Multidimensional Monotonicity and Economic Applications

Frank Yang and Kai Hao Yang
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Frank Yang: University of Chicago
Kai Hao Yang: Yale University

No 2428, Cowles Foundation Discussion Papers from Cowles Foundation for Research in Economics, Yale University

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.

Pages: 70 pages
Date: 2025-02-26
New Economics Papers: this item is included in nep-des, nep-gth and nep-mic
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