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AIMS Electronics and Electrical Engineering

2017, Volume 1, Issue 1: 18-73. doi: 10.3934/ElectrEng.2017.1.18
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Review

Mean-Field-Type Games in Engineering

  • 1.
    Department of Mathematics, KTH Royal Institute of Technology, Stockholm, Sweden
  • 2.
    Learning and Game Theory Laboratory, New York University, Abu Dhabi
  • Received: 12 July 2017 Accepted: 27 September 2017 Published: 24 November 2017

  • A mean-field-type game is a game in which the instantaneous payoffs and/or the statedynamics functions involve not only the state and the action profile but also the joint distributionsof state-action pairs. This article presents some engineering applications of mean-field-type gamesincluding road traffic networks, multi-level building evacuation, millimeter wave wireless communications,distributed power networks, virus spread over networks, virtual machine resource management incloud networks, synchronization of oscillators, energy-effcient buildings, online meeting and mobilecrowdsensing.

    Citation: Boualem Djehiche, Alain Tcheukam, Hamidou Tembine. Mean-Field-Type Games in Engineering[J]. AIMS Electronics and Electrical Engineering, 2017, 1(1): 18-73. doi: 10.3934/ElectrEng.2017.1.18

    Related Papers:

  • A mean-field-type game is a game in which the instantaneous payoffs and/or the statedynamics functions involve not only the state and the action profile but also the joint distributionsof state-action pairs. This article presents some engineering applications of mean-field-type gamesincluding road traffic networks, multi-level building evacuation, millimeter wave wireless communications,distributed power networks, virus spread over networks, virtual machine resource management incloud networks, synchronization of oscillators, energy-effcient buildings, online meeting and mobilecrowdsensing.


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    [1] Wald A (1951) On some systems of equations of mathematical economics. Econometrica 19: 368-403. doi: 10.2307/1907464
    [2] von Neumann J, Morgenstern O (1953) Theory of Games and Economic Behavior, Princeton: Princeton University Press.
    [3] Nash J (1951) Non-cooperative games, Annals of Mathematics, Second Series, 54: 286-295.
    [4] Wardrop JG (1952) Some theoretical aspects of road traffic research. P I Civil Eng 1: 325-378.
    [5] Beckmann MJ, McGuire CB,Winsten CB (1956) Studies in the economics of transportation. Econ J 67: 116-118.
    [6] Knight FH (1924) Some fallacies in the interpretation of social cost. Q J Econ 38: 582-606. doi: 10.2307/1884592
    [7] Dafermos SC, Sparrow FT (1969) The traffic assignment problem for a general network. J Res US Natl Bur Stand 73B: 91-118. doi: 10.6028/jres.073B.010
    [8] Larsson T, PatrikssonM(1999) Side constrained traffic equilibrium models-analysis, computation and applications. Transport Res B-Math 33: 233-264.
    [9] Aashtiani HZ , Magnanti TL (1981) Equilibria on a congested transportation network. SIAM J Algebr Discrete Method 2: 213-226. doi: 10.1137/0602024
    [10] Kohl JG (1841) Der verkehr und die ansiedelungen der menschen in ihrer abhangigkeit von der gestaltung der erdoberflache. Dresden/Leipzig: Arnold.
    [11] Smith MJ (1979) The existence, uniqueness and stability of traffic equilibria. Transport Res BMath 13: 295-304.
    [12] Dafermos SC (1980) Traffic equilibrium and variational inequalities. Transport Sci 14: 42-54. doi: 10.1287/trsc.14.1.42
    [13] Weibull J (1995) Evolutionary Game Theory. Cambridge, MA: The M.I.T. Press.
    [14] Hofbauer J, Sigmund K (1988) Theory of Evolution and Dynamical Systems. Cambridge: Cambridge University Press.
    [15] Hofbauer J, Sigmund K (1998) Evolutionary Games and Population Dynamics. Cambridge: Cambridge University Press.
    [16] Carlsson H, van Damme E (1993) Global games and equilibrium selection. Econometrica 61: 989-1018. doi: 10.2307/2951491
    [17] Morris S, Shin HS (1998) Unique equilibrium in a model of self-fulfilling currency attacks. Am Econ Rev 88: 587-597.
