Large Ranking Games with Diffusion Control

References

• [1] Baldacci B, Possamaï D (2022) Governmental incentives for green bonds investment. Math. Financial Econom. 16(3):539–585.Crossref, Google Scholar
• [2] Barrasso A, Touzi N (2022) Controlled diffusion mean field games with common noise and McKean-Vlasov second order backward SDEs. Theory Probab. Its Appl. 66(4):613–639.Crossref, Google Scholar
• [3] Bayraktar E, Zhang Y (2016) A rank-based mean field game in the strong formulation. Electronic Comm. Probab. 21:1–12.Crossref, Google Scholar
• [4] Bayraktar E, Zhang Y (2021) Terminal ranking games. Math. Oper. Res. 46(4):1349–1365.Link, Google Scholar
• [5] Bayraktar E, Cvitanić J, Zhang Y (2019) Large tournament games. Ann. Appl. Probab. 29(6):3695–3744.Crossref, Google Scholar
• [6] Cardaliaguet P, Delarue F, Lasry JM, Lions PL (2019) The Master Equation and the Convergence Problem in Mean Field Games (Princeton University Press, Princeton, NJ).Google Scholar
• [7] Carmona R, Delarue F (2018a) Probabilistic Theory of Mean Field Games with Applications I, Probability Theory and Stochastic Modelling, vol. 83 (Springer, Cham, Switzerland).Crossref, Google Scholar
• [8] Carmona R, Delarue F (2018b) Probabilistic Theory of Mean Field Games with Applications II, Probability Theory and Stochastic Modelling, vol. 84 (Springer, Cham, Switzerland).Crossref, Google Scholar
• [9] Chevalier J, Ellison G (1997) Risk taking by mutual funds as a response to incentives. J. Political Econom. 105(6):1167–1200.Crossref, Google Scholar
• [10] Deng C, Su X, Zhou C (2020) Relative wealth concerns with partial information and heterogeneous priors. Preprint, submitted July 23, https://doi.org/10.48550/arXiv.2007.11781.Google Scholar
• [11] Elie R, Possamaï D (2019) Contracting theory with competitive interacting agents. SIAM J. Control Optim. 57(2):1157–1188.Crossref, Google Scholar
• [12] Élie R, Hubert E, Mastrolia T, Possamaï D (2021) Mean-field moral hazard for optimal energy demand response management. Math. Finance 31(1):399–473.Crossref, Google Scholar
• [13] Espinosa GE, Touzi N (2015) Optimal investment under relative performance concerns. Math. Finance 25(2):221–257.Crossref, Google Scholar
• [14] Fu G, Zhou C (2023) Mean field portfolio games. Finance Stochastics 27(1):189–231.Google Scholar
• [15] Fu G, Su X, Zhou C (2020) Mean field exponential utility game: A probabilistic approach. Preprint, submitted July 16, https://doi.org/10.48550/arXiv.2006.07684.Google Scholar
• [16] Hoeffding W (1963) Probability inequalities for sums of bounded random variables. J. Amer. Statist. Assoc. 58:13–30.Crossref, Google Scholar
• [17] 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.Crossref, Google Scholar
• [18] 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):221–251.Crossref, Google Scholar
• [19] Hubert E (2020) Continuous-time incentives in hierarchies. Preprint, submitted July 21, https://doi.org/10.48550/arXiv.2007.10758.Google Scholar
• [20] Karatzas I, Shreve SE (1991) Brownian Motion and Stochastic Calculus, 2nd ed., Graduate Texts in Mathematics, vol. 113 (Springer-Verlag, New York).Google Scholar
• [21] Keilson J, Wellner JA (1978) Oscillating Brownian motion. J. Appl. Probab. 15(2):300–310.Crossref, Google Scholar
• [22] Krylov NV (1969) On Itô’s stochastic integral equations. Theory Probab. Appl. 14(2):330–336.Crossref, Google Scholar
• [23] Krylov NV (1980) Controlled Diffusion Processes, vol. 14 (Springer Science & Business Media, New York).Crossref, Google Scholar
• [24] Krylov NV (2021) On time inhomogeneous stochastic Itô equations with drift in LD+1. Ukrainian Math. J. 72(9):1420–1444.Crossref, Google Scholar
• [25] Lacker D (2016) A general characterization of the mean field limit for stochastic differential games. Probab. Theory Related Fields 165(3):581–648.Crossref, Google Scholar
• [26] 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
• [27] Lacker D, Webster K (2015) Translation invariant mean field games with common noise. Electronic Comm. Probab. 20(42):13.Google Scholar
• [28] Lasry JM, Lions PL (2006a) Jeux à champ moyen. I. Le cas stationnaire. Comptes Rendus Math. 343(9):619–625.Crossref, Google Scholar
• [29] Lasry JM, Lions PL (2006b) Jeux à champ moyen. II. Horizon fini et contrôle optimal. Comptes Rendus Math. 343(10):679–684.Crossref, Google Scholar
• [30] Lasry JM, Lions PL (2007) Mean field games. Japanese J. Math. 2(1):229–260.Crossref, Google Scholar
• [31] Lejay A, Pigato P (2018) Statistical estimation of the oscillating Brownian motion. Bernoulli 24(4B):3568–3602.Crossref, Google Scholar
• [32] McNamara JM (1983) Optimal control of the diffusion coefficient of a simple diffusion process. Math. Oper. Res. 8(3):373–380.Link, Google Scholar
• [33] McNamara JM (1985) A regularity condition on the transition probability measure of a diffusion process. Stochastics 15(3):161–182.Crossref, Google Scholar
• [34] McNamara JM (1988) A stochastic differential game with safe and risky choices. Probab. Engrg. Inform. Sci. 2(1):31–39.Crossref, Google Scholar
• [35] Nakao S (1972) On the pathwise uniqueness of solutions of one-dimensional stochastic differential equations. Osaka J. Math. 9(3):513–518.Google Scholar
• [36] Nutz M, Zhang Y (2019) A mean field competition. Math. Oper. Res. 44(4):1245–1263.Link, Google Scholar
• [37] Seel C, Strack P (2013) Gambling in contests. J. Econom. Theory 148(5):2033–2048.Crossref, Google Scholar
• [38] Seel C, Strack P (2016) Continuous time contests with private information. Math. Oper. Res. 41(3):1093–1107.Link, Google Scholar