Multidimensional Monotonicity and Economic Applications

Frank Yang and Kai Hao Yang

Papers from arXiv.org

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 in various mechanism design and information design problems, including public good provision with interdependent values; interim efficient bilateral trade mechanisms; asymmetric reduced form auctions; and optimal private private information structure. As another application, we also present a mechanism anti-equivalence theorem for two-agent, two-alternative social choice problems: A mechanism is payoff-equivalent to a deterministic DIC mechanism if and only if they are ex-post equivalent.

Date: 2025-02
New Economics Papers: this item is included in nep-des and nep-mic
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