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Dynamic Contracting with Many Agents

Author

Listed:
  • Biais, Bruno

    (HEC Paris)

  • Gersbach, Hans

    (ETH Zurich)

  • Rochet, Jean-Charles

    (University of Toulouse Capitole)

  • von Thadden, Ernst-Ludwig

    (Universitaet Mannheim)

  • Villeneuve, Stéphane

    (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

  • Biais, Bruno & Gersbach, Hans & Rochet, Jean-Charles & von Thadden, Ernst-Ludwig & Villeneuve, Stéphane, 2024. "Dynamic Contracting with Many Agents," HEC Research Papers Series 1516, HEC Paris.
    • Handle: RePEc:ebg:heccah:1516
    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:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design
    • D86 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Economics of Contract Law
    • D92 - Microeconomics - - Micro-Based Behavioral Economics - - - Intertemporal Firm Choice, Investment, Capacity, and Financing
    • E22 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment - - - Investment; Capital; Intangible Capital; Capacity

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