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Contracting theory with competitive interacting agents

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  • Romuald Elie
  • Dylan Possamai

Abstract

In a framework close to the one developed by Holmstr\"om and Milgrom [44], we study the optimal contracting scheme between a Principal and several Agents. Each hired Agent is in charge of one project, and can make efforts towards managing his own project, as well as impact (positively or negatively) the projects of the other Agents. Considering economic Agents in competition with relative performance concerns, we derive the optimal contracts in both first best and moral hazard settings. The enhanced resolution methodology relies heavily on the connection between Nash equilibria and multidimensional quadratic BSDEs. The optimal contracts are linear and each agent is paid a fixed proportion of the terminal value of all the projects of the firm. Besides, each Agent receives his reservation utility, and those with high competitive appetence are assigned less volatile projects, and shall even receive help from the other Agents. From the principal point of view, it is in the firm interest in our model to strongly diversify the competitive appetence of the Agents.

Suggested Citation

  • Romuald Elie & Dylan Possamai, 2016. "Contracting theory with competitive interacting agents," Papers 1605.08099, arXiv.org.
    • Handle: RePEc:arx:papers:1605.08099
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    as
    1. Pedro Rey‐Biel, 2008. "Inequity Aversion and Team Incentives," Scandinavian Journal of Economics, Wiley Blackwell, vol. 110(2), pages 297-320, June.
    2. Boualem Djehiche & Peter Helgesson, 2015. "The Principal-Agent Problem With Time Inconsistent Utility Functions," Papers 1503.05416, arXiv.org.
    3. Patrick Bolton & Mathias Dewatripont, 2005. "Contract Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262025760, April.
    4. Ernst Fehr & Alexander Klein & Klaus M. Schmidt, "undated". "Fairness, Incentives and Contractual Incompleteness," IEW - Working Papers 072, Institute for Empirical Research in Economics - University of Zurich.
    5. Jenny Kragl, 2015. "Group versus Individual Performance Pay in Relational Employment Contracts when Workers are Envious," Journal of Economics & Management Strategy, Wiley Blackwell, vol. 24(1), pages 131-150, March.
    6. Englmaier, Florian & Muehlheusser, Gerd & Roider, Andreas, 2010. "Optimal Incentive Contracts under Moral Hazard When the Agent Is Free to Leave," IZA Discussion Papers 5027, Institute of Labor Economics (IZA).
    7. Hui Ou-Yang, 2005. "An Equilibrium Model of Asset Pricing and Moral Hazard," The Review of Financial Studies, Society for Financial Studies, vol. 18(4), pages 1253-1303.
    8. Green, Jerry R & Stokey, Nancy L, 1983. "A Comparison of Tournaments and Contracts," Journal of Political Economy, University of Chicago Press, vol. 91(3), pages 349-364, June.
    9. Ernst Fehr & Klaus M. Schmidt, 1999. "A Theory of Fairness, Competition, and Cooperation," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 114(3), pages 817-868.
    10. Dilip Mookherjee, 1984. "Optimal Incentive Schemes with Many Agents," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 51(3), pages 433-446.
    11. James A. Mirrlees, 1976. "The Optimal Structure of Incentives and Authority Within an Organization," Bell Journal of Economics, The RAND Corporation, vol. 7(1), pages 105-131, Spring.
    12. Martin F. Hellwig & Klaus M. Schmidt, 2002. "Discrete-Time Approximations of the Holmstrom-Milgrom Brownian-Motion Model of Intertemporal Incentive Provision," Econometrica, Econometric Society, vol. 70(6), pages 2225-2264, November.
    13. Yuliy Sannikov, 2008. "A Continuous-Time Version of the Principal-Agent Problem," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 75(3), pages 957-984.
    14. Christian Grund & Dirk Sliwka, 2005. "Envy and Compassion in Tournaments," Journal of Economics & Management Strategy, Wiley Blackwell, vol. 14(1), pages 187-207, March.
    15. Dominique Demougin & Claude Fluet & Carsten Helm, 2006. "Output and wages with inequality averse agents," Canadian Journal of Economics/Revue canadienne d'économique, John Wiley & Sons, vol. 39(2), pages 399-413, May.
