A Tale of a Principal and Many, Many Agents

References

• Bayraktar E, Cosso A, Pham H (2018) Randomized dynamic programming principle and Feynman-Kac representation for optimal control of McKean-Vlasov dynamics. Trans. Amer. Math. Soc. 370(3):2115–2160.Crossref, Google Scholar
• Bensoussan A, Frehse J, Yam S (2013) Mean Field Games and Mean Field Type Control Theory. SpringerBriefs in Mathematics, Vol. 101 (Springer-Verlag, New York).Crossref, Google Scholar
• Bolton P, Dewatripont M (2005) Contract Theory (MIT Press, Cambridge, MA).Google Scholar
• Buckdahn R, Li J, Peng S (2009) Mean-field backward stochastic differential equations and related partial differential equations. Stochastic Processes and Their Appl. 119(10):3133–3154.Crossref, Google Scholar
• Buckdahn R, Djehiche B, Li J, Peng S (2009) Mean-field backward stochastic differential equations: A limit approach. Ann. Probab. 37(4):1524–1565.Crossref, Google Scholar
• Buckdahn R, Li J, Peng S, Rainer C (2017) Mean-field stochastic differential equations and associated PDEs. Ann. Probab. 45(2):824–878.Crossref, Google Scholar
• Cardaliaguet P (2010) Notes on mean field games (from P.-L. Lions’ lectures at Collège de France), lecture given at Tor Vergata, April–May 2010.Google Scholar
• Cardaliaguet P, Delarue F, Lasry JM, Lions P-L (2015) The master equation and the convergence problem in mean field games. arXiv preprint arXiv:1509.02505.Google Scholar
• Carmona R, Delarue F (2013) Mean field forward–backward stochastic differential equations. Electronic Comm. Probab. 18(68):1–15.Google Scholar
• Carmona R, Delarue F (2015) Forward–backward stochastic differential equations and controlled McKean-Vlasov dynamics. Ann. Probab. 43(5):2647–2700.Crossref, Google Scholar
• Carmona R, Lacker D (2015) A probabilistic weak formulation of mean field games and applications. Ann. Appl. Probab. 25(3):1189–1231.Crossref, Google Scholar
• Carmona R, Fouque JP, Sun LH (2015) Mean field games and systemic risk. Comm. Math. Sci. 13(4):911–933.Crossref, Google Scholar
• Chassagneux JF, Crisan D, Delarue F (2014) A probabilistic approach to classical solutions of the master equation for large population equilibria. arXiv preprint arXiv:1411.3009.Google Scholar
• Chiang TS (1994) McKean-Vlasov equations with discontinuous coefficients. Soochow J. Math. 20(4):507–526.Google Scholar
• Cvitanić J, Zhang J (2012) Contract Theory in Continuous-Time Models (Springer).Google Scholar
• Cvitanić J, Possamaï D, Touzi N (2018) Dynamic programming approach to principal-agent problems. Finance and Stochastics 22(1):1–37.Crossref, Google Scholar
• Cvitanić J, Possamaï D, Touzi N (2017) Moral hazard in dynamic risk management. Management Sci. 63(10):3328–3346.Link, Google Scholar
• Dellacherie C, Lenglart E (1981) Sur des problèmes de régularisation, de recollement et d’interpolation en théorie des martingales. Séminaire de probabilités de Strasbourg XV, 328–346.Google Scholar
• Demski J, Sappington D (1984) Optimal incentive contracts with multiple agents. J. Econom. Theory 33(1):152–171.Crossref, Google Scholar
• Djehiche B, Helgesson P (2015) The principal-agent problem with time inconsistent utility functions. arXiv preprint arXiv:1503.05416.Google Scholar
• El Karoui N, Tan X (2013) Capacities, measurable selection and dynamic programming part II: Application in stochastic control problems. arXiv preprint arXiv:1310.3364.Google Scholar
• El Karoui N, Peng S, Quenez MC (1997) Backward stochastic differential equations in finance. Math. Finance 7(1):1–71.Crossref, Google Scholar
• Élie R, Possamaï D (2016) Contracting theory with competitive interacting agents. arXiv preprint arXiv:1605.08099.Google Scholar
• Green J, Stokey N (1983) A comparison of tournaments and contracts. J. Political Econom. 91(3):349–364.Crossref, Google Scholar
• Harter J, Richou A (2016) A stability approach for solving multidimensional quadratic BSDEs. arXiv preprint arXiv:1606.08627.Google Scholar
• Holmström B (1982) Moral hazard in teams. The Bell J. Econom. 13(2):324–340.Crossref, Google Scholar
• Holmström B, Milgrom P (1987) Aggregation and linearity in the provision of intertemporal incentives. Econometrica 55(2):303–328.Crossref, Google Scholar
