regularity for principal-agent problems
arXiv:2303.04937
Abstract
We prove the interior 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 The original ideas for this proof arise from an earlier, unpublished, result of Caffarelli and Lions for bilinear preferences which we extend here to general quasilinear benefit functions.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 regularity is optimal.
19 pages, 1 figure; updated based on reviewer's comment to include additional exposition