Approximate Nash Equilibria in Partially Observed Stochastic Games with Mean-Field Interactions
Published Online:30 May 2019https://doi.org/10.1287/moor.2018.0957
References
- [1] (2015) Equilibria of dynamic games with many players: Existence, approximation, and market structure. J. Econom. Theory 156(3):269–316.Crossref, Google Scholar
- [2] (2006) Infinite Dimensional Analysis, 3rd ed. (Springer-Verlag, Berlin).Google Scholar
- [3] (2013) Mean Field Games and Mean Field Type Control Theory (Springer, New York).Crossref, Google Scholar
- [4] (1978) Stochastic Optimal Control: The Discrete Time Case (Academic Press, New York).Google Scholar
- [5] (1995) Probability and Measure, 3rd ed. (Wiley, New York).Google Scholar
- [6] (1999) Convergence of Probability Measures, 2nd ed. (Wiley, New York).Crossref, Google Scholar
- [7] (2015) Mean field games with ergodic cost for discrete time Markov processes. Working paper, IISER, Pune, India.Google Scholar
- [8] (2007) Measure Theory, vol. 2 (Springer, New York).Crossref, Google Scholar
- [9] (2015) Long time results for a weakly interacting particle system in discrete time. Stochastic Anal. Appl. 33(3):429–463.Crossref, Google Scholar
- [10] (2011) Notes on mean-field games (from P.-L. Lions’ lectures at Collège de France). Lecture notes, April–May 2010, Tor Vergata, Rome.Google Scholar
- [11] (2013) Probabilistic analysis of mean-field games. SIAM J. Control Optim. 51(4):2705–2734.Crossref, Google Scholar
- [12] (2015) A probabilistic weak formulation of mean field games and applications. Ann. Appl. Probab. 25(3):1189–1231.Crossref, Google Scholar
- [13] (2004) Real Analysis and Probability (Cambridge University Press, Cambridge, UK).Google Scholar
- [14] (2016) Partially observable total-cost Markov decision process with weakly continuous transition probabilities. Math. Oper. Res. 41(2):656–681.Link, Google Scholar
- [15] (2014) Mean field games models—A brief survey. Dynam. Games Appl. 4(2):110–154.Crossref, Google Scholar
- [16] (2010) Discrete time, finite state space mean field games. J. Math. Pures Appl. 93(3):308–328.Crossref, Google Scholar
- [17] (1989) Adaptive Markov Control Processes (Springer-Verlag, Berlin).Crossref, Google Scholar
- [18] (1996) Discrete-Time Markov Control Processes: Basic Optimality Criteria (Springer-Verlag, New York).Crossref, Google Scholar
- [19] (1970) Foundations of Non-stationary Dynamic Programming with Discrete Time Parameter (Springer-Verlag, Berlin).Crossref, Google Scholar
- [20] (2014) A class of mean-field LQG games with partial information. Working paper, Hong Kong Polytechnic University, Hong Kong.Google Scholar
- [21] (2010) Large-population LQG games involving a major player: The Nash certainty equivalence principle. SIAM J. Control Optim. 48(5):3318–3353.Crossref, Google Scholar
- [22] (2006) Distributed multi-agent decision-making with partial observations: Asymptotic Nash equilibria. Proc. 17th Internat. Sympos. Math. Theory Networks Systems, Kyoto, Japan, 2725–2730.Google Scholar
- [23] (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.Crossref, Google Scholar
- [24] (2006) Large population stochastic dynamic games: Closed loop McKean-Vlasov systems and the Nash certainity equivalence principle. Comm. Inform. Systems 6(3):221–252.Crossref, Google Scholar
- [25] (1988) Anonymous sequential games. J. Math. Econom. 17(1):77–87.Crossref, Google Scholar
- [26] (2015) Stochastic differential mean field game theory. Unpublished doctoral dissertation, Princeton University, Princeton, NJ.Google Scholar
- [27] (1981) Convergence of dynamic programming models. Math. Oper. Res. 6(4):493–512.Link, Google Scholar
- [28] (2007) Mean field games. Japan. J. Math. 2(1):229–260.Crossref, Google Scholar
- [29] (2016) Robust mean field games for coupled Markov jump linear systems. Internat. J. Control 89(7):1367–1381.Crossref, Google Scholar
- [30] (1967) Probability Measures on Metric Spaces (AMS Bookstore, Providence, RI).Crossref, Google Scholar
- [31] (2001) Lecture on Choquet’s Theorem (Springer-Verlag, Berlin).Crossref, Google Scholar
- [32] (1974) Incomplete information in Markovian decision models. Ann. Statist. 2(6):1327–1334.Crossref, Google Scholar
- [33] (2017) Markov-Nash equilibria in mean-field games with discounted cost. Proc. 2017 Amer. Control Conf. (Institute of Electrical and Electronics Engineers, Piscataway, NJ), 3676–3681.Crossref, Google Scholar
- [34] (2018). Markov-Nash equilibria in mean-field games with discounted cost. SIAM J. Control Optim. 56(6):4256–4287.Google Scholar
- [35] (2014) Mean field games with partially observed major player and stochastic mean field. Proc. 53rd IEEE Conf. Decision Control (Institute of Electrical and Electronics Engineers, Piscataway, NJ), 2709–2715.Crossref, Google Scholar
- [36] (2015) ε -Nash equilibria for a partially observed mean field game with major player. Proc. 2015 Amer. Control Conf. (Institute of Electrical and Electronics Engineers, Piscataway, NJ), 4791–4797.Crossref, Google Scholar
- [37] (2016) Nonlinear filtering theory for McKean-Vlasov type stochastic differential equations. SIAM J. Control Optim. 54(1):153–174.Crossref, Google Scholar
- [38] (2016) On mean field games and nonlinear filtering for agents with individual-state partial observations. Proc. 2016 Amer. Control Conf. (Institute of Electrical and Electronics Engineers, Piscataway, NJ), 4681–4686.Crossref, Google Scholar
- [39] (2016) Mean field game theory with a partially observed major agent. SIAM J. Control Optim. 54(6):3174–3224.Crossref, Google Scholar
- [40] (2016) Partially observed optimal control for mean-field SDEs. Working paper, Department of Mathematics, Huzhou University, Zhejiang, China.Google Scholar
- [41] (2014) Risk-sensitive mean field games. IEEE. Trans. Automatic Control 59(4):835–850.Crossref, Google Scholar
- [42] (2009) Optimal Transport: Old and New (Springer-Verlag, Berlin).Crossref, Google Scholar
- [43] (1976) Reduction of a controlled Markov model with incomplete data to a problem with complete information in the case of Borel state and control spaces. Theory Probab. Appl. 21(1):153–158.Crossref, Google Scholar

