Information Design and Mechanism Design: An Integrated Framework

TL;DR

This paper develops an integrated framework for information design and mechanism design in screening environments with quasilinear utility by using majorization and quantile representations. Revenue and consumer surplus are shown to be bilinear in quantile value and allocation functions, and optimal policies arise from concavification (ironing) under majorization constraints. When information and allocation are jointly optimized, pooling becomes universally optimal, yielding robust predictions and a welfare frontier characterized by censoring patterns in efficient auctions. The approach unifies classic auction and screening results, extends them to information design, and yields insights into welfare and competition under joint design, with practical relevance to data-driven pricing and platform design. The paper also provides extensive comparative statics and outlines broad extensions, including endogenous inventory and asymmetric settings.

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.

Figures (6)

• Figure 1: Revenue function $r_{W}(t)$ and its concavification $\overline{r}_{W}(t)$ when $W(t)=t^{4}$.
• Figure 2: Allocation in the Optimal Auction: Feasible Allocation $Q(t)$ and Optimal Allocation $X(t)$, with $Q \succ_{w} X$.
• Figure 3: The excess function $e_{X}$ and its concavification $\overline{e}_{X}$ when $X(t)=t^{4}$.
• Figure 4: Optimal Information Design with $V(t)$ and $W(t)$, where $V(t) \succ W(t)$.
• Figure 5: The given distributions of values $V(t)=t^{4}$ and qualities $Q(t)=t^{4}$ are depicted on the left. The associated optimal distributions $W(t)$ and $X(t)$, which are monotone partitional distributions, are depicted on the right.

Theorems & Definitions (7)

• Theorem 1: Optimal Mechanism via Concavification
• Corollary 1: Monotone Virtual Values
• Theorem 2: Optimal Information Structure via Concavification
• Proposition 1: Optimal Disclosure
• Proposition 2: Monotone Partitional Distribution
• Theorem 3: Optimality of Pooling
• Theorem 4: Optimal Information Structure for Weighted Social Welfare