• Huang M, Caines P, Malhamé R (2007) An invariance principle in large population stochastic dynamic games. J. Systems Sci. Complexity 20(2):162–172.Crossref, Google Scholar
• Huang M, Malhamé R, Caines P (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
• Koo H, Shim G, Sung J (2008) Optimal multi-agent performance measures for team contracts. Math. Finance 18(4):649–667.Crossref, Google Scholar
• Laffont JJ, Martimort D (2002) The Theory of Incentives: The Principal-Agent Model (Princeton University Press, Princeton, NJ).Crossref, Google Scholar
• Lasry JM, Lions P-L (2006) Jeux à champ moyen. i—le cas stationnaire. Comptes Rendus Mathématique 343(9):619–625.Crossref, Google Scholar
• Lasry JM, Lions P-L (2006) Jeux à champ moyen. ii—horizon fini et contrôle optimal. Comptes Rendus Mathématique 343(10):679–684.Crossref, Google Scholar
• Lasry JM, Lions P-L (2007) Mean field games. Japanese J. Math. 2(1):229–260.Crossref, Google Scholar
• Lépingle D, Mémin J (1978) Intégrabilité uniforme et dans lr des martingales exponentielles. Publications des séminaires de mathématiques et informatique de Rennes 1:1–14.Google Scholar
• Lions P-L (1988) Viscosity solutions of fully nonlinear second-order equations and optimal stochastic control in infinite dimensions. Part I: The case of bounded stochastic evolutions. Acta Mathematica 161(1):243–278.Crossref, Google Scholar
• Lions P-L (1989) Viscosity solutions of fully nonlinear second-order equations and optimal stochastic control in infinite dimensions. III. Uniqueness of viscosity solutions for general second-order equations. J. Functional Anal. 86(1):1–18.Crossref, Google Scholar
• Lions P-L (1989) Viscosity solutions of fully nonlinear second order equations and optimal stochastic control in infinite dimensions. Part II: Optimal control of Zakai’s equation. da Prato G, Tubaro L, eds. Stochastic Partial Differential Equations and Appl. II. Proc. Conf. Held in Trento, Italy February 1–6, 1988, Lecture Notes in Mathematics, Vol. 1390 (Springer), 147–170.Google Scholar
• Lions P-L (2006–2012) Théorie des jeux de champ moyen et applications. Cours du Collège de France. http://www.college-de-france.fr/default/EN/all/equder/audiovideo.jsp.Google Scholar
• Mastrolia T (2017) Moral hazard in welfare economics: On the advantage of planner’s advices to manage employees’ actions. arXiv preprint arXiv:1706.01254.Google Scholar
• Mishura Y, Veretennikov A (2016) Existence and uniqueness theorems for solutions of McKean-Vlasov stochastic equations. arXiv preprint arXiv:1603.02212.Google Scholar
• Mookherjee D (1984) Optimal incentive schemes with many agents. Rev. Econom. Stud. 51(3):433–446.Crossref, Google Scholar
• Pham H (2016) Linear quadratic optimal control of conditional McKean-Vlasov equation with random coefficients and applications. Probab., Uncertainty Quant. Risk 1(7).Google Scholar
• Pham H, Wei X (2015) Bellman equation and viscosity solutions for mean-field stochastic control problem. arXiv preprint arXiv:1512.07866.Google Scholar
• Pham H, Wei X (2016) Discrete time McKean-Vlasov control problem: A dynamic programming approach. Appl. Math. Optim. 74(3):487–506.Crossref, Google Scholar
• Pham H, Wei X (2017) Dynamic programming for optimal control of stochastic McKean-Vlasov dynamics. SIAM J. Control and Optim. 55(2):1069–1101.Crossref, Google Scholar
• Revuz D, Yor M (1999) Continuous Martingales and Brownian Motion. Grundlehren der Mathematischen Wissenschaften, 3rd ed., Vol. 293 (Springer).Crossref, Google Scholar
• Schättler H, Sung J (1993) The first-order approach to the continuous-time principal-agent problem with exponential utility. J. Econom. Theory 61(2):331–371.Crossref, Google Scholar
• Schättler H, Sung J (1997) On optimal sharing rules in discrete-and continuous-time principal-agent problems with exponential utility. J. Econom. Dynam. Control 21(2):551–574.Crossref, Google Scholar
• Sung J (1995) Linearity with project selection and controllable diffusion rate in continuous-time principal-agent problems. RAND J. Econom. 26(4):720–743.Crossref, Google Scholar
• Williams N (2009) On dynamic principal-agent problems in continuous time. University of Wisconsin, Madison.Google Scholar
• Xing H, Žitković G (2018) A class of globally solvable Markovian quadratic BSDE systems and applications. Ann. Probab. 46(1):491–550.Crossref, Google Scholar