    [18] Dubey P, Mas-Colell A, Shubik M (1980) Effciency properties of strategic market games: An axiomatic approach. J Econ Theor 22: 339-362. doi: 10.1016/0022-0531(80)90047-2
    [19] Sandholm WH (2010) Population Games and Evolutionary Dynamics. Cambridge: MIT Press.
    [20] Samuelson L (1997) Evolutionary Games and Equilibrium Selection. Cambridge: MIT Press.
    [21] Friedman D (1991) Evolutionary games in economics. Econometrica 59: 637-666. doi: 10.2307/2938222
    [22] Scarf H (1962) An analysis of markets with a large number of participants. In recent advances in Game Theory.
    [23] Davis M (1961) Symmetric solutions to symmetric games with a continuum of players. In recent advances in Game Theory.
    [24] Debreu G (1963) On a theorem of scarf. Rev Econ Stud 30: 177-180. doi: 10.2307/2296318
    [25] Shapley LS, Milnor JW (1978) Values of large games II: Oceanic games. Math Oper Res 3: 290-307. doi: 10.1287/moor.3.4.290
    [26] Peleg B (1963) Quota games with a continuum of players. Israel J Math 1: 48-53. doi: 10.1007/BF02759800
    [27] Aumann RJ (1964): Markets with a continuum of traders. Econometrica 32: 39-50.
    [28] Jovanovic B (1982) Selection and the evolution of industry. Econometrica 50: 649-670. doi: 10.2307/1912606
    [29] Jovanovic B, Rosenthal RW (1988) Anonymous sequential games. J Math Econ 17: 77-87. doi: 10.1016/0304-4068(88)90029-8
    [30] Bergin J, Bernhardt D (1992) Anonymous sequential games with aggregate uncertainty. J Math Econ 21: 543-562. doi: 10.1016/0304-4068(92)90026-4
    [31] Benamou JD, Brenier Y (2000) A computational fluid mechanics solution to the Monge-Kantorovich mass transfer problem. Numer Math 84: 375-393. doi: 10.1007/s002110050002
    [32] Benamou JD, Brenier Y (2001) Mixed L2-Wasserstein optimal mapping between prescribed density functions. J Optim Theor Appl 111: 255-271. doi: 10.1023/A:1011926116573
    [33] Lasry JM, Lions PL (2007) Mean field games. Jpn J Math 2: 229-260. doi: 10.1007/s11537-007-0657-8
    [34] Huang MY, Malhame RP, Caines PE (2006) Large population stochastic dynamic games: Closedloop McKean-Vlasov systems and the Nash certainty equivalence principle. Commun Inf Syst 6: 221-252.
    [35] Zamir S, Maschler M, Solan E (2013) Game Theory, 1st Edition, Cambridge University Press.
    [36] Bensoussan A, Frehse J, Yam SCP (2013) Mean field games and mean field type control theory, Springerbriefs in mathematics, Springer.
    [37] Carmona R, Delarue F (2013) Probabilistic Analysis of Mean-Field Games. SIAM J Contr Opt 51: 2705-2734. doi: 10.1137/120883499
    [38] Gomes D, Patrizi S, Voskanyan V (2014) On the existence of classical solutions for stationary extended mean field games. Nonlinear Anal 99: 49-79. doi: 10.1016/j.na.2013.12.016
    [39] Diogo AG, Vardan KV (2016) Extended deterministic mean-field games. SIAM J Contr Opt 54: 1030-1055. doi: 10.1137/130944503
    [40] Noha A, Rita F, Diogo G (2017) Two numerical approaches to stationary mean-field games. Dynam Games Appl 7: 657-682. doi: 10.1007/s13235-016-0203-5
    [41] Diogo AG, Vardan KV (2015) Short-time existence of solutions for mean-field games with congestion. J London Math Soc 92: 778-799. doi: 10.1112/jlms/jdv052
    [42] Wilfrid G, Andrzej S (2015) Existence of a solution to an equation arising from the theory of mean-field games. J Differ Equa 259: 6573-6643. doi: 10.1016/j.jde.2015.08.001
    [43] Lasry JM, Lions PL (2006) Jeux à champ moyen. I. Le cas stationnaire. C R Math Acad Sci Paris 343: 619-625. doi: 10.1016/j.crma.2006.09.019
    [44] Lasry JM, Lions PL (2006) Jeux à champ moyen. II. Horizon fini et controle optimal. C R Math Acad Sci Paris 343: 679-684. doi: 10.1016/j.crma.2006.09.018
    [45] Lions PL (2007-2011) College de France course on mean-field games.
