Contracts with Information Acquisition, via Scoring Rules

TL;DR

This paper develops a unified framework using proper scoring rules for principal-agent problems involving information acquisition and hidden actions, providing novel solutions and algorithms for these complex contract design issues.

Contribution

It introduces a scoring rule-based approach to generalize and solve principal-agent problems with information acquisition, including new geometric solutions and an efficient algorithm.

Findings

Closed-form solutions for multidimensional information acquisition

Geometric scoring-rule based solutions for classic contracts

Efficient algorithm for general information acquisition contracts

Abstract

We consider a principal-agent problem where the agent may privately choose to acquire relevant information prior to taking a hidden action. This model generalizes two special cases: a classic moral hazard setting, and a more recently studied problem of incentivizing information acquisition (IA). We show that all of these problems can be reduced to the design of a proper scoring rule. Under a limited liability condition, we consider the special cases separately and then the general problem. We give novel results for the special case of IA, giving a closed form "pointed polyhedral cone" solution for the general multidimensional problem. We also describe a geometric, scoring-rules based solution to the case of the classic contracts problem. Finally, we give an efficient algorithm for the general problem of Contracts with Information Acquisition.