http://dx.doi.org/10.1137/120883499.

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31

Achdou, Yves, Martino Bardi, and Marco Cirant. "Mean field games models of segregation." Mathematical Models and Methods in Applied Sciences 27, no. 01 (2017): 75–113. http://dx.doi.org/10.1142/s0218202517400036.

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This paper introduces and analyzes some models in the framework of mean field games (MFGs) describing interactions between two populations motivated by the studies on urban settlements and residential choice by Thomas Schelling. For static games, a large population limit is proved. For differential games with noise, the existence of solutions is established for the systems of partial differential equations of MFG theory, in the stationary and in the evolutive case. Numerical methods are proposed with several simulations. In the examples and in the numerical results, particular emphasis is put

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32

Cesaroni, Annalisa, Marco Cirant, Serena Dipierro, Matteo Novaga, and Enrico Valdinoci. "On stationary fractional mean field games." Journal de Mathématiques Pures et Appliquées 122 (February 2019): 1–22. http://dx.doi.org/10.1016/j.matpur.2017.10.013.

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33

Chan, Patrick, and Ronnie Sircar. "Bertrand and Cournot Mean Field Games." Applied Mathematics & Optimization 71, no. 3 (2014): 533–69. http://dx.doi.org/10.1007/s00245-014-9269-x.

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34

Carmona, René, François Delarue, and Daniel Lacker. "Mean field games with common noise." Annals of Probability 44, no. 6 (2016): 3740–803. http://dx.doi.org/10.1214/15-aop1060.

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35

Carmona, René, Jean-Pierre Fouque, and Li-Hsien Sun. "Mean Field Games and systemic risk." Communications in Mathematical Sciences 13, no. 4 (2015): 911–33. http://dx.doi.org/10.4310/cms.2015.v13.n4.a4.

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36

Popov, Bojan, and Vladimir Tomov. "Central schemes for mean field games." Communications in Mathematical Sciences 13, no. 8 (2015): 2177–94. http://dx.doi.org/10.4310/cms.2015.v13.n8.a9.

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37

Fu, Guanxing, and Ulrich Horst. "Mean Field Games with Singular Controls." SIAM Journal on Control and Optimization 55, no. 6 (2017): 3833–68. http://dx.doi.org/10.1137/17m1123742.

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38

Şen, Nevroz, and Peter E. Caines. "Mean Field Games with Partial Observation." SIAM Journal on Control and Optimization 57, no. 3 (2019): 2064–91. http://dx.doi.org/10.1137/17m1140133.

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39

Tang, Qing, and Fabio Camilli. "Variational Time-Fractional Mean Field Games." Dynamic Games and Applications 10, no. 2 (2019): 573–88. http://dx.doi.org/10.1007/s13235-019-00330-2.

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40

Doncel, Josu, Nicolas Gast, and Bruno Gaujal. "Are Mean-field Games the Limits of Finite Stochastic Games?" ACM SIGMETRICS Performance Evaluation Review 44, no. 2 (2016): 18–20. http://dx.doi.org/10.1145/3003977.3003984.

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41

Mou, Chenchen, and Jianfeng Zhang. "Mean field games of controls: Propagation of monotonicities." Probability, Uncertainty and Quantitative Risk 7, no. 3 (2022): 247. http://dx.doi.org/10.3934/puqr.2022015.

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<p style='text-indent:20px;'>The theory of Mean Field Game of Controls considers a class of mean field games where the interaction is through the joint distribution of the state and control. It is well known that, for standard mean field games, certain monotonicity conditions are crucial to guarantee the uniqueness of mean field equilibria and then the global wellposedness for master equations. In the literature the monotonicity condition could be the Lasry–Lions monotonicity, the displacement monotonicity, or the anti-monotonicity conditions. In this paper, we investigate these three ty

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42

Carmona, René, Christy V. Graves, and Zongjun Tan. "Price of anarchy for Mean Field Games." ESAIM: Proceedings and Surveys 65 (2019): 349–83. http://dx.doi.org/10.1051/proc/201965349.

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The price of anarchy, originally introduced to quantify the inefficiency of selfish behavior in routing games, is extended to mean field games. The price of anarchy is defined as the ratio of a worst case social cost computed for a mean field game equilibrium to the optimal social cost as computed by a central planner. We illustrate properties of such a price of anarchy on linear quadratic extended mean field games, for which explicit computations are possible. A sufficient and necessary condition to have no price of anarchy is presented. Various asymptotic behaviors of the price of anarchy ar

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43

Huang, Minyi, and Xuwei Yang. "Mean Field Stackelberg Games: State Feedback Equilibrium." IFAC-PapersOnLine 53, no. 2 (2020): 2237–42. http://dx.doi.org/10.1016/j.ifacol.2020.12.010.

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44

Tembine, Hamidou. "Distributed Planning in Mean-Field-Type Games." IFAC-PapersOnLine 53, no. 2 (2020): 2183–88. http://dx.doi.org/10.1016/j.ifacol.2020.12.2609.

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45

Sarrazin, Clément. "Lagrangian Discretization of Variational Mean Field Games." SIAM Journal on Control and Optimization 60, no. 3 (2022): 1365–92. http://dx.doi.org/10.1137/20m1377291.

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46

Caines, Peter E., and Minyi Huang. "Graphon Mean Field Games and Their Equations." SIAM Journal on Control and Optimization 59, no. 6 (2021): 4373–99. http://dx.doi.org/10.1137/20m136373x.

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47

Sun, Jingrui, Hanxiao Wang, and Zhen Wu. "Mean-field linear-quadratic stochastic differential games." Journal of Differential Equations 296 (September 2021): 299–334. http://dx.doi.org/10.1016/j.jde.2021.06.004.

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48

Tembine, Hamidou, Quanyan Zhu, and Tamer Basar. "Risk-Sensitive Mean-Field Stochastic Differential Games." IFAC Proceedings Volumes 44, no. 1 (2011): 3222–27. http://dx.doi.org/10.3182/20110828-6-it-1002.02247.

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49

Cardaliaguet, Pierre, Jean-Michel Lasry, Pierre-Louis Lions, and Alessio Porretta. "Long time average of mean field games." Networks and Heterogeneous Media 7, no. 2 (2012): 279–301. http://dx.doi.org/10.3934/nhm.2012.7.279.

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50

Cardaliaguet, Pierre, and P. Jameson Graber. "Mean field games systems of first order." ESAIM: Control, Optimisation and Calculus of Variations 21, no. 3 (2015): 690–722. http://dx.doi.org/10.1051/cocv/2014044.

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