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Multidimensional Monotonicity and Economic Applications

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  • Frank Yang

    (University of Chicago)

  • Kai Hao Yang

    (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.

Suggested Citation

  • Frank Yang & Kai Hao Yang, 2025. "Multidimensional Monotonicity and Economic Applications," Cowles Foundation Discussion Papers 2428, Cowles Foundation for Research in Economics, Yale University.
    • Handle: RePEc:cwl:cwldpp:2428
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    File URL: https://cowles.yale.edu/sites/default/files/2025-02/d2428.pdf
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