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Agency Contracts under Maximum-Entropy.

Oscar Gutiérrez¹, Vicente Salas-Fumás²

¹Department of Business Economics, Universitat Autònoma de Barcelona, 08193 Barcelona, Spain.

Entropy (Basel, Switzerland)

|August 27, 2021

Summary

This study applies the maximum-entropy principle (MEP) to agency contracting with incomplete information. It finds that optimal contracts often resemble simple, increasing affine functions of output, reflecting real-world compensation schemes.

Keywords:

agency relationship first-order approach likelihood ratio maximum-entropy moral hazard worst-case scenario

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Area of Science:

Economics
Decision Theory
Information Theory

Background:

Agency contracting involves principals and agents with potentially misaligned goals.
Information asymmetry regarding output probabilities complicates contract design.
Existing models often assume complete knowledge of output distributions.

Purpose of the Study:

To apply the maximum-entropy principle (MEP) to agency contracting under partial information.
To characterize second-best agency contracts derived from maximum entropy distributions (MED).
To explore how information availability influences optimal contract structures.

Main Methods:

Application of the maximum-entropy principle (MEP) to model agency relationships.
Derivation of maximum entropy distributions (MED) consistent with available information.
Characterization of second-best agency contracts based on MED.

Main Results:

Under minimal shared information, the second-best contract is an increasing affine function of output.
Increased information about output distributions can lead to more complex optimal contracts.
The MEP framework theoretically supports observed real-world compensation schemes.

Conclusions:

The MEP provides a robust framework for designing agency contracts with incomplete information.
Simple, output-based compensation is optimal under limited information, aligning with practical scenarios.
The model's flexibility allows for complex contracts when more data is available.