Dynamic Contracting with Many Agents
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Date
2024-02
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Working Paper
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yes
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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.
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published
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1511
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Toulouse School of Economics
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03729 - Gersbach, Hans / Gersbach, Hans
02525 - KOF Konjunkturforschungsstelle / KOF Swiss Economic Institute
06338 - KOF FB KOF Lab / KOF FB KOF Lab