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Extreme Points and Majorization

Author

Listed:
  • Andreas Kleiner
  • Benny Moldovanu
  • Philipp Strack

Abstract

A key insight is that many, seemingly different, economic problems share a com mon mathematical structure: they all involve the maximization of a functional over sets of monotonic functions that are either majorized by, or majorize, a given func tion. We first present new, simpler proofs for the main characterization results of the extreme points of sets defined by monotonicity and majorization constraints obtained by Kleiner, Moldovanu, and Strack (2021). We then demonstrate how the charac terization results can be fruitfully applied to a broad range of economic applications, from auction and information design to decision problems under risk such as optimal stopping. Finally, we conclude with an overview of recent, related work that extends these characterizations to settings with additional constraints, multidimensional state spaces, and alternative stochastic orders.

Suggested Citation

  • Andreas Kleiner & Benny Moldovanu & Philipp Strack, 2026. "Extreme Points and Majorization," CRC TR 224 Discussion Paper Series crctr224_2025_749, University of Bonn and University of Mannheim, Germany.
    • Handle: RePEc:bon:boncrc:crctr224_2025_749
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    File URL: https://www.crctr224.de/research/discussion-papers/archive/dp749
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    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness

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