Approximate Markov-Nash Equilibria for Discrete-Time Risk-Sensitive Mean-Field Games

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.Crossref, Google Scholar
• [2] Aliprantis CD, Border KC (2006) Infinite Dimensional Analysis, 3rd ed. (Springer, Berlin).Google Scholar
• [3] Avila-Godoy G, Brau A, Fernandez-Gaucherand E (1997) Controlled Markov chains with discounted risk-sensitive criteria: Applications to machine replacement. Proc. 36th IEEE Conf. Decision Control, vol. 2 (IEEE, Piscataway, NJ), 1115–1120.Google Scholar
• [4] Bauerle N, Rieder U (2014) More risk-sensitive Markov decision processes. Math. Oper. Res. 39(1):105–120.Link, Google Scholar
• [5] Bensoussan A, Frehse J, Yam P (2013) Mean Field Games and Mean Field Type Control Theory (Springer, New York).Crossref, Google Scholar
• [6] Billingsley P (1999) Convergence of Probability Measures, 2nd ed. (Wiley, New York).Crossref, Google Scholar
• [7] 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
• [8] Bogachev VI (2007) Measure Theory, vol. II (Springer, Berlin).Crossref, Google Scholar
• [9] Budhiraja A, Majumder AP (2015) Long time results for a weakly interacting particle system in discrete time. Stochastic Anal. Appl. 33(3):429–463.Crossref, Google Scholar
• [10] Cardaliaguet P (2011) Notes on mean-field games. Working paper, Université Paris-Dauphine, Paris.Google Scholar
• [11] Carmona R, Delarue F (2013) Probabilistic analysis of mean-field games. SIAM J. Control Optim. 51(4):2705–2734.Crossref, Google Scholar
• [12] Chung K, Sobel MJ (1987) Discounted MDP’s: Distribution functions and exponential utility maximization. SIAM J. Control Optim. 25(1):49–62.Crossref, Google Scholar
• [13] Dai Pra P, Meneghini L, Runggaldier WJ (1996) Connections between stochastic control and dynamic games. Math. Control Signals Systems 9(4):303–326.Crossref, Google Scholar
• [14] Djehiche B, Tembine H (2016) Risk-sensitive mean-field type control under partial observation. Benth FE, Di Nunno G, eds. Stochastics of Environmental and Financial Economics (Springer, Cham, Switzerland), 243–263.Google Scholar
• [15] Dudley RM (2004) Real Analysis and Probability (Cambridge University Press, New York).Google Scholar
• [16] Elliot R, Li X, Ni Y (2013) Discrete time mean-field stochastic linear-quadratic optimal control problems. Automatica J. IFAC 49(11):3222–3233.Crossref, Google Scholar
• [17] Gomes DA, Saúde J (2014) Mean field games models - a brief survey. Dynam. Games Appl. 4(2):110–154.Crossref, Google Scholar
• [18] Gomes DA, Mohr J, Souza RR (2010) Discrete time, finite state space mean field games. J. Math. Pures Appl. 93(3):308–328.Crossref, Google Scholar
• [19] Hernandez-Hernandez D, Marcus SI (1996) Risk sensitive control of Markov processes in countable state space. Systems Control Lett. 29(3):147–155.Crossref, Google Scholar
• [20] Hernández-Lerma O, Lasserre JB (1996) Discrete-Time Markov Control Processes: Basic Optimality Criteria (Springer, New York).Crossref, Google Scholar
• [21] Howard RA, Matheson JE (1972) Risk-sensitive Markov decision processes. Management Sci. 18(7):356–369.Link, Google Scholar
• [22] Huang M (2010) Large-population LQG games involving major player: The Nash certainity equivalence principle. SIAM J. Control Optim. 48(5):3318–3353.Crossref, Google Scholar
• [23] Huang M, Caines PE, Malhamé RP (2007) Large-population cost coupled LQG problems with nonuniform agents: Individual-mass behavior and decentralizedε-Nash equilibria. IEEE Trans. Automat. Control 52(9):1560–1571.Crossref, Google Scholar
• [24] Huang M, Malhamé RP, Caines PE (2006) Large population stochastic dynamic games: Closed loop McKean-Vlasov sysyems and the Nash certainity equivalence principle. Comm. Inform. Systems 6(3):221–252.Crossref, Google Scholar
• [25] Jaskiewicz A (2007) Average optimality for risk-sensitive control with general state space. Ann. Appl. Probab. 17(2):654–675.Crossref, Google Scholar
• [26] Jovanovic B, Rosenthal RW (1988) Anonymous sequential games. J. Math. Econom. 17(1):77–87.Crossref, Google Scholar
• [27] Langen HJ (1981) Convergence of dynamic programming models. Math. Oper. Res. 6(4):493–512.Link, Google Scholar
• [28] Lasry J, Lions P (2007) Mean field games. Japanese J. Math. 2(1):229–260.Crossref, Google Scholar
• [29] Moon J, Başar 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) (IEEE, Piscataway, NJ), 4779–4784.Google Scholar
• [30] Moon J, Başar T (2016) Discrete-time mean field Stackelberg games with a large number of followers. Proc. 2016 IEEE 55th Conf. Decision Control (IEEE, Piscataway, NJ), 3578–3583.Google Scholar
• [31] Moon J, Başar T (2016) Robust mean field games for coupled Markov jump linear systems. Internat. J. Control 89(7):1367–1381.Crossref, Google Scholar
• [32] Moon J, Başar T (2017) Linear quadratic risk-sensitive and robust mean field games. IEEE Trans. Automat. Control 62(3):1062–1077.Crossref, Google Scholar
• [33] Nourian M, Nair GN (2013) Linear-quadratic-Gaussian mean field games under high rate quantization. Proc. 52nd IEEE Conf. Decision Control (IEEE, Piscataway, NJ), 1898–1903.Google Scholar
• [34] Parthasarathy KR (1967) Probability Measures on Metric Spaces (American Mathematical Society, Providence, RI).Crossref, Google Scholar
• [35] 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.Google Scholar
• [36] 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.Crossref, Google Scholar
• [37] Şen N, Caines PE (2016) Mean field game theory with a partially observed major agent. SIAM J. Control Optim. 54(6):3174–3224.Crossref, Google Scholar
• [38] Şen N, Caines PE (2016) On mean field games and nonlinear filtering for agents with individual-state partial observations. 2016 American Control Conf. (IEEE, Piscataway, NJ), 4681–4686.Google Scholar
• [39] Serfozo R (1982) Convergence of Lebesgue integrals with varying measures. Sankhya Ser. A 44(3):380–402.Google Scholar
• [40] Tembine H (2015) Risk-sensitive mean-field-type games with Lp-norm drifts. Automatica J. IFAC 59:224–237.Crossref, Google Scholar
• [41] Tembine H, Zhu Q, Başar T (2014) Risk-sensitive mean field games. IEEE Trans. Automat. Control 59(4):835–850.Crossref, Google Scholar
• [42] Villani C (2009) Optimal Transport: Old and New (Springer, Berlin).Crossref, Google Scholar