Multidimensional Monotonicity and Economic Applications

TL;DR

This paper characterizes the extreme points of multidimensional monotone functions and their marginals, leading to new insights and results in mechanism design and information structure problems.

Contribution

It provides novel characterizations of extreme points in multidimensional monotonicity, advancing theoretical understanding and applications in economic mechanism design.

Findings

New characterizations of extreme points for multidimensional monotone functions.

Applications to mechanism design problems like public goods and bilateral trade.

Enhanced understanding of information structures in economic mechanisms.

Abstract

We characterize the extreme points of multidimensional monotone functions from $[0,1]^n$ to $[0,1]$, as well as the extreme points of the set of one-dimensional marginals of these functions. These characterizations lead to new results for various mechanism design and information design problems, including public good provision with interdependent values; interim efficient bilateral trade mechanisms; mechanism (anti) equivalence; asymmetric reduced form auctions; and optimal private private information structure.