Information Design and Mechanism Design: An Integrated Framework

TL;DR

This paper introduces an integrated framework combining information design and mechanism design using majorization theory, enabling joint optimization of information structures and mechanisms in screening environments with quasilinear utility.

Contribution

It unifies classic auction and screening results with information design, extending analysis to joint optimization of information and mechanisms using majorization constraints.

Findings

Pooling of values and allocations is always optimal when jointly optimizing.

The framework unifies and extends classic auction and screening results.

Joint optimization of information and mechanisms impacts welfare analysis.

Abstract

We develop an integrated framework for information design and mechanism design in screening environments with quasilinear utility. Using the tools of majorization theory and quantile functions, we show that both information design and mechanism design problems reduce to maximizing linear functionals subject to majorization constraints. For mechanism design, the designer chooses allocations weakly majorized by the exogenous inventory. For information design, the designer chooses information structures that are majorized by the prior distribution. When the designer can choose both the mechanism and the information structure simultaneously, then the joint optimization problem becomes bilinear with two majorization constraints. We show that pooling of values and associated allocations is always optimal in this case. Our approach unifies classic results in auction theory and screening, extends them to information design settings, and provides new insights into the welfare effects of jointly optimizing allocation and information.