Optimal Delegation in a Multidimensional World

TL;DR

This paper analyzes optimal delegation mechanisms in a multidimensional setting where a principal and agent have private information, providing conditions for mechanism optimality and incentive compatibility.

Contribution

It offers necessary and sufficient conditions for optimal mechanisms in multidimensional delegation problems, including simple criteria for convex delegation sets.

Findings

Mechanisms are incentive compatible iff their induced utility is convex and below the first-best payoff.

Provides a characterization of optimal mechanisms in multidimensional contexts.

Discusses conditions under which convex delegation sets are optimal.

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 of the world. The principal can design any direct mechanism, including stochastic ones. We provide necessary and sufficient conditions for an arbitrary mechanism to maximize the principal's expected payoff. We also discuss simple conditions which ensure that some convex delegation set is optimal. A key step of our analysis shows that a mechanism is incentive compatible if and only if its induced indirect utility is convex and lies below the agent's first-best payoff.