    [46] Lions PL. IMA, University of Minessota. Course on mean-field games. Video. Available from: http://www.ima.umn.edu/2012-2013/sw11.12-13.12/. 2012.
    [47] Cardaliaguet P, Delarue F, Lasry JM, et al. (2015) The master equation and the convergence problem in mean field games. Preprint.
    [48] Porretta A (2015) Weak solutions to Fokker-Planck equations. Arch Ration Mech Anal 216: 1-62. doi: 10.1007/s00205-014-0799-9
    [49] Wang BC, Zhang JF (2011) Distributed control of multiagent systems with random parameters and a major agent. Automatica.
    [50] Wang BC, Zhang JF (2010) Mean field games for large population stochastic multi-agent systems with Markov jumps. Proceedings of the 29th Chinese Control Conference, Beijing, China, 4572-4577.
    [51] Nourian M, Caines PE, Malhame RP, et al. (2012) Mean field LQG control in leader-follower stochastic multi-agent systems: Likelihood ratio based adaptation. IEEE T Autom Cont 57: 2801-2816. doi: 10.1109/TAC.2012.2195797
    [52] Weintraub GY, Benkard L, Van Roy B (2005) Oblivious equilibrium: A mean field approximation for large-scale dynamic games. Adv Neural Inform Process Syst 18.
    [53] Weintraub GY, Benkard L, Van Roy B (2008) Markov perfect industry dynamics with many firms. Econometrica 76: 1375-1411. doi: 10.3982/ECTA6158
    [54] Tembine H, Le Boudec JY, El Azouzi R, et al. (2009) Mean field asymptotics of Markov decision evolutionary games and teams. Gamenets: 140-150.
    [55] Gomes D, Velho RM,Wolfram MT (2014) Dual two-state mean-field games. Proceedings of IEEE CDC.
    [56] Gomes D, Mohr J, Souza RR (2010) Discrete time, finite state space mean field games. J de Math Pures et Appl 93: 308-328. doi: 10.1016/j.matpur.2009.10.010
    [57] Gomes D, Mohr J, Souza RR (2013) Continuous time finite state mean-field games. Appl Math Opt 68: 99-143. doi: 10.1007/s00245-013-9202-8
    [58] Gomes DA (2011) Continuous time finite state space mean field games-a variational approach. 49th Annual Allerton Conference on Communication, Control, and Computing, Allerton, 998-1001.
    [59] Adlakha S, Johari R, Weintraub G, et al. (2008) Oblivious equilibrium for large-scale stochastic games with unbounded costs. Proceedings of the IEEE Conference on Decision and Control.
    [60] Arabneydi J, Mahajan A (2014) Team optimal control of coupled subsystems with mean field sharing, Proceedings of the 53rd IEEE Conference on Decision and Control, 1669-1674.
    [61] Huang M, Caines PE, Malhame RP (2012) Social optima in mean field LQG control: centralized and decentralized strategies, IEEE T Autom Contr 57: 1736-1751.
    [62] Elliott R, Li X, Ni YH (2013) Discrete time mean-field stochastic linear-quadratic optimal control problems, Automatica 49: 3222-3233.
    [63] Bauso D, Dia BM, Djehiche B, et al. (2014) Mean-Field Games for Marriage. PloS One 9: 5.
    [64] Sznitman AS (1991) Topics in propagation of chaos. Ecole d'Ete de Probabilites de Saint-Flour 165-251.
    [65] Aldous D (1985) Exchangeability and related topics. In: Hennequin P Editor, Ecole d'Ete de Probabilites de Saint-Flour XIII-1983. Heidelberg: Springer. Lecture notes in mathematics 1117: 1-198.
    [66] Tembine H, Huang M (2011) Mean field difference games: McKean-Vlasov dynamics. IEEE Conference on Decision and Control CDC-ECE 1006-1011.
