Reduced Forms: Feasibility, Extremality, Optimality

Pasha Andreyanov, Ilia Krasikov and Alex Suzdaltsev

Papers from arXiv.org

Abstract: We study independent private values auction environments in which the auctioneer's revenue depends nonlinearly on bidders' interim winning probabilities. Our framework accommodates heterogeneity among bidders and places no ad hoc constraints on the mechanisms available to the auctioneer. Within this general setting, we show that feasibility of interim winning probabilities can be tested along a unidimensional curve -- the principal curve -- and use this insight to explicitly characterize the extreme points of the feasible set. We then combine our results on feasibility and extremality to solve for the optimal auction under a natural regularity condition. We show that the optimal mechanism allocates the good based on principal virtual values, which extend Myerson's virtual values to nonlinear settings and are constructed to equalize bidders' marginal revenue along the principal curve. We apply our approach to the classical linear model, settings with endogenous valuations due to ex ante investments, and settings with non-expected utility preferences, where previous results were largely limited either to symmetric environments with symmetric allocations or to two-bidder environments.

Date: 2026-02
References: Add references at CitEc
Citations:

Downloads: (external link)
http://arxiv.org/pdf/2602.17812 Latest version (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:2602.17812

Access Statistics for this paper

More papers in Papers from arXiv.org
Bibliographic data for series maintained by arXiv administrators ().