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Dynamic Contracting with Many Agents

Author

Listed:
  • Bruno Biais

    (HEC Paris - Ecole des Hautes Etudes Commerciales)

  • Hans Gersbach

    (ETH Zürich - Eidgenössische Technische Hochschule - Swiss Federal Institute of Technology [Zürich], IZA - Forschungsinstitut zur Zukunft der Arbeit - Institute of Labor Economics, CESifo - CESifo, CEPR - Center for Economic Policy Research)

  • Jean-Charles Rochet

    (TSE-R - Toulouse School of Economics - UT Capitole - Université Toulouse Capitole - Comue de Toulouse - Communauté d'universités et établissements de Toulouse - EHESS - École des hautes études en sciences sociales - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement)

  • Ernst-Ludwig von Thadden

    (University of Mannheim = Universität Mannheim, CEPR - Center for Economic Policy Research, ECGI - European Corporate Governance Institute)

  • Stéphane Villeneuve

    (University of Toulouse 1)

Abstract

This paper analyzes dynamic capital allocation and risk sharing between a principal and many agents, who privately observe their output. The state variables of the mechanism design problem are aggregate capital and the distribution of continuation utilities across agents. This gives rise to a Bellman equation in an infinite dimensional space, which we solve with mean-field techniques. We fully characterize the optimal mechanism and show that the level of risk agents must be exposed to for incentive reasons is decreasing in their initial reservation utility. We extend classical welfare theorems by showing that any incentive-constrained optimal allocation can be implemented as an equilibrium allocation, with appropriate transfers and wealth taxation by the principal.

Suggested Citation

  • Bruno Biais & Hans Gersbach & Jean-Charles Rochet & Ernst-Ludwig von Thadden & Stéphane Villeneuve, 2024. "Dynamic Contracting with Many Agents," Working Papers hal-04759186, HAL.
    • Handle: RePEc:hal:wpaper:hal-04759186
    DOI: 10.2139/ssrn.4769204
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    Cited by:

    1. Heng-fu Zou, 2025. "Mean-Field Principal-Agent Contracts with Relative Performance: An Explicit Formula under Sannikov-Style Primitives," CEMA Working Papers 789, China Economics and Management Academy, Central University of Finance and Economics.

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    JEL classification:

    • E44 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Financial Markets and the Macroeconomy
    • E62 - Macroeconomics and Monetary Economics - - Macroeconomic Policy, Macroeconomic Aspects of Public Finance, and General Outlook - - - Fiscal Policy; Modern Monetary Theory

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