    [67] Achdou Y (2013) Finite difference methods for mean field games, Hamilton-Jacobi equations: Approximations, numerical analysis 1 and applications, Lecture Notes in Mathematics 2074, Heidelberg: Sp inger-Verlag Berlin.
    [68] Achdou Y, Camilli F, Dolcetta IC (2012) Mean field games: numerical methods for the planning problem. SIAM J Contr Optim 50: 77-109. doi: 10.1137/100790069
    [69] Achdou Y, Dolcetta IC (2010) Mean field games: numerical methods. SIAM J Numer Anal 48: 1136-1162. doi: 10.1137/090758477
    [70] Achdou Y, Perez V (2012) Iterative strategies for solving linearized discrete mean field games. Netw Heterogeneous Media 7: 197-217. doi: 10.3934/nhm.2012.7.197
    [71] Tembine H (2014) Nonasymptotic mean-field games. IEEE T Cybern 44: 2744-2756. doi: 10.1109/TCYB.2014.2315171
    [72] Porretta A (2013) On the planning problem for the mean-field games system. Dyn Games Appl.
    [73] Law K, Tembine H, Tempone R (2016) Deterministic mean-field ensemble Kalman filtering. SIAM J Sci Comput (SISC).
    [74] Pequito S, Aguiar AP, Sinopoli B, et al. (2011) Nonlinear estimation using mean field games. International Conference on NETwork Games, Control and Optimization, Paris, France.
    [75] Yin H, Mehta PG, Meyn SP, et al. (2012) Synchronization of coupled oscillators is a game. IEEE T Autom Contr 57: 920-935. doi: 10.1109/TAC.2011.2168082
    [76] Yin H, Mehta PG, Meyn SP, et al. (2011) Bifurcation analysis of a heterogeneous mean-field oscillator game. Proceedings of the IEEE Conference on Decision and Control, Orlando, 3895-3900.
    [77] Yin H, Mehta PG, Meyn SP, et al. (2011) On the efficiency of equilibria in mean-field oscillatorgames. Proceedings of the American Control Conference, San Francisco, 53540-5359.
    [78] Yin H, Mehta PG, Meyn SP, et al. (2010) Learning in mean-field oscillator games. Proceedings of the IEEE Conference on Decision and Control, Atlanta, 3125-3132.
    [79] Stella L, Bagagiolo F, Bauso D, et al. (2013) Opinion dynamics and stubbornness through mean-field games. 52nd IEEE Conference on Decision and Control Florence, Italy, 10-13.
    [80] Siwe AT, Tembine H (2016) Network security as public good: A mean-field-type game theory approach. 13th International Multi-Conference on Systems, Signals & Devices, Conference on Systems, Automation & Control, Leipzig, Germany.
    [81] Wang Y, Yu FR, Tang H, et al. (2014) A mean field game theoretic approach for security enhance ments in mobile ad hoc networks. IEEE T wirel commun 13.
    [82] Moon J, Basar T (2014) Discrete-time LQG mean field games with unreliable communication. Proceedings of the 53rd IEEE Conference on Decision and Control, Los Angeles, 2697-2702.
    [83] Bauso D, Tembine H, Basar T (2016) Robust mean field games. J Dyn Games Appl.
    [84] Tcheukam A, Tembine H (2016) Spatial mean-field games for combatting corruption propagation, 28th Chinese Control and Decision Conference (CCDC), Yinchuan, China.
    [85] Huang M, Caines PE, Malhame RP (2003) Individual and mass behavior in large population stochastic wireless power control problems: centralized and Nash equilibrium solutions, Proceeding of 42nd IEEE Conference Decision Control, Maui, HI, 98-103.
    [86] Meriaux F, Varma V, Lasaulce S (2012) Mean-field energy games in wireless networks, Proceeding of Asilomar Conference Signals, System, Compute, 2012.
    [87] Meriaux F, Lasaulce S, Tembine H (2012) Stochastic differential games and energy-efficient power control. Dyn Games Appl.
    [88] Tembine H, Vilanova P, Assaad M (2011) Mean field stochastic games for SINR-based medium access control, Proceeding of International Conference Performance Evaluation Methodologies Tools.