    16. Holmstrom, Bengt & Milgrom, Paul, 1987. "Aggregation and Linearity in the Provision of Intertemporal Incentives," Econometrica, Econometric Society, vol. 55(2), pages 303-328, March.
    17. Demski, Joel S. & Sappington, David, 1984. "Optimal incentive contracts with multiple agents," Journal of Economic Theory, Elsevier, vol. 33(1), pages 152-171, June.
    18. Dominique Demougin & Claude Fluet, 2003. "Inequity Aversion in Tournaments," Cahiers de recherche 0322, CIRPEE.
    19. Grossman, Sanford J & Hart, Oliver D, 1983. "An Analysis of the Principal-Agent Problem," Econometrica, Econometric Society, vol. 51(1), pages 7-45, January.
    20. Barry J. Nalebuff & Joseph E. Stiglitz, 1983. "Prices and Incentives: Towards a General Theory of Compensation and Competition," Bell Journal of Economics, The RAND Corporation, vol. 14(1), pages 21-43, Spring.
    21. Englmaier, Florian & Wambach, Achim, 2010. "Optimal incentive contracts under inequity aversion," Games and Economic Behavior, Elsevier, vol. 69(2), pages 312-328, July.
    22. Mirrlees, James A., 1972. "Population policy and the taxation of family size," Journal of Public Economics, Elsevier, vol. 1(2), pages 169-198, August.
    23. Hyeng Keun Koo & Gyoocheol Shim & Jaeyoung Sung, 2008. "Optimal Multi‐Agent Performance Measures For Team Contracts," Mathematical Finance, Wiley Blackwell, vol. 18(4), pages 649-667, October.
    24. Hideshi Itoh, 2004. "Moral Hazard and Other‐Regarding Preferences," The Japanese Economic Review, Japanese Economic Association, vol. 55(1), pages 18-45, March.
    25. Spence, Michael & Zeckhauser, Richard, 1971. "Insurance, Information, and Individual Action," American Economic Review, American Economic Association, vol. 61(2), pages 380-387, May.
    26. Florian Englmaier & Achim Wambach, 2002. "Contracts and Inequity Aversion," CESifo Working Paper Series 809, CESifo.
    27. Schattler, Heinz & Sung, Jaeyoung, 1997. "On optimal sharing rules in discrete-and continuous-time principal-agent problems with exponential utility," Journal of Economic Dynamics and Control, Elsevier, vol. 21(2-3), pages 551-574.
    28. Zeckhauser, Richard, 1970. "Medical insurance: A case study of the tradeoff between risk spreading and appropriate incentives," Journal of Economic Theory, Elsevier, vol. 2(1), pages 10-26, March.
    29. Gilles-Edouard Espinosa & Nizar Touzi, 2015. "Optimal Investment Under Relative Performance Concerns," Mathematical Finance, Wiley Blackwell, vol. 25(2), pages 221-257, April.
    30. J. A. Mirrlees, 1999. "The Theory of Moral Hazard and Unobservable Behaviour: Part I," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 66(1), pages 3-21.
    31. Sung, Jaeyoung, 1997. "Corporate Insurance and Managerial Incentives," Journal of Economic Theory, Elsevier, vol. 74(2), pages 297-332, June.
    32. Jaeyoung Sung, 1995. "Linearity with Project Selection and Controllable Diffusion Rate in Continuous-Time Principal-Agent Problems," RAND Journal of Economics, The RAND Corporation, vol. 26(4), pages 720-743, Winter.
    33. Constantinos Kardaras & Hao Xing & Gordan v{Z}itkovi'c, 2015. "Incomplete stochastic equilibria for dynamic monetary utility," Papers 1505.07224, arXiv.org, revised Feb 2017.
    34. Hui Ou-Yang, 2003. "Optimal Contracts in a Continuous-Time Delegated Portfolio Management Problem," The Review of Financial Studies, Society for Financial Studies, vol. 16(1), pages 173-208.
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    Cited by:

    1. Yasuaki Wasa & Ken-Ichi Akao & Kenko Uchida, 2020. "Optimal Dynamic Incentive Contracts between a Principal and Multiple Agents in Controlled Markov Processes: A Constructive Approach," RIEEM Discussion Paper Series 2001, Research Institute for Environmental Economics and Management, Waseda University.
    2. Marcel Nutz & Yuchong Zhang, 2019. "A Mean Field Competition," Management Science, INFORMS, vol. 44(4), pages 1245-1263, November.
    3. Marcel Nutz & Yuchong Zhang, 2017. "A Mean Field Competition," Papers 1708.01308, arXiv.org.
    4. Qi Luo & Romesh Saigal, 2017. "A Note on the Multi-Agent Contracts in Continuous Time," Papers 1710.00377, arXiv.org, revised Oct 2017.

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