Cited By
View all- Baldacci BManziuk IMastrolia TRosenbaum M(2023)Market Making and Incentives Design in the Presence of a Dark PoolOperations Research10.1287/opre.2022.240671:2(727-749)Online publication date: 1-Mar-2023
Principal-Agent Problem with Common Agency Without Communication
Pages 775 - 799
Abstract
In this paper, we consider a problem of contract theory in which several Principals hire a common Agent and we study the model in the continuous time setting. We show that optimal contracts should satisfy some equilibrium conditions and we reduce the optimization problem of the Principals to a system of coupled Hamilton--Jacobi--Bellman (HJB) equations. We provide conditions ensuring that for risk-neutral Principals, the system of coupled HJB equations admits a solution. Further, we apply our study in a more specific linear-quadratic model where two interacting Principals hire one common Agent. In this continuous time model, we extend the result of [B. D. Bernheim and M. D. Whinston, Econometrica, 54 (1986), pp. 923--942] in which the authors compare the optimal effort of the Agent in a noncooperative Principals model and that in the aggregate model, by showing that these two optimizations coincide only in the first best case. We also study the sensibility of the optimal effort and the optimal remunerations with respect to appetence parameters and the correlation between the projects.
References
[1]
D. P. Baron, Noncooperative regulation of a nonlocalized externality, RAND J. Econ., 16 (1985), pp. 553--568.
[2]
G. Biglaiser and C. Mezzetti, Principals competing for an agent in the presence of adverse selection and moral hazard, J. Econom. Theory, 61 (1993), pp. 302--330.
[3]
J. M Buchanan and W. C Stubblebine, Externality, in Classic Papers in Natural Resource Economics, Springer, New York, 1962, pp. 138--154.
[4]
A. Braverman and J. E. Stiglitz, Sharecropping and the interlinking of agrarian markets, Amer. Econ. Rev., 72 (1982), pp. 695--715.
[5]
B. D. Bernheim and M. D. Whinston, Common marketing agency as a device for facilitating collusion, RAND J. Econ., 16 (1985), pp. 269--281.
[6]
B. D. Bernheim and M. D. Whinston, Common agency, Econometrica, 54 (1986), pp. 923--942.
[7]
R. Carmona, Lectures on BSDEs, Stochastic Control, and Stochastic Differential Games with Financial Applications, Vol. 1, SIAM, Philadelphia, 2016.
[8]
U. Çetin and A. Danilova, Markovian Nash equilibrium in financial markets with asymmetric information and related forward--backward systems, Ann. Appl. Probab., 26 (2016), pp. 1996--2029.
[9]
J. Cvitanić, D. Possamaï, and N. Touzi, Moral Hazard in Dynamic Risk Management, preprint, arXiv:1406.5852, 2014.
[10]
J. Cvitanić, D. Possamaï, and N. Touzi, Dynamic Programming Approach to Principal-Agent Problems, preprint, arXiv:1510.07111, 2015.
[11]
R. Carmona and J. Yang, Predatory Trading: A Game on Volatility and Liquidity, preprint, 2011, https://www.princeton.edu/~rcarmona/download/fe/PredatoryTradingGameQF.pdf.
[12]
J Cvitanic and J Zhang, Contract Theory in Continuous-Time Methods, Springer, New York, 2013.
[13]
A. Dixit, G. M Grossman, and E. Helpman, Common agency and coordination: General theory and application to government policy making, J. Political Econ., 105 (1997), pp. 752--769.
[14]
E. Dockner, S. Jorgensen, N. V. Long, and G. Sorger, Differential Games in Economics and Management Science, Cambridge University Press, Cambridge, 2000.
[15]
N. El Karoui, S. Peng, and M. C. Quenez, Backward stochastic differential equations in finance, Math. Finance, 7 (1997), pp. 1--71.
[16]
R. Elie, T. Mastrolia, and D. Possamaï, A Tale of a Principal and Many Many Agents, preprint, arXiv:1608.05226, 2016.
[17]
R. Elie and D. Possamaï, Contracting Theory with Competitive Interacting Agents, preprint, arXiv:1605.08099, 2016.
[18]
Y. Hu, P. Imkeller, and M. Müller, Utility maximization in incomplete markets, Ann. Appl. Probab., 15 (2005), pp. 1691--1712.