    [89] Tembine H, Altman E, El Azouzi R, et al. (2010) Evolutionary games in wireless networks. IEEE T Syst, Man, Cybern, Part B 40: 634-646. doi: 10.1109/TSMCB.2009.2034631
    [90] Tembine H, Tempone R, Vilanova P (2012) Mean-field games for cognitive radio networks, American Control Conference (ACC), 6388-6393.
    [91] Tembine H (2014) Energy-constrained mean-field games in wireless networks. Strateg Behav Environ 4: 187-221. doi: 10.1561/102.00000040
    [92] Couillet R, Perlaza SM, Tembine H (2012) A mean-field game analysis of electric vehicles in the smart grid, The 1st IEEE INFOCOM Workshop on Communications and Control for Sustainable Energy Systems: Green Networking and Smart Grids, Orlando.
    [93] Kamgarpour M, Tembine H (2013) A Bayesian mean-field game approach to supply demand analysis of the smart grid, First International Black Sea Conference on Communications and Networking (BlackSeaCom), 211-215.
    [94] Manjrekar M, Ramaswamy V, Shakkottai S (2014) A mean-field game approach to scheduling in cellular systems. INFOCOM 1554-1562
    [95] Hanif AF, Tembine H, Assaad M, et al. (2016) Mean-field games for resource sharing in cloudbased networks IEEE/ACM T Network 24: 624-637.
    [96] Hanif AF, Tembine H, Assaad M, et al. (2012) Cloud networking mean field games, IEEE 1st International Conference on Cloud Networking (CLOUDNET), 46-50.
    [97] Khiyaita A, Zbakh M (2013) Mean-field game among cloud computing end users. Secur Days (JNS3) 19: 1-5
    [98] Ghazzai H, Tembine H, Alouini MS (2017) Mobile user association for heterogeneous networks using optimal transport theory, Proceedings of The Sixth International Conference on Communications and Networking, ComNet'2017.
    [99] Iyer K, Johari R, Sundararajan M (2011) Mean-field equilibria of dynamic auctions with learning, EC'11, San Jose, California, USA.
    [100] Lyer K, Johari R, Sundararajan M (2014) Mean field equilibria of dynamic auctions with learning. Manage Sci 60: 2949-2970. doi: 10.1287/mnsc.2014.2018
    [101] Bauso D, Tembine H (2016) Crowd-averse cyber-physical systems: The paradigm of robust mean field games. IEEE T Autom Control 61: 2312-2317. doi: 10.1109/TAC.2015.2492038
    [102] Li J, Bhattacharyya R, Paul S, et al. (2016) Incentivizing sharing in realtime D2D streaming networks: A mean field game perspective. IEEE/ACM T Network.
    [103] Siwe AT, Tembine H (2016) Mean-field-type games on airline networks and airport queues, 13th International Multi-Conference on Systems, Signals and Devices. Conference on Systems, Au tomation and Control, Leipzig, Germany.
    [104] Aziz M, Caines PE (2014) Computational investigations of decentralized cellular network optimization via mean field control. IEEE CDC 5560-5567.
    [105] Gao J, Tembine H (2017) Distributed mean-field-type filter for vehicle tracking, 2017 American Control Conference, Seattle, WA, USA.
    [106] Gao J, Tembine H (2017) Correlative mean-field filter for sequential and spatial data processing, 17th IEEE International Conference on Smart Technologies, IEEE EUROCON, Ohrid, Macedonia.
    [107] Kachroo P, Agarwal S, Sastry S (2016) Inverse problem for non-viscous mean field control: Example from traffic. IEEE T Autom Control.
    [108] Tembine H (2017) Mean-field-type games, workshop on mean-field games, IPAM UCLA, Los Angeles, USA.
    [109] Gao J, Tembine H (2016) Distributed mean-field-type filters for big data assimilation, IEEE International Conference on Data Science Systems (DSS 2016), Sydney, Australia.
    [110] Li J, Xia B, Geng X, et al. (2015) Mean field games in nudge systems for societal networks, ACM Sigmetrics.
    [111] Rossi G, Tcheukam A, Tembine H (2016) How much does users' psychology matter in engineering mean-field-type games, Workshop on Game Theory and Experimental Methods.
