A Unifying Framework for Submodular 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] Aïd R, Dumitrescu R, Tankov P (2020) The entry and exit game in the electricity markets: A mean-field game approach. Preprint, submitted April 29, https://arxiv.org/abs/2004.14057.Google Scholar
• [3] Bardi M, Fischer M (2019) On non-uniqueness and uniqueness of solutions in finite-horizon mean field games. ESAIM Control Optim. Calculus Variations 25:1–33.Crossref, Google Scholar
• [4] Bayraktar E, Zhang X (2020) On non-uniqueness in mean field games. Proc. Amer. Math. Soc. 148(9):4091–4106.Crossref, Google Scholar
• [5] Bayraktar E, Budhiraja A, Cohen A (2018) A numerical scheme for a mean field game in some queueing systems based on Markov chain approximation method. SIAM J. Control Optim. 56(6):4017–4044.Crossref, Google Scholar
• [6] Bayraktar E, Budhiraja A, Cohen A (2019) Rate control under heavy traffic with strategic servers. Ann. Appl. Probab. 29(1):1–35.Crossref, Google Scholar
• [7] Bayraktar E, Cecchin A, Cohen A, Delarue F (2021) Finite state mean field games with Wright Fisher common noise. J. Math. Pures Appl. 147:98–162.Crossref, Google Scholar
• [8] Bayraktar E, Cecchin A, Cohen A, Delarue F (2022) Finite state mean field games with Wright–Fisher common noise as limits of N-player weighted games. Math. Oper. Res., ePub ahead of print March 16, https://doi.org/10.1287/moor.2021.1230.Link, Google Scholar
• [9] Bensoussan A, Sung K, Yam SCP, Yung SP (2016) Linear-quadratic mean field games. J. Optim. Theory Appl. 169(2):496–529.Crossref, Google Scholar
• [10] Bertucci C (2018) Optimal stopping in mean field games, an obstacle problem approach. J. Math. Pures Appl. 120:165–194.Crossref, Google Scholar
• [11] Birkhoff G (1967) Lattice Theory, 3rd ed. (American Mathematical Society, Providence, RI).Google Scholar
• [12] Bonnans JF, Lavigne P, Pfeiffer L (2021) Discrete-time mean field games with risk-averse agents. ESAIM Control Optim. Calculus Variations 27(44):1–27.Google Scholar
• [13] Bouveret G, Dumitrescu R, Tankov P (2020) Mean-field games of optimal stopping: A relaxed solution approach. SIAM J. Control Optim. 58(4):1795–1821.Crossref, Google Scholar
• [14] Campi L, De Angelis T, Ghio M, Livieri G (2020) Mean-field games of finite-fuel capacity expansion with singular controls. Preprint, submitted June 3, https://arxiv.org/abs/2006.02074v1.Google Scholar
• [15] Cao H, Guo X (2022) MFGs for partially reversible investment. Stochastic Processes Their Appl. 150(2022):995–1014.Crossref, Google Scholar
• [16] Cao H, Dianetti J, Ferrari G (2021) Stationary discounted and ergodic mean field games of singular control. Preprint, submitted May 15, https://doi.org/10.48550/arXiv.2105.07213.Google Scholar
• [17] Cardaliaguet P (2012) Notes. Lion’s lectures. Report, Collége de France, Paris.Google Scholar
• [18] Cardaliaguet P, Hadikhanloo S (2017) Learning in mean field games: The fictitious play. ESAIM Control Optim. Calculus Variations 23(2):569–591.Crossref, Google Scholar
• [19] Carmona R, Delarue F (2018) Probabilistic Theory of Mean Field Games with Applications I: Mean Field FBSDEs, Control, and Games, Probability Theory and Stochastic Modelling, vol. 83 (Springer, Cham, Switzerland).Google Scholar
• [20] Carmona R, Delarue F, Lacker D (2016) Mean field games with common noise. Ann. Probab. 44(6):3740–3803.Crossref, Google Scholar