[19]
B. Holmstrom and P. Milgrom, Aggregation and linearity in the provision of intertemporal incentives, Econometrica, 55 (1987), pp. 303--328.
[20]
M. F. Hellwig and K. M. Schmidt, Discrete-time approximations of the Holmström--Milgrom Brownian-motion model of intertemporal incentive provision, Econometerica, 70 (2002), pp. 2225--2264.
[21]
H. K. Koo, G. Shim, and J. Sung, Optimal multi-agent performance measures for team contracts, Math. Finance, 18 (2008), pp. 649--667.
[22]
M. Kobylanski, Backward stochastic differential equations and partial differential equations with quadratic growth, Ann. Probab., 28 (2000), pp. 558--602.
[23]
J.-J. Laffont, Externalities, in Allocation, Information and Markets, Springer, New York, 1989, pp. 112--116.
[24]
G. M. Lieberman, Second Order Parabolic Differential Equations, World Scientific, Singapore, 1996.
[25]
S. J. Liebowitz and S. E. Margolis, Network externality: An uncommon tragedy, J. Econ. Perspect., 8 (1994), pp. 133--150.
[26]
J.-J. Laffont and D. Martimort, The Theory of Incentives: The Principal-Agent Model, Princeton University Press, Princeton, NJ, 2009.
[27]
J.-J. Laffont and J. Tirole, A Theory of Incentives in Procurement and Regulation, MIT Press, Cambridge, MA, 1993.
[28]
T. Mastrolia, Moral Hazard in Welfare Economics: On the Advantage of Planner's Advices to Manage Employees' Actions, hal-01504473, 2017.
[29]
J. A. Mirrlees, The optimal structure of incentives and authority within an organization, Bell J. Econom., 117 (1976), pp. 105--131.
[30]
S. G. Potts, V. L. Imperatriz-Fonseca, H. T. Ngo, J. C. Biesmeijer, T. D. Breeze, L. V. Dicks, L. A. Garibaldi, R. Hill, J. Settele, and A. J. Vanbergen, Summary for Policymakers of the Assessment Report of the Intergovernmental Science-Policy Platform on Biodiversity and Ecosystem Services on Pollinators, Pollination and Food Production, Central Archive at the University of Reading, 2016.
[31]
E. Pardoux and S. Peng, Adapted solution of a backward stochastic differential equation, Systems Control Lett., 14 (1990), pp. 55--61.
[32]
R. Rouge and N. El Karoui, Pricing via utility maximization and entropy, Math. Finance, 10 (2000), pp. 259--276.
[33]
M. Rothschild and J. Stiglitz, Equilibrium in competitive insurance markets: An essay on the economics of imperfect information, Q. J. Econ., 1976, pp. 629--649.
[34]
Y. Sannikov, A continuous-time version of the principal-agent problem, Rev. Econ. Stud., 75 (2008), pp. 957--984.
[35]
H. Schättler and J. Sung, The first-order approach to the continuous-time principal--agent problem with exponential utility, J. Econom. Theory, 61 (1993), pp. 331--371.
[36]
H. M. Soner, N. Touzi, and J. Zhang, Wellposedness of second order backward sdes, Probab. Theory Related Fields, 153 (2012), pp. 149--190.
[37]
J. Sung, Linearity with project selection and controllable diffusion rate in continuous-time principal-agent problems, RAND J. Econ., 1995, pp. 720--743.
[38]
J. Sung, Lectures on the Theory of Contracts in Corporate Finance: From Discrete-Time to Continuous-Time Models, Com2Mac Lecture Note Ser. 4, 2001.
[39]
J. Tirole, Inefficient foreign borrowing: A dual-and common-agency perspective, Amer. Econ. Rev., 93 (2003), pp. 1678--1702.
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© 2018, Society for Industrial and Applied Mathematics.
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Published: 01 January 2018
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View all- Baldacci BManziuk IMastrolia TRosenbaum M(2023)Market Making and Incentives Design in the Presence of a Dark PoolOperations Research10.1287/opre.2022.240671:2(727-749)Online publication date: 1-Mar-2023