    [112] Gao J, Tembine H (2017) Empathy and berge equilibria in the forwarding dilemma in relayenabled networks, The International Conference on Wireless Networks and Mobile Communications (WINCOM'17).
    [113] Grammatico S, Parise F, Colombino M, et al. (2016) Decentralized convergence to Nash equilib ria in constrained mean field control. IEEE T Autom Control.
    [114] Parise F, Colombino M, Grammatico S, et al. (2014) Mean-field constrained charging policy for large populations of plug-in electric vehicles, Proceeding of the IEEE Conference on Decision and Control, Los Angeles, California, USA, 5101-5106.
    [115] Parise F, Grammatico S, Gentile B, et al. (2016) Network aggregative games and distributed mean field control via consensus theory, Preprint.
    [116] Grammatico S, Gentile B, Parise F, et al. (2015) A mean field control approach for demand side management of large populations of thermostatically controlled loads, Control Conference (ECC), European, 3548-3553.
    [117] Bagagiolo F, Bauso D (2014) Mean-field games and dynamic demand management in power grids. Dyn Games Appl 4: 155-176. doi: 10.1007/s13235-013-0097-4
    [118] Chen H, Li Y, Louie R, et al. (2014) Autonomous demand side management based on energy consumption scheduling and instantaneous load billing: An aggregative game approach. IEEE T Smart Grid 5: 1744-1754. doi: 10.1109/TSG.2014.2311122
    [119] Ma Z, Callaway D, Hiskens I (2013) Decentralized charging control of large populations of plugin electric vehicles. IEEE T Control Syst Technol 21: 67-78. doi: 10.1109/TCST.2011.2174059
    [120] Kizilkale A, Mannor S, Caines P (2012) Large scale real-time bidding in the smart grid: A mean field framework, Proceeding of the IEEE Conference on Decision and Control, 3680-3687.
    [121] Couillet R, Perlaza SM, Tembine H, et al. (2012) Electrical vehicles in the smart grid: A mean field game analysis. IEEE J Sel Area Comm 30: 1086-1096. doi: 10.1109/JSAC.2012.120707
    [122] Tembine H (2015) Mean-field-type optimization for demand-supply management under operational constraints in smart grid. Energ Syst 1-24.
    [123] Tcheukam A, Tembine H (2016) Mean-field-type games for distributed power networks in presence of prosumers, 28th Chinese Control and Decision Conference (CCDC), Yinchuan, China.
    [124] Ye M, Hu G (2016) Game design and analysis for price based demand response: An aggregate game approach. IEEE T Cybern.
    [125] Kun D, Barooah P, Mehta PG (2012) Mean-field control for energy efficient buildings, American Control Conference (ACC), 3044-3049.
    [126] Kizilkale AC, Malhame RP (2014) Collective target tracking mean field control for electric space heaters, 22nd Mediterranean Conference on Control and Automation (MED) University of Palermo.
    [127] Klein S (1976) A design procedure for solar heating systems. PhD Thesis, Department of Chem ical Engineering, University of Wisconsin-Madison.
    [128] Gentile B, Grammatico S, Lygeros J (2015) Mean field modeling of large-scale energy systems,IFAC-PapersOnLine, 48: 918-919.
    [129] Kizilkale A, Malhame R (2013) Mean field based control of power system dispersed energy storage devices for peak load relief, IEEE Conference on Decision and Control (CDC), 4971-4976.
    [130] Tembine H, Zhu Q, Basar T (2014) Risk-sensitive mean-field games. IEEE T Autom Contr 59: 835-850. doi: 10.1109/TAC.2013.2289711
    [131] Smith JM (1982) Evolution and the theory of games. Cambridge University Press.
    [132] Tembine H (2015) Risk-sensitive mean-field-type games with p-norm drifts, Automatica 59: 224-237.
    [133] Fornasier M, Solombrino F (2014) Mean-field optimal control. ESAIM Contr Optim Calc Var 20: 1123-1152. doi: 10.1051/cocv/2014009
    [134] Andersson D, Djehiche B (2010) A maximum principle for SDEs of mean-field type. Appl Math Optim 63: 341-356.