• [21] Carmona R, Delarue F, Lacker D (2017) Mean field games of timing and models for bank runs. Appl. Math. Optim. 76(1):217–260.Crossref, Google Scholar
• [22] Cecchin A, Dai Pra P, Fischer M, Pelino G (2019) On the convergence problem in mean field games: A two state model without uniqueness. SIAM J. Control Optim. 57(4):2443–2466.Crossref, Google Scholar
• [23] Delarue F, Tchuendom RF (2020) Selection of equilibria in a linear quadratic mean-field game. Stochastic Processes Their Appl. 130(2):1000–1040.Crossref, Google Scholar
• [24] Dianetti J, Ferrari G (2020) Nonzero-sum submodular monotone-follower games: Existence and approximation of Nash equilibria. SIAM J. Control Optim. 58(3):1257–1288.Crossref, Google Scholar
• [25] Dianetti J, Ferrari G, Fischer M, Nendel M (2021) Submodular mean field games: Existence and approximation of solutions. Ann. Appl. Probab. 31(6):2538–2566.Crossref, Google Scholar
• [26] Doncel J, Gast N, Gaujal B (2019) Discrete mean field games: Existence of equilibria and convergence. J. Dynamics Games 6(3):221–239.Google Scholar
• [27] Dudley RM (1968) Distances of probability measures and random variables. Ann. Math. Statist. 39(5):1563–1572.Crossref, Google Scholar
• [28] Elie R, Pérolat J, Laurière M, Geist M, Pietquin O (2019) Approximate fictitious play for mean field games. Preprint, submitted July 4, https://www.researchgate.net/publication/334288784_Approximate_Fictitious_Play_for_Mean_Field_Games.Google Scholar
• [29] Frink O Jr (1942) Topology in lattices. Trans. Amer. Math. Soc. 51(3):569–582.Google Scholar
• [30] Fu G (2019) Extended mean field games with singular controls. Preprint, submitted September 9, https://arxiv.org/abs/1909.04154v1.Google Scholar
• [31] Fu G, Horst U (2017) Mean field games with singular controls. SIAM J. Control Optim. 55(6):3833–3868.Crossref, Google Scholar
• [32] Gomes D, Mohr J, Souza RR (2010) Discrete mean field games: Existence of equilibria and convergence. J. Math. Pures Appl. 93:308–328.Crossref, Google Scholar
• [33] Gomes D, Velho RM, Wolfram MT (2013) Socio-economic applications of finite state mean field games. Philos. Trans. Roy. Soc. A Math. Physical Engrg. Sci. 372(2028):20130405.Google Scholar
• [34] Graber PJ, Mouzouni C (2020) On mean field games models for exhaustible commodities trade. ESAIM Control Optim. Calculus Variations 26:1–38.Google Scholar
• [35] Guo X, Xu R (2019) Stochastic games for fuel follower problem: N vs. mean field game. SIAM J. Control Optim. 57(1):659–692.Crossref, Google Scholar
• [36] Hadikhanloo S, Silva F (2019) Finite mean field games: Fictitious play and convergence to a first order continuous mean field game. J. Math. Pures Appl. 132:369–397.Crossref, Google Scholar
• [37] Haussmann UG, Suo W (1995) Singular optimal stochastic controls. I. Existence. SIAM J. Control Optim. 33(3):916–936.Crossref, Google Scholar
• [38] Hofbauer J, Sandholm WH (2002) On the global convergence of stochastic fictitious play. Econometrica 70(6):2265–2294.Crossref, Google Scholar
• [39] 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.Crossref, Google Scholar
• [40] Kabanov YM (1999) Hedging and liquidation under transaction costs in currency markets. Finance Stochastics 3(2):237–248.Crossref, Google Scholar
• [41] Lacker D (2015) Mean field games via controlled martingale problems: Existence of Markovian equilibria. Stochastic Processes Their Appl. 125(7):2856–2894.Crossref, Google Scholar
