메뉴 건너뛰기




Volumn 6, Issue 3, 2019, Pages 221-239

Discrete mean field games: Existence of equilibria and convergence

Author keywords

Discrete state space; Mean field game

Indexed keywords

CONDITION; CONTINOUS TIME; DISCRETE STATE SPACE; DISCRETE TIME; FINITE STATE SPACES; FINITE TIME HORIZON; INFINITE TIME HORIZON; MEAN-FIELD; MEAN-FIELD GAMES; N-PLAYER GAMES;

EID: 85075781529     PISSN: None     EISSN: 21646074     Source Type: Journal    
DOI: 10.3934/jdg.2019016     Document Type: Article
Times cited : (862)

References (38)
  • 3
    • 85044051351 scopus 로고    scopus 로고
    • Strong solutions for time-dependent mean field games with non-separable hamiltonians
    • D. M. Ambrose, Strong solutions for time-dependent mean field games with non-separable hamiltonians, Journal de Mathe´matiques Pures et Appliquées, 113 (2018), 141-154
    • (2018) Journal de Mathe´matiques Pures et Appliquées , vol.113 , pp. 141-154
    • Ambrose, D.M.1
  • 4
    • 84996455505 scopus 로고    scopus 로고
    • An epsilon-nash equilibrium for non-linear markov games of mean-field-type on finite spaces
    • R. Basna, A. Hilbert and V. N. Kolokoltsov, An epsilon-nash equilibrium for non-linear markov games of mean-field-type on finite spaces, Commun. Stoch. Anal, 8 (2014), 449-468
    • (2014) Commun. Stoch. Anal , vol.8 , pp. 449-468
    • Basna, R.1    Hilbert, A.2    Kolokoltsov, V.N.3
  • 5
    • 85056088593 scopus 로고    scopus 로고
    • Analysis of a finite state many player game using its master equation
    • E. Bayraktar and A. Cohen, Analysis of a finite state many player game using its master equation, SIAM J. Control Optim., 56 (2018), 3538-3568
    • (2018) SIAM J. Control Optim , vol.56 , pp. 3538-3568
    • Bayraktar, E.1    Cohen, A.2
  • 6
    • 53649095038 scopus 로고    scopus 로고
    • A class of mean field interaction models for computer and communication systems
    • M. Benaim and J.-Y. Le Boudec, A class of mean field interaction models for computer and communication systems, Performance Evaluation, 65 (2008), 823-838
    • (2008) Performance Evaluation , vol.65 , pp. 823-838
    • Benaim, M.1    Le Boudec, J.-Y.2
  • 11
    • 84925426147 scopus 로고    scopus 로고
    • A probabilistic weak formulation of mean field games and applications
    • R. Carmona, D. Lacker, et al., A probabilistic weak formulation of mean field games and applications, The Annals of Applied Probability, 25 (2015), 1189-1231
    • (2015) The Annals of Applied Probability , vol.25 , pp. 1189-1231
    • Carmona, R.1    Lacker, D.2
  • 14
    • 84960608031 scopus 로고
    • The existence of equilibrium in discontinuous economic games
    • P. Dasgupta and E. Maskin, The existence of equilibrium in discontinuous economic games, i: Theory, Review of Economic Studies, 53 (1986), 1-26
    • (1986) i: Theory, Review of Economic Studies , vol.53 , pp. 1-26
    • Dasgupta, P.1    Maskin, E.2
  • 15
    • 85011304362 scopus 로고    scopus 로고
    • Are mean-field games the limits of finite stochastic games?
    • J. Doncel, N. Gast and B. Gaujal, Are mean-field games the limits of finite stochastic games?, SIGMETRICS Perform. Eval. Rev., 44 (2016), 18-20
    • (2016) SIGMETRICS Perform. Eval. Rev , vol.44 , pp. 18-20
    • Doncel, J.1    Gast, N.2    Gaujal, B.3
  • 16
    • 84972535636 scopus 로고
    • Equilibrium in a stochastic n-person game
    • A. M. Fink, Equilibrium in a stochastic n-person game, J. Sci. Hiroshima Univ. Ser. A-I Math., 28 (1964), 89-93
    • (1964) J. Sci. Hiroshima Univ. Ser. A-I Math , vol.28 , pp. 89-93
    • Fink, A.M.1
  • 17
    • 0000028492 scopus 로고
    • The folk theorem in repeated games with discounting or with incomplete information
    • D. Fudenberg and E. Maskin, The folk theorem in repeated games with discounting or with incomplete information, Econometrica, 54 (1986), 533-554
    • (1986) Econometrica , vol.54 , pp. 533-554
    • Fudenberg, D.1    Maskin, E.2
  • 18
    • 79951558493 scopus 로고    scopus 로고
    • A mean field approach for optimization in discrete time
    • N. Gast and B. Gaujal, A mean field approach for optimization in discrete time, Discrete Event Dynamic Systems, 21 (2011), 63-101