    [135] Cisse AK, Tembine H (2014) Cooperative mean-field type games, 19th World Congress The International Federation of Automatic Control, Cape Town, South Africa.
    [136] Luo X, Tembine H (2016) Evolutionary coalitional games for random access control. Ann Oper Res 1-34.
    [137] Siwe AT, Tembine H (2016) On the distributed mean-variance paradigm, 13th International Multi-Conference on Systems, Signals and Devices, Conference on Systems, Automation and Control, Leipzig, Germany.
    [138] Tembine H (2009) Population games with networking applications, PhD Thesis, Universite d'Avignon.
    [139] Taylor P, Jonker L (1978) Evolutionarily stable strategies and game dynamics. Math Biosci 40: 145-156. doi: 10.1016/0025-5564(78)90077-9
    [140] Djehiche B, Tcheukam A, Tembine H (2016) A mean-field game of evacuation in a multi-level building, Special Session 118: Mean field games and applications, The 11th AIMS Conference on Dynamical Systems, Differential Equations and Applications, Orlando, Florida, USA.
    [141] Djehiche B, Tcheukam A, Tembine H (2016) Evacuation of multi-level building: Design, control and strategic flow, 35th Chinese Control Conference (CCC2016), Chengdu.
    [142] Djehiche B, Tcheukam A, Tembine H (2016) A mean-field game of evacuation in a multi-level building, 17th International Symposium on Dynamic Games and Applications, Urbino, Italy.
    [143] Djehiche B, Tcheukam A, Tembine H (2017) A mean-field game of evacuation in a multi-level building. IEEE T Autom Contr 62: 5154-5169. doi: 10.1109/TAC.2017.2679487
    [144] Duives D, Daamen W, Hoogendoorn S (2013) State-of-the-art crowd motion simulation models. Transport Res C-Emer 37: 193-209. doi: 10.1016/j.trc.2013.02.005
    [145] Helbing D, Johansson A (2010) Pedestrian, crowd and evacuation dynamics. Encyclopedia complex Syst Sci 16: 6476-6495.
    [146] Hoogendoorn SP, van Wageningen-Kessels F, Daamen W, et al. (2015) Continuum theory for pedestrian traffic flow: Local route choice modelling and its implications. Transport Res Procedia 7: 381-397. doi: 10.1016/j.trpro.2015.06.020
    [147] Degond P, Hua J (2013) Self-organized hydrodynamics with congestion and path formation in crowds, J Comput Phys.
    [148] Hughes R (2002) A continuum theory for the flow of pedestrians. Transport Res B: Meth 36: 507-535. doi: 10.1016/S0191-2615(01)00015-7
    [149] Villani C (2009) Optimal transport: old and new, Grundlehren der mathematischen Wissenschaften, Springer Book, 338.
    [150] Bellomo N, Dogbe C (2011) On the modelling of traffic and crowds, A survey of models, speculations, and perspectives. SIAM Rev 53: 409-463. doi: 10.1137/090746677
    [151] Lachapelle A, Wolfram MT (2011) On a mean field game approach modeling congestion and aversion in pedestrian crowds. Transport Res B-Meth 45: 1572-1589 doi: 10.1016/j.trb.2011.07.011
    [152] Burger M, Di Francesco M, Markowich PA, et al. (2014) Mean field games with nonlinear mobilities in pedestrian dynamics. DCDS 19: 1311–1333. doi: 10.3934/dcdsb.2014.19.1311
    [153] Burger M, Di Francesco M, Markowich P, et al. (2013) On a mean field game optimal control approach modeling fast exit scenarios in human crowds, 52nd IEEE Conference on Decision and Control, Firence, Italy.
    [154] Gomes DA, Patrizi S (2015) Obstacle mean-field game problem. Interface Free Bound 17: 55-68. doi: 10.4171/IFB/333
    [155] Tembine H, Vilanova P, Debbah M (2012) Noisy mean field game model for malware propagation in opportunistic networks. Game Theor Netw 459-474.
    [156] Kuramoto Y (1975) Self-entrainment of a population of coupled non-linear oscillators international symposium on mathematical problems in theoretical physics, Lecture Notes in Physics, 39: 420-422, New York: Springer.
