A Label-State Formulation of Stochastic Graphon Games and Approximate Equilibria on Large Networks

References

• [1] Aliprantis C, Border K (2007) Infinite Dimensional Analysis: A Hitchhiker’s Guide, 3rd ed. (Springer, Berlin).Google Scholar
• [2] Aurell A, Carmona R, Lauriere M (2022) Stochastic graphon games. II. The linear-quadratic case. Appl. Math. Optim. 85(3):1–33.Google Scholar
• [3] Basak A, Mukherjee S (2017) Universality of the mean-field for the Potts model. Probab. Theory Related Fields 168(3-4):557–600.Crossref, Google Scholar
• [4] Bayraktar E, Chakraborty S, Wu R (2020) Graphon mean field systems. Preprint, submitted October 6, https://arxiv.org/abs/2003.13180v2.Google Scholar
• [5] Bayraktar E, Wu R, Zhang X (2022) Propagation of chaos of forward-backward stochastic differential equations with graphon interactions. Preprint, submitted February 16, https://arxiv.org/abs/2202.08163.Google Scholar
• [6] Beiglböck M, Lacker D (2020) Denseness of adapted processes among causal couplings. Preprint, submitted May 27, https://arxiv.org/abs/1805.03185v3.Google Scholar
• [7] Bertsekas DP, Shreve SE (1996) Stochastic Optimal Control: The Discrete-Time Case, vol. 5 (Athena Scientific, Nashua, NH).Google Scholar
• [8] Bet G, Coppini F, Nardi FR (2020) Weakly interacting oscillators on dense random graphs. Preprint, submitted June 13, https://arxiv.org/abs/2006.07670v1.Google Scholar
• [9] Bhamidi S, Budhiraja A, Wu R (2019) Weakly interacting particle systems on inhomogeneous random graphs. Stochastic Processes Their Appl. 129(6):2174–2206.Crossref, Google Scholar
• [10] Bogachev VI (2007) Measure Theory (Springer, Berlin).Crossref, Google Scholar
• [11] Borgs C, Chayes J, Cohn H, Zhao Y (2019) An Lp theory of sparse graph convergence. I. Limits, sparse random graph models, and power law distributions. Trans. Amer. Math. Soc. 372(5):3019–3062.Crossref, Google Scholar
• [12] Brunick G, Shreve S (2013) Mimicking an Itô process by a solution of a stochastic differential equation. Ann. Appl. Probab. 23(4):1584–1628.Google Scholar
• [13] Caines PE, Huang M (2018) Graphon mean field games and the GMFG equations. 2018 IEEE Conf. Decision Control (CDC) (IEEE, Philadelphia), 4129–4134.Google Scholar
• [14] Caines P-E, Huang M (2019) Graphon mean field games and the GMFG equations: ε-Nash equilibria. 2019 IEEE 58th Conf. Decision Control (CDC) (IEEE, Philadelphia), 286–292.Google Scholar
• [15] Cardaliaguet P, Delarue F, Lasry J-M, Lions P-L (2019) The Master Equation and the Convergence Problem in Mean Field Games (Princeton University Press, Princeton, NJ).Google Scholar
• [16] Carmona G (2004) Nash equilibria of games with a continuum of players. FEUNL Working Paper No. 466, Faculdade de Economia da Universidade Nova de Lisboa, Lisbon, Portugal.Google Scholar
• [17] Carmona R, Delarue F (2013) Probabilistic analysis of mean-field games. SIAM J. Control Optim. 51(4):2705–2734.Crossref, Google Scholar
• [18] Carmona R, Delarue F (2018) Probabilistic Theory of Mean Field Games with Applications I-II (Springer, Berlin).Crossref, Google Scholar
• [19] Carmona R, Fouque J-P, Sun L-H (2013) Mean field games and systemic risk. Preprint, submitted August 9, https://arxiv.org/abs/1308.2172.Google Scholar
• [20] Carmona R, Cooney DB, Graves CV, Lauriere M (2022) Stochastic graphon games: I. The static case. Math. Oper. Res. 47(1):750–778.Google Scholar
• [21] Coppini F (2022) Long time dynamics for interacting oscillators on graphs. Ann. Appl. Probab. 32(1):360–391.Google Scholar
• [22] Coppini F (2022) A note on Fokker-Planck equations and graphons. J. Statist. Phys. 187(2):1–12.Google Scholar
• [23] Coppini F, Dietert H, Giacomin G (2020) A law of large numbers and large deviations for interacting diffusions on Erdös–Rényi graphs. Stochastic Dynam. 20(2):2050010.Crossref, Google Scholar
