Linear Mean-Field Games with Discounted Cost

Published Online:https://doi.org/10.1287/moor.2023.0148

References

  • [1] Adlakha S, Johari R, Weintraub GY (2015) Equilibria of dynamic games with many players: Existence, approximation, and market structure. J. Econom. Theory 156:269–316.CrossrefGoogle Scholar
  • [2] Aliprantis CD, Border KC (2006) Infinite Dimensional Analysis, 3rd ed. (Springer, Berlin, Heidelberg).Google Scholar
  • [3] Anahtarcı B, Karıksız CD, Saldi N (2020) Value iteration algorithm for mean-field games. Systems Control Lett. 143:104744.CrossrefGoogle Scholar
  • [4] Anahtarci B, Kariksiz CD, Saldi N (2022) Q-learning in regularized mean-field games. Dynam. Games Appl. 13:89–117.Google Scholar
  • [5] Anahtarci B, Kariksiz CD, Saldi N (2023) Learning mean-field games with discounted and average costs. J. Machine Learn. Res. 24(17):1–59.Google Scholar
  • [6] Anahtarci B, Kariksiz CD, Saldi N (2024) Maximum causal entropy inverse reinforcement learning for mean-field games. Preprint, submitted January 12, https://arxiv.org/abs/2401.06566.Google Scholar
  • [7] Bapat RB, Raghavan TES (1997) Nonnegative Matrices and Applications. Encyclopedia of Mathematics and Its Applications, vol. 64 (Cambridge University Press, Cambridge, UK).CrossrefGoogle Scholar
  • [8] Başar T (2018) A consensus problem in mean field setting with noisy measurements of target. 2018 Annual Amer. Control Conf. (ACC) (IEEE, New York), 6521–6526.Google Scholar
  • [9] Bensoussan A, Frehse J, Yam P (2013) Mean Field Games and Mean Field Type Control Theory (Springer, New York).CrossrefGoogle Scholar
  • [10] Billingsley P (1995) Probability and Measure, 3rd ed. (Wiley, New York).Google Scholar
  • [11] Biswas A (2015) Mean field games with ergodic cost for discrete time Markov processes. Preprint, submitted October 30, https://arxiv.org/abs/1510.08968.Google Scholar
  • [12] Cardaliaguet P (2011) Notes on mean-field games. Technical report, Université Paris - DAUPHINE, France.Google Scholar
  • [13] Carmona R, Delarue F (2013) Probabilistic analysis of mean-field games. SIAM J. Control Optim. 51(4):2705–2734.CrossrefGoogle Scholar
  • [14] Dreves A, Facchinei F, Kanzow C, Sagratella S (2011) On the solution of the KKT conditions of generalized Nash equilibrium problems. SIAM J. Optim. 21(3):1082–1108.CrossrefGoogle Scholar
  • [15] Dudley RM (2004) Real Analysis and Probability (Cambridge University Press, Cambridge, UK).Google Scholar
  • [16] Elliot R, Li X, Ni Y (2013) Discrete time mean-field stochastic linear-quadratic optimal control problems. Automatica 49(11):3222–3233.CrossrefGoogle Scholar
  • [17] Facchinei F, Kanzow C (2010) Generalized Nash equilibrium problems. Ann. Oper. Res. 175:177–211.CrossrefGoogle Scholar
  • [18] Facchinei F, Pang J-S (2003) Finite-Dimensional Variational Inequalities and Complementarity Problems (Springer, New York).Google Scholar
  • [19] Fournier N, Guillin A (2015) On the rate of convergence in Wasserstein distance of the empirical measure. Probab. Theory Related Fields 162(3):707–738.CrossrefGoogle Scholar
  • [20] Gomes DA, Saúde J (2014) Mean field games models - A brief survey. Dynam. Games Appl. 4(2):110–154.CrossrefGoogle Scholar
  • [21] Gomes DA, Mohr J, Souza RR (2010) Discrete time, finite state space mean field games. J. Math. Pures Appl. 93(3):308–328.CrossrefGoogle Scholar
  • [22] Gottlieb L-A, Kontorovich A, Krauthgamer R (2016) Adaptive metric dimensionality reduction. Theoret. Comput. Sci. 620:105–118.CrossrefGoogle Scholar
  • [23] Gottlieb L-A, Kontorovich A, Krauthgamer R (2017) Efficient regression in metric spaces via approximate Lipschitz extension. IEEE Trans. Inform. Theory 63(8):4838–4849.CrossrefGoogle Scholar
  • [24] Hernández-Lerma O, González-Hernández J (2000) Constrained Markov control processes in Borel spaces: The discounted case. Math. Methods Oper. Res. 52:271–285.CrossrefGoogle Scholar
  • [25] Hernández-Lerma O, Lasserre JB (1996) Discrete-Time Markov Control Processes: Basic Optimality Criteria (Springer, New York).CrossrefGoogle Scholar
  • [26] Huang M (2010) Large-population LQG games involving a major player: The Nash certainty equivalence principle. SIAM J. Control Optim. 48(5):3318–3353.CrossrefGoogle Scholar
  • [27] Huang M, Ma Y (2019) Binary mean field stochastic games: Stationary equilibria and comparative statics. Yin G, Zhang Q, eds. Modeling, Stochastic Control, Optimization, and Applications. The IMA Volumes in Mathematics and Its Applications, vol. 164 (Springer, Cham, Switzerland), 283–313.CrossrefGoogle Scholar
