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Dynamic Contracting with Many Agents

Author

Listed:
  • Biais, Bruno
  • Gersbach, Hans
  • Rochet, Jean-Charles
  • von Thadden, Ernst-Ludwig
  • Villeneuve, Stéphane

Abstract

We analyze 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 outside utility. We extend classical welfare theorems by showing that any incentive- constrained optimal allocation can be implemented as an equilibrium allocation, with appropriate money issuance and wealth taxation by the principal.

Suggested Citation

  • Biais, Bruno & Gersbach, Hans & Rochet, Jean-Charles & von Thadden, Ernst-Ludwig & Villeneuve, Stéphane, 2025. "Dynamic Contracting with Many Agents," TSE Working Papers 25-1642, Toulouse School of Economics (TSE).
  • Handle: RePEc:tse:wpaper:130553
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    References listed on IDEAS

    as
    1. Zhigu He & Arvind Krishnamurthy, 2012. "A Model of Capital and Crises," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 79(2), pages 735-777.
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    5. Bruno Biais & Thomas Mariotti & Jean-Charles Rochet & StÈphane Villeneuve, 2010. "Large Risks, Limited Liability, and Dynamic Moral Hazard," Econometrica, Econometric Society, vol. 78(1), pages 73-118, January.
    6. Yves Achdou & Jiequn Han & Jean-Michel Lasry & Pierre-Louis Lionse & Benjamin Moll, 2022. "Income and Wealth Distribution in Macroeconomics: A Continuous-Time Approach," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 89(1), pages 45-86.
    7. Sebastian Di Tella & Yuliy Sannikov, 2021. "Optimal Asset Management Contracts With Hidden Savings," Econometrica, Econometric Society, vol. 89(3), pages 1099-1139, May.
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    More about this item

    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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