• [24] Cui K, Koeppl H (2021) Learning graphon mean field games and approximate Nash equilibria. Preprint, submitted December 17, https://arxiv.org/abs/2112.01280v2.Google Scholar
• [25] Delarue F (2017) Mean field games: A toy model on an Erdös-Renyi graph. ESAIM Proc. Surveys 60:1–26.Crossref, Google Scholar
• [26] Delattre S, Giacomin G, Luçon E (2016) A note on dynamical models on random graphs and Fokker–Planck equations. J. Statist. Phys. 165(4):785–798.Crossref, Google Scholar
• [27] El Karoui N, Nguyen DH, Jeanblanc-Picqué M (1987) Compactification methods in the control of degenerate diffusions: Existence of an optimal control. Stochastics 20(3):169–219.Crossref, Google Scholar
• [28] Fan K (1952) Fixed-point and minimax theorems in locally convex topological linear spaces. Proc. Natl. Acad. Sci. USA 38(2):121–126.Google Scholar
• [29] Feng Y, Fouque J-P, Ichiba T (2020) Linear-quadratic stochastic differential games on directed chain networks. Preprint, submitted May 29, https://arxiv.org/abs/2003.08840.Google Scholar
• [30] Gao S, Foguen Tchuendom R, Caines PE (2020) Linear quadratic graphon field games. Preprint, submitted September 30, https://arxiv.org/abs/2006.03964.Google Scholar
• [31] Haussmann UG, Lepeltier JP (1990) On the existence of optimal controls. SIAM J. Control Optim. 28(4):851–902.Crossref, Google Scholar
• [32] 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
• [33] Jabin P-E, Poyato D, Soler J (2021) Mean-field limit of non-exchangeable systems. Preprint, submitted December 31, https://arxiv.org/abs/2112.15406.Google Scholar
• [34] Jackson MO (2010) Social and Economic Networks (Princeton University Press, Princeton, NJ).Crossref, Google Scholar
• [35] 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
• [36] Lacker D (2018) Mean field games and interacting particle systems. Working paper, Columbia University, New York.Google Scholar
• [37] Lacker D (2020) On the convergence of closed-loop Nash equilibria to the mean field game limit. Ann. Appl. Probab. 30(4):1693–1761.Crossref, Google Scholar
• [38] Lacker D, Soret A (2022) A case study on stochastic games on large graphs in mean field and sparse regimes. Math. Oper. Res. 47(2):1530–1565.Link, Google Scholar
• [39] Lasry J-M, Lions P-L (2007) Mean field games. Japanese J. Math. 2(1):229–260.Crossref, Google Scholar
• [40] Lovász L (2012) Large Networks and Graph Limits, vol. 60 (American Mathematical Society, Providence, RI).Crossref, Google Scholar
• [41] Luçon E (2020) Quenched asymptotics for interacting diffusions on inhomogeneous random graphs. Stochastic Processes Their Appl. 130(11):6783–6842.Crossref, Google Scholar
• [42] Parise F, Ozdaglar A (2019) Graphon games. Proc. 2019 ACM Conf. Econom. Comput. (Association for Computing Machinery, New York), 457–458.Google Scholar
• [43] Parise F, Ozdaglar A (2021) Analysis and interventions in large network games. Annual Rev. Control Robotics Autonomous Systems 4:455–486.Crossref, Google Scholar
• [44] Stroock DW, Varadhan SRS (1997) Multidimensional Diffusion Processes, vol. 233 (Springer Science & Business Media, New York).Google Scholar
• [45] Sun Y (2006) The exact law of large numbers via Fubini extension and characterization of insurable risks. J. Econom. Theory 126(1):31–69.Crossref, Google Scholar
• [46] Sznitman A-S (1991) Topics in propagation of chaos. Hennequin P-L, ed. Ecole d’été de Probabilités de Saint-Flour XIX-1989 (Springer, Berlin), 165–251.Crossref, Google Scholar
• [47] Tangpi L, Zhou X (2022) Optimal investment in a large population of competitive and heterogeneous agents. Preprint, submitted February 23, https://arxiv.org/abs/2202.11314.Google Scholar
• [48] Vasal D, Mishra R, Vishwanath S (2021) Sequential decomposition of graphon mean field games. 2021 Amer. Control Conf. (ACC), 730–736.Google Scholar
• [49] Veretennikov AJ (1981) On strong solutions and explicit formulas for solutions of stochastic integral equations. Math. USSR Sbornik 39(3):387–403.Crossref, Google Scholar