    • (2011) Discrete Event Dynamic Systems , vol.21 , pp. 63-101
    • Gast, N.1    Gaujal, B.2
  • 21
    • 84947474862 scopus 로고    scopus 로고
    • Time-dependent mean-field games with logarithmic nonlinear-ities
    • D. A. Gomes and E. Pimentel, Time-dependent mean-field games with logarithmic nonlinear-ities, SIAM Journal on Mathematical Analysis, 47 (2015), 3798-3812
    • (2015) SIAM Journal on Mathematical Analysis , vol.47 , pp. 3798-3812
    • Gomes, D.A.1    Pimentel, E.2
  • 23
    • 85045388079 scopus 로고    scopus 로고
    • Regularity for mean-field games systems with initial-initial boundary conditions: The subquadratic case
    • D. A. Gomes and E. A. Pimentel, Regularity for mean-field games systems with initial-initial boundary conditions: The subquadratic case, In Dynamics, Games and Science, 2015, 291-304
    • (2015) In Dynamics, Games and Science , pp. 291-304
    • Gomes, D.A.1    Pimentel, E.A.2
  • 25
    • 1842512912 scopus 로고    scopus 로고
    • Springer Monographs in Mathematics. Springer-Verlag, New York
    • A. Granas and J. Dugundji, Fixed Point Theory, Springer Monographs in Mathematics. Springer-Verlag, New York, 2003
    • (2003) Fixed Point Theory
    • Granas, A.1    Dugundji, J.2
  • 26
    • 84941422568 scopus 로고    scopus 로고
    • Existence and uniqueness result for mean field games with congestion effect on graphs
    • O. Guéant, Existence and uniqueness result for mean field games with congestion effect on graphs, Applied Mathematics & Optimization, 72 (2014), 291-303
    • (2014) Applied Mathematics & Optimization , vol.72 , pp. 291-303
    • Guéant, O.1
  • 28
    • 84873949201 scopus 로고    scopus 로고
    • Mean field stochastic games with discrete states and mixed players
    • M. Huang, Mean field stochastic games with discrete states and mixed players, In Game Theory for Networks, Springer, 2012, 138-151
    • (2012) In Game Theory for Networks, Springer , pp. 138-151
    • Huang, M.1
  • 29
    • 39549087376 scopus 로고    scopus 로고
    • Large population stochastic dynamic games: Closed-loop mckean vlasov systems and the nash certainty equivalence principle
    • Special issue in honor of the 65th birthday of Tyrone Duncan
    • M. Huang, R. Malhame and P. Caines, Large population stochastic dynamic games: Closed-loop mckean vlasov systems and the nash certainty equivalence principle, Communications in Information and Systems, 6 (2006), 221-252, Special issue in honor of the 65th birthday of Tyrone Duncan
    • (2006) Communications in Information and Systems , vol.6 , pp. 221-252
    • Huang, M.1    Malhame, R.2    Caines, P.3
  • 30
    • 84936864615 scopus 로고    scopus 로고
    • A general characterization of the mean field limit for stochastic differential games
    • D. Lacker, A general characterization of the mean field limit for stochastic differential games, Probability Theory and Related Fields, 165 (2016), 581-648
    • (2016) Probability Theory and Related Fields , vol.165 , pp. 581-648
    • Lacker, D.1
  • 31
  • 32
    • 33751077273 scopus 로고    scopus 로고
    • Jeux à champ moyen. ii-horizon fini et contr^ole optimal
    • J.-M. Lasry and P.-L. Lions, Jeux à champ moyen. ii-horizon fini et contr^ole optimal, Comptes Rendus Mathématique, 343 (2006), 679-684
    • (2006) Comptes Rendus Mathématique , vol.343 , pp. 679-684
    • Lasry, J.-M.1    Lions, P.-L.2
  • 34
    • 38249018546 scopus 로고
    • Anonymous repeated games with a large number of players and random out-comes
    • H. Sabourian, Anonymous repeated games with a large number of players and random out-comes, Journal Of Economic Theory, 51 (1990), 92-110
    • (1990) Journal Of Economic Theory , vol.51 , pp. 92-110
    • Sabourian, H.1
  • 36
    • 80053146604 scopus 로고    scopus 로고
    • Mean field stochastic games: Convergence q/h-learning and optimality
    • H. Tembine, Mean field stochastic games: Convergence, q/h-learning and optimality, In American Control Conference (ACC), 2011, IEEE, 2011, 2423-2428
    • (2011) In American Control Conference (ACC), 2011, IEEE , pp. 2423-2428
    • Tembine, H.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.