  • [28] Huang M, Caines PE, Malhamé RP (2007) Large-population cost-coupled LQG problems with nonuniform agents: Individual-mass behavior and decentralized ϵ-Nash equilibria. IEEE Trans. Automatic Control 52(9):1560–1571.CrossrefGoogle Scholar
  • [29] Huang M, Malhamé RP, Caines PE (2006) Large population stochastic dynamic games: Closed-loop McKean-Vlasov systems and the Nash certainty equivalence principle. Comm. Inform. Systems 6(3):221–252.CrossrefGoogle Scholar
  • [30] Lasry J, Lions P (2007) Mean field games. Japanese J. Math. 2:229–260.CrossrefGoogle Scholar
  • [31] Light B, Weintraub GY (2022) Mean field equilibrium: Uniqueness, existence, and comparative statics. Oper. Res. 70(1):585–605.LinkGoogle Scholar
  • [32] Monteiro RDC, Pang J-S (1999) A potential reduction Newton method for constrained equations. SIAM J. Optim. 9(3):729–754.CrossrefGoogle Scholar
  • [33] Moon J, Basar T (2015) Discrete-time decentralized control using the risk-sensitive performance criterion in the large population regime: A mean field approach. 2015 Amer. Control Conf. (ACC 2015) (IEEE, New York), 4779–4784.Google Scholar
  • [34] Moon J, Başar T (2016) Discrete-time stochastic Stackelberg dynamic games with a large number of followers. 2016 IEEE 55th Conf. Decision Control (CDC) (IEEE, New York), 3578–3583.Google Scholar
  • [35] Moon J, Başar T (2016) Robust mean field games for coupled Markov jump linear systems. Internat. J. Control 89(7):1367–1381.CrossrefGoogle Scholar
  • [36] Moon J, Başar T (2018) Linear quadratic mean field Stackelberg differential games. Automatica 97:200–213.CrossrefGoogle Scholar
  • [37] Moon J, Başar T (2019) Risk-sensitive mean field games via the stochastic maximum principle. Dynam. Games Appl. 9:1100–1125.CrossrefGoogle Scholar
  • [38] Nourian M, Nair GN (2013) Linear-quadratic-Gaussian mean field games under high rate quantization. 52nd IEEE Conf. Decision Control (IEEE, New York), 1898–1903.Google Scholar
  • [39] Saldi N (2020) Discrete-time average-cost mean-field games on Polish spaces. Turkish J. Math. 44(2):463–480.Google Scholar
  • [40] Saldi N (2023) Linear mean-field games with discounted cost. Preprint, submitted January 15, https://arxiv.org/abs/2301.06074.Google Scholar
  • [41] Saldi N, Başar T, Raginsky M (2018) Markov–Nash equilibria in mean-field games with discounted cost. SIAM J. Control Optim. 56(6):4256–4287.CrossrefGoogle Scholar
  • [42] Saldi N, Başar T, Raginsky M (2019) Approximate Nash equilibria in partially observed stochastic games with mean-field interactions. Math. Oper. Res. 44(3):1006–1033.LinkGoogle Scholar
  • [43] Saldi N, Başar T, Raginsky M (2020) Approximate Markov-Nash equilibria for discrete-time risk-sensitive mean-field games. Math. Oper. Res. 45(4):1596–1620.LinkGoogle Scholar
  • [44] Saldi N, Yüksel S, Linder T (2017) On the asymptotic optimality of finite approximations to Markov decision processes with Borel spaces. Math. Oper. Res. 42(4):945–978.LinkGoogle Scholar
  • [45] Subramanian J, Mahajan A (2019) Reinforcement learning in stationary mean-field games. Proc. 18th Internat. Conf. Autonomous Agents Multiagent Systems (International Foundation for Autonomous Agents and Multiagent Systems, Richland, SC), 251–259.Google Scholar
  • [46] Tembine H, Zhu Q, Basar T (2014) Risk-sensitive mean field games. IEEE. Trans. Automatic Control 59(4):835–850.CrossrefGoogle Scholar
  • [47] Villani C (2009) Optimal Transport: Old and New (Springer, Berlin, Heidelberg).CrossrefGoogle Scholar
  • [48] Weintraub G, Benkard L, Van Roy B (2005) Oblivious equilibrium: A mean field approximation for large-scale dynamic games. Weiss Y, Schölkopf B, Platt J, eds. Advances in Neural Information Processing Systems, vol. 18 (MIT Press, Cambridge, MA).Google Scholar
  • [49] Weintraub GY, Benkard CL, Van Roy B (2008) Markov perfect industry dynamics with many firms. Econometrica 76(6):1375–1411.CrossrefGoogle Scholar
  • [50] Weintraub GY, Benkard CL, Van Roy B (2010) Computational methods for oblivious equilibrium. Oper. Res. 58(4-part-2):1247–1265.LinkGoogle Scholar
  • [51] Wiecek P (2020) Discrete-time ergodic mean-field games with average reward on compact spaces. Dynam. Games Appl. 10(1):222–256.CrossrefGoogle Scholar
  • [52] Więcek P, Altman E (2015) Stationary anonymous sequential games with undiscounted rewards. J. Optim. Theory Appl. 166(2):686–710.CrossrefGoogle Scholar
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