Multidimensional Monotonicity and Economic Applications
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.
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