C1,1 regularity for principal-agent problems

We prove the interior C1,1 regularity of the indirect utilities which solve a subclass of principal-agent problems originally considered by Figalli, Kim, and McCann. Our approach is based on construction of a suitable comparison function which, essentially, allows one to pinch the solution between p...

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Bibliographic Details
Published inAdvances in mathematics (New York. 1965) Vol. 478; p. 110396
Main Authors McCann, Robert J., Rankin, Cale, Zhang, Kelvin Shuangjian
Format Journal Article
LanguageEnglish
Published Elsevier Inc 01.10.2025
Subjects
Bilevel optimization
Elliptic PDE
Monopolist nonlinear pricing
Multidimensional asymmetric information
Principal-agent problem
Regularity theory
secondary
Multidimensional asymmetric information
Bilevel optimization
Elliptic PDE
Principal-agent problem
Regularity theory
Monopolist nonlinear pricing
primary
Online AccessGet full text
ISSN0001-8708
DOI10.1016/j.aim.2025.110396

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Summary:We prove the interior C1,1 regularity of the indirect utilities which solve a subclass of principal-agent problems originally considered by Figalli, Kim, and McCann. Our approach is based on construction of a suitable comparison function which, essentially, allows one to pinch the solution between parabolas. The original ideas for this proof arise from an earlier, unpublished, result of Caffarelli and Lions for bilinear preferences which we extend here to general quasilinear benefit functions. We give a simple example which shows the C1,1 regularity is optimal.
ISSN:0001-8708
DOI:10.1016/j.aim.2025.110396