    [157] Xu Z, Egerstedt M, Droge G, et al. (2013) Balanced deployment of multiple robots using a modified Kuramoto model, American Control Conference (ACC) Washington, DC, USA.
    [158] Djehiche B, Tembine H, Tempone R (2015) A stochastic maximum principle for risk-sensitive mean-field type control. IEEE T Autom Contr 60: 2640-2649. doi: 10.1109/TAC.2015.2406973
    [159] Djehiche B, Tembine H (2016) Risk-sensitive mean-field type control under partial observation, Stochastics of Environmental and Financial Economics, vol 138 of the series Springer Proceedings in Mathematics and Statistics.
    [160] Tembine H (2015) Uncertainty quantification in mean-field-type teams and games. IEEE CDC, 4418-4423.
    [161] Jourdain B, Meleard S, Woyczynski W (2008) Nonlinear SDEs driven by Lévy processes and related PDEs. Alea 4: 1-29.
    [162] Buckdahn R, Djehiche B, Li J (2011) A general stochastic maximum principle for SDEs of mean-field type. Appl Math Opt 64: 197-216. doi: 10.1007/s00245-011-9136-y
    [163] Cucker F, Smale S (2007) Emergent behavior in flocks. IEEE T Autom Contr 52: 852-862. doi: 10.1109/TAC.2007.895842
    [164] Millikan FR (2012) Joseph Henry: Father of weather service? Joseph Henry Papers Project, Smithsonian Institution.
    [165] Henson PM (2006) Spencer F Baird's Vision for a National Museum.
    [166] Krause A, Horvitz E, Kansal A, et al. (2008) Toward Community Sensing, 481-492, St. Louis, MO.
    [167] Schwartz G, Tembine H, Amin S, et al. (2014) Demand response scheme based on lottery-like rebates, Proceedings of the 19th IFAC World Congress.
    [168] Tembine H (2015) Learning and game theory lab: the game of life. Int Innovat 49-51.
    [169] Tembine H (2011) Large-scale games in large-scale systems, Proceedings of the 5th International Conference on Performance Evaluation Methodologies and Tools, 9-17.
    [170] Bauso D, Tembine H, Bas?ar T (2016) Opinion dynamics in social networks through mean-field games. SIAM J Contr Opt 54: 3225-3257. doi: 10.1137/140985676
    [171] Tembine H (2017) Reverse Ishikawa-Nesterov learning scheme for fractional mean-field games, 20th World Congress of the International Federation of Automatic Control (IFAC), Toulouse, France.
    [172] 173. Tembine H (2017) The price of simplicity of mean-field-type optimization is unbounded, Conference on Communication, Signal Processing and Information Technology, International MultiConference on Systems, Signals and Devices.
    [173] 174. Tembine H (2017) Quantile-based mean-field games, Conference on Power Systems and Smart Energies, International Multi-Conference on Systems, Signals and Devices.
    [174] 175. Tembine H (2017) Payoff measurement noise in risk-sensitive mean-field-type games, 29th Chinese Control and Decision Conference, Chongqing, China.
    [175] 176. Duncan TE, Tembine H (2017) Linear-quadratic mean-field-type games: A direct method, Preprint.
    [176] 177. Duncan TE, Tembine H (2017) Linear-quadratic mean-field-type games with common noise: A direct method, Preprint.
    [177] 178. Duncan TE, Tembine H (2017) Other-regarding payoffs in linear-quadratic mean-field-type games with common noise: A direct method, Preprint.
    [178] 179. Tembine H, Djehiche B, Yam P, et al. (2017) Mean-field-type games with jumps and switching regimes, Preprint.
    [179] 180. Dubey P (1986) Inefficiency of Nash equilibria. Math Oper Res 11: 1-8. doi: 10.1287/moor.11.1.1
    [180] 181. Koutsoupias E, Papadimitriou C (1999) Worst-case equilibria. Proceeding STACS'99 Proceedings of the 16th annual conference on Theoretical aspects of computer science, 404-413.
    [181] 182. Koutsoupias E, Papadimitriou C (2009) Worst-case equilibria. Comput Sci Rev 3: 65-69. doi: 10.1016/j.cosrev.2009.04.003
    [182] 183. Tanimoto J (2015) Fundamentals of evolutionary game theory and its applications, Springer.
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