• [42] Lasry JM, Lions PL (2007) Mean field games. Japanese J. Math. 2(1):229–260.Crossref, Google Scholar
• [43] Lee K, Rengarajan D, Kalathil D, Shakkottai S (2021) Reinforcement learning for mean field games with strategic complementarities. Banerjee A, Fukumizu K, eds. Proc. 24th Internat. Conf. Artificial Intelligence Statist., vol. 130. Proceedings of Machine Learning Research (PMLR), 2458–2466.Google Scholar
• [44] Li J, Žitković G (2017) Existence, characterization, and approximation in the generalized monotone-follower problem. SIAM J. Control Optim. 55(1):94–118.Crossref, Google Scholar
• [45] Luttmer EG (2007) Selection, growth, and the size distribution of firms. Quart. J. Econom. 122(3):1103–1144.Crossref, Google Scholar
• [46] Menaldi JL, Taksar MI (1989) Optimal correction problem of a multidimensional stochastic system. Automatica J. IFAC 25(2):223–232.Crossref, Google Scholar
• [47] Meyer PA, Zheng W (1984) Tightness criteria for laws of semimartingales. Ann. Inst. Henri Poincare Probab. Statist. 20(4):353–372.Google Scholar
• [48] Miao J (2005) Optimal capital structure and industry dynamics. J. Finance 60(6):2621–2659.Crossref, Google Scholar
• [49] Müller A, Scarsini M (2006) Stochastic order relations and lattices of probability measures. SIAM J. Optim. 16(4):1024–1043.Crossref, Google Scholar
• [50] Nendel M (2020) A note on stochastic dominance, uniform integrability and lattice properties. Bull. London Math. Soc. 52(5):907–923.Crossref, Google Scholar
• [51] Perrin S, Pérolat J, Laurière M, Geist M, Elie R, Pietquin O (2020) Fictitious play for mean field games: Continuous time analysis and applications. Preprint, submitted October 26, https://arxiv.org/abs/2007.03458.Google Scholar
• [52] Protter PE (2005) Stochastic Integration and Differential Equations, 2nd ed., Stochastic Modelling and Applied Probability, vol. 21 (Springer, Berlin).Crossref, Google Scholar
• [53] Saldi N, Basar T, Raginsky M (2018) Markov-Nash equilibria in mean-field games with discounted costs. SIAM J. Control Optim. 56(6):4256–4287.Crossref, Google Scholar
• [54] Saldi N, Basar T, Raginsky M (2020) Approximate Markov-Nash equilibria for discrete-time risk-sensitive mean-field games. Math. Oper. Res. 45(4):1596–1620.Link, Google Scholar
• [55] Shaked M, Shanthikumar JG, eds. (2007) Stochastic Orders, Springer Series in Statistics (Springer Science & Business Media, New York).Crossref, Google Scholar
• [56] Tchuendom RF (2018) Uniqueness for linear-quadratic mean field games with common noise. Dynamic Games Appl. 8(1):199–210.Crossref, Google Scholar
• [57] Topkis DM (1979) Equilibrium points in nonzero-sum n-person submodular games. SIAM J. Control Optim. 17(6):773–787.Crossref, Google Scholar
• [58] Topkis DM (2011) Supermodularity and Complementarity (Princeton University Press, Princeton, NJ).Crossref, Google Scholar
• [59] Vives X (1990) Nash equilibrium with strategic complementarities. J. Math. Econom. 19(3):305–321.Crossref, Google Scholar
• [60] Więcek P (2017) Total reward semi-Markov mean-field games with complementarity properties. Dynamic Games Appl. 7(3):507–529.Crossref, Google Scholar
• [61] Więcek P (2020) Discrete-time ergodic mean-field games with average reward on compact spaces. Dynamic Games Appl. 10:222–256.Crossref, Google Scholar
• [62] Xie Q, Yang Z, Wang Z, Minca A (2020) Provable fictitious play for general mean-field games. Preprint, submitted October 8, https://arxiv.org/abs/2010.04211.Google Scholar