Multivariate Majorization in Principal-Agents Models

TL;DR

This paper introduces a novel multivariate majorization concept that extends the 'ironing' technique to complex principal-agent problems with multidimensional externalities, enhancing contract theory and decision-making under risk.

Contribution

It develops a new multivariate majorization framework applicable to diverse type spaces, generalizing second-order stochastic dominance for multidimensional risk analysis.

Findings

Generalizes Mussa and Rosen's ironing to multivariate settings

Provides a new tool for contract design with externalities

Extends stochastic dominance to multiple dimensions

Abstract

We introduce a definition of multivariate majorization that is new to the economics literature. Our majorization technique allows us to generalize Mussa and Rosen's (1978) "ironing" to a broad class of multivariate principal-agents problems. Specifically, we consider adverse selection problems in which agents' types are one dimensional but informational externalities create a multidimensional ironing problem. Our majorization technique applies to discrete and continuous type spaces alike and we demonstrate its usefulness for contract theory and mechanism design. We further show that multivariate majorization yields a natural extension of second-order stochastic dominance to multiple dimensions and derive its implications for decision making under multivariate risk.