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Optimal Delegation in a Multidimensional World

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  • Andreas Kleiner

Abstract

We study a model of delegation in which a principal takes a multidimensional action and an agent has private information about a multidimensional state. We provide necessary and sufficient conditions for an arbitrary mechanism to maximize the principal’s expected payoff. A key step shows that a function is the indirect utility of an incentive-compatible mechanism if and only if it is convex and lies below the agent’s full-discretion payoff. We apply our optimality conditions to convex delegation sets and characterize when a single budget optimally links decisions. Linking can preserve discretion even when separate dele gation would eliminate it. Optimal linking can also require a nonconvex delegation set, even with uniformly distributed types. If the principal cares little about aligned decisions, every optimal mechanism randomizes: risk in an aligned decision provides incentives in the biased ones at little cost to her.

Suggested Citation

  • Andreas Kleiner, 2026. "Optimal Delegation in a Multidimensional World," CRC TR 224 Discussion Paper Series crctr224_2025_784, University of Bonn and University of Mannheim, Germany.
    • Handle: RePEc:bon:boncrc:crctr224_2025_784
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    References listed on IDEAS

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    Keywords

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    JEL classification:

    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design
    • D86 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Economics of